ITP001 Axioms: ITP051^5.ax
%------------------------------------------------------------------------------
% File : ITP051^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : readerMonad^2.ax [Gau20]
% : HL4051^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 25 ( 0 unt; 5 typ; 0 def)
% Number of atoms : 187 ( 16 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 478 ( 0 ~; 0 |; 1 &; 449 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 11 avg; 449 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 87 ( 1 ^ 86 !; 0 ?; 87 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EreaderMonad_2EBIND,type,
c_2EreaderMonad_2EBIND: del > del > del > $i ).
thf(mem_c_2EreaderMonad_2EBIND,axiom,
! [A_27a: del,A_27b: del,A_27s: del] : ( mem @ ( c_2EreaderMonad_2EBIND @ A_27a @ A_27b @ A_27s ) @ ( arr @ ( arr @ A_27s @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27s @ A_27b ) ) @ ( arr @ A_27s @ A_27b ) ) ) ) ).
thf(tp_c_2EreaderMonad_2EFMAP,type,
c_2EreaderMonad_2EFMAP: del > del > del > $i ).
thf(mem_c_2EreaderMonad_2EFMAP,axiom,
! [A_27a: del,A_27b: del,A_27s: del] : ( mem @ ( c_2EreaderMonad_2EFMAP @ A_27a @ A_27b @ A_27s ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27s @ A_27a ) @ ( arr @ A_27s @ A_27b ) ) ) ) ).
thf(tp_c_2EreaderMonad_2EJOIN,type,
c_2EreaderMonad_2EJOIN: del > del > $i ).
thf(mem_c_2EreaderMonad_2EJOIN,axiom,
! [A_27a: del,A_27s: del] : ( mem @ ( c_2EreaderMonad_2EJOIN @ A_27a @ A_27s ) @ ( arr @ ( arr @ A_27s @ ( arr @ A_27s @ A_27a ) ) @ ( arr @ A_27s @ A_27a ) ) ) ).
thf(tp_c_2EreaderMonad_2EMCOMPOSE,type,
c_2EreaderMonad_2EMCOMPOSE: del > del > del > del > $i ).
thf(mem_c_2EreaderMonad_2EMCOMPOSE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27s: del] : ( mem @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27b @ A_27c @ A_27s ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27s @ A_27b ) ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27s @ A_27c ) ) @ ( arr @ A_27a @ ( arr @ A_27s @ A_27c ) ) ) ) ) ).
thf(tp_c_2EreaderMonad_2EUNIT,type,
c_2EreaderMonad_2EUNIT: del > del > $i ).
thf(mem_c_2EreaderMonad_2EUNIT,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2EreaderMonad_2EUNIT @ A_27a @ A_27b ) @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) ) ).
thf(ax_thm_2EreaderMonad_2EBIND__def,axiom,
! [A_27a: del,A_27b: del,A_27s: del,V0M: $i] :
( ( mem @ V0M @ ( arr @ A_27s @ A_27a ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ A_27s @ A_27b ) ) )
=> ! [V2s: $i] :
( ( mem @ V2s @ A_27s )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EreaderMonad_2EBIND @ A_27a @ A_27b @ A_27s ) @ V0M ) @ V1f ) @ V2s )
= ( ap @ ( ap @ V1f @ ( ap @ V0M @ V2s ) ) @ V2s ) ) ) ) ) ).
thf(ax_thm_2EreaderMonad_2EUNIT__def,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1s: $i] :
( ( mem @ V1s @ A_27b )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EUNIT @ A_27a @ A_27b ) @ V0x ) @ V1s )
= V0x ) ) ) ).
thf(ax_thm_2EreaderMonad_2EMCOMPOSE__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27s: del,V0f1: $i] :
( ( mem @ V0f1 @ ( arr @ A_27a @ ( arr @ A_27s @ A_27b ) ) )
=> ! [V1f2: $i] :
( ( mem @ V1f2 @ ( arr @ A_27b @ ( arr @ A_27s @ A_27c ) ) )
=> ! [V2a: $i] :
( ( mem @ V2a @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27b @ A_27c @ A_27s ) @ V0f1 ) @ V1f2 ) @ V2a )
= ( ap @ ( ap @ ( c_2EreaderMonad_2EBIND @ A_27b @ A_27c @ A_27s ) @ ( ap @ V0f1 @ V2a ) ) @ V1f2 ) ) ) ) ) ).
thf(conj_thm_2EreaderMonad_2EBIND__UNITR,axiom,
! [A_27a: del,A_27b: del,V0m: $i] :
( ( mem @ V0m @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EBIND @ A_27b @ A_27b @ A_27a ) @ V0m ) @ ( c_2EreaderMonad_2EUNIT @ A_27b @ A_27a ) )
= V0m ) ) ).
thf(conj_thm_2EreaderMonad_2EBIND__UNITL,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
( ( mem @ V0x @ A_27c )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27c @ ( arr @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EBIND @ A_27c @ A_27b @ A_27a ) @ ( ap @ ( c_2EreaderMonad_2EUNIT @ A_27c @ A_27a ) @ V0x ) ) @ V1f )
= ( ap @ V1f @ V0x ) ) ) ) ).
thf(conj_thm_2EreaderMonad_2EMCOMPOSE__LEFT__ID,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0g: $i] :
( ( mem @ V0g @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27a @ A_27c @ A_27b ) @ ( c_2EreaderMonad_2EUNIT @ A_27a @ A_27b ) ) @ V0g )
= V0g ) ) ).
