ITP001 Axioms: ITP005^7.ax
%------------------------------------------------------------------------------
% File : ITP005^7 : 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 : marker.ax [Gau19]
% : HL4005^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 36 ( 12 unt; 18 typ; 0 def)
% Number of atoms : 21 ( 7 equ; 1 cnn)
% Maximal formula atoms : 2 ( 0 avg)
% Number of connectives : 148 ( 1 ~; 21 |; 30 &; 75 @)
% ( 20 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg; 75 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 0 ^ 37 !; 1 ?; 43 :)
% ( 5 !>; 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_2Emin_2Eind,type,
tyop_2Emin_2Eind: $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_2Emarker_2E_3A_2D,type,
c_2Emarker_2E_3A_2D: tyop_2Emin_2Eind > $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_2Emarker_2EAC,type,
c_2Emarker_2EAC: $o > $o > $o ).
thf(c_2Emarker_2EAbbrev,type,
c_2Emarker_2EAbbrev: $o > $o ).
thf(c_2Emarker_2ECong,type,
c_2Emarker_2ECong: $o > $o ).
thf(c_2Emarker_2EIfCases,type,
c_2Emarker_2EIfCases: $o ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Emarker_2Estmarker,type,
c_2Emarker_2Estmarker:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
thf(c_2Emarker_2Eunint,type,
c_2Emarker_2Eunint:
!>[A_27a: $tType] : ( A_27a > 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_2Emarker_2Estmarker__def,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( c_2Emarker_2Estmarker @ A_27a @ V0x )
= V0x ) ).
thf(thm_2Emarker_2Eunint__def,axiom,
! [A_27a: $tType,V0x: A_27a] :
( ( c_2Emarker_2Eunint @ A_27a @ V0x )
= V0x ) ).
thf(thm_2Emarker_2EAbbrev__def,axiom,
! [V0x: $o] :
( ( c_2Emarker_2EAbbrev @ V0x )
= V0x ) ).
thf(thm_2Emarker_2EIfCases__def,axiom,
c_2Emarker_2EIfCases = c_2Ebool_2ET ).
thf(thm_2Emarker_2EAC__DEF,axiom,
! [V0b1: $o,V1b2: $o] :
( ( c_2Emarker_2EAC @ V0b1 @ V1b2 )
<=> ( V0b1
& V1b2 ) ) ).
thf(thm_2Emarker_2ECong__def,axiom,
! [V0x: $o] :
( ( c_2Emarker_2ECong @ V0x )
= V0x ) ).
thf(thm_2Emarker_2Elabel__def,axiom,
! [V0lab: tyop_2Emin_2Eind,V1argument: $o] :
( ( c_2Emarker_2E_3A_2D @ V0lab @ V1argument )
= V1argument ) ).
thf(thm_2Emarker_2Emove__left__conj,axiom,
! [V0p: $o,V1q: $o,V2m: $o] :
( ( ( V0p
& ( c_2Emarker_2Estmarker @ $o @ V2m ) )
<=> ( ( c_2Emarker_2Estmarker @ $o @ V2m )
& V0p ) )
& ( ( ( c_2Emarker_2Estmarker @ $o @ V2m )
& V0p
& V1q )
<=> ( ( c_2Emarker_2Estmarker @ $o @ V2m )
& V0p
& V1q ) )
& ( ( V0p
& ( c_2Emarker_2Estmarker @ $o @ V2m )
& V1q )
<=> ( ( c_2Emarker_2Estmarker @ $o @ V2m )
& V0p
& V1q ) ) ) ).
thf(thm_2Emarker_2Emove__right__conj,axiom,
! [V0p: $o,V1q: $o,V2m: $o] :
( ( ( ( c_2Emarker_2Estmarker @ $o @ V2m )
& V0p )
<=> ( V0p
& ( c_2Emarker_2Estmarker @ $o @ V2m ) ) )
& ( ( V0p
& V1q
& ( c_2Emarker_2Estmarker @ $o @ V2m ) )
<=> ( V0p
& V1q
& ( c_2Emarker_2Estmarker @ $o @ V2m ) ) )
& ( ( V0p
& ( c_2Emarker_2Estmarker @ $o @ V2m )
& V1q )
<=> ( V0p
& V1q
& ( c_2Emarker_2Estmarker @ $o @ V2m ) ) ) ) ).
thf(thm_2Emarker_2Emove__left__disj,axiom,
! [V0p: $o,V1q: $o,V2m: $o] :
( ( ( V0p
| ( c_2Emarker_2Estmarker @ $o @ V2m ) )
<=> ( ( c_2Emarker_2Estmarker @ $o @ V2m )
| V0p ) )
& ( ( ( c_2Emarker_2Estmarker @ $o @ V2m )
| V0p
| V1q )
<=> ( ( c_2Emarker_2Estmarker @ $o @ V2m )
| V0p
| V1q ) )
& ( ( V0p
| ( c_2Emarker_2Estmarker @ $o @ V2m )
| V1q )
<=> ( ( c_2Emarker_2Estmarker @ $o @ V2m )
| V0p
| V1q ) ) ) ).
thf(thm_2Emarker_2Emove__right__disj,axiom,
! [V0p: $o,V1q: $o,V2m: $o] :
( ( ( ( c_2Emarker_2Estmarker @ $o @ V2m )
| V0p )
<=> ( V0p
| ( c_2Emarker_2Estmarker @ $o @ V2m ) ) )
& ( ( V0p
| V1q
| ( c_2Emarker_2Estmarker @ $o @ V2m ) )
<=> ( V0p
| V1q
| ( c_2Emarker_2Estmarker @ $o @ V2m ) ) )
& ( ( V0p
| ( c_2Emarker_2Estmarker @ $o @ V2m )
| V1q )
<=> ( V0p
| V1q
| ( c_2Emarker_2Estmarker @ $o @ V2m ) ) ) ) ).
%------------------------------------------------------------------------------