SET007 Axioms: SET007+96.ax
%------------------------------------------------------------------------------
% File : SET007+96 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : N-Tuples and Cartesian Products for n=9
% 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_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 21 unt; 0 def)
% Number of atoms : 653 ( 394 equ)
% Maximal formula atoms : 30 ( 9 avg)
% Number of connectives : 787 ( 202 ~; 91 |; 297 &)
% ( 12 <=>; 185 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 23 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 1 con; 0-10 aty)
% Number of variables : 928 ( 897 !; 31 ?)
% 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_6,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( ( 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,L)
& r2_hidden(L,M)
& r2_hidden(M,N)
& r2_hidden(N,O)
& r2_hidden(O,P)
& r2_hidden(P,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(t2_mcart_6,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q] :
( ( 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,L)
& r2_hidden(L,M)
& r2_hidden(M,N)
& r2_hidden(N,O)
& r2_hidden(O,P)
& r2_hidden(P,Q)
& r2_hidden(Q,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(d1_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k4_tarski(k1_mcart_5(A,B,C,D,E,F,G,H),I) ).
fof(t3_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(A,B),C),D),E),F),G),H),I) ).
fof(t4_mcart_6,axiom,
$true ).
fof(t5_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k3_mcart_1(k1_mcart_4(A,B,C,D,E,F,G),H,I) ).
fof(t6_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k4_mcart_1(k1_mcart_3(A,B,C,D,E,F),G,H,I) ).
fof(t7_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_2(k1_mcart_2(A,B,C,D,E),F,G,H,I) ).
fof(t8_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_3(k4_mcart_1(A,B,C,D),E,F,G,H,I) ).
fof(t9_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_4(k3_mcart_1(A,B,C),D,E,F,G,H,I) ).
fof(t10_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_5(k4_tarski(A,B),C,D,E,F,G,H,I) ).
fof(t11_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
( k1_mcart_6(A,B,C,D,E,F,G,H,I) = k1_mcart_6(J,K,L,M,N,O,P,Q,R)
=> ( A = J
& B = K
& C = L
& D = M
& E = N
& F = O
& G = P
& H = Q
& I = R ) ) ).
fof(d2_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_zfmisc_1(k2_mcart_5(A,B,C,D,E,F,G,H),I) ).
fof(t12_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D),E),F),G),H),I) ).
fof(t13_mcart_6,axiom,
$true ).
fof(t14_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k3_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G),H,I) ).
fof(t15_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k4_zfmisc_1(k2_mcart_3(A,B,C,D,E,F),G,H,I) ).
fof(t16_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_2(k2_mcart_2(A,B,C,D,E),F,G,H,I) ).
fof(t17_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_3(k4_zfmisc_1(A,B,C,D),E,F,G,H,I) ).
fof(t18_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_4(k3_zfmisc_1(A,B,C),D,E,F,G,H,I) ).
fof(t19_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_5(k2_zfmisc_1(A,B),C,D,E,F,G,H,I) ).
fof(t20_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0 )
<=> k2_mcart_6(A,B,C,D,E,F,G,H,I) != k1_xboole_0 ) ).
fof(t21_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
( k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_6(J,K,L,M,N,O,P,Q,R)
=> ( 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
| ( A = J
& B = K
& C = L
& D = M
& E = N
& F = O
& G = P
& H = Q
& I = R ) ) ) ).
fof(t22_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
( k2_mcart_6(A,B,C,D,E,F,G,H,I) = k2_mcart_6(J,K,L,M,N,O,P,Q,R)
=> ( k2_mcart_6(A,B,C,D,E,F,G,H,I) = k1_xboole_0
| ( A = J
& B = K
& C = L
& D = M
& E = N
& F = O
& G = P
& H = Q
& I = R ) ) ) ).
fof(t23_mcart_6,axiom,
! [A,B] :
( k2_mcart_6(A,A,A,A,A,A,A,A,A) = k2_mcart_6(B,B,B,B,B,B,B,B,B)
=> A = B ) ).
fof(t24_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ? [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
& ! [K] :
( m1_subset_1(K,A)
=> ! [L] :
( m1_subset_1(L,B)
=> ! [M] :
( m1_subset_1(M,C)
=> ! [N] :
( m1_subset_1(N,D)
=> ! [O] :
( m1_subset_1(O,E)
=> ! [P] :
( m1_subset_1(P,F)
=> ! [Q] :
( m1_subset_1(Q,G)
=> ! [R] :
( m1_subset_1(R,H)
=> ! [S] :
( m1_subset_1(S,I)
=> J != k1_mcart_6(K,L,M,N,O,P,Q,R,S) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,A)
=> ( K = k3_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = L ) ) ) ) ) ).
