SET007 Axioms: SET007+94.ax
%------------------------------------------------------------------------------
% File : SET007+94 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : N-Tuples and Cartesian Products for n=7
% 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 60 ( 17 unt; 0 def)
% Number of atoms : 486 ( 285 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 586 ( 160 ~; 58 |; 224 &)
% ( 10 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 19 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 1 con; 0-8 aty)
% Number of variables : 642 ( 617 !; 25 ?)
% 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_4,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J,K,L] :
( ( 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,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(t2_mcart_4,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J,K,L,M] :
( ( 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,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(d1_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k4_tarski(k1_mcart_3(A,B,C,D,E,F),G) ).
fof(t3_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(A,B),C),D),E),F),G) ).
fof(t4_mcart_4,axiom,
$true ).
fof(t5_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k3_mcart_1(k1_mcart_2(A,B,C,D,E),F,G) ).
fof(t6_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k4_mcart_1(k4_mcart_1(A,B,C,D),E,F,G) ).
fof(t7_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k1_mcart_2(k3_mcart_1(A,B,C),D,E,F,G) ).
fof(t8_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k1_mcart_4(A,B,C,D,E,F,G) = k1_mcart_3(k4_tarski(A,B),C,D,E,F,G) ).
fof(t9_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
( k1_mcart_4(A,B,C,D,E,F,G) = k1_mcart_4(H,I,J,K,L,M,N)
=> ( A = H
& B = I
& C = J
& D = K
& E = L
& F = M
& G = N ) ) ).
fof(t10_mcart_4,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I] :
~ ( ( r2_hidden(C,A)
| r2_hidden(D,A) )
& B = k1_mcart_4(C,D,E,F,G,H,I) ) ) ) ).
fof(d2_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_zfmisc_1(k2_mcart_3(A,B,C,D,E,F),G) ).
fof(t11_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = 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) ).
fof(t12_mcart_4,axiom,
$true ).
fof(t13_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k3_zfmisc_1(k2_mcart_2(A,B,C,D,E),F,G) ).
fof(t14_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k4_zfmisc_1(k4_zfmisc_1(A,B,C,D),E,F,G) ).
fof(t15_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_2(k3_zfmisc_1(A,B,C),D,E,F,G) ).
fof(t16_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_3(k2_zfmisc_1(A,B),C,D,E,F,G) ).
fof(t17_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
( ( 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 )
<=> k2_mcart_4(A,B,C,D,E,F,G) != k1_xboole_0 ) ).
fof(t18_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
( k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_4(H,I,J,K,L,M,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
| ( A = H
& B = I
& C = J
& D = K
& E = L
& F = M
& G = N ) ) ) ).
fof(t19_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
( k2_mcart_4(A,B,C,D,E,F,G) = k2_mcart_4(H,I,J,K,L,M,N)
=> ( k2_mcart_4(A,B,C,D,E,F,G) = k1_xboole_0
| ( A = H
& B = I
& C = J
& D = K
& E = L
& F = M
& G = N ) ) ) ).
fof(t20_mcart_4,axiom,
! [A,B] :
( k2_mcart_4(A,A,A,A,A,A,A) = k2_mcart_4(B,B,B,B,B,B,B)
=> A = B ) ).
fof(t21_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
& ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> H != k1_mcart_4(I,J,K,L,M,N,O) ) ) ) ) ) ) ) ) ) ).
fof(d3_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ! [I] :
( m1_subset_1(I,A)
=> ( I = k3_mcart_4(A,B,C,D,E,F,G,H)
<=> ! [J,K,L,M,N,O,P] :
( H = k1_mcart_4(J,K,L,M,N,O,P)
=> I = J ) ) ) ) ) ).
fof(d4_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ! [I] :
( m1_subset_1(I,B)
=> ( I = k4_mcart_4(A,B,C,D,E,F,G,H)
<=> ! [J,K,L,M,N,O,P] :
( H = k1_mcart_4(J,K,L,M,N,O,P)
=> I = K ) ) ) ) ) ).
fof(d5_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ! [I] :
( m1_subset_1(I,C)
=> ( I = k5_mcart_4(A,B,C,D,E,F,G,H)
<=> ! [J,K,L,M,N,O,P] :
( H = k1_mcart_4(J,K,L,M,N,O,P)
=> I = L ) ) ) ) ) ).
