ITP001 Axioms: ITP051^7.ax
%------------------------------------------------------------------------------
% File : ITP051^7 : 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 : readerMonad.ax [Gau19]
% : HL4051^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 38 ( 19 unt; 16 typ; 0 def)
% Number of atoms : 25 ( 17 equ; 1 cnn)
% Maximal formula atoms : 2 ( 0 avg)
% Number of connectives : 199 ( 1 ~; 1 |; 2 &; 187 @)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg; 187 nst)
% Number of types : 2 ( 1 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 1 con; 0-8 aty)
% Number of variables : 110 ( 1 ^ 87 !; 1 ?; 110 :)
% ( 21 !>; 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_2EreaderMonad_2EBIND,type,
c_2EreaderMonad_2EBIND:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : ( ( A_27s > A_27a ) > ( A_27a > A_27s > A_27b ) > A_27s > A_27b ) ).
thf(c_2EreaderMonad_2EFMAP,type,
c_2EreaderMonad_2EFMAP:
!>[A_27a: $tType,A_27b: $tType,A_27s: $tType] : ( ( A_27a > A_27b ) > ( A_27s > A_27a ) > A_27s > A_27b ) ).
thf(c_2Ecombin_2EI,type,
c_2Ecombin_2EI:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
thf(c_2EreaderMonad_2EJOIN,type,
c_2EreaderMonad_2EJOIN:
!>[A_27a: $tType,A_27s: $tType] : ( ( A_27s > A_27s > A_27a ) > A_27s > A_27a ) ).
thf(c_2EreaderMonad_2EMCOMPOSE,type,
c_2EreaderMonad_2EMCOMPOSE:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType] : ( ( A_27a > A_27s > A_27b ) > ( A_27b > A_27s > A_27c ) > A_27a > A_27s > A_27c ) ).
thf(c_2EreaderMonad_2EUNIT,type,
c_2EreaderMonad_2EUNIT:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ecombin_2Eo,type,
c_2Ecombin_2Eo:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27c > A_27b ) > ( A_27a > A_27c ) > A_27a > A_27b ) ).
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_2EreaderMonad_2EBIND__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27s: $tType,V0M: A_27s > A_27a,V1f: A_27a > A_27s > A_27b,V2s: A_27s] :
( ( c_2EreaderMonad_2EBIND @ A_27a @ A_27b @ A_27s @ V0M @ V1f @ V2s )
= ( V1f @ ( V0M @ V2s ) @ V2s ) ) ).
thf(thm_2EreaderMonad_2EUNIT__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0x: A_27a,V1s: A_27b] :
( ( c_2EreaderMonad_2EUNIT @ A_27a @ A_27b @ V0x @ V1s )
= V0x ) ).
thf(thm_2EreaderMonad_2EMCOMPOSE__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27s: $tType,V0f1: A_27a > A_27s > A_27b,V1f2: A_27b > A_27s > A_27c,V2a: A_27a] :
( ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27b @ A_27c @ A_27s @ V0f1 @ V1f2 @ V2a )
= ( c_2EreaderMonad_2EBIND @ A_27b @ A_27c @ A_27s @ ( V0f1 @ V2a ) @ V1f2 ) ) ).
thf(thm_2EreaderMonad_2EFMAP__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27s: $tType,V0f: A_27a > A_27b,V1M1: A_27s > A_27a] :
( ( c_2EreaderMonad_2EFMAP @ A_27a @ A_27b @ A_27s @ V0f @ V1M1 )
= ( c_2Ecombin_2Eo @ A_27s @ A_27b @ A_27a @ V0f @ V1M1 ) ) ).
thf(thm_2EreaderMonad_2EJOIN__def,axiom,
! [A_27a: $tType,A_27s: $tType,V0MM: A_27s > A_27s > A_27a,V1s: A_27s] :
( ( c_2EreaderMonad_2EJOIN @ A_27a @ A_27s @ V0MM @ V1s )
= ( V0MM @ V1s @ V1s ) ) ).
thf(thm_2EreaderMonad_2EBIND__UNITR,axiom,
! [A_27a: $tType,A_27b: $tType,V0m: A_27a > A_27b] :
( ( c_2EreaderMonad_2EBIND @ A_27b @ A_27b @ A_27a @ V0m @ ( c_2EreaderMonad_2EUNIT @ A_27b @ A_27a ) )
= V0m ) ).