fof(d4_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,B)
=> ( K = k4_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = M ) ) ) ) ) ).
fof(d5_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,C)
=> ( K = k5_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = N ) ) ) ) ) ).
fof(d6_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,D)
=> ( K = k6_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = O ) ) ) ) ) ).
fof(d7_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,E)
=> ( K = k7_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = P ) ) ) ) ) ).
fof(d8_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,F)
=> ( K = k8_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = Q ) ) ) ) ) ).
fof(d9_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,G)
=> ( K = k9_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = R ) ) ) ) ) ).
fof(d10_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,H)
=> ( K = k10_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = S ) ) ) ) ) ).
fof(d11_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ! [K] :
( m1_subset_1(K,I)
=> ( K = k11_mcart_6(A,B,C,D,E,F,G,H,I,J)
<=> ! [L,M,N,O,P,Q,R,S,T] :
( J = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> K = T ) ) ) ) ) ).
fof(t25_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ? [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
& ? [K,L,M,N,O,P,Q,R,S] :
( J = k1_mcart_6(K,L,M,N,O,P,Q,R,S)
& ~ ( k3_mcart_6(A,B,C,D,E,F,G,H,I,J) = K
& k4_mcart_6(A,B,C,D,E,F,G,H,I,J) = L
& k5_mcart_6(A,B,C,D,E,F,G,H,I,J) = M
& k6_mcart_6(A,B,C,D,E,F,G,H,I,J) = N
& k7_mcart_6(A,B,C,D,E,F,G,H,I,J) = O
& k8_mcart_6(A,B,C,D,E,F,G,H,I,J) = P
& k9_mcart_6(A,B,C,D,E,F,G,H,I,J) = Q
& k10_mcart_6(A,B,C,D,E,F,G,H,I,J) = R
& k11_mcart_6(A,B,C,D,E,F,G,H,I,J) = S ) ) ) ) ).
fof(t26_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> J = k1_mcart_6(k3_mcart_6(A,B,C,D,E,F,G,H,I,J),k4_mcart_6(A,B,C,D,E,F,G,H,I,J),k5_mcart_6(A,B,C,D,E,F,G,H,I,J),k6_mcart_6(A,B,C,D,E,F,G,H,I,J),k7_mcart_6(A,B,C,D,E,F,G,H,I,J),k8_mcart_6(A,B,C,D,E,F,G,H,I,J),k9_mcart_6(A,B,C,D,E,F,G,H,I,J),k10_mcart_6(A,B,C,D,E,F,G,H,I,J),k11_mcart_6(A,B,C,D,E,F,G,H,I,J)) ) ) ).
fof(t27_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ~ ! [J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( k3_mcart_6(A,B,C,D,E,F,G,H,I,J) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))))))
& k4_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))))))
& k5_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J)))))))
& k6_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))))
& k7_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J)))))
& k8_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(J))))
& k9_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(k1_mcart_1(J)))
& k10_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(k1_mcart_1(J))
& k11_mcart_6(A,B,C,D,E,F,G,H,I,J) = k2_mcart_1(J) ) ) ) ).
fof(t28_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
( ~ r1_xboole_0(k2_mcart_6(A,B,C,D,E,F,G,H,I),k2_mcart_6(J,K,L,M,N,O,P,Q,R))
=> ( ~ r1_xboole_0(A,J)
& ~ r1_xboole_0(B,K)
& ~ r1_xboole_0(C,L)
& ~ r1_xboole_0(D,M)
& ~ r1_xboole_0(E,N)
& ~ r1_xboole_0(F,O)
& ~ r1_xboole_0(G,P)
& ~ r1_xboole_0(H,Q)
& ~ r1_xboole_0(I,R) ) ) ).
fof(t29_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I] : k2_mcart_6(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D),k1_tarski(E),k1_tarski(F),k1_tarski(G),k1_tarski(H),k1_tarski(I)) = k1_tarski(k1_mcart_6(A,B,C,D,E,F,G,H,I)) ).
