ITP001 Axioms: ITP039^5.ax
%------------------------------------------------------------------------------
% File : ITP039^5 : 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 : defCNF^2.ax [Gau20]
% : HL4039^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 31 ( 2 unt; 10 typ; 0 def)
% Number of atoms : 1410 ( 4 equ; 0 cnn)
% Maximal formula atoms : 261 ( 45 avg)
% Number of connectives : 1676 ( 0 ~; 0 |; 25 &;1571 @)
% ( 23 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 15 avg;1571 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 26 con; 0-2 aty)
% Number of variables : 95 ( 0 ^ 92 !; 3 ?; 95 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(stp_c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,type,
tp__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,type,
inj__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o: tp__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,type,
surj__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o: $i > tp__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o] :
( ( surj__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ ( inj__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ X ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ ( surj__c_ty_2Epair_2Eprod_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ X ) ) ) ) ).
thf(stp_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,type,
tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o: $tType ).
thf(stp_inj_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,type,
inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o: tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o > $i ).
thf(stp_surj_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,type,
surj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o: $i > tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o ).
thf(stp_inj_surj_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,axiom,
! [X: tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o] :
( ( surj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ ( inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,axiom,
! [X: tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o] : ( mem @ ( inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ X ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ).
thf(stp_iso_mem_c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) )
=> ( X
= ( inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ ( surj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ X ) ) ) ) ).
thf(tp_c_2EdefCNF_2EDEF,type,
c_2EdefCNF_2EDEF: $i ).
thf(mem_c_2EdefCNF_2EDEF,axiom,
mem @ c_2EdefCNF_2EDEF @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ bool ) ) ) ).
thf(tp_c_2EdefCNF_2EOK,type,
c_2EdefCNF_2EOK: $i ).
thf(mem_c_2EdefCNF_2EOK,axiom,
mem @ c_2EdefCNF_2EOK @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ bool ) ) ).
thf(tp_c_2EdefCNF_2EOKDEF,type,
c_2EdefCNF_2EOKDEF: $i ).
thf(mem_c_2EdefCNF_2EOKDEF,axiom,
mem @ c_2EdefCNF_2EOKDEF @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ bool ) ) ).
thf(tp_c_2EdefCNF_2EUNIQUE,type,
c_2EdefCNF_2EUNIQUE: $i ).
thf(mem_c_2EdefCNF_2EUNIQUE,axiom,
mem @ c_2EdefCNF_2EUNIQUE @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ bool ) ) ) ).
thf(conj_thm_2EdefCNF_2EUNIQUE__ind,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ bool ) ) ) )
=> ( ( ! [V1v: $i] :
( ( mem @ V1v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2n: tp__ty_2Enum_2Enum,V3conn: $i] :
( ( mem @ V3conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V4i: tp__ty_2Enum_2Enum,V5j: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ V0P @ V1v ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V3conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V4i ) ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V5j ) ) ) ) ) ) ) )
& ! [V6v: $i] :
( ( mem @ V6v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V7n: tp__ty_2Enum_2Enum,V8conn: $i] :
( ( mem @ V8conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V9i: tp__ty_2Enum_2Enum,V10b: $i] :
( ( mem @ V10b @ bool )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V6v ) @ ( inj__ty_2Enum_2Enum @ V7n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V8conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V9i ) ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V10b ) ) ) ) ) ) ) )
& ! [V11v: $i] :
( ( mem @ V11v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V12n: tp__ty_2Enum_2Enum,V13conn: $i] :
( ( mem @ V13conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V14a: $i] :
( ( mem @ V14a @ bool )
=> ! [V15j: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ ( ap @ V0P @ V11v ) @ ( inj__ty_2Enum_2Enum @ V12n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V13conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V14a ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V15j ) ) ) ) ) ) ) ) )
& ! [V16v: $i] :
( ( mem @ V16v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V17n: tp__ty_2Enum_2Enum,V18conn: $i] :
( ( mem @ V18conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V19a: $i] :
( ( mem @ V19a @ bool )
=> ! [V20b: $i] :
( ( mem @ V20b @ bool )
=> ( p @ ( ap @ ( ap @ ( ap @ V0P @ V16v ) @ ( inj__ty_2Enum_2Enum @ V17n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V18conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V19a ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V20b ) ) ) ) ) ) ) ) ) )
=> ! [V21v: $i] :
( ( mem @ V21v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V22v1: tp__ty_2Enum_2Enum,V23v2: $i] :
( ( mem @ V23v2 @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V24v3: tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,V25v4: tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o] : ( p @ ( ap @ ( ap @ ( ap @ V0P @ V21v ) @ ( inj__ty_2Enum_2Enum @ V22v1 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V23v2 ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ V24v3 ) ) @ ( inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ V25v4 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2EUNIQUE__def,axiom,
! [V0v: $i] :
( ( mem @ V0v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2conn: $i] :
( ( mem @ V2conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V3i: tp__ty_2Enum_2Enum,V4j: tp__ty_2Enum_2Enum,V5b: $i] :
( ( mem @ V5b @ bool )
=> ! [V6a: $i] :
( ( mem @ V6a @ bool )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EUNIQUE @ V0v ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V2conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V4j ) ) ) ) ) )
<=> ( ( p @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ ( ap @ ( ap @ V2conn @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V4j ) ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EUNIQUE @ V0v ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V2conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V5b ) ) ) ) )
<=> ( ( p @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ ( ap @ ( ap @ V2conn @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ V5b ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EUNIQUE @ V0v ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V2conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V6a ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V4j ) ) ) ) ) )
<=> ( ( p @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ ( ap @ ( ap @ V2conn @ V6a ) @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V4j ) ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EUNIQUE @ V0v ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V2conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V6a ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V5b ) ) ) ) )
<=> ( ( p @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ ( ap @ ( ap @ V2conn @ V6a ) @ V5b ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2EdefCNF_2EDEF__def,axiom,