thf(conj_thm_2EreaderMonad_2EMCOMPOSE__RIGHT__ID,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27c ) ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27c @ A_27c @ A_27b ) @ V0f ) @ ( c_2EreaderMonad_2EUNIT @ A_27c @ A_27b ) )
= V0f ) ) ).
thf(conj_thm_2EreaderMonad_2EMCOMPOSE__ASSOC,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ( arr @ A_27b @ A_27d ) ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27d @ ( arr @ A_27b @ A_27e ) ) )
=> ! [V2h: $i] :
( ( mem @ V2h @ ( arr @ A_27e @ ( arr @ A_27b @ A_27c ) ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27d @ A_27c @ A_27b ) @ V0f ) @ ( ap @ ( ap @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27d @ A_27e @ A_27c @ A_27b ) @ V1g ) @ V2h ) )
= ( ap @ ( ap @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27e @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2EreaderMonad_2EMCOMPOSE @ A_27a @ A_27d @ A_27e @ A_27b ) @ V0f ) @ V1g ) ) @ V2h ) ) ) ) ) ).
thf(ax_thm_2EreaderMonad_2EFMAP__def,axiom,
! [A_27a: del,A_27b: del,A_27s: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1M1: $i] :
( ( mem @ V1M1 @ ( arr @ A_27s @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27a @ A_27b @ A_27s ) @ V0f ) @ V1M1 )
= ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27s @ A_27b @ A_27a ) @ V0f ) @ V1M1 ) ) ) ) ).
thf(conj_thm_2EreaderMonad_2EFMAP__ID,axiom,
! [A_27a: del,A_27b: del,V0M: $i] :
( ( mem @ V0M @ ( arr @ A_27a @ A_27b ) )
=> ( ( ( ap
@ ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27b @ A_27a )
@ ( lam @ A_27b
@ ^ [V1x: $i] : V1x ) )
@ V0M )
= V0M )
& ( ( ap @ ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27b @ A_27a ) @ ( c_2Ecombin_2EI @ A_27b ) ) @ V0M )
= V0M ) ) ) ).
thf(conj_thm_2EreaderMonad_2EFMAP__o,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27d @ A_27c ) )
=> ! [V1g: $i] :
( ( mem @ V1g @ ( arr @ A_27b @ A_27d ) )
=> ( ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27c @ A_27a ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27b @ A_27c @ A_27d ) @ V0f ) @ V1g ) )
= ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( arr @ A_27a @ A_27b ) @ ( arr @ A_27a @ A_27c ) @ ( arr @ A_27a @ A_27d ) ) @ ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27d @ A_27c @ A_27a ) @ V0f ) ) @ ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27b @ A_27d @ A_27a ) @ V1g ) ) ) ) ) ).
thf(conj_thm_2EreaderMonad_2EFMAP__BIND,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27c @ A_27b ) )
=> ! [V1M: $i] :
( ( mem @ V1M @ ( arr @ A_27a @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27c @ A_27b @ A_27a ) @ V0f ) @ V1M )
= ( ap @ ( ap @ ( c_2EreaderMonad_2EBIND @ A_27c @ A_27b @ A_27a ) @ V1M ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ A_27c @ ( arr @ A_27a @ A_27b ) @ A_27b ) @ ( c_2EreaderMonad_2EUNIT @ A_27b @ A_27a ) ) @ V0f ) ) ) ) ) ).
thf(ax_thm_2EreaderMonad_2EJOIN__def,axiom,
! [A_27a: del,A_27s: del,V0MM: $i] :
( ( mem @ V0MM @ ( arr @ A_27s @ ( arr @ A_27s @ A_27a ) ) )
=> ! [V1s: $i] :
( ( mem @ V1s @ A_27s )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EJOIN @ A_27a @ A_27s ) @ V0MM ) @ V1s )
= ( ap @ ( ap @ V0MM @ V1s ) @ V1s ) ) ) ) ).
thf(conj_thm_2EreaderMonad_2EBIND__JOIN,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0M: $i] :
( ( mem @ V0M @ ( arr @ A_27a @ A_27c ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27c @ ( arr @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( ap @ ( c_2EreaderMonad_2EBIND @ A_27c @ A_27b @ A_27a ) @ V0M ) @ V1f )
= ( ap @ ( c_2EreaderMonad_2EJOIN @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( c_2EreaderMonad_2EFMAP @ A_27c @ ( arr @ A_27a @ A_27b ) @ A_27a ) @ V1f ) @ V0M ) ) ) ) ) ).
thf(conj_thm_2EreaderMonad_2EJOIN__BIND,axiom,
! [A_27a: del,A_27b: del,V0M: $i] :
( ( mem @ V0M @ ( arr @ A_27a @ ( arr @ A_27a @ A_27b ) ) )
=> ( ( ap @ ( c_2EreaderMonad_2EJOIN @ A_27b @ A_27a ) @ V0M )
= ( ap @ ( ap @ ( c_2EreaderMonad_2EBIND @ ( arr @ A_27a @ A_27b ) @ A_27b @ A_27a ) @ V0M ) @ ( c_2Ecombin_2EI @ ( arr @ A_27a @ A_27b ) ) ) ) ) ).
%------------------------------------------------------------------------------