ITP001 Axioms: ITP108^7.ax
%------------------------------------------------------------------------------
% File : ITP108^7 : 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 : fmsp.ax [Gau19]
% : HL4108^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 49 ( 6 unt; 34 typ; 0 def)
% Number of atoms : 49 ( 1 equ; 1 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 358 ( 1 ~; 1 |; 5 &; 337 @)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 12 avg; 337 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 1 con; 0-8 aty)
% Number of variables : 107 ( 3 ^ 59 !; 1 ?; 107 :)
% ( 44 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Efinite__map_2Efmap,type,
tyop_2Efinite__map_2Efmap: $tType > $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(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(tyop_2Esptree_2Espt,type,
tyop_2Esptree_2Espt: $tType > $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_2Ecombin_2EC,type,
c_2Ecombin_2EC:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a > A_27b > A_27c ) > A_27b > A_27a > A_27c ) ).
thf(c_2Efinite__map_2EFDOM,type,
c_2Efinite__map_2EFDOM:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > A_27a > $o ) ).
thf(c_2Efinite__map_2EFEMPTY,type,
c_2Efinite__map_2EFEMPTY:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ).
thf(c_2Efinite__map_2EFLOOKUP,type,
c_2Efinite__map_2EFLOOKUP:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > A_27a > ( tyop_2Eoption_2Eoption @ A_27b ) ) ).
thf(c_2Efmsp_2EFMSP,type,
c_2Efmsp_2EFMSP:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a > tyop_2Enum_2Enum > $o ) > ( A_27b > A_27c > $o ) > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > ( tyop_2Esptree_2Espt @ A_27c ) > $o ) ).
thf(c_2Efinite__map_2EFUNION,type,
c_2Efinite__map_2EFUNION:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ).
thf(c_2Etransfer_2EFUN__REL,type,
c_2Etransfer_2EFUN__REL:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( A_27a > A_27b > $o ) > ( A_27c > A_27d > $o ) > ( A_27a > A_27c ) > ( A_27b > A_27d ) > $o ) ).
thf(c_2Efinite__map_2EFUPDATE,type,
c_2Efinite__map_2EFUPDATE:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ).
thf(c_2Esptree_2ELN,type,
c_2Esptree_2ELN:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt @ A_27a ) ).
thf(c_2Eoption_2EOPTREL,type,
c_2Eoption_2EOPTREL:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > $o ) > ( tyop_2Eoption_2Eoption @ A_27a ) > ( tyop_2Eoption_2Eoption @ A_27b ) > $o ) ).
thf(c_2Etransfer_2EPAIR__REL,type,
c_2Etransfer_2EPAIR__REL:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( A_27a > A_27b > $o ) > ( A_27c > A_27d > $o ) > ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) > ( tyop_2Epair_2Eprod @ A_27b @ A_27d ) > $o ) ).
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_2Etransfer_2Ebi__unique,type,
c_2Etransfer_2Ebi__unique:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > $o ) > $o ) ).
thf(c_2Etransfer_2Ebitotal,type,
c_2Etransfer_2Ebitotal:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b > $o ) > $o ) ).
thf(c_2Esptree_2Edelete,type,
c_2Esptree_2Edelete:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Esptree_2Espt @ A_27a ) > ( tyop_2Esptree_2Espt @ A_27a ) ) ).
thf(c_2Esptree_2Edomain,type,
c_2Esptree_2Edomain:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt @ A_27a ) > tyop_2Enum_2Enum > $o ) ).
thf(c_2Efinite__map_2Efdomsub,type,
c_2Efinite__map_2Efdomsub:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > A_27a > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ).
thf(c_2Esptree_2Einsert,type,
c_2Esptree_2Einsert:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > A_27a > ( tyop_2Esptree_2Espt @ A_27a ) > ( tyop_2Esptree_2Espt @ A_27a ) ) ).
thf(c_2Esptree_2Elookup,type,
c_2Esptree_2Elookup:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Esptree_2Espt @ A_27a ) > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).
thf(c_2Esptree_2Eunion,type,
c_2Esptree_2Eunion:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt @ A_27a ) > ( tyop_2Esptree_2Espt @ A_27a ) > ( tyop_2Esptree_2Espt @ 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_2Efmsp_2EFMSP__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0AN: A_27a > tyop_2Enum_2Enum > $o,V1BC: A_27b > A_27c > $o,V2fm: tyop_2Efinite__map_2Efmap @ A_27a @ A_27b,V3sp: tyop_2Esptree_2Espt @ A_27c] :
( ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V0AN @ V1BC @ V2fm @ V3sp )
<=> ! [V4a: A_27a,V5n: tyop_2Enum_2Enum] :
( ( V0AN @ V4a @ V5n )
=> ( c_2Eoption_2EOPTREL @ A_27b @ A_27c @ V1BC @ ( c_2Efinite__map_2EFLOOKUP @ A_27a @ A_27b @ V2fm @ V4a ) @ ( c_2Esptree_2Elookup @ A_27c @ V5n @ V3sp ) ) ) ) ).