fof(t30_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,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 != k1_xboole_0
& H != k1_xboole_0
& I != k1_xboole_0
& ? [K,L,M,N,O,P,Q,R,S] :
( J = k1_mcart_6(K,L,M,N,O,P,Q,R,S)
& ~ ( k3_mcart_6(A,B,C,D,E,F,G,H,I,J) = K
& k4_mcart_6(A,B,C,D,E,F,G,H,I,J) = L
& k5_mcart_6(A,B,C,D,E,F,G,H,I,J) = M
& k6_mcart_6(A,B,C,D,E,F,G,H,I,J) = N
& k7_mcart_6(A,B,C,D,E,F,G,H,I,J) = O
& k8_mcart_6(A,B,C,D,E,F,G,H,I,J) = P
& k9_mcart_6(A,B,C,D,E,F,G,H,I,J) = Q
& k10_mcart_6(A,B,C,D,E,F,G,H,I,J) = R
& k11_mcart_6(A,B,C,D,E,F,G,H,I,J) = S ) ) ) ) ).
fof(t31_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = 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 = k3_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t32_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = 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 = k1_xboole_0
| H = k1_xboole_0
| I = k1_xboole_0
| J = k4_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t33_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = 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 = k1_xboole_0
| H = k1_xboole_0
| I = k1_xboole_0
| J = k5_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t34_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = O ) ) ) ) ) ) ) ) ) )
=> ( 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 = k6_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t35_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = P ) ) ) ) ) ) ) ) ) )
=> ( 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 = k7_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t36_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = Q ) ) ) ) ) ) ) ) ) )
=> ( 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 = k8_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t37_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = R ) ) ) ) ) ) ) ) ) )
=> ( 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 = k9_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t38_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = S ) ) ) ) ) ) ) ) ) )
=> ( 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 = k10_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t39_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K] :
( m1_subset_1(K,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,B)
=> ! [N] :
( m1_subset_1(N,C)
=> ! [O] :
( m1_subset_1(O,D)
=> ! [P] :
( m1_subset_1(P,E)
=> ! [Q] :
( m1_subset_1(Q,F)
=> ! [R] :
( m1_subset_1(R,G)
=> ! [S] :
( m1_subset_1(S,H)
=> ! [T] :
( m1_subset_1(T,I)
=> ( K = k1_mcart_6(L,M,N,O,P,Q,R,S,T)
=> J = T ) ) ) ) ) ) ) ) ) )
=> ( 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 = k11_mcart_6(A,B,C,D,E,F,G,H,I,K) ) ) ) ).
fof(t40_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
~ ( r2_hidden(A,k2_mcart_6(B,C,D,E,F,G,H,I,J))
& ! [K,L,M,N,O,P,Q,R,S] :
~ ( r2_hidden(K,B)
& r2_hidden(L,C)
& r2_hidden(M,D)
& r2_hidden(N,E)
& r2_hidden(O,F)
& r2_hidden(P,G)
& r2_hidden(Q,H)
& r2_hidden(R,I)
& r2_hidden(S,J)
& A = k1_mcart_6(K,L,M,N,O,P,Q,R,S) ) ) ).
fof(t41_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
( r2_hidden(k1_mcart_6(A,B,C,D,E,F,G,H,I),k2_mcart_6(J,K,L,M,N,O,P,Q,R))
<=> ( r2_hidden(A,J)
& r2_hidden(B,K)
& r2_hidden(C,L)
& r2_hidden(D,M)
& r2_hidden(E,N)
& r2_hidden(F,O)
& r2_hidden(G,P)
& r2_hidden(H,Q)
& r2_hidden(I,R) ) ) ).
fof(t42_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ! [K] :
( r2_hidden(K,A)
<=> ? [L,M,N,O,P,Q,R,S,T] :
( r2_hidden(L,B)
& r2_hidden(M,C)
& r2_hidden(N,D)
& r2_hidden(O,E)
& r2_hidden(P,F)
& r2_hidden(Q,G)
& r2_hidden(R,H)
& r2_hidden(S,I)
& r2_hidden(T,J)
& K = k1_mcart_6(L,M,N,O,P,Q,R,S,T) ) )
=> A = k2_mcart_6(B,C,D,E,F,G,H,I,J) ) ).
fof(t43_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
~ ( 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 != k1_xboole_0
& N != k1_xboole_0
& O != k1_xboole_0
& P != k1_xboole_0
& Q != k1_xboole_0
& R != k1_xboole_0
& ? [S] :
( m1_subset_1(S,k2_mcart_6(A,B,C,D,E,F,G,H,I))
& ? [T] :
( m1_subset_1(T,k2_mcart_6(J,K,L,M,N,O,P,Q,R))
& S = T
& ~ ( k3_mcart_6(A,B,C,D,E,F,G,H,I,S) = k3_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k4_mcart_6(A,B,C,D,E,F,G,H,I,S) = k4_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k5_mcart_6(A,B,C,D,E,F,G,H,I,S) = k5_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k6_mcart_6(A,B,C,D,E,F,G,H,I,S) = k6_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k7_mcart_6(A,B,C,D,E,F,G,H,I,S) = k7_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k8_mcart_6(A,B,C,D,E,F,G,H,I,S) = k8_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k9_mcart_6(A,B,C,D,E,F,G,H,I,S) = k9_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k10_mcart_6(A,B,C,D,E,F,G,H,I,S) = k10_mcart_6(J,K,L,M,N,O,P,Q,R,T)
& k11_mcart_6(A,B,C,D,E,F,G,H,I,S) = k11_mcart_6(J,K,L,M,N,O,P,Q,R,T) ) ) ) ) ).