( ! [V0v: $i] :
( ( mem @ V0v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EDEF @ V0v ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( c_2Elist_2ENIL @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) ) )
<=> $true ) )
& ! [V2v: $i] :
( ( mem @ V2v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V3n: tp__ty_2Enum_2Enum,V4x: $i] :
( ( mem @ V4x @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) )
=> ! [V5xs: $i] :
( ( mem @ V5xs @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EDEF @ V2v ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ V4x ) @ V5xs ) ) )
<=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EUNIQUE @ V2v ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ V4x ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EDEF @ V2v ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V5xs ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2EOK__ind,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ bool ) ) )
=> ( ( ! [V1n: tp__ty_2Enum_2Enum,V2conn: $i] :
( ( mem @ V2conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V3i: tp__ty_2Enum_2Enum,V4j: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V2conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V4j ) ) ) ) ) ) )
& ! [V5n: tp__ty_2Enum_2Enum,V6conn: $i] :
( ( mem @ V6conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V7i: tp__ty_2Enum_2Enum,V8b: $i] :
( ( mem @ V8b @ bool )
=> ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V5n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V6conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V7i ) ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V8b ) ) ) ) ) ) )
& ! [V9n: tp__ty_2Enum_2Enum,V10conn: $i] :
( ( mem @ V10conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V11a: $i] :
( ( mem @ V11a @ bool )
=> ! [V12j: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V9n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V10conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V11a ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V12j ) ) ) ) ) ) ) )
& ! [V13n: tp__ty_2Enum_2Enum,V14conn: $i] :
( ( mem @ V14conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V15a: $i] :
( ( mem @ V15a @ bool )
=> ! [V16b: $i] :
( ( mem @ V16b @ bool )
=> ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V13n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V14conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V15a ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V16b ) ) ) ) ) ) ) ) )
=> ! [V17v: tp__ty_2Enum_2Enum,V18v1: $i] :
( ( mem @ V18v1 @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V19v2: tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o,V20v3: tp__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V17v ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V18v1 ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ V19v2 ) ) @ ( inj__c_ty_2Esum_2Esum_ty_2Enum_2Enum_o @ V20v3 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2EOK__def,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1conn: $i] :
( ( mem @ V1conn @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V2i: tp__ty_2Enum_2Enum,V3j: tp__ty_2Enum_2Enum,V4b: $i] :
( ( mem @ V4b @ bool )
=> ! [V5a: $i] :
( ( mem @ V5a @ bool )
=> ( ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOK @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V1conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V3j ) ) ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3j ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOK @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V1conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V4b ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOK @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V1conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V5a ) ) @ ( ap @ ( c_2Esum_2EINL @ ty_2Enum_2Enum @ bool ) @ ( inj__ty_2Enum_2Enum @ V3j ) ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3j ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOK @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) @ V1conn ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V5a ) ) @ ( ap @ ( c_2Esum_2EINR @ ty_2Enum_2Enum @ bool ) @ V4b ) ) ) ) )
<=> $true ) ) ) ) ) ).
thf(ax_thm_2EdefCNF_2EOKDEF__def,axiom,
( ! [V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOKDEF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( c_2Elist_2ENIL @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) ) )
<=> $true )
& ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) )
=> ! [V3xs: $i] :
( ( mem @ V3xs @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOKDEF @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ V2x ) @ V3xs ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOK @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2x ) )
& ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOKDEF @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V3xs ) ) ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2EDEF__SNOC,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: $i] :
( ( mem @ V1x @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) )
=> ! [V3v: $i] :
( ( mem @ V3v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EDEF @ V3v ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ V1x ) @ V2l ) ) )
<=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EDEF @ V3v ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EUNIQUE @ V3v ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ V2l ) ) ) @ V1x ) ) ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2EOKDEF__SNOC,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1x: $i] :
( ( mem @ V1x @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) )
=> ! [V2l: $i] :
( ( mem @ V2l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOKDEF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ V1x ) @ V2l ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOKDEF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l ) )
& ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOK @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) @ V2l ) ) ) @ V1x ) ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2ECONSISTENCY,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1l: $i] :
( ( mem @ V1l @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2EdefCNF_2EOKDEF @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) )
=> ? [V2v: $i] :
( ( mem @ V2v @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EDEF @ V2v ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1l ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2EBIGSTEP,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ! [V2R: $i] :
( ( mem @ V2R @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ bool ) )
=> ( ! [V3v: $i] :
( ( mem @ V3v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ V0P @ V3v ) )
=> ( ( p @ V1Q )
<=> ( p @ ( ap @ V2R @ V3v ) ) ) ) )
=> ( ( ? [V4v: $i] :
( ( mem @ V4v @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V0P @ V4v ) ) )
& ( p @ V1Q ) )
<=> ? [V5v: $i] :
( ( mem @ V5v @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V0P @ V5v ) )
& ( p @ ( ap @ V2R @ V5v ) ) ) ) ) ) ) ) ).
thf(conj_thm_2EdefCNF_2EFINAL__DEF,axiom,
! [V0v: $i] :
( ( mem @ V0v @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1n: tp__ty_2Enum_2Enum,V2x: $i] :
( ( mem @ V2x @ bool )
=> ( ( ( p @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ V2x ) )
<=> ( ( ( p @ ( ap @ V0v @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ V2x ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2EdefCNF_2EDEF @ V0v ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( c_2Elist_2ENIL @ ( ty_2Epair_2Eprod @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) @ ( ty_2Esum_2Esum @ ty_2Enum_2Enum @ bool ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------