TPTP Problem File: ITP011^2.p
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%------------------------------------------------------------------------------
% File : ITP011^2 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Equotient__option_2EOPTION__REL__def.p, bushy 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 : thm_2Equotient__option_2EOPTION__REL__def.p [Gau19]
% : HL405001^2.p [TPAP]
% Status : Theorem
% Rating : 0.62 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.55 v7.5.0
% Syntax : Number of formulae : 74 ( 5 unt; 28 typ; 0 def)
% Number of atoms : 399 ( 30 equ; 0 cnn)
% Maximal formula atoms : 69 ( 8 avg)
% Number of connectives : 839 ( 11 ~; 7 |; 48 &; 659 @)
% ( 41 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 15 con; 0-2 aty)
% Number of variables : 101 ( 0 ^; 97 !; 4 ?; 101 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001^2.ax').
%------------------------------------------------------------------------------
thf(tp_ty_2Eoption_2Eoption,type,
ty_2Eoption_2Eoption: del > del ).
thf(tp_c_2Eoption_2EOPTION__JOIN,type,
c_2Eoption_2EOPTION__JOIN: del > $i ).
thf(mem_c_2Eoption_2EOPTION__JOIN,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__MAP,type,
c_2Eoption_2EOPTION__MAP: del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__MAP,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ).
thf(tp_c_2Eoption_2Eoption__CASE,type,
c_2Eoption_2Eoption__CASE: del > del > $i ).
thf(mem_c_2Eoption_2Eoption__CASE,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ A_27b @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27b ) ) ) ) ).
thf(tp_c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
thf(ax_imp_p,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
<=> ( ( p @ Q )
=> ( p @ R ) ) ) ) ) ).
thf(tp_c_2Eoption_2EIS__NONE,type,
c_2Eoption_2EIS__NONE: del > $i ).
thf(mem_c_2Eoption_2EIS__NONE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
thf(tp_c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
thf(mem_c_2Ebool_2EF,axiom,
mem @ c_2Ebool_2EF @ bool ).
thf(ax_false_p,axiom,
~ ( p @ c_2Ebool_2EF ) ).
thf(tp_c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
thf(mem_c_2Ebool_2ET,axiom,
mem @ c_2Ebool_2ET @ bool ).
thf(ax_true_p,axiom,
p @ c_2Ebool_2ET ).
thf(tp_c_2Eoption_2EIS__SOME,type,
c_2Eoption_2EIS__SOME: del > $i ).
thf(mem_c_2Eoption_2EIS__SOME,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ bool ) ) ).
thf(tp_c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
thf(mem_c_2Ebool_2E_7E,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ) ).
thf(ax_neg_p,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ Q ) )
<=> ~ ( p @ Q ) ) ) ).
thf(tp_c_2Eoption_2ETHE,type,
c_2Eoption_2ETHE: del > $i ).
thf(mem_c_2Eoption_2ETHE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ETHE @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ A_27a ) ) ).
thf(tp_c_2Eoption_2ESOME,type,
c_2Eoption_2ESOME: del > $i ).
thf(mem_c_2Eoption_2ESOME,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ESOME @ A_27a ) @ ( arr @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
thf(tp_c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F: del > $i ).
thf(mem_c_2Ebool_2E_3F,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_3F @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
thf(ax_ex_p,axiom,
! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ Q ) )
<=> ? [X: $i] :
( ( mem @ X @ A )
& ( p @ ( ap @ Q @ X ) ) ) ) ) ).
thf(tp_c_2Eoption_2ENONE,type,
c_2Eoption_2ENONE: del > $i ).
thf(mem_c_2Eoption_2ENONE,axiom,
! [A_27a: del] : ( mem @ ( c_2Eoption_2ENONE @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ).
thf(tp_c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
thf(mem_c_2Ebool_2E_2F_5C,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
thf(ax_and_p,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ Q ) @ R ) )
<=> ( ( p @ Q )
& ( p @ R ) ) ) ) ) ).
thf(tp_c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
thf(mem_c_2Ebool_2E_5C_2F,axiom,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).
