TPTP Problem File: ITP020^2.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ITP020^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 set theory export of thm_2Eutil__prob_2ENUM__2D__BIJ__INV.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_2Eutil__prob_2ENUM__2D__BIJ__INV.p [Gau19]
% : HL409501^2.p [TPAP]
% Status : Theorem
% Rating : 0.60 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0
% Syntax : Number of formulae : 95 ( 8 unt; 29 typ; 0 def)
% Number of atoms : 506 ( 12 equ; 0 cnn)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 955 ( 41 ~; 36 |; 45 &; 667 @)
% ( 51 <=>; 115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 5 ( 3 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 16 con; 0-2 aty)
% Number of variables : 141 ( 0 ^; 125 !; 16 ?; 141 :)
% 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_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_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_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_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_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_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_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(tp_c_2Epred__set_2EUNIV,type,
c_2Epred__set_2EUNIV: del > $i ).
thf(mem_c_2Epred__set_2EUNIV,axiom,
! [A_27a: del] : ( mem @ ( c_2Epred__set_2EUNIV @ A_27a ) @ ( arr @ A_27a @ bool ) ) ).
thf(tp_ty_2Epair_2Eprod,type,
ty_2Epair_2Eprod: del > del > del ).
thf(tp_c_2Epred__set_2ECROSS,type,
c_2Epred__set_2ECROSS: del > del > $i ).
thf(mem_c_2Epred__set_2ECROSS,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2ECROSS @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ A_27a @ A_27b ) @ bool ) ) ) ) ).
thf(tp_c_2Epred__set_2EBIJ,type,
c_2Epred__set_2EBIJ: del > del > $i ).
thf(mem_c_2Epred__set_2EBIJ,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ bool ) @ ( arr @ ( arr @ A_27b @ bool ) @ bool ) ) ) ) ).
thf(tp_ty_2Enum_2Enum,type,
ty_2Enum_2Enum: del ).
thf(stp_ty_2Enum_2Enum,type,
tp__ty_2Enum_2Enum: $tType ).
thf(stp_inj_ty_2Enum_2Enum,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
thf(stp_surj_ty_2Enum_2Enum,type,
surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum ).
thf(stp_inj_surj_ty_2Enum_2Enum,axiom,
! [X: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) )
= X ) ).
thf(stp_inj_mem_ty_2Enum_2Enum,axiom,
! [X: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ) ).
thf(stp_iso_mem_ty_2Enum_2Enum,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Enum_2Enum )
=> ( X
= ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,type,
surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum: $i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_ty_2Enum_2Enum @ X ) ) ) ) ).
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(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_2EIMP__F,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( p @ V0t )
=> $false )
=> ~ ( p @ V0t ) ) ) ).
thf(conj_thm_2Ebool_2EF__IMP,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ~ ( p @ V0t )
=> ( ( p @ V0t )
=> $false ) ) ) ).
thf(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ( ( $true
=> ( p @ V0t ) )
<=> ( p @ V0t ) )
& ( ( ( p @ V0t )
=> $true )
<=> $true )
& ( ( $false
=> ( p @ V0t ) )
<=> $true )
& ( ( ( p @ V0t )
=> ( p @ V0t ) )
<=> $true )
& ( ( ( p @ V0t )
=> $false )
<=> ~ ( 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_2EEQ__SYM__EQ,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1y: $i] :
( ( mem @ V1y @ A_27a )
=> ( ( V0x = V1y )
<=> ( V1y = V0x ) ) ) ) ).