thf(thm_2EreaderMonad_2EBIND__UNITL,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x: A_27c,V1f: A_27c > A_27a > A_27b] :
( ( c_2EreaderMonad_2EBIND @ A_27c @ A_27b @ A_27a @ ( c_2EreaderMonad_2EUNIT @ A_27c @ A_27a @ V0x ) @ V1f )
= ( V1f @ V0x ) ) ).
thf(thm_2EreaderMonad_2EMCOMPOSE__LEFT__ID,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0g: A_27a > A_27b > A_27c] :
( ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27a @ A_27c @ A_27b @ ( c_2EreaderMonad_2EUNIT @ A_27a @ A_27b ) @ V0g )
= V0g ) ).
thf(thm_2EreaderMonad_2EMCOMPOSE__RIGHT__ID,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27a > A_27b > A_27c] :
( ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27c @ A_27c @ A_27b @ V0f @ ( c_2EreaderMonad_2EUNIT @ A_27c @ A_27b ) )
= V0f ) ).
thf(thm_2EreaderMonad_2EMCOMPOSE__ASSOC,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,V0h: A_27e > A_27b > A_27c,V1g: A_27d > A_27b > A_27e,V2f: A_27a > A_27b > A_27d] :
( ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27d @ A_27c @ A_27b @ V2f @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27d @ A_27e @ A_27c @ A_27b @ V1g @ V0h ) )
= ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27e @ A_27c @ A_27b @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27d @ A_27e @ A_27b @ V2f @ V1g ) @ V0h ) ) ).
thf(thm_2EreaderMonad_2EFMAP__ID,axiom,
! [A_27a: $tType,A_27b: $tType,V0M: A_27a > A_27b] :
( ( ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27b @ A_27a
@ ^ [V1x: A_27b] : V1x
@ V0M )
= V0M )
& ( ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27b @ A_27a @ ( c_2Ecombin_2EI @ A_27b ) @ V0M )
= V0M ) ) ).
thf(thm_2EreaderMonad_2EFMAP__o,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g: A_27b > A_27d,V1f: A_27d > A_27c] :
( ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27c @ A_27a @ ( c_2Ecombin_2Eo @ A_27b @ A_27c @ A_27d @ V1f @ V0g ) )
= ( c_2Ecombin_2Eo @ ( A_27a > A_27b ) @ ( A_27a > A_27c ) @ ( A_27a > A_27d ) @ ( c_2EreaderMonad_2EFMAP @ A_27d @ A_27c @ A_27a @ V1f ) @ ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27d @ A_27a @ V0g ) ) ) ).
thf(thm_2EreaderMonad_2EFMAP__BIND,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27c > A_27b,V1M: A_27a > A_27c] :
( ( c_2EreaderMonad_2EFMAP @ A_27c @ A_27b @ A_27a @ V0f @ V1M )
= ( c_2EreaderMonad_2EBIND @ A_27c @ A_27b @ A_27a @ V1M @ ( c_2Ecombin_2Eo @ A_27c @ ( A_27a > A_27b ) @ A_27b @ ( c_2EreaderMonad_2EUNIT @ A_27b @ A_27a ) @ V0f ) ) ) ).
thf(thm_2EreaderMonad_2EBIND__JOIN,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27c > A_27a > A_27b,V1M: A_27a > A_27c] :
( ( c_2EreaderMonad_2EBIND @ A_27c @ A_27b @ A_27a @ V1M @ V0f )
= ( c_2EreaderMonad_2EJOIN @ A_27b @ A_27a @ ( c_2EreaderMonad_2EFMAP @ A_27c @ ( A_27a > A_27b ) @ A_27a @ V0f @ V1M ) ) ) ).
thf(thm_2EreaderMonad_2EJOIN__BIND,axiom,
! [A_27a: $tType,A_27b: $tType,V0M: A_27a > A_27a > A_27b] :
( ( c_2EreaderMonad_2EJOIN @ A_27b @ A_27a @ V0M )
= ( c_2EreaderMonad_2EBIND @ ( A_27a > A_27b ) @ A_27b @ A_27a @ V0M @ ( c_2Ecombin_2EI @ ( A_27a > A_27b ) ) ) ) ).
%------------------------------------------------------------------------------