fof(d6_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ! [I] :
( m1_subset_1(I,D)
=> ( I = k6_mcart_4(A,B,C,D,E,F,G,H)
<=> ! [J,K,L,M,N,O,P] :
( H = k1_mcart_4(J,K,L,M,N,O,P)
=> I = M ) ) ) ) ) ).
fof(d7_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ! [I] :
( m1_subset_1(I,E)
=> ( I = k7_mcart_4(A,B,C,D,E,F,G,H)
<=> ! [J,K,L,M,N,O,P] :
( H = k1_mcart_4(J,K,L,M,N,O,P)
=> I = N ) ) ) ) ) ).
fof(d8_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ! [I] :
( m1_subset_1(I,F)
=> ( I = k8_mcart_4(A,B,C,D,E,F,G,H)
<=> ! [J,K,L,M,N,O,P] :
( H = k1_mcart_4(J,K,L,M,N,O,P)
=> I = O ) ) ) ) ) ).
fof(d9_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ! [I] :
( m1_subset_1(I,G)
=> ( I = k9_mcart_4(A,B,C,D,E,F,G,H)
<=> ! [J,K,L,M,N,O,P] :
( H = k1_mcart_4(J,K,L,M,N,O,P)
=> I = P ) ) ) ) ) ).
fof(t22_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
& ? [I,J,K,L,M,N,O] :
( H = k1_mcart_4(I,J,K,L,M,N,O)
& ~ ( k3_mcart_4(A,B,C,D,E,F,G,H) = I
& k4_mcart_4(A,B,C,D,E,F,G,H) = J
& k5_mcart_4(A,B,C,D,E,F,G,H) = K
& k6_mcart_4(A,B,C,D,E,F,G,H) = L
& k7_mcart_4(A,B,C,D,E,F,G,H) = M
& k8_mcart_4(A,B,C,D,E,F,G,H) = N
& k9_mcart_4(A,B,C,D,E,F,G,H) = O ) ) ) ) ).
fof(t23_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> H = k1_mcart_4(k3_mcart_4(A,B,C,D,E,F,G,H),k4_mcart_4(A,B,C,D,E,F,G,H),k5_mcart_4(A,B,C,D,E,F,G,H),k6_mcart_4(A,B,C,D,E,F,G,H),k7_mcart_4(A,B,C,D,E,F,G,H),k8_mcart_4(A,B,C,D,E,F,G,H),k9_mcart_4(A,B,C,D,E,F,G,H)) ) ) ).
fof(t24_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
~ ( 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] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ( k3_mcart_4(A,B,C,D,E,F,G,H) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H))))))
& k4_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H))))))
& k5_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H)))))
& k6_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(H))))
& k7_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(k1_mcart_1(H)))
& k8_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(k1_mcart_1(H))
& k9_mcart_4(A,B,C,D,E,F,G,H) = k2_mcart_1(H) ) ) ) ).
fof(t25_mcart_4,axiom,
! [A,B,C,D,E,F,G] :
( ~ ( ~ r1_tarski(A,k2_mcart_4(A,B,C,D,E,F,G))
& ~ r1_tarski(A,k2_mcart_4(B,C,D,E,F,G,A))
& ~ r1_tarski(A,k2_mcart_4(C,D,E,F,G,A,B))
& ~ r1_tarski(A,k2_mcart_4(D,E,F,G,A,B,C))
& ~ r1_tarski(A,k2_mcart_4(E,F,G,A,B,C,D))
& ~ r1_tarski(A,k2_mcart_4(F,G,A,B,C,D,E))
& ~ r1_tarski(A,k2_mcart_4(G,A,B,C,D,E,F)) )
=> A = k1_xboole_0 ) ).
fof(t26_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
( ~ r1_xboole_0(k2_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N))
=> ( ~ r1_xboole_0(A,H)
& ~ r1_xboole_0(B,I)
& ~ r1_xboole_0(C,J)
& ~ r1_xboole_0(D,K)
& ~ r1_xboole_0(E,L)
& ~ r1_xboole_0(F,M)
& ~ r1_xboole_0(G,N) ) ) ).
fof(t27_mcart_4,axiom,
! [A,B,C,D,E,F,G] : k2_mcart_4(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D),k1_tarski(E),k1_tarski(F),k1_tarski(G)) = k1_tarski(k1_mcart_4(A,B,C,D,E,F,G)) ).
