SET007 Axioms: SET007+93.ax
%------------------------------------------------------------------------------
% File : SET007+93 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : N-Tuples and Cartesian Products for n=6
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 55 ( 15 unt; 0 def)
% Number of atoms : 404 ( 235 equ)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 484 ( 135 ~; 44 |; 185 &)
% ( 9 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 17 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 1 con; 0-7 aty)
% Number of variables : 510 ( 488 !; 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_3,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J] :
( ( 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,J)
& r2_hidden(J,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(t2_mcart_3,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J,K] :
( ( 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,J)
& r2_hidden(J,K)
& r2_hidden(K,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(d1_mcart_3,axiom,
! [A,B,C,D,E,F] : k1_mcart_3(A,B,C,D,E,F) = k4_tarski(k1_mcart_2(A,B,C,D,E),F) ).
fof(t3_mcart_3,axiom,
! [A,B,C,D,E,F] : k1_mcart_3(A,B,C,D,E,F) = k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(A,B),C),D),E),F) ).
fof(t4_mcart_3,axiom,
$true ).
fof(t5_mcart_3,axiom,
! [A,B,C,D,E,F] : k1_mcart_3(A,B,C,D,E,F) = k3_mcart_1(k4_mcart_1(A,B,C,D),E,F) ).
fof(t6_mcart_3,axiom,
! [A,B,C,D,E,F] : k1_mcart_3(A,B,C,D,E,F) = k4_mcart_1(k3_mcart_1(A,B,C),D,E,F) ).
fof(t7_mcart_3,axiom,
! [A,B,C,D,E,F] : k1_mcart_3(A,B,C,D,E,F) = k1_mcart_2(k4_tarski(A,B),C,D,E,F) ).
fof(t8_mcart_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( k1_mcart_3(A,B,C,D,E,F) = k1_mcart_3(G,H,I,J,K,L)
=> ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ).
fof(t9_mcart_3,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H] :
~ ( ( r2_hidden(C,A)
| r2_hidden(D,A) )
& B = k1_mcart_3(C,D,E,F,G,H) ) ) ) ).
fof(d2_mcart_3,axiom,
! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k2_zfmisc_1(k2_mcart_2(A,B,C,D,E),F) ).
fof(t10_mcart_3,axiom,
! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D),E),F) ).
fof(t11_mcart_3,axiom,
$true ).
fof(t12_mcart_3,axiom,
! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k3_zfmisc_1(k4_zfmisc_1(A,B,C,D),E,F) ).
fof(t13_mcart_3,axiom,
! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k4_zfmisc_1(k3_zfmisc_1(A,B,C),D,E,F) ).
fof(t14_mcart_3,axiom,
! [A,B,C,D,E,F] : k2_mcart_3(A,B,C,D,E,F) = k2_mcart_2(k2_zfmisc_1(A,B),C,D,E,F) ).
fof(t15_mcart_3,axiom,
! [A,B,C,D,E,F] :
( ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& F != k1_xboole_0 )
<=> k2_mcart_3(A,B,C,D,E,F) != k1_xboole_0 ) ).
fof(t16_mcart_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( k2_mcart_3(A,B,C,D,E,F) = k2_mcart_3(G,H,I,J,K,L)
=> ( A = k1_xboole_0
| B = k1_xboole_0
| C = k1_xboole_0
| D = k1_xboole_0
| E = k1_xboole_0
| F = k1_xboole_0
| ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
fof(t17_mcart_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( k2_mcart_3(A,B,C,D,E,F) = k2_mcart_3(G,H,I,J,K,L)
=> ( k2_mcart_3(A,B,C,D,E,F) = k1_xboole_0
| ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
fof(t18_mcart_3,axiom,
! [A,B] :
( k2_mcart_3(A,A,A,A,A,A) = k2_mcart_3(B,B,B,B,B,B)
=> A = B ) ).
fof(t19_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
& ! [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)
=> ! [M] :
( m1_subset_1(M,F)
=> G != k1_mcart_3(H,I,J,K,L,M) ) ) ) ) ) ) ) ) ).
fof(d3_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ! [H] :
( m1_subset_1(H,A)
=> ( H = k3_mcart_3(A,B,C,D,E,F,G)
<=> ! [I,J,K,L,M,N] :
( G = k1_mcart_3(I,J,K,L,M,N)
=> H = I ) ) ) ) ) ).
