ITP001 Axioms: ITP111^7.ax
%------------------------------------------------------------------------------
% File : ITP111^7 : 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 : intto.ax [Gau19]
% : HL4111^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 53 ( 20 unt; 29 typ; 0 def)
% Number of atoms : 29 ( 18 equ; 3 cnn)
% Maximal formula atoms : 2 ( 0 avg)
% Number of connectives : 115 ( 3 ~; 1 |; 1 &; 102 @)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg; 102 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 7 con; 0-4 aty)
% Number of variables : 44 ( 0 ^ 37 !; 1 ?; 44 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: $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_2EternaryComparisons_2Eordering,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
thf(tyop_2Etoto_2Etoto,type,
tyop_2Etoto_2Etoto: $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_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_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2EternaryComparisons_2EEQUAL,type,
c_2EternaryComparisons_2EEQUAL: tyop_2EternaryComparisons_2Eordering ).
thf(c_2EternaryComparisons_2EGREATER,type,
c_2EternaryComparisons_2EGREATER: tyop_2EternaryComparisons_2Eordering ).
thf(c_2EternaryComparisons_2ELESS,type,
c_2EternaryComparisons_2ELESS: tyop_2EternaryComparisons_2Eordering ).
thf(c_2Etoto_2ETO,type,
c_2Etoto_2ETO:
!>[A_27a: $tType] : ( ( A_27a > A_27a > tyop_2EternaryComparisons_2Eordering ) > ( tyop_2Etoto_2Etoto @ A_27a ) ) ).
thf(c_2Etoto_2ETO__of__LinearOrder,type,
c_2Etoto_2ETO__of__LinearOrder:
!>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > A_27a > A_27a > tyop_2EternaryComparisons_2Eordering ) ).
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_2Etoto_2Eapto,type,
c_2Etoto_2Eapto:
!>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto @ A_27a ) > A_27a > A_27a > tyop_2EternaryComparisons_2Eordering ) ).
thf(c_2Eintto_2EintOrd,type,
c_2Eintto_2EintOrd: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > tyop_2EternaryComparisons_2Eordering ).
thf(c_2Einteger_2Eint__lt,type,
c_2Einteger_2Eint__lt: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o ).
thf(c_2Einteger_2Eint__neg,type,
c_2Einteger_2Eint__neg: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
thf(c_2Einteger_2Eint__of__num,type,
c_2Einteger_2Eint__of__num: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
thf(c_2Eintto_2Eintto,type,
c_2Eintto_2Eintto: tyop_2Etoto_2Etoto @ tyop_2Einteger_2Eint ).
thf(c_2Etoto_2EnumOrd,type,
c_2Etoto_2EnumOrd: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2EternaryComparisons_2Eordering ).
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_2Eintto_2EintOrd,axiom,
( c_2Eintto_2EintOrd
= ( c_2Etoto_2ETO__of__LinearOrder @ tyop_2Einteger_2Eint @ c_2Einteger_2Eint__lt ) ) ).
thf(thm_2Eintto_2Eintto,axiom,
( c_2Eintto_2Eintto
= ( c_2Etoto_2ETO @ tyop_2Einteger_2Eint @ c_2Eintto_2EintOrd ) ) ).
thf(thm_2Eintto_2Eapintto__thm,axiom,
( ( c_2Etoto_2Eapto @ tyop_2Einteger_2Eint @ c_2Eintto_2Eintto )
= c_2Eintto_2EintOrd ) ).
thf(thm_2Eintto_2Epos__pos__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__of__num @ V0m ) @ ( c_2Einteger_2Eint__of__num @ V1n ) )
= ( c_2Etoto_2EnumOrd @ V0m @ V1n ) ) ).
thf(thm_2Eintto_2Eneg__neg__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V0m ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V1n ) ) )
= ( c_2Etoto_2EnumOrd @ V1n @ V0m ) ) ).
thf(thm_2Eintto_2EBIT1__nz,axiom,
! [V0n: tyop_2Enum_2Enum] :
( (~)
@ ( ( c_2Earithmetic_2EBIT1 @ V0n )
= c_2Enum_2E0 ) ) ).
thf(thm_2Eintto_2EBIT2__nz,axiom,
! [V0n: tyop_2Enum_2Enum] :
( (~)
@ ( ( c_2Earithmetic_2EBIT2 @ V0n )
= c_2Enum_2E0 ) ) ).
thf(thm_2Eintto_2Eneg__lt__BIT1__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V0m ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) )
= c_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__lt__BIT2__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V0m ) ) @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT2 @ V1n ) ) )
= c_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__BIT1__lt__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT1 @ V0m ) ) ) @ ( c_2Einteger_2Eint__of__num @ V1n ) )
= c_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__BIT2__lt__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT2 @ V0m ) ) ) @ ( c_2Einteger_2Eint__of__num @ V1n ) )
= c_2EternaryComparisons_2ELESS ) ).
thf(thm_2Eintto_2Eneg__ZERO__eq__ZERO__thm,axiom,
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Earithmetic_2EZERO ) ) @ ( c_2Einteger_2Eint__of__num @ c_2Earithmetic_2EZERO ) )
= c_2EternaryComparisons_2EEQUAL ) ).
thf(thm_2Eintto_2EBIT1__gt__neg__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT1 @ V0m ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V1n ) ) )
= c_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2EBIT2__gt__neg__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT2 @ V0m ) ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ V1n ) ) )
= c_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2Egt__neg__BIT1__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__of__num @ V0m ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= c_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2Egt__neg__BIT2__thm,axiom,
! [V0m: tyop_2Enum_2Enum,V1n: tyop_2Enum_2Enum] :
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__of__num @ V0m ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ ( c_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= c_2EternaryComparisons_2EGREATER ) ).
thf(thm_2Eintto_2EZERO__eq__neg__ZERO__thm,axiom,
( ( c_2Eintto_2EintOrd @ ( c_2Einteger_2Eint__of__num @ c_2Earithmetic_2EZERO ) @ ( c_2Einteger_2Eint__neg @ ( c_2Einteger_2Eint__of__num @ c_2Earithmetic_2EZERO ) ) )
= c_2EternaryComparisons_2EEQUAL ) ).
%------------------------------------------------------------------------------