fof(t28_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> ~ ( 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
& ? [I,J,K,L,M,N,O] :
( H = k1_mcart_4(I,J,K,L,M,N,O)
& ~ ( k3_mcart_4(A,B,C,D,E,F,G,H) = I
& k4_mcart_4(A,B,C,D,E,F,G,H) = J
& k5_mcart_4(A,B,C,D,E,F,G,H) = K
& k6_mcart_4(A,B,C,D,E,F,G,H) = L
& k7_mcart_4(A,B,C,D,E,F,G,H) = M
& k8_mcart_4(A,B,C,D,E,F,G,H) = N
& k9_mcart_4(A,B,C,D,E,F,G,H) = O ) ) ) ) ).
fof(t29_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
=> ( ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> ! [P] :
( m1_subset_1(P,H)
=> ( I = k1_mcart_4(J,K,L,M,N,O,P)
=> A = J ) ) ) ) ) ) ) )
=> ( 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
| A = k3_mcart_4(B,C,D,E,F,G,H,I) ) ) ) ).
fof(t30_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
=> ( ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> ! [P] :
( m1_subset_1(P,H)
=> ( I = k1_mcart_4(J,K,L,M,N,O,P)
=> A = K ) ) ) ) ) ) ) )
=> ( 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
| A = k4_mcart_4(B,C,D,E,F,G,H,I) ) ) ) ).
fof(t31_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
=> ( ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> ! [P] :
( m1_subset_1(P,H)
=> ( I = k1_mcart_4(J,K,L,M,N,O,P)
=> A = L ) ) ) ) ) ) ) )
=> ( 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
| A = k5_mcart_4(B,C,D,E,F,G,H,I) ) ) ) ).
fof(t32_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
=> ( ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> ! [P] :
( m1_subset_1(P,H)
=> ( I = k1_mcart_4(J,K,L,M,N,O,P)
=> A = M ) ) ) ) ) ) ) )
=> ( 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
| A = k6_mcart_4(B,C,D,E,F,G,H,I) ) ) ) ).
fof(t33_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
=> ( ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> ! [P] :
( m1_subset_1(P,H)
=> ( I = k1_mcart_4(J,K,L,M,N,O,P)
=> A = N ) ) ) ) ) ) ) )
=> ( 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
| A = k7_mcart_4(B,C,D,E,F,G,H,I) ) ) ) ).
fof(t34_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
=> ( ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> ! [P] :
( m1_subset_1(P,H)
=> ( I = k1_mcart_4(J,K,L,M,N,O,P)
=> A = O ) ) ) ) ) ) ) )
=> ( 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
| A = k8_mcart_4(B,C,D,E,F,G,H,I) ) ) ) ).
fof(t35_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_4(B,C,D,E,F,G,H))
=> ( ! [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)
=> ! [O] :
( m1_subset_1(O,G)
=> ! [P] :
( m1_subset_1(P,H)
=> ( I = k1_mcart_4(J,K,L,M,N,O,P)
=> A = P ) ) ) ) ) ) ) )
=> ( 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
| A = k9_mcart_4(B,C,D,E,F,G,H,I) ) ) ) ).
fof(t36_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( r2_hidden(A,k2_mcart_4(B,C,D,E,F,G,H))
& ! [I,J,K,L,M,N,O] :
~ ( r2_hidden(I,B)
& r2_hidden(J,C)
& r2_hidden(K,D)
& r2_hidden(L,E)
& r2_hidden(M,F)
& r2_hidden(N,G)
& r2_hidden(O,H)
& A = k1_mcart_4(I,J,K,L,M,N,O) ) ) ).
fof(t37_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
( r2_hidden(k1_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N))
<=> ( r2_hidden(A,H)
& r2_hidden(B,I)
& r2_hidden(C,J)
& r2_hidden(D,K)
& r2_hidden(E,L)
& r2_hidden(F,M)
& r2_hidden(G,N) ) ) ).
fof(t38_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( ! [I] :
( r2_hidden(I,H)
<=> ? [J,K,L,M,N,O,P] :
( r2_hidden(J,A)
& r2_hidden(K,B)
& r2_hidden(L,C)
& r2_hidden(M,D)
& r2_hidden(N,E)
& r2_hidden(O,F)
& r2_hidden(P,G)
& I = k1_mcart_4(J,K,L,M,N,O,P) ) )
=> H = k2_mcart_4(A,B,C,D,E,F,G) ) ).