fof(d4_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ! [H] :
( m1_subset_1(H,B)
=> ( H = k4_mcart_3(A,B,C,D,E,F,G)
<=> ! [I,J,K,L,M,N] :
( G = k1_mcart_3(I,J,K,L,M,N)
=> H = J ) ) ) ) ) ).
fof(d5_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ! [H] :
( m1_subset_1(H,C)
=> ( H = k5_mcart_3(A,B,C,D,E,F,G)
<=> ! [I,J,K,L,M,N] :
( G = k1_mcart_3(I,J,K,L,M,N)
=> H = K ) ) ) ) ) ).
fof(d6_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ! [H] :
( m1_subset_1(H,D)
=> ( H = k6_mcart_3(A,B,C,D,E,F,G)
<=> ! [I,J,K,L,M,N] :
( G = k1_mcart_3(I,J,K,L,M,N)
=> H = L ) ) ) ) ) ).
fof(d7_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ! [H] :
( m1_subset_1(H,E)
=> ( H = k7_mcart_3(A,B,C,D,E,F,G)
<=> ! [I,J,K,L,M,N] :
( G = k1_mcart_3(I,J,K,L,M,N)
=> H = M ) ) ) ) ) ).
fof(d8_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ! [H] :
( m1_subset_1(H,F)
=> ( H = k8_mcart_3(A,B,C,D,E,F,G)
<=> ! [I,J,K,L,M,N] :
( G = k1_mcart_3(I,J,K,L,M,N)
=> H = N ) ) ) ) ) ).
fof(t20_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
& ? [H,I,J,K,L,M] :
( G = k1_mcart_3(H,I,J,K,L,M)
& ~ ( k3_mcart_3(A,B,C,D,E,F,G) = H
& k4_mcart_3(A,B,C,D,E,F,G) = I
& k5_mcart_3(A,B,C,D,E,F,G) = J
& k6_mcart_3(A,B,C,D,E,F,G) = K
& k7_mcart_3(A,B,C,D,E,F,G) = L
& k8_mcart_3(A,B,C,D,E,F,G) = M ) ) ) ) ).
fof(t21_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> G = k1_mcart_3(k3_mcart_3(A,B,C,D,E,F,G),k4_mcart_3(A,B,C,D,E,F,G),k5_mcart_3(A,B,C,D,E,F,G),k6_mcart_3(A,B,C,D,E,F,G),k7_mcart_3(A,B,C,D,E,F,G),k8_mcart_3(A,B,C,D,E,F,G)) ) ) ).
fof(t22_mcart_3,axiom,
! [A,B,C,D,E,F] :
~ ( 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] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ( k3_mcart_3(A,B,C,D,E,F,G) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(G)))))
& k4_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(G)))))
& k5_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(G))))
& k6_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(k1_mcart_1(G)))
& k7_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(k1_mcart_1(G))
& k8_mcart_3(A,B,C,D,E,F,G) = k2_mcart_1(G) ) ) ) ).
fof(t23_mcart_3,axiom,
! [A,B,C,D,E,F] :
( ~ ( ~ r1_tarski(A,k2_mcart_3(A,B,C,D,E,F))
& ~ r1_tarski(A,k2_mcart_3(B,C,D,E,F,A))
& ~ r1_tarski(A,k2_mcart_3(C,D,E,F,A,B))
& ~ r1_tarski(A,k2_mcart_3(D,E,F,A,B,C))
& ~ r1_tarski(A,k2_mcart_3(E,F,A,B,C,D))
& ~ r1_tarski(A,k2_mcart_3(F,A,B,C,D,E)) )
=> A = k1_xboole_0 ) ).
fof(t24_mcart_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( ~ r1_xboole_0(k2_mcart_3(A,B,C,D,E,F),k2_mcart_3(G,H,I,J,K,L))
=> ( ~ r1_xboole_0(A,G)
& ~ r1_xboole_0(B,H)
& ~ r1_xboole_0(C,I)
& ~ r1_xboole_0(D,J)
& ~ r1_xboole_0(E,K)
& ~ r1_xboole_0(F,L) ) ) ).
fof(t25_mcart_3,axiom,
! [A,B,C,D,E,F] : k2_mcart_3(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D),k1_tarski(E),k1_tarski(F)) = k1_tarski(k1_mcart_3(A,B,C,D,E,F)) ).
