ITP001 Axioms: ITP007^7.ax
%------------------------------------------------------------------------------
% File : ITP007^7 : 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 : sat.ax [Gau19]
% : HL4007^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 43 ( 7 unt; 12 typ; 0 def)
% Number of atoms : 79 ( 5 equ; 52 cnn)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 241 ( 52 ~; 39 |; 20 &; 72 @)
% ( 25 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg; 72 nst)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 67 ( 0 ^ 62 !; 1 ?; 67 :)
% ( 4 !>; 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(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_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $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_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_2Esat_2EAND__IMP,axiom,
! [V0A: $o,V1B: $o,V2C: $o] :
( ( ( V0A
& V1B )
=> V2C )
<=> ( V0A
=> ( V1B
=> V2C ) ) ) ).
thf(thm_2Esat_2ENOT__NOT,axiom,
! [V0t: $o] :
( ( (~) @ ( (~) @ V0t ) )
<=> V0t ) ).
thf(thm_2Esat_2EAND__INV,axiom,
! [V0A: $o] :
( ( ( (~) @ V0A )
& V0A )
<=> c_2Ebool_2EF ) ).
thf(thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A: $o] :
( V0A
=> ( ( (~) @ V0A )
=> c_2Ebool_2EF ) ) ).
thf(thm_2Esat_2EOR__DUAL,axiom,
! [V0B: $o,V1A: $o] :
( ( ( (~)
@ ( V1A
| V0B ) )
=> c_2Ebool_2EF )
<=> ( ( (~) @ V1A )
=> ( ( (~) @ V0B )
=> c_2Ebool_2EF ) ) ) ).
thf(thm_2Esat_2EOR__DUAL2,axiom,
! [V0B: $o,V1A: $o] :
( ( ( (~)
@ ( V1A
| V0B ) )
=> c_2Ebool_2EF )
<=> ( ( V1A
=> c_2Ebool_2EF )
=> ( ( (~) @ V0B )
=> c_2Ebool_2EF ) ) ) ).
thf(thm_2Esat_2EOR__DUAL3,axiom,
! [V0B: $o,V1A: $o] :
( ( ( (~)
@ ( ( (~) @ V1A )
| V0B ) )
=> c_2Ebool_2EF )
<=> ( V1A
=> ( ( (~) @ V0B )
=> c_2Ebool_2EF ) ) ) ).
thf(thm_2Esat_2EAND__INV2,axiom,
! [V0A: $o] :
( ( ( (~) @ V0A )
=> c_2Ebool_2EF )
=> ( ( V0A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ) ).
thf(thm_2Esat_2ENOT__ELIM2,axiom,
! [V0A: $o] :
( ( ( (~) @ V0A )
=> c_2Ebool_2EF )
<=> V0A ) ).
thf(thm_2Esat_2EEQT__Imp1,axiom,
! [V0b: $o] :
( V0b
=> ( V0b = c_2Ebool_2ET ) ) ).
thf(thm_2Esat_2EEQF__Imp1,axiom,
! [V0b: $o] :
( ( (~) @ V0b )
=> ( V0b = c_2Ebool_2EF ) ) ).
thf(thm_2Esat_2Edc__eq,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q = V0r ) )
<=> ( ( V2p
| V1q
| V0r )
& ( V2p
| ( (~) @ V0r )
| ( (~) @ V1q ) )
& ( V1q
| ( (~) @ V0r )
| ( (~) @ V2p ) )
& ( V0r
| ( (~) @ V1q )
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__conj,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q
& V0r ) )
<=> ( ( V2p
| ( (~) @ V1q )
| ( (~) @ V0r ) )
& ( V1q
| ( (~) @ V2p ) )
& ( V0r
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__disj,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q
| V0r ) )
<=> ( ( V2p
| ( (~) @ V1q ) )
& ( V2p
| ( (~) @ V0r ) )
& ( V1q
| V0r
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__imp,axiom,
! [V0r: $o,V1q: $o,V2p: $o] :
( ( V2p
<=> ( V1q
=> V0r ) )
<=> ( ( V2p
| V1q )
& ( V2p
| ( (~) @ V0r ) )
& ( ( (~) @ V1q )
| V0r
| ( (~) @ V2p ) ) ) ) ).
thf(thm_2Esat_2Edc__neg,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
<=> ( (~) @ V0q ) )
<=> ( ( V1p
| V0q )
& ( ( (~) @ V0q )
| ( (~) @ V1p ) ) ) ) ).
thf(thm_2Esat_2Edc__cond,axiom,
! [V0s: $o,V1r: $o,V2q: $o,V3p: $o] :
( ( V3p
= ( c_2Ebool_2ECOND @ $o @ V2q @ V1r @ V0s ) )
<=> ( ( V3p
| V2q
| ( (~) @ V0s ) )
& ( V3p
| ( (~) @ V1r )
| ( (~) @ V2q ) )
& ( V3p
| ( (~) @ V1r )
| ( (~) @ V0s ) )
& ( ( (~) @ V2q )
| V1r
| ( (~) @ V3p ) )
& ( V2q
| V0s
| ( (~) @ V3p ) ) ) ) ).
thf(thm_2Esat_2Epth__ni1,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
=> V0q ) )
=> V1p ) ).
thf(thm_2Esat_2Epth__ni2,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
=> V0q ) )
=> ( (~) @ V0q ) ) ).
thf(thm_2Esat_2Epth__no1,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
| V0q ) )
=> ( (~) @ V1p ) ) ).
thf(thm_2Esat_2Epth__no2,axiom,
! [V0q: $o,V1p: $o] :
( ( (~)
@ ( V1p
| V0q ) )
=> ( (~) @ V0q ) ) ).
thf(thm_2Esat_2Epth__an1,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& V0q )
=> V1p ) ).
thf(thm_2Esat_2Epth__an2,axiom,
! [V0q: $o,V1p: $o] :
( ( V1p
& V0q )
=> V0q ) ).
thf(thm_2Esat_2Epth__nn,axiom,
! [V0p: $o] :
( ( (~) @ ( (~) @ V0p ) )
=> V0p ) ).
%------------------------------------------------------------------------------