SET007 Axioms: SET007+95.ax
%------------------------------------------------------------------------------
% File : SET007+95 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : N-Tuples and Cartesian Products for n=8
% 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_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 65 ( 19 unt; 0 def)
% Number of atoms : 574 ( 339 equ)
% Maximal formula atoms : 27 ( 8 avg)
% Number of connectives : 696 ( 187 ~; 74 |; 265 &)
% ( 11 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 21 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 1 con; 0-9 aty)
% Number of variables : 788 ( 760 !; 28 ?)
% 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_5,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J,K,L,M,N] :
( ( 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,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(t2_mcart_5,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J,K,L,M,N,O] :
( ( 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,B) )
=> r1_xboole_0(C,A) ) ) ) ).
fof(d1_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k4_tarski(k1_mcart_4(A,B,C,D,E,F,G),H) ).
fof(t3_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(k4_tarski(A,B),C),D),E),F),G),H) ).
fof(t4_mcart_5,axiom,
$true ).
fof(t5_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k3_mcart_1(k1_mcart_3(A,B,C,D,E,F),G,H) ).
fof(t6_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k4_mcart_1(k1_mcart_2(A,B,C,D,E),F,G,H) ).
fof(t7_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k1_mcart_2(k4_mcart_1(A,B,C,D),E,F,G,H) ).
fof(t8_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k1_mcart_3(k3_mcart_1(A,B,C),D,E,F,G,H) ).
fof(t9_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k1_mcart_5(A,B,C,D,E,F,G,H) = k1_mcart_4(k4_tarski(A,B),C,D,E,F,G,H) ).
fof(t10_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( k1_mcart_5(A,B,C,D,E,F,G,H) = k1_mcart_5(I,J,K,L,M,N,O,P)
=> ( A = I
& B = J
& C = K
& D = L
& E = M
& F = N
& G = O
& H = P ) ) ).
fof(t11_mcart_5,axiom,
! [A] :
~ ( A != k1_xboole_0
& ! [B] :
~ ( r2_hidden(B,A)
& ! [C,D,E,F,G,H,I,J] :
~ ( ( r2_hidden(C,A)
| r2_hidden(D,A) )
& B = k1_mcart_5(C,D,E,F,G,H,I,J) ) ) ) ).
fof(d2_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_zfmisc_1(k2_mcart_4(A,B,C,D,E,F,G),H) ).
fof(t12_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = 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) ).
fof(t13_mcart_5,axiom,
$true ).
fof(t14_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k3_zfmisc_1(k2_mcart_3(A,B,C,D,E,F),G,H) ).
fof(t15_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k4_zfmisc_1(k2_mcart_2(A,B,C,D,E),F,G,H) ).
fof(t16_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_mcart_2(k4_zfmisc_1(A,B,C,D),E,F,G,H) ).
fof(t17_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_mcart_3(k3_zfmisc_1(A,B,C),D,E,F,G,H) ).
fof(t18_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(A,B,C,D,E,F,G,H) = k2_mcart_4(k2_zfmisc_1(A,B),C,D,E,F,G,H) ).
fof(t19_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
( ( 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 )
<=> k2_mcart_5(A,B,C,D,E,F,G,H) != k1_xboole_0 ) ).
fof(t20_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( k2_mcart_5(A,B,C,D,E,F,G,H) = k2_mcart_5(I,J,K,L,M,N,O,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
| ( A = I
& B = J
& C = K
& D = L
& E = M
& F = N
& G = O
& H = P ) ) ) ).
fof(t21_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( k2_mcart_5(A,B,C,D,E,F,G,H) = k2_mcart_5(I,J,K,L,M,N,O,P)
=> ( k2_mcart_5(A,B,C,D,E,F,G,H) = k1_xboole_0
| ( A = I
& B = J
& C = K
& D = L
& E = M
& F = N
& G = O
& H = P ) ) ) ).
fof(t22_mcart_5,axiom,
! [A,B] :
( k2_mcart_5(A,A,A,A,A,A,A,A) = k2_mcart_5(B,B,B,B,B,B,B,B)
=> A = B ) ).