thf(thm_2Efmsp_2EFMSP__FDOM,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0BC: A_27b > A_27c > $o,V1AN: A_27a > tyop_2Enum_2Enum > $o] : ( c_2Etransfer_2EFUN__REL @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( A_27a > $o ) @ ( tyop_2Enum_2Enum > $o ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) @ ( c_2Etransfer_2EFUN__REL @ A_27a @ tyop_2Enum_2Enum @ $o @ $o @ V1AN @ ( c_2Emin_2E_3D @ $o ) ) @ ( c_2Efinite__map_2EFDOM @ A_27a @ A_27b ) @ ( c_2Esptree_2Edomain @ A_27c ) ) ).
thf(thm_2Efmsp_2EFMSP__FEMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0BC: A_27b > A_27c > $o,V1AN: A_27a > tyop_2Enum_2Enum > $o] : ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC @ ( c_2Efinite__map_2EFEMPTY @ A_27a @ A_27b ) @ ( c_2Esptree_2ELN @ A_27c ) ) ).
thf(thm_2Efmsp_2EFMSP__FUPDATE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0BC: A_27b > A_27c > $o,V1AN: A_27a > tyop_2Enum_2Enum > $o] :
( ( c_2Etransfer_2Ebi__unique @ A_27a @ tyop_2Enum_2Enum @ V1AN )
=> ( c_2Etransfer_2EFUN__REL @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) > ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) @ ( c_2Etransfer_2EFUN__REL @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Etransfer_2EPAIR__REL @ A_27a @ tyop_2Enum_2Enum @ A_27b @ A_27c @ V1AN @ V0BC ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) ) @ ( c_2Efinite__map_2EFUPDATE @ A_27a @ A_27b )
@ ^ [V2sp: tyop_2Esptree_2Espt @ A_27c] :
( c_2Epair_2EUNCURRY @ tyop_2Enum_2Enum @ A_27c @ ( tyop_2Esptree_2Espt @ A_27c )
@ ^ [V3n: tyop_2Enum_2Enum,V4v: A_27c] : ( c_2Esptree_2Einsert @ A_27c @ V3n @ V4v @ V2sp ) ) ) ) ).
thf(thm_2Efmsp_2EFMSP__bitotal,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0BC: A_27b > A_27c > $o,V1AN: A_27a > tyop_2Enum_2Enum > $o] :
( ( ( c_2Etransfer_2Ebitotal @ A_27a @ tyop_2Enum_2Enum @ V1AN )
& ( c_2Etransfer_2Ebitotal @ A_27b @ A_27c @ V0BC )
& ( c_2Etransfer_2Ebi__unique @ A_27a @ tyop_2Enum_2Enum @ V1AN ) )
=> ( c_2Etransfer_2Ebitotal @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) ) ) ).
thf(thm_2Efmsp_2EFMSP__FORALL,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0BC: A_27b > A_27c > $o,V1AN: A_27a > tyop_2Enum_2Enum > $o] :
( ( ( c_2Etransfer_2Ebitotal @ A_27a @ tyop_2Enum_2Enum @ V1AN )
& ( c_2Etransfer_2Ebitotal @ A_27b @ A_27c @ V0BC )
& ( c_2Etransfer_2Ebi__unique @ A_27a @ tyop_2Enum_2Enum @ V1AN ) )
=> ( c_2Etransfer_2EFUN__REL @ ( ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > $o ) @ ( ( tyop_2Esptree_2Espt @ A_27c ) > $o ) @ $o @ $o @ ( c_2Etransfer_2EFUN__REL @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ $o @ $o @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) @ ( c_2Emin_2E_3D @ $o ) ) @ ( c_2Emin_2E_3D @ $o ) @ ( c_2Ebool_2E_21 @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( c_2Ebool_2E_21 @ ( tyop_2Esptree_2Espt @ A_27c ) ) ) ) ).
thf(thm_2Efmsp_2EFMSP__FUNION,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0BC: A_27b > A_27c > $o,V1AN: A_27a > tyop_2Enum_2Enum > $o] : ( c_2Etransfer_2EFUN__REL @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( ( tyop_2Esptree_2Espt @ A_27c ) > ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) @ ( c_2Etransfer_2EFUN__REL @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) ) @ ( c_2Efinite__map_2EFUNION @ A_27a @ A_27b ) @ ( c_2Esptree_2Eunion @ A_27c ) ) ).
thf(thm_2Efmsp_2EFMSP__FDOMSUB,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0BC: A_27b > A_27c > $o,V1AN: A_27a > tyop_2Enum_2Enum > $o] :
( ( c_2Etransfer_2Ebi__unique @ A_27a @ tyop_2Enum_2Enum @ V1AN )
=> ( c_2Etransfer_2EFUN__REL @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( A_27a > ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Enum_2Enum > ( tyop_2Esptree_2Espt @ A_27c ) ) @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) @ ( c_2Etransfer_2EFUN__REL @ A_27a @ tyop_2Enum_2Enum @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ V1AN @ ( c_2Efmsp_2EFMSP @ A_27a @ A_27b @ A_27c @ V1AN @ V0BC ) ) @ ( c_2Efinite__map_2Efdomsub @ A_27a @ A_27b ) @ ( c_2Ecombin_2EC @ tyop_2Enum_2Enum @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( tyop_2Esptree_2Espt @ A_27c ) @ ( c_2Esptree_2Edelete @ A_27c ) ) ) ) ).
%------------------------------------------------------------------------------