fof(t44_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k1_zfmisc_1(A))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(B))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(C))
=> ! [M] :
( m1_subset_1(M,k1_zfmisc_1(D))
=> ! [N] :
( m1_subset_1(N,k1_zfmisc_1(E))
=> ! [O] :
( m1_subset_1(O,k1_zfmisc_1(F))
=> ! [P] :
( m1_subset_1(P,k1_zfmisc_1(G))
=> ! [Q] :
( m1_subset_1(Q,k1_zfmisc_1(H))
=> ! [R] :
( m1_subset_1(R,k1_zfmisc_1(I))
=> ! [S] :
( m1_subset_1(S,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> ( r2_hidden(S,k2_mcart_6(J,K,L,M,N,O,P,Q,R))
=> ( r2_hidden(k3_mcart_6(A,B,C,D,E,F,G,H,I,S),J)
& r2_hidden(k4_mcart_6(A,B,C,D,E,F,G,H,I,S),K)
& r2_hidden(k5_mcart_6(A,B,C,D,E,F,G,H,I,S),L)
& r2_hidden(k6_mcart_6(A,B,C,D,E,F,G,H,I,S),M)
& r2_hidden(k7_mcart_6(A,B,C,D,E,F,G,H,I,S),N)
& r2_hidden(k8_mcart_6(A,B,C,D,E,F,G,H,I,S),O)
& r2_hidden(k9_mcart_6(A,B,C,D,E,F,G,H,I,S),P)
& r2_hidden(k10_mcart_6(A,B,C,D,E,F,G,H,I,S),Q)
& r2_hidden(k11_mcart_6(A,B,C,D,E,F,G,H,I,S),R) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R] :
( ( 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(M,N)
& r1_tarski(O,P)
& r1_tarski(Q,R) )
=> r1_tarski(k2_mcart_6(A,C,E,G,I,K,M,O,Q),k2_mcart_6(B,D,F,H,J,L,N,P,R)) ) ).
fof(t46_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k1_zfmisc_1(A))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(B))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(C))
=> ! [M] :
( m1_subset_1(M,k1_zfmisc_1(D))
=> ! [N] :
( m1_subset_1(N,k1_zfmisc_1(E))
=> ! [O] :
( m1_subset_1(O,k1_zfmisc_1(F))
=> ! [P] :
( m1_subset_1(P,k1_zfmisc_1(G))
=> ! [Q] :
( m1_subset_1(Q,k1_zfmisc_1(H))
=> ! [R] :
( m1_subset_1(R,k1_zfmisc_1(I))
=> m1_subset_1(k2_mcart_6(J,K,L,M,N,O,P,Q,R),k1_zfmisc_1(k2_mcart_6(A,B,C,D,E,F,G,H,I))) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_mcart_6,axiom,
$true ).
fof(dt_k2_mcart_6,axiom,
$true ).
fof(dt_k3_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k3_mcart_6(A,B,C,D,E,F,G,H,I,J),A) ) ).
fof(dt_k4_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k4_mcart_6(A,B,C,D,E,F,G,H,I,J),B) ) ).
fof(dt_k5_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k5_mcart_6(A,B,C,D,E,F,G,H,I,J),C) ) ).
fof(dt_k6_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k6_mcart_6(A,B,C,D,E,F,G,H,I,J),D) ) ).
fof(dt_k7_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k7_mcart_6(A,B,C,D,E,F,G,H,I,J),E) ) ).
fof(dt_k8_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k8_mcart_6(A,B,C,D,E,F,G,H,I,J),F) ) ).
fof(dt_k9_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k9_mcart_6(A,B,C,D,E,F,G,H,I,J),G) ) ).
fof(dt_k10_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k10_mcart_6(A,B,C,D,E,F,G,H,I,J),H) ) ).
fof(dt_k11_mcart_6,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_6(A,B,C,D,E,F,G,H,I))
=> m1_subset_1(k11_mcart_6(A,B,C,D,E,F,G,H,I,J),I) ) ).
%------------------------------------------------------------------------------