fof(t26_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> ~ ( A != k1_xboole_0
& B != k1_xboole_0
& C != k1_xboole_0
& D != k1_xboole_0
& E != k1_xboole_0
& F != k1_xboole_0
& ? [H,I,J,K,L,M] :
( G = k1_mcart_3(H,I,J,K,L,M)
& ~ ( k3_mcart_3(A,B,C,D,E,F,G) = H
& k4_mcart_3(A,B,C,D,E,F,G) = I
& k5_mcart_3(A,B,C,D,E,F,G) = J
& k6_mcart_3(A,B,C,D,E,F,G) = K
& k7_mcart_3(A,B,C,D,E,F,G) = L
& k8_mcart_3(A,B,C,D,E,F,G) = M ) ) ) ) ).
fof(t27_mcart_3,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_3(A,B,C,D,E,F))
=> ( ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,B)
=> ! [K] :
( m1_subset_1(K,C)
=> ! [L] :
( m1_subset_1(L,D)
=> ! [M] :
( m1_subset_1(M,E)
=> ! [N] :
( m1_subset_1(N,F)
=> ( H = k1_mcart_3(I,J,K,L,M,N)
=> G = I ) ) ) ) ) ) )
=> ( 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 = k3_mcart_3(A,B,C,D,E,F,H) ) ) ) ).
fof(t28_mcart_3,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_3(A,B,C,D,E,F))
=> ( ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,B)
=> ! [K] :
( m1_subset_1(K,C)
=> ! [L] :
( m1_subset_1(L,D)
=> ! [M] :
( m1_subset_1(M,E)
=> ! [N] :
( m1_subset_1(N,F)
=> ( H = k1_mcart_3(I,J,K,L,M,N)
=> G = 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 = k4_mcart_3(A,B,C,D,E,F,H) ) ) ) ).
fof(t29_mcart_3,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_3(A,B,C,D,E,F))
=> ( ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,B)
=> ! [K] :
( m1_subset_1(K,C)
=> ! [L] :
( m1_subset_1(L,D)
=> ! [M] :
( m1_subset_1(M,E)
=> ! [N] :
( m1_subset_1(N,F)
=> ( H = k1_mcart_3(I,J,K,L,M,N)
=> G = K ) ) ) ) ) ) )
=> ( 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 = k5_mcart_3(A,B,C,D,E,F,H) ) ) ) ).
fof(t30_mcart_3,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_3(A,B,C,D,E,F))
=> ( ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,B)
=> ! [K] :
( m1_subset_1(K,C)
=> ! [L] :
( m1_subset_1(L,D)
=> ! [M] :
( m1_subset_1(M,E)
=> ! [N] :
( m1_subset_1(N,F)
=> ( H = k1_mcart_3(I,J,K,L,M,N)
=> G = L ) ) ) ) ) ) )
=> ( 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 = k6_mcart_3(A,B,C,D,E,F,H) ) ) ) ).
fof(t31_mcart_3,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_3(A,B,C,D,E,F))
=> ( ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,B)
=> ! [K] :
( m1_subset_1(K,C)
=> ! [L] :
( m1_subset_1(L,D)
=> ! [M] :
( m1_subset_1(M,E)
=> ! [N] :
( m1_subset_1(N,F)
=> ( H = k1_mcart_3(I,J,K,L,M,N)
=> G = M ) ) ) ) ) ) )
=> ( 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 = k7_mcart_3(A,B,C,D,E,F,H) ) ) ) ).
fof(t32_mcart_3,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_3(A,B,C,D,E,F))
=> ( ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,B)
=> ! [K] :
( m1_subset_1(K,C)
=> ! [L] :
( m1_subset_1(L,D)
=> ! [M] :
( m1_subset_1(M,E)
=> ! [N] :
( m1_subset_1(N,F)
=> ( H = k1_mcart_3(I,J,K,L,M,N)
=> G = N ) ) ) ) ) ) )
=> ( 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 = k8_mcart_3(A,B,C,D,E,F,H) ) ) ) ).
fof(t33_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
~ ( r2_hidden(A,k2_mcart_3(B,C,D,E,F,G))
& ! [H,I,J,K,L,M] :
~ ( r2_hidden(H,B)
& r2_hidden(I,C)
& r2_hidden(J,D)
& r2_hidden(K,E)
& r2_hidden(L,F)
& r2_hidden(M,G)
& A = k1_mcart_3(H,I,J,K,L,M) ) ) ).
fof(t34_mcart_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( r2_hidden(k1_mcart_3(A,B,C,D,E,F),k2_mcart_3(G,H,I,J,K,L))
<=> ( r2_hidden(A,G)
& r2_hidden(B,H)
& r2_hidden(C,I)
& r2_hidden(D,J)
& r2_hidden(E,K)
& r2_hidden(F,L) ) ) ).
