ITP001 Axioms: ITP035^7.ax
%------------------------------------------------------------------------------
% File : ITP035^7 : 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 : listRange.ax [Gau19]
% : HL4035^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 48 ( 11 unt; 28 typ; 0 def)
% Number of atoms : 33 ( 11 equ; 1 cnn)
% Maximal formula atoms : 4 ( 0 avg)
% Number of connectives : 157 ( 1 ~; 1 |; 3 &; 137 @)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg; 137 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 2 con; 0-3 aty)
% Number of variables : 56 ( 2 ^ 42 !; 1 ?; 56 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
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(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_2Earithmetic_2E_2D,type,
c_2Earithmetic_2E_2D: 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_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $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_2Elist_2EALL__DISTINCT,type,
c_2Elist_2EALL__DISTINCT:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Elist_2ECONS,type,
c_2Elist_2ECONS:
!>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Elist_2EEL,type,
c_2Elist_2EEL:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) > A_27a ) ).
thf(c_2Elist_2EGENLIST,type,
c_2Elist_2EGENLIST:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum > A_27a ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ A_27a ) ) ).
thf(c_2Ebool_2EIN,type,
c_2Ebool_2EIN:
!>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).
thf(c_2Elist_2ELENGTH,type,
c_2Elist_2ELENGTH:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > tyop_2Enum_2Enum ) ).
thf(c_2Elist_2ELIST__TO__SET,type,
c_2Elist_2ELIST__TO__SET:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a > $o ) ).
thf(c_2Elist_2ENIL,type,
c_2Elist_2ENIL:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2ElistRange_2ElistRangeINC,type,
c_2ElistRange_2ElistRangeINC: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ).
thf(c_2ElistRange_2ElistRangeLHI,type,
c_2ElistRange_2ElistRangeLHI: tyop_2Enum_2Enum > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ 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_2ElistRange_2ElistRangeINC__def,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2ElistRange_2ElistRangeINC @ V0m @ V1n )
= ( c_2Elist_2EGENLIST @ tyop_2Enum_2Enum
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B @ V0m @ V2i )
@ ( c_2Earithmetic_2E_2D @ ( c_2Earithmetic_2E_2B @ V1n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0m ) ) ) ).
thf(thm_2ElistRange_2ElistRangeLHI__def,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2ElistRange_2ElistRangeLHI @ V0m @ V1n )
= ( c_2Elist_2EGENLIST @ tyop_2Enum_2Enum
@ ^ [V2i: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B @ V0m @ V2i )
@ ( c_2Earithmetic_2E_2D @ V1n @ V0m ) ) ) ).
thf(thm_2ElistRange_2ElistRangeINC__SING,axiom,
! [V0m: tyop_2Enum_2Enum] :
( ( c_2ElistRange_2ElistRangeINC @ V0m @ V0m )
= ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ V0m @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) ) ) ).
thf(thm_2ElistRange_2EMEM__listRangeINC,axiom,
! [V0x: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2m: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EIN @ tyop_2Enum_2Enum @ V0x @ ( c_2Elist_2ELIST__TO__SET @ tyop_2Enum_2Enum @ ( c_2ElistRange_2ElistRangeINC @ V2m @ V1n ) ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ V2m @ V0x )
& ( c_2Earithmetic_2E_3C_3D @ V0x @ V1n ) ) ) ).
thf(thm_2ElistRange_2ElistRangeINC__CONS,axiom,
! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V1m @ V0n )
=> ( ( c_2ElistRange_2ElistRangeINC @ V1m @ V0n )
= ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ V1m @ ( c_2ElistRange_2ElistRangeINC @ ( c_2Earithmetic_2E_2B @ V1m @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0n ) ) ) ) ).
thf(thm_2ElistRange_2ElistRangeINC__EMPTY,axiom,
! [V0n: tyop_2Enum_2Enum,V1m: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0n @ V1m )
=> ( ( c_2ElistRange_2ElistRangeINC @ V1m @ V0n )
= ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) ) ) ).
thf(thm_2ElistRange_2ElistRangeLHI__EQ,axiom,
! [V0m: tyop_2Enum_2Enum] :
( ( c_2ElistRange_2ElistRangeLHI @ V0m @ V0m )
= ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) ) ).
thf(thm_2ElistRange_2EMEM__listRangeLHI,axiom,
! [V0x: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum,V2m: tyop_2Enum_2Enum] :
( ( c_2Ebool_2EIN @ tyop_2Enum_2Enum @ V0x @ ( c_2Elist_2ELIST__TO__SET @ tyop_2Enum_2Enum @ ( c_2ElistRange_2ElistRangeLHI @ V2m @ V1n ) ) )
<=> ( ( c_2Earithmetic_2E_3C_3D @ V2m @ V0x )
& ( c_2Eprim__rec_2E_3C @ V0x @ V1n ) ) ) ).
thf(thm_2ElistRange_2ElistRangeLHI__EMPTY,axiom,
! [V0lo: tyop_2Enum_2Enum,V1hi: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V1hi @ V0lo )
=> ( ( c_2ElistRange_2ElistRangeLHI @ V0lo @ V1hi )
= ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) ) ) ).
thf(thm_2ElistRange_2ElistRangeLHI__CONS,axiom,
! [V0lo: tyop_2Enum_2Enum,V1hi: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0lo @ V1hi )
=> ( ( c_2ElistRange_2ElistRangeLHI @ V0lo @ V1hi )
= ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ V0lo @ ( c_2ElistRange_2ElistRangeLHI @ ( c_2Earithmetic_2E_2B @ V0lo @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V1hi ) ) ) ) ).
thf(thm_2ElistRange_2ElistRangeLHI__ALL__DISTINCT,axiom,
! [V0lo: tyop_2Enum_2Enum,V1hi: tyop_2Enum_2Enum] : ( c_2Elist_2EALL__DISTINCT @ tyop_2Enum_2Enum @ ( c_2ElistRange_2ElistRangeLHI @ V0lo @ V1hi ) ) ).
thf(thm_2ElistRange_2ELENGTH__listRangeLHI,axiom,
! [V0lo: tyop_2Enum_2Enum,V1hi: tyop_2Enum_2Enum] :
( ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ ( c_2ElistRange_2ElistRangeLHI @ V0lo @ V1hi ) )
= ( c_2Earithmetic_2E_2D @ V1hi @ V0lo ) ) ).
thf(thm_2ElistRange_2EEL__listRangeLHI,axiom,
! [V0lo: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum,V2hi: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2E_2B @ V0lo @ V1i ) @ V2hi )
=> ( ( c_2Elist_2EEL @ tyop_2Enum_2Enum @ V1i @ ( c_2ElistRange_2ElistRangeLHI @ V0lo @ V2hi ) )
= ( c_2Earithmetic_2E_2B @ V0lo @ V1i ) ) ) ).
%------------------------------------------------------------------------------