thf(ax_or_p,axiom,
! [Q: $i] :
( ( mem @ Q @ bool )
=> ! [R: $i] :
( ( mem @ R @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ Q ) @ R ) )
<=> ( ( p @ Q )
| ( p @ R ) ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTREL,type,
c_2Eoption_2EOPTREL: del > del > $i ).
thf(mem_c_2Eoption_2EOPTREL,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27a ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ bool ) ) ) ) ).
thf(tp_c_2Emin_2E_3D,type,
c_2Emin_2E_3D: del > $i ).
thf(mem_c_2Emin_2E_3D,axiom,
! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).
thf(ax_eq_p,axiom,
! [A: del,X: $i] :
( ( mem @ X @ A )
=> ! [Y: $i] :
( ( mem @ Y @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
<=> ( X = Y ) ) ) ) ).
thf(tp_c_2Ebool_2E_21,type,
c_2Ebool_2E_21: del > $i ).
thf(mem_c_2Ebool_2E_21,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2E_21 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ bool ) ) ).
thf(ax_all_p,axiom,
! [A: del,Q: $i] :
( ( mem @ Q @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ Q ) )
<=> ! [X: $i] :
( ( mem @ X @ A )
=> ( p @ ( ap @ Q @ X ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ETRUTH,axiom,
$true ).
thf(conj_thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1: $i] :
( ( mem @ V0t1 @ bool )
=> ! [V1t2: $i] :
( ( mem @ V1t2 @ bool )
=> ( ( ( p @ V0t1 )
=> ( p @ V1t2 ) )
=> ( ( ( p @ V1t2 )
=> ( p @ V0t1 ) )
=> ( ( p @ V0t1 )
<=> ( p @ V1t2 ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2EFALSITY,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( $false
=> ( p @ V0t ) ) ) ).
thf(conj_thm_2Ebool_2EEXISTS__SIMP,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ? [V1x: $i] :
( ( mem @ V1x @ A_27a )
& ( p @ V0t ) )
<=> ( p @ V0t ) ) ) ).
thf(conj_thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( $true
& ( p @ V0t ) )
<=> ( p @ V0t ) )
& ( ( ( p @ V0t )
& $true )
<=> ( p @ V0t ) )
& ( ( $false
& ( p @ V0t ) )
<=> $false )
& ( ( ( p @ V0t )
& $false )
<=> $false )
& ( ( ( p @ V0t )
& ( p @ V0t ) )
<=> ( p @ V0t ) ) ) ) ).
thf(conj_thm_2Ebool_2EOR__CLAUSES,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( $true
| ( p @ V0t ) )
<=> $true )
& ( ( ( p @ V0t )
| $true )
<=> $true )
& ( ( $false
| ( p @ V0t ) )
<=> ( p @ V0t ) )
& ( ( ( p @ V0t )
| $false )
<=> ( p @ V0t ) )
& ( ( ( p @ V0t )
| ( p @ V0t ) )
<=> ( p @ V0t ) ) ) ) ).
thf(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ~ ~ ( p @ V0t )
<=> ( p @ V0t ) ) )
& ( ~ $true
<=> $false )
& ( ~ $false
<=> $true ) ) ).
thf(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( V0x = V0x )
<=> $true ) ) ).
thf(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( $true
<=> ( p @ V0t ) )
<=> ( p @ V0t ) )
& ( ( ( p @ V0t )
<=> $true )
<=> ( p @ V0t ) )
& ( ( $false
<=> ( p @ V0t ) )
<=> ~ ( p @ V0t ) )
& ( ( ( p @ V0t )
<=> $false )
<=> ~ ( p @ V0t ) ) ) ) ).
