SET007 Axioms: SET007+92.ax
%------------------------------------------------------------------------------
% File : SET007+92 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : N-Tuples and Cartesian Products for n=5
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : mcart_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 358 ( 202 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 431 ( 127 ~; 32 |; 168 &)
% ( 8 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 15 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 1 con; 0-10 aty)
% Number of variables : 423 ( 401 !; 22 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_mcart_2,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H] :
( ( r2_hidden(C,D)
& r2_hidden(D,E)
& r2_hidden(E,F)
& r2_hidden(F,G)
& r2_hidden(G,H)
& r2_hidden(H,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(t2_mcart_2,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I] :
( ( r2_hidden(C,D)
& r2_hidden(D,E)
& r2_hidden(E,F)
& r2_hidden(F,G)
& r2_hidden(G,H)
& r2_hidden(H,I)
& r2_hidden(I,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(d1_mcart_2,axiom,
! [A,B,C,D,E] : k1_mcart_2(A,B,C,D,E) = k4_tarski(k4_mcart_1(A,B,C,D),E) ).
fof(t3_mcart_2,axiom,
! [A,B,C,D,E] : k1_mcart_2(A,B,C,D,E) = k4_tarski(k4_tarski(k4_tarski(k4_tarski(A,B),C),D),E) ).
fof(t4_mcart_2,axiom,
$true ).
fof(t5_mcart_2,axiom,
! [A,B,C,D,E] : k1_mcart_2(A,B,C,D,E) = k3_mcart_1(k3_mcart_1(A,B,C),D,E) ).
fof(t6_mcart_2,axiom,
! [A,B,C,D,E] : k1_mcart_2(A,B,C,D,E) = k4_mcart_1(k4_tarski(A,B),C,D,E) ).
fof(t7_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( k1_mcart_2(A,B,C,D,E) = k1_mcart_2(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ).
fof(t8_mcart_2,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G] :
~ ( ( r2_hidden(C,A)
| r2_hidden(D,A) )
& B = k1_mcart_2(C,D,E,F,G) ) ) ) ).
fof(d2_mcart_2,axiom,
! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k2_zfmisc_1(k4_zfmisc_1(A,B,C,D),E) ).
fof(t9_mcart_2,axiom,
! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D),E) ).
fof(t10_mcart_2,axiom,
$true ).
fof(t11_mcart_2,axiom,
! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k3_zfmisc_1(k3_zfmisc_1(A,B,C),D,E) ).
fof(t12_mcart_2,axiom,
! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k4_zfmisc_1(k2_zfmisc_1(A,B),C,D,E) ).
fof(t13_mcart_2,axiom,
! [A,B,C,D,E] :
( ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0 )
<=> k2_mcart_2(A,B,C,D,E) != k1_xboole_0 ) ).
fof(t14_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( k2_mcart_2(A,B,C,D,E) = k2_mcart_2(F,G,H,I,J)
=> ( A = k1_xboole_0
| B = k1_xboole_0
| C = k1_xboole_0
| D = k1_xboole_0
| E = k1_xboole_0
| ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(t15_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( k2_mcart_2(A,B,C,D,E) = k2_mcart_2(F,G,H,I,J)
=> ( k2_mcart_2(A,B,C,D,E) = k1_xboole_0
| ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(t16_mcart_2,axiom,
! [A,B] :
( k2_mcart_2(A,A,A,A,A) = k2_mcart_2(B,B,B,B,B)
=> A = B ) ).
fof(t17_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ? [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
& ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,B)
=> ! [I] :
( m1_subset_1(I,C)
=> ! [J] :
( m1_subset_1(J,D)
=> ! [K] :
( m1_subset_1(K,E)
=> F != k1_mcart_2(G,H,I,J,K) ) ) ) ) ) ) ) ).
fof(d3_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> ! [G] :
( m1_subset_1(G,A)
=> ( G = k3_mcart_2(A,B,C,D,E,F)
<=> ! [H,I,J,K,L] :
( F = k1_mcart_2(H,I,J,K,L)
=> G = H ) ) ) ) ) ).
fof(d4_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> ! [G] :
( m1_subset_1(G,B)
=> ( G = k4_mcart_2(A,B,C,D,E,F)
<=> ! [H,I,J,K,L] :
( F = k1_mcart_2(H,I,J,K,L)
=> G = I ) ) ) ) ) ).