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_2Ebool_2ENOT__EXISTS__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ( ~ ? [V1x: $i] :
( ( mem @ V1x @ A_27a )
& ( p @ ( ap @ V0P @ V1x ) ) )
<=> ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ~ ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ELEFT__AND__FORALL__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ( ( ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( p @ ( ap @ V0P @ V2x ) ) )
& ( p @ V1Q ) )
<=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ ( ap @ V0P @ V3x ) )
& ( p @ V1Q ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ( ( ( p @ V0P )
& ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( p @ ( ap @ V1Q @ V2x ) ) ) )
<=> ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( ( p @ V0P )
& ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ELEFT__OR__EXISTS__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ( ( ? [V2x: $i] :
( ( mem @ V2x @ A_27a )
& ( p @ ( ap @ V0P @ V2x ) ) )
| ( p @ V1Q ) )
<=> ? [V3x: $i] :
( ( mem @ V3x @ A_27a )
& ( ( p @ ( ap @ V0P @ V3x ) )
| ( p @ V1Q ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ( ( ( p @ V0P )
| ? [V2x: $i] :
( ( mem @ V2x @ A_27a )
& ( p @ ( ap @ V1Q @ V2x ) ) ) )
<=> ? [V3x: $i] :
( ( mem @ V3x @ A_27a )
& ( ( p @ V0P )
| ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ bool ) )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ bool )
=> ( ? [V2x: $i] :
( ( mem @ V2x @ A_27a )
& ( p @ ( ap @ V0P @ V2x ) )
& ( p @ V1Q ) )
<=> ( ? [V3x: $i] :
( ( mem @ V3x @ A_27a )
& ( p @ ( ap @ V0P @ V3x ) ) )
& ( p @ V1Q ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ( ? [V2x: $i] :
( ( mem @ V2x @ A_27a )
& ( p @ V0P )
& ( p @ ( ap @ V1Q @ V2x ) ) )
<=> ( ( p @ V0P )
& ? [V3x: $i] :
( ( mem @ V3x @ A_27a )
& ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM,axiom,
! [A_27a: del,V0Q: $i] :
( ( mem @ V0Q @ bool )
=> ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ A_27a @ bool ) )
=> ( ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ ( ap @ V1P @ V2x ) )
| ( p @ V0Q ) ) )
<=> ( ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( p @ ( ap @ V1P @ V3x ) ) )
| ( p @ V0Q ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ bool )
=> ! [V1Q: $i] :
( ( mem @ V1Q @ ( arr @ A_27a @ bool ) )
=> ( ! [V2x: $i] :
( ( mem @ V2x @ A_27a )
=> ( ( p @ V0P )
| ( p @ ( ap @ V1Q @ V2x ) ) ) )
<=> ( ( p @ V0P )
| ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ( p @ ( ap @ V1Q @ V3x ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebool_2EDISJ__SYM,axiom,
! [V0A: $i] :
( ( mem @ V0A @ bool )
=> ! [V1B: $i] :
( ( mem @ V1B @ bool )
=> ( ( ( p @ V0A )
| ( p @ V1B ) )
<=> ( ( p @ V1B )
| ( p @ V0A ) ) ) ) ) ).
thf(conj_thm_2Ebool_2ESKOLEM__THM,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ A_27a @ ( arr @ A_27b @ bool ) ) )
=> ( ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ? [V2y: $i] :
( ( mem @ V2y @ A_27b )
& ( p @ ( ap @ ( ap @ V0P @ V1x ) @ V2y ) ) ) )
<=> ? [V3f: $i] :
( ( mem @ V3f @ ( arr @ A_27a @ A_27b ) )
& ! [V4x: $i] :
( ( mem @ V4x @ A_27a )
=> ( p @ ( ap @ ( ap @ V0P @ V4x ) @ ( ap @ V3f @ V4x ) ) ) ) ) ) ) ).
thf(conj_thm_2Epred__set_2EBIJ__SYM,axiom,
! [A_27a: del,A_27b: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ A_27a @ bool ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( arr @ A_27b @ bool ) )
=> ( ? [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ A_27b ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27a @ A_27b ) @ V2f ) @ V0s ) @ V1t ) ) )
<=> ? [V3g: $i] :
( ( mem @ V3g @ ( arr @ A_27b @ A_27a ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ A_27b @ A_27a ) @ V3g ) @ V1t ) @ V0s ) ) ) ) ) ) ).
thf(conj_thm_2Esat_2ENOT__NOT,axiom,
! [V0t: $i] :
( ( mem @ V0t @ bool )
=> ( ~ ~ ( p @ V0t )
<=> ( p @ V0t ) ) ) ).
thf(conj_thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A: $i] :
( ( mem @ V0A @ bool )
=> ( ( p @ V0A )
=> ( ~ ( p @ V0A )
=> $false ) ) ) ).
