TPTP Problem File: ITP002^2.p
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%------------------------------------------------------------------------------
% File : ITP002^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Eoption_2EOPTION__MAP2__THM.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_2Eoption_2EOPTION__MAP2__THM.p [Gau19]
% : HL400501^2.p [TPAP]
% Status : Theorem
% Rating : 1.00 v7.5.0
% Syntax : Number of formulae : 53 ( 5 unt; 21 typ; 0 def)
% Number of atoms : 190 ( 17 equ; 0 cnn)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 406 ( 1 ~; 0 |; 15 &; 348 @)
% ( 12 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 12 con; 0-3 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP001^2.ax').
%------------------------------------------------------------------------------
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_ty_2Eoption_2Eoption,type,
ty_2Eoption_2Eoption: del > del ).
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_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_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_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_2ECOND,type,
c_2Ebool_2ECOND: del > $i ).
thf(mem_c_2Ebool_2ECOND,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebool_2ECOND @ A_27a ) @ ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ) ).
thf(tp_c_2Eoption_2EOPTION__MAP2,type,
c_2Eoption_2EOPTION__MAP2: del > del > del > $i ).
thf(mem_c_2Eoption_2EOPTION__MAP2,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27b ) @ ( arr @ ( ty_2Eoption_2Eoption @ A_27c ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ) ).
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_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_2EREFL__CLAUSE,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( V0x = V0x )
<=> $true ) ) ).
thf(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
! [A_27a: del,V0t1: $i] :
( ( mem @ V0t1 @ A_27a )
=> ! [V1t2: $i] :
( ( mem @ V1t2 @ A_27a )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ V1t2 )
= V0t1 )
& ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V0t1 ) @ V1t2 )
= V1t2 ) ) ) ) ).
thf(conj_thm_2Eoption_2ESOME__11,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ( ( ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V1y ) )
<=> ( V0x = V1y ) ) ) ) ).
thf(ax_thm_2Eoption_2EIS__SOME__DEF,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) ) )
<=> $true ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27a ) @ ( c_2Eoption_2ENONE @ A_27a ) ) )
<=> $false ) ) ).
thf(ax_thm_2Eoption_2ETHE__DEF,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ V0x ) )
= V0x ) ) ).
thf(ax_thm_2Eoption_2EOPTION__MAP2__DEF,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ ( ty_2Eoption_2Eoption @ A_27b ) )
=> ! [V2y: $i] :
( ( mem @ V2y @ ( ty_2Eoption_2Eoption @ A_27c ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1x ) @ V2y )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A_27a ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ A_27c ) @ V2y ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ ( ap @ ( c_2Eoption_2ETHE @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ETHE @ A_27c ) @ V2y ) ) ) ) @ ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Eoption_2EOPTION__MAP2__THM,conjecture,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27b @ ( arr @ A_27c @ A_27a ) ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ A_27b )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27c )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( ap @ ( c_2Eoption_2ESOME @ A_27a ) @ ( ap @ ( ap @ V0f @ V1x ) @ V2y ) ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27b ) @ V1x ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A_27c ) @ V2y ) )
= ( c_2Eoption_2ENONE @ A_27a ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A_27a @ A_27b @ A_27c ) @ V0f ) @ ( c_2Eoption_2ENONE @ A_27b ) ) @ ( c_2Eoption_2ENONE @ A_27c ) )
= ( c_2Eoption_2ENONE @ A_27a ) ) ) ) ) ) ).
%------------------------------------------------------------------------------