fof(d5_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> ! [G] :
( m1_subset_1(G,C)
=> ( G = k5_mcart_2(A,B,C,D,E,F)
<=> ! [H,I,J,K,L] :
( F = k1_mcart_2(H,I,J,K,L)
=> G = J ) ) ) ) ) ).
fof(d6_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> ! [G] :
( m1_subset_1(G,D)
=> ( G = k6_mcart_2(A,B,C,D,E,F)
<=> ! [H,I,J,K,L] :
( F = k1_mcart_2(H,I,J,K,L)
=> G = K ) ) ) ) ) ).
fof(d7_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> ! [G] :
( m1_subset_1(G,E)
=> ( G = k7_mcart_2(A,B,C,D,E,F)
<=> ! [H,I,J,K,L] :
( F = k1_mcart_2(H,I,J,K,L)
=> G = L ) ) ) ) ) ).
fof(t18_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ? [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
& ? [G,H,I,J,K] :
( F = k1_mcart_2(G,H,I,J,K)
& ~ ( k3_mcart_2(A,B,C,D,E,F) = G
& k4_mcart_2(A,B,C,D,E,F) = H
& k5_mcart_2(A,B,C,D,E,F) = I
& k6_mcart_2(A,B,C,D,E,F) = J
& k7_mcart_2(A,B,C,D,E,F) = K ) ) ) ) ).
fof(t19_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> F = k1_mcart_2(k3_mcart_2(A,B,C,D,E,F),k4_mcart_2(A,B,C,D,E,F),k5_mcart_2(A,B,C,D,E,F),k6_mcart_2(A,B,C,D,E,F),k7_mcart_2(A,B,C,D,E,F)) ) ) ).
fof(t20_mcart_2,axiom,
! [A,B,C,D,E] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> ( k3_mcart_2(A,B,C,D,E,F) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(F))))
& k4_mcart_2(A,B,C,D,E,F) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(F))))
& k5_mcart_2(A,B,C,D,E,F) = k2_mcart_1(k1_mcart_1(k1_mcart_1(F)))
& k6_mcart_2(A,B,C,D,E,F) = k2_mcart_1(k1_mcart_1(F))
& k7_mcart_2(A,B,C,D,E,F) = k2_mcart_1(F) ) ) ) ).
fof(t21_mcart_2,axiom,
! [A,B,C,D,E] :
( ~ ( ~ r1_tarski(A,k2_mcart_2(A,B,C,D,E))
& ~ r1_tarski(A,k2_mcart_2(B,C,D,E,A))
& ~ r1_tarski(A,k2_mcart_2(C,D,E,A,B))
& ~ r1_tarski(A,k2_mcart_2(D,E,A,B,C))
& ~ r1_tarski(A,k2_mcart_2(E,A,B,C,D)) )
=> A = k1_xboole_0 ) ).
fof(t22_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ~ r1_xboole_0(k2_mcart_2(A,B,C,D,E),k2_mcart_2(F,G,H,I,J))
=> ( ~ r1_xboole_0(A,F)
& ~ r1_xboole_0(B,G)
& ~ r1_xboole_0(C,H)
& ~ r1_xboole_0(D,I)
& ~ r1_xboole_0(E,J) ) ) ).
fof(t23_mcart_2,axiom,
! [A,B,C,D,E] : k2_mcart_2(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D),k1_tarski(E)) = k1_tarski(k1_mcart_2(A,B,C,D,E)) ).
fof(t24_mcart_2,axiom,
! [A,B,C,D,E,F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> ~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& ? [G,H,I,J,K] :
( F = k1_mcart_2(G,H,I,J,K)
& ~ ( k3_mcart_2(A,B,C,D,E,F) = G
& k4_mcart_2(A,B,C,D,E,F) = H
& k5_mcart_2(A,B,C,D,E,F) = I
& k6_mcart_2(A,B,C,D,E,F) = J
& k7_mcart_2(A,B,C,D,E,F) = K ) ) ) ) ).
fof(t25_mcart_2,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_2(A,B,C,D,E))
=> ( ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,C)
=> ! [K] :
( m1_subset_1(K,D)
=> ! [L] :
( m1_subset_1(L,E)
=> ( G = k1_mcart_2(H,I,J,K,L)
=> F = H ) ) ) ) ) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| C = k1_xboole_0
| D = k1_xboole_0
| E = k1_xboole_0
| F = k3_mcart_2(A,B,C,D,E,G) ) ) ) ).