fof(t35_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( ! [H] :
( r2_hidden(H,A)
<=> ? [I,J,K,L,M,N] :
( r2_hidden(I,B)
& r2_hidden(J,C)
& r2_hidden(K,D)
& r2_hidden(L,E)
& r2_hidden(M,F)
& r2_hidden(N,G)
& H = k1_mcart_3(I,J,K,L,M,N) ) )
=> A = k2_mcart_3(B,C,D,E,F,G) ) ).
fof(t36_mcart_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
~ ( 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 != k1_xboole_0
& L != k1_xboole_0
& ? [M] :
( m1_subset_1(M,k2_mcart_3(A,B,C,D,E,F))
& ? [N] :
( m1_subset_1(N,k2_mcart_3(G,H,I,J,K,L))
& M = N
& ~ ( k3_mcart_3(A,B,C,D,E,F,M) = k3_mcart_3(G,H,I,J,K,L,N)
& k4_mcart_3(A,B,C,D,E,F,M) = k4_mcart_3(G,H,I,J,K,L,N)
& k5_mcart_3(A,B,C,D,E,F,M) = k5_mcart_3(G,H,I,J,K,L,N)
& k6_mcart_3(A,B,C,D,E,F,M) = k6_mcart_3(G,H,I,J,K,L,N)
& k7_mcart_3(A,B,C,D,E,F,M) = k7_mcart_3(G,H,I,J,K,L,N)
& k8_mcart_3(A,B,C,D,E,F,M) = k8_mcart_3(G,H,I,J,K,L,N) ) ) ) ) ).
fof(t37_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k1_zfmisc_1(A))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(B))
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(C))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(D))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(E))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(F))
=> ! [M] :
( m1_subset_1(M,k2_mcart_3(A,B,C,D,E,F))
=> ( r2_hidden(M,k2_mcart_3(G,H,I,J,K,L))
=> ( r2_hidden(k3_mcart_3(A,B,C,D,E,F,M),G)
& r2_hidden(k4_mcart_3(A,B,C,D,E,F,M),H)
& r2_hidden(k5_mcart_3(A,B,C,D,E,F,M),I)
& r2_hidden(k6_mcart_3(A,B,C,D,E,F,M),J)
& r2_hidden(k7_mcart_3(A,B,C,D,E,F,M),K)
& r2_hidden(k8_mcart_3(A,B,C,D,E,F,M),L) ) ) ) ) ) ) ) ) ) ).
fof(t38_mcart_3,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( ( r1_tarski(A,B)
& r1_tarski(C,D)
& r1_tarski(E,F)
& r1_tarski(G,H)
& r1_tarski(I,J)
& r1_tarski(K,L) )
=> r1_tarski(k2_mcart_3(A,C,E,G,I,K),k2_mcart_3(B,D,F,H,J,L)) ) ).
fof(t39_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k1_zfmisc_1(A))
=> ! [H] :
( m1_subset_1(H,k1_zfmisc_1(B))
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(C))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(D))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(E))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(F))
=> m1_subset_1(k2_mcart_3(G,H,I,J,K,L),k1_zfmisc_1(k2_mcart_3(A,B,C,D,E,F))) ) ) ) ) ) ) ).
fof(dt_k1_mcart_3,axiom,
$true ).
fof(dt_k2_mcart_3,axiom,
$true ).
fof(dt_k3_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> m1_subset_1(k3_mcart_3(A,B,C,D,E,F,G),A) ) ).
fof(dt_k4_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> m1_subset_1(k4_mcart_3(A,B,C,D,E,F,G),B) ) ).
fof(dt_k5_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> m1_subset_1(k5_mcart_3(A,B,C,D,E,F,G),C) ) ).
fof(dt_k6_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> m1_subset_1(k6_mcart_3(A,B,C,D,E,F,G),D) ) ).
fof(dt_k7_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> m1_subset_1(k7_mcart_3(A,B,C,D,E,F,G),E) ) ).
fof(dt_k8_mcart_3,axiom,
! [A,B,C,D,E,F,G] :
( m1_subset_1(G,k2_mcart_3(A,B,C,D,E,F))
=> m1_subset_1(k8_mcart_3(A,B,C,D,E,F,G),F) ) ).
%------------------------------------------------------------------------------