TPTP Problem File: ITP011^5.p
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%------------------------------------------------------------------------------
% File : ITP011^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Equotient__option_2EOPTION__REL__def.p, 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 : thm_2Equotient__option_2EOPTION__REL__def.p [Gau20]
% : HL405001^5.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 8837 ( 617 unt;1255 typ; 0 def)
% Number of atoms : 176223 (9032 equ; 0 cnn)
% Maximal formula atoms : 7693 ( 23 avg)
% Number of connectives : 432662 ( 916 ~; 485 |;19437 &;389016 @)
% (3767 <=>;19041 =>; 0 <=; 0 <~>)
% Maximal formula depth : 368 ( 13 avg)
% Number of types : 37 ( 35 usr)
% Number of type conns : 1427 (1427 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1234 (1231 usr; 284 con; 0-5 aty)
% Number of variables : 42982 (2775 ^;27329 !;12878 ?;42982 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001^2.ax').
include('Axioms/ITP001/ITP002^5.ax').
include('Axioms/ITP001/ITP003^5.ax').
include('Axioms/ITP001/ITP004^5.ax').
include('Axioms/ITP001/ITP007^5.ax').
include('Axioms/ITP001/ITP006^5.ax').
include('Axioms/ITP001/ITP005^5.ax').
include('Axioms/ITP001/ITP008^5.ax').
include('Axioms/ITP001/ITP009^5.ax').
include('Axioms/ITP001/ITP010^5.ax').
include('Axioms/ITP001/ITP012^5.ax').
include('Axioms/ITP001/ITP011^5.ax').
include('Axioms/ITP001/ITP013^5.ax').
include('Axioms/ITP001/ITP014^5.ax').
include('Axioms/ITP001/ITP015^5.ax').
include('Axioms/ITP001/ITP017^5.ax').
include('Axioms/ITP001/ITP016^5.ax').
include('Axioms/ITP001/ITP019^5.ax').
include('Axioms/ITP001/ITP018^5.ax').
include('Axioms/ITP001/ITP021^5.ax').
include('Axioms/ITP001/ITP022^5.ax').
include('Axioms/ITP001/ITP020^5.ax').
include('Axioms/ITP001/ITP024^5.ax').
include('Axioms/ITP001/ITP023^5.ax').
include('Axioms/ITP001/ITP025^5.ax').
include('Axioms/ITP001/ITP026^5.ax').
include('Axioms/ITP001/ITP027^5.ax').
include('Axioms/ITP001/ITP028^5.ax').
include('Axioms/ITP001/ITP031^5.ax').
include('Axioms/ITP001/ITP029^5.ax').
include('Axioms/ITP001/ITP033^5.ax').
include('Axioms/ITP001/ITP030^5.ax').
include('Axioms/ITP001/ITP032^5.ax').
include('Axioms/ITP001/ITP038^5.ax').
include('Axioms/ITP001/ITP035^5.ax').
include('Axioms/ITP001/ITP034^5.ax').
include('Axioms/ITP001/ITP036^5.ax').
include('Axioms/ITP001/ITP037^5.ax').
include('Axioms/ITP001/ITP039^5.ax').
include('Axioms/ITP001/ITP041^5.ax').
include('Axioms/ITP001/ITP042^5.ax').
include('Axioms/ITP001/ITP040^5.ax').
include('Axioms/ITP001/ITP044^5.ax').
include('Axioms/ITP001/ITP051^5.ax').
include('Axioms/ITP001/ITP045^5.ax').
include('Axioms/ITP001/ITP056^5.ax').
include('Axioms/ITP001/ITP046^5.ax').
include('Axioms/ITP001/ITP043^5.ax').
include('Axioms/ITP001/ITP052^5.ax').
include('Axioms/ITP001/ITP057^5.ax').
include('Axioms/ITP001/ITP048^5.ax').
include('Axioms/ITP001/ITP047^5.ax').
include('Axioms/ITP001/ITP055^5.ax').
include('Axioms/ITP001/ITP053^5.ax').
include('Axioms/ITP001/ITP054^5.ax').
include('Axioms/ITP001/ITP058^5.ax').
include('Axioms/ITP001/ITP049^5.ax').
include('Axioms/ITP001/ITP050^5.ax').
include('Axioms/ITP001/ITP061^5.ax').
include('Axioms/ITP001/ITP069^5.ax').
include('Axioms/ITP001/ITP062^5.ax').
include('Axioms/ITP001/ITP068^5.ax').
include('Axioms/ITP001/ITP078^5.ax').
include('Axioms/ITP001/ITP064^5.ax').
include('Axioms/ITP001/ITP060^5.ax').
include('Axioms/ITP001/ITP067^5.ax').
include('Axioms/ITP001/ITP075^5.ax').
include('Axioms/ITP001/ITP074^5.ax').
include('Axioms/ITP001/ITP063^5.ax').
include('Axioms/ITP001/ITP059^5.ax').
include('Axioms/ITP001/ITP065^5.ax').
include('Axioms/ITP001/ITP076^5.ax').
include('Axioms/ITP001/ITP066^5.ax').
include('Axioms/ITP001/ITP077^5.ax').
include('Axioms/ITP001/ITP070^5.ax').
%------------------------------------------------------------------------------
thf(conj_thm_2Equotient__option_2EOPTION__MAP__I,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Eoption_2EOPTION__MAP @ A_27a @ A_27a ) @ ( c_2Ecombin_2EI @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ).
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 ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------