fof(t26_mcart_2,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_2(A,B,C,D,E))
=> ( ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,C)
=> ! [K] :
( m1_subset_1(K,D)
=> ! [L] :
( m1_subset_1(L,E)
=> ( G = k1_mcart_2(H,I,J,K,L)
=> F = I ) ) ) ) ) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| C = k1_xboole_0
| D = k1_xboole_0
| E = k1_xboole_0
| F = k4_mcart_2(A,B,C,D,E,G) ) ) ) ).
fof(t27_mcart_2,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_2(A,B,C,D,E))
=> ( ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,C)
=> ! [K] :
( m1_subset_1(K,D)
=> ! [L] :
( m1_subset_1(L,E)
=> ( G = k1_mcart_2(H,I,J,K,L)
=> F = J ) ) ) ) ) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| C = k1_xboole_0
| D = k1_xboole_0
| E = k1_xboole_0
| F = k5_mcart_2(A,B,C,D,E,G) ) ) ) ).
fof(t28_mcart_2,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_2(A,B,C,D,E))
=> ( ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,C)
=> ! [K] :
( m1_subset_1(K,D)
=> ! [L] :
( m1_subset_1(L,E)
=> ( G = k1_mcart_2(H,I,J,K,L)
=> F = K ) ) ) ) ) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| C = k1_xboole_0
| D = k1_xboole_0
| E = k1_xboole_0
| F = k6_mcart_2(A,B,C,D,E,G) ) ) ) ).
fof(t29_mcart_2,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_2(A,B,C,D,E))
=> ( ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,C)
=> ! [K] :
( m1_subset_1(K,D)
=> ! [L] :
( m1_subset_1(L,E)
=> ( G = k1_mcart_2(H,I,J,K,L)
=> F = L ) ) ) ) ) )
=> ( A = k1_xboole_0
| B = k1_xboole_0
| C = k1_xboole_0
| D = k1_xboole_0
| E = k1_xboole_0
| F = k7_mcart_2(A,B,C,D,E,G) ) ) ) ).
fof(t30_mcart_2,axiom,
! [A,B,C,D,E,F] :
~ ( r2_hidden(A,k2_mcart_2(B,C,D,E,F))
& ! [G,H,I,J,K] :
~ ( r2_hidden(G,B)
& r2_hidden(H,C)
& r2_hidden(I,D)
& r2_hidden(J,E)
& r2_hidden(K,F)
& A = k1_mcart_2(G,H,I,J,K) ) ) ).
fof(t31_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( r2_hidden(k1_mcart_2(A,B,C,D,E),k2_mcart_2(F,G,H,I,J))
<=> ( r2_hidden(A,F)
& r2_hidden(B,G)
& r2_hidden(C,H)
& r2_hidden(D,I)
& r2_hidden(E,J) ) ) ).
fof(t32_mcart_2,axiom,
! [A,B,C,D,E,F] :
( ! [G] :
( r2_hidden(G,A)
<=> ? [H,I,J,K,L] :
( r2_hidden(H,B)
& r2_hidden(I,C)
& r2_hidden(J,D)
& r2_hidden(K,E)
& r2_hidden(L,F)
& G = k1_mcart_2(H,I,J,K,L) ) )
=> A = k2_mcart_2(B,C,D,E,F) ) ).
fof(t33_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& F != k1_xboole_0
& G != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& J != k1_xboole_0
& ? [K] :
( m1_subset_1(K,k2_mcart_2(A,B,C,D,E))
& ? [L] :
( m1_subset_1(L,k2_mcart_2(F,G,H,I,J))
& K = L
& ~ ( k3_mcart_2(A,B,C,D,E,K) = k3_mcart_2(F,G,H,I,J,L)
& k4_mcart_2(A,B,C,D,E,K) = k4_mcart_2(F,G,H,I,J,L)
& k5_mcart_2(A,B,C,D,E,K) = k5_mcart_2(F,G,H,I,J,L)
& k6_mcart_2(A,B,C,D,E,K) = k6_mcart_2(F,G,H,I,J,L)
& k7_mcart_2(A,B,C,D,E,K) = k7_mcart_2(F,G,H,I,J,L) ) ) ) ) ).