thf(conj_thm_2Esat_2EOR__DUAL2,axiom,
! [V0A: $i] :
( ( mem @ V0A @ bool )
=> ! [V1B: $i] :
( ( mem @ V1B @ bool )
=> ( ( ~ ( ( p @ V0A )
| ( p @ V1B ) )
=> $false )
<=> ( ( ( p @ V0A )
=> $false )
=> ( ~ ( p @ V1B )
=> $false ) ) ) ) ) ).
thf(conj_thm_2Esat_2EOR__DUAL3,axiom,
! [V0A: $i] :
( ( mem @ V0A @ bool )
=> ! [V1B: $i] :
( ( mem @ V1B @ bool )
=> ( ( ~ ( ~ ( p @ V0A )
| ( p @ V1B ) )
=> $false )
<=> ( ( p @ V0A )
=> ( ~ ( p @ V1B )
=> $false ) ) ) ) ) ).
thf(conj_thm_2Esat_2EAND__INV2,axiom,
! [V0A: $i] :
( ( mem @ V0A @ bool )
=> ( ( ~ ( p @ V0A )
=> $false )
=> ( ( ( p @ V0A )
=> $false )
=> $false ) ) ) ).
thf(conj_thm_2Esat_2Edc__eq,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2r: $i] :
( ( mem @ V2r @ bool )
=> ( ( ( p @ V0p )
<=> ( ( p @ V1q )
<=> ( p @ V2r ) ) )
<=> ( ( ( p @ V0p )
| ( p @ V1q )
| ( p @ V2r ) )
& ( ( p @ V0p )
| ~ ( p @ V2r )
| ~ ( p @ V1q ) )
& ( ( p @ V1q )
| ~ ( p @ V2r )
| ~ ( p @ V0p ) )
& ( ( p @ V2r )
| ~ ( p @ V1q )
| ~ ( p @ V0p ) ) ) ) ) ) ) ).
thf(conj_thm_2Esat_2Edc__conj,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2r: $i] :
( ( mem @ V2r @ bool )
=> ( ( ( p @ V0p )
<=> ( ( p @ V1q )
& ( p @ V2r ) ) )
<=> ( ( ( p @ V0p )
| ~ ( p @ V1q )
| ~ ( p @ V2r ) )
& ( ( p @ V1q )
| ~ ( p @ V0p ) )
& ( ( p @ V2r )
| ~ ( p @ V0p ) ) ) ) ) ) ) ).
thf(conj_thm_2Esat_2Edc__disj,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2r: $i] :
( ( mem @ V2r @ bool )
=> ( ( ( p @ V0p )
<=> ( ( p @ V1q )
| ( p @ V2r ) ) )
<=> ( ( ( p @ V0p )
| ~ ( p @ V1q ) )
& ( ( p @ V0p )
| ~ ( p @ V2r ) )
& ( ( p @ V1q )
| ( p @ V2r )
| ~ ( p @ V0p ) ) ) ) ) ) ) ).
thf(conj_thm_2Esat_2Edc__imp,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ! [V2r: $i] :
( ( mem @ V2r @ bool )
=> ( ( ( p @ V0p )
<=> ( ( p @ V1q )
=> ( p @ V2r ) ) )
<=> ( ( ( p @ V0p )
| ( p @ V1q ) )
& ( ( p @ V0p )
| ~ ( p @ V2r ) )
& ( ~ ( p @ V1q )
| ( p @ V2r )
| ~ ( p @ V0p ) ) ) ) ) ) ) ).
thf(conj_thm_2Esat_2Edc__neg,axiom,
! [V0p: $i] :
( ( mem @ V0p @ bool )
=> ! [V1q: $i] :
( ( mem @ V1q @ bool )
=> ( ( ( p @ V0p )
<=> ~ ( p @ V1q ) )
<=> ( ( ( p @ V0p )
| ( p @ V1q ) )
& ( ~ ( p @ V1q )
| ~ ( p @ V0p ) ) ) ) ) ) ).
thf(conj_thm_2Eutil__prob_2ENUM__2D__BIJ,axiom,
? [V0f: $i] :
( ( mem @ V0f @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ V0f ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ).
thf(conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV,conjecture,
? [V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ V0f ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ) ).
%------------------------------------------------------------------------------