fof(t39_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,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 != k1_xboole_0
& K != k1_xboole_0
& L != k1_xboole_0
& M != k1_xboole_0
& N != k1_xboole_0
& ? [O] :
( m1_subset_1(O,k2_mcart_4(A,B,C,D,E,F,G))
& ? [P] :
( m1_subset_1(P,k2_mcart_4(H,I,J,K,L,M,N))
& O = P
& ~ ( k3_mcart_4(A,B,C,D,E,F,G,O) = k3_mcart_4(H,I,J,K,L,M,N,P)
& k4_mcart_4(A,B,C,D,E,F,G,O) = k4_mcart_4(H,I,J,K,L,M,N,P)
& k5_mcart_4(A,B,C,D,E,F,G,O) = k5_mcart_4(H,I,J,K,L,M,N,P)
& k6_mcart_4(A,B,C,D,E,F,G,O) = k6_mcart_4(H,I,J,K,L,M,N,P)
& k7_mcart_4(A,B,C,D,E,F,G,O) = k7_mcart_4(H,I,J,K,L,M,N,P)
& k8_mcart_4(A,B,C,D,E,F,G,O) = k8_mcart_4(H,I,J,K,L,M,N,P)
& k9_mcart_4(A,B,C,D,E,F,G,O) = k9_mcart_4(H,I,J,K,L,M,N,P) ) ) ) ) ).
fof(t40_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k1_zfmisc_1(A))
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(B))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(C))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(D))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(E))
=> ! [M] :
( m1_subset_1(M,k1_zfmisc_1(F))
=> ! [N] :
( m1_subset_1(N,k1_zfmisc_1(G))
=> ! [O] :
( m1_subset_1(O,k2_mcart_4(A,B,C,D,E,F,G))
=> ( r2_hidden(O,k2_mcart_4(H,I,J,K,L,M,N))
=> ( r2_hidden(k3_mcart_4(A,B,C,D,E,F,G,O),H)
& r2_hidden(k4_mcart_4(A,B,C,D,E,F,G,O),I)
& r2_hidden(k5_mcart_4(A,B,C,D,E,F,G,O),J)
& r2_hidden(k6_mcart_4(A,B,C,D,E,F,G,O),K)
& r2_hidden(k7_mcart_4(A,B,C,D,E,F,G,O),L)
& r2_hidden(k8_mcart_4(A,B,C,D,E,F,G,O),M)
& r2_hidden(k9_mcart_4(A,B,C,D,E,F,G,O),N) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_mcart_4,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N] :
( ( r1_tarski(A,H)
& r1_tarski(B,I)
& r1_tarski(C,J)
& r1_tarski(D,K)
& r1_tarski(E,L)
& r1_tarski(F,M)
& r1_tarski(G,N) )
=> r1_tarski(k2_mcart_4(A,B,C,D,E,F,G),k2_mcart_4(H,I,J,K,L,M,N)) ) ).
fof(t42_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k1_zfmisc_1(A))
=> ! [I] :
( m1_subset_1(I,k1_zfmisc_1(B))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(C))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(D))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(E))
=> ! [M] :
( m1_subset_1(M,k1_zfmisc_1(F))
=> ! [N] :
( m1_subset_1(N,k1_zfmisc_1(G))
=> m1_subset_1(k2_mcart_4(H,I,J,K,L,M,N),k1_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G))) ) ) ) ) ) ) ) ).
fof(dt_k1_mcart_4,axiom,
$true ).
fof(dt_k2_mcart_4,axiom,
$true ).
fof(dt_k3_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> m1_subset_1(k3_mcart_4(A,B,C,D,E,F,G,H),A) ) ).
fof(dt_k4_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> m1_subset_1(k4_mcart_4(A,B,C,D,E,F,G,H),B) ) ).
fof(dt_k5_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> m1_subset_1(k5_mcart_4(A,B,C,D,E,F,G,H),C) ) ).
fof(dt_k6_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> m1_subset_1(k6_mcart_4(A,B,C,D,E,F,G,H),D) ) ).
fof(dt_k7_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> m1_subset_1(k7_mcart_4(A,B,C,D,E,F,G,H),E) ) ).
fof(dt_k8_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> m1_subset_1(k8_mcart_4(A,B,C,D,E,F,G,H),F) ) ).
fof(dt_k9_mcart_4,axiom,
! [A,B,C,D,E,F,G,H] :
( m1_subset_1(H,k2_mcart_4(A,B,C,D,E,F,G))
=> m1_subset_1(k9_mcart_4(A,B,C,D,E,F,G,H),G) ) ).
%------------------------------------------------------------------------------