fof(t34_mcart_2,axiom,
! [A,B,C,D,E,F] :
( m1_subset_1(F,k1_zfmisc_1(A))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(B))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(C))
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(D))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(E))
=> ! [K] :
( m1_subset_1(K,k2_mcart_2(A,B,C,D,E))
=> ( r2_hidden(K,k2_mcart_2(F,G,H,I,J))
=> ( r2_hidden(k3_mcart_2(A,B,C,D,E,K),F)
& r2_hidden(k4_mcart_2(A,B,C,D,E,K),G)
& r2_hidden(k5_mcart_2(A,B,C,D,E,K),H)
& r2_hidden(k6_mcart_2(A,B,C,D,E,K),I)
& r2_hidden(k7_mcart_2(A,B,C,D,E,K),J) ) ) ) ) ) ) ) ) ).
fof(t35_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( r1_tarski(A,B)
& r1_tarski(C,D)
& r1_tarski(E,F)
& r1_tarski(G,H)
& r1_tarski(I,J) )
=> r1_tarski(k2_mcart_2(A,C,E,G,I),k2_mcart_2(B,D,F,H,J)) ) ).
fof(t36_mcart_2,axiom,
! [A,B] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& ? [C] :
( m1_subset_1(C,k2_zfmisc_1(A,B))
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,B)
=> C != k4_tarski(D,E) ) ) ) ) ).
fof(t37_mcart_2,axiom,
! [A,B,C] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& ? [D] :
( m1_subset_1(D,k3_zfmisc_1(A,B,C))
& ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> ! [G] :
( m1_subset_1(G,C)
=> D != k3_mcart_1(E,F,G) ) ) ) ) ) ).
fof(t38_mcart_2,axiom,
! [A,B,C,D] :
~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& ? [E] :
( m1_subset_1(E,k4_zfmisc_1(A,B,C,D))
& ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,B)
=> ! [H] :
( m1_subset_1(H,C)
=> ! [I] :
( m1_subset_1(I,D)
=> E != k4_mcart_1(F,G,H,I) ) ) ) ) ) ) ).
fof(dt_k1_mcart_2,axiom,
$true ).
fof(dt_k2_mcart_2,axiom,
$true ).
fof(dt_k3_mcart_2,axiom,
! [A,B,C,D,E,F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> m1_subset_1(k3_mcart_2(A,B,C,D,E,F),A) ) ).
fof(dt_k4_mcart_2,axiom,
! [A,B,C,D,E,F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> m1_subset_1(k4_mcart_2(A,B,C,D,E,F),B) ) ).
fof(dt_k5_mcart_2,axiom,
! [A,B,C,D,E,F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> m1_subset_1(k5_mcart_2(A,B,C,D,E,F),C) ) ).
fof(dt_k6_mcart_2,axiom,
! [A,B,C,D,E,F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> m1_subset_1(k6_mcart_2(A,B,C,D,E,F),D) ) ).
fof(dt_k7_mcart_2,axiom,
! [A,B,C,D,E,F] :
( m1_subset_1(F,k2_mcart_2(A,B,C,D,E))
=> m1_subset_1(k7_mcart_2(A,B,C,D,E,F),E) ) ).
fof(dt_k8_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( m1_subset_1(F,k1_zfmisc_1(A))
& m1_subset_1(G,k1_zfmisc_1(B))
& m1_subset_1(H,k1_zfmisc_1(C))
& m1_subset_1(I,k1_zfmisc_1(D))
& m1_subset_1(J,k1_zfmisc_1(E)) )
=> m1_subset_1(k8_mcart_2(A,B,C,D,E,F,G,H,I,J),k1_zfmisc_1(k2_mcart_2(A,B,C,D,E))) ) ).
fof(redefinition_k8_mcart_2,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( m1_subset_1(F,k1_zfmisc_1(A))
& m1_subset_1(G,k1_zfmisc_1(B))
& m1_subset_1(H,k1_zfmisc_1(C))
& m1_subset_1(I,k1_zfmisc_1(D))
& m1_subset_1(J,k1_zfmisc_1(E)) )
=> k8_mcart_2(A,B,C,D,E,F,G,H,I,J) = k2_mcart_2(F,G,H,I,J) ) ).
%------------------------------------------------------------------------------