thf(conj_thm_2Eoption_2Eoption__CLAUSES,axiom,
! [A_27a: del,A_27b: del,V0e: $i] :
( ( mem @ V0e @ A_27b )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ A_27b ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27a )
=> ( ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V4y ) )
<=> ( V3x = V4y ) ) ) )
& ! [V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V5x ) )
= V5x ) )
& ! [V6x: $i] :
( ( mem @ V6x @ A_27a )
=> ( ( c_2Eoption_2ENONE @ A_27a )
!= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V6x ) ) )
& ! [V7x: $i] :
( ( mem @ V7x @ A_27a )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V7x )
!= ( c_2Eoption_2ENONE @ A_27a ) ) )
& ! [V8x: $i] :
( ( mem @ V8x @ A_27a )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V8x ) ) )
<=> $true ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
<=> $false )
& ! [V9x: $i] :
( ( mem @ V9x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V9x ) )
<=> ( V9x
= ( c_2Eoption_2ENONE @ A_27a ) ) ) )
& ! [V10x: $i] :
( ( mem @ V10x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V10x ) )
<=> ( V10x
= ( c_2Eoption_2ENONE @ A_27a ) ) ) )
& ! [V11x: $i] :
( ( mem @ V11x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V11x ) )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V11x ) )
= V11x ) ) )
& ! [V12x: $i] :
( ( mem @ V12x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V12x ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( c_2Eoption_2ESOME @ A_27a ) )
= V12x ) )
& ! [V13x: $i] :
( ( mem @ V13x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V13x ) @ V13x ) @ ( c_2Eoption_2ESOME @ A_27a ) )
= V13x ) )
& ! [V14x: $i] :
( ( mem @ V14x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A_27a ) @ V14x ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V14x ) @ V0e ) @ V1f )
= V0e ) ) )
& ! [V15x: $i] :
( ( mem @ V15x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V15x ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ V15x ) @ V0e ) @ V1f )
= ( ap @ V1f @ ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ V15x ) ) ) ) )
& ! [V16x: $i] :
( ( mem @ V16x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ V16x ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V16x ) @ V2e ) @ ( c_2Eoption_2ESOME @ A_27a ) )
= V16x ) ) )
& ! [V17v: $i] :
( ( mem @ V17v @ A_27b )
=> ! [V18f: $i] :
( ( mem @ V18f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ V17v ) @ V18f )
= V17v ) ) )
& ! [V19x: $i] :
( ( mem @ V19x @ A_27a )
=> ! [V20v: $i] :
( ( mem @ V20v @ A_27b )
=> ! [V21f: $i] :
( ( mem @ V21f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A_27a @ A_27b ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V19x ) ) @ V20v ) @ V21f )
= ( ap @ V21f @ V19x ) ) ) ) )
& ! [V22f: $i] :
( ( mem @ V22f @ ( arr @ A_27a @ A_27b ) )
=> ! [V23x: $i] :
( ( mem @ V23x @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V22f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V23x ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ ( ap @ V22f @ V23x ) ) ) ) )
& ! [V24f: $i] :
( ( mem @ V24f @ ( arr @ A_27a @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27b ) @ V24f ) @ ( c_2Eoption_2ENONE @ A_27a ) )
= ( c_2Eoption_2ENONE @ A_27b ) ) )
& ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A_27a ) ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ! [V25x: $i] :
( ( mem @ V25x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ V25x ) )
= V25x ) ) ) ) ) ) ).
thf(ax_thm_2Eoption_2EOPTREL__def,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27a ) )
=> ! [V2y: $i] :
( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27b ) @ V0R ) @ V1x ) @ V2y ) )
<=> ( ( ( V1x
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( V2y
= ( c_2Eoption_2ENONE @ A_27b ) ) )
| ? [V3x0: $i] :
( ( mem @ V3x0 @ A_27a )
& ? [V4y0: $i] :
( ( mem @ V4y0 @ A_27b )
& ( V1x
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V3x0 ) )
& ( V2y
= ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V4y0 ) )
& ( p @ ( ap @ ( ap @ V0R @ V3x0 ) @ V4y0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__option_2EOPTION__REL__def,conjecture,
! [A_27a: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27a )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
<=> $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( c_2Eoption_2ENONE @ A_27a ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) )
<=> $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V2y ) ) )
<=> ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------