fof(t23_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
& ! [J] :
( m1_subset_1(J,A)
=> ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> I != k1_mcart_5(J,K,L,M,N,O,P,Q) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,A)
=> ( J = k3_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = K ) ) ) ) ) ).
fof(d4_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,B)
=> ( J = k4_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = L ) ) ) ) ) ).
fof(d5_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,C)
=> ( J = k5_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = M ) ) ) ) ) ).
fof(d6_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,D)
=> ( J = k6_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = N ) ) ) ) ) ).
fof(d7_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,E)
=> ( J = k7_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = O ) ) ) ) ) ).
fof(d8_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,F)
=> ( J = k8_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = P ) ) ) ) ) ).
fof(d9_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,G)
=> ( J = k9_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = Q ) ) ) ) ) ).
fof(d10_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ! [J] :
( m1_subset_1(J,H)
=> ( J = k10_mcart_5(A,B,C,D,E,F,G,H,I)
<=> ! [K,L,M,N,O,P,Q,R] :
( I = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> J = R ) ) ) ) ) ).
fof(t24_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
& ? [J,K,L,M,N,O,P,Q] :
( I = k1_mcart_5(J,K,L,M,N,O,P,Q)
& ~ ( k3_mcart_5(A,B,C,D,E,F,G,H,I) = J
& k4_mcart_5(A,B,C,D,E,F,G,H,I) = K
& k5_mcart_5(A,B,C,D,E,F,G,H,I) = L
& k6_mcart_5(A,B,C,D,E,F,G,H,I) = M
& k7_mcart_5(A,B,C,D,E,F,G,H,I) = N
& k8_mcart_5(A,B,C,D,E,F,G,H,I) = O
& k9_mcart_5(A,B,C,D,E,F,G,H,I) = P
& k10_mcart_5(A,B,C,D,E,F,G,H,I) = Q ) ) ) ) ).
fof(t25_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> I = k1_mcart_5(k3_mcart_5(A,B,C,D,E,F,G,H,I),k4_mcart_5(A,B,C,D,E,F,G,H,I),k5_mcart_5(A,B,C,D,E,F,G,H,I),k6_mcart_5(A,B,C,D,E,F,G,H,I),k7_mcart_5(A,B,C,D,E,F,G,H,I),k8_mcart_5(A,B,C,D,E,F,G,H,I),k9_mcart_5(A,B,C,D,E,F,G,H,I),k10_mcart_5(A,B,C,D,E,F,G,H,I)) ) ) ).
fof(t26_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
~ ( 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] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ( k3_mcart_5(A,B,C,D,E,F,G,H,I) = k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(I)))))))
& k4_mcart_5(A,B,C,D,E,F,G,H,I) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(I)))))))
& k5_mcart_5(A,B,C,D,E,F,G,H,I) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(I))))))
& k6_mcart_5(A,B,C,D,E,F,G,H,I) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(I)))))
& k7_mcart_5(A,B,C,D,E,F,G,H,I) = k2_mcart_1(k1_mcart_1(k1_mcart_1(k1_mcart_1(I))))
& k8_mcart_5(A,B,C,D,E,F,G,H,I) = k2_mcart_1(k1_mcart_1(k1_mcart_1(I)))
& k9_mcart_5(A,B,C,D,E,F,G,H,I) = k2_mcart_1(k1_mcart_1(I))
& k10_mcart_5(A,B,C,D,E,F,G,H,I) = k2_mcart_1(I) ) ) ) ).
fof(t27_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] :
( ~ ( ~ r1_tarski(A,k2_mcart_5(A,B,C,D,E,F,G,H))
& ~ r1_tarski(A,k2_mcart_5(B,C,D,E,F,G,H,A))
& ~ r1_tarski(A,k2_mcart_5(C,D,E,F,G,H,A,B))
& ~ r1_tarski(A,k2_mcart_5(D,E,F,G,H,A,B,C))
& ~ r1_tarski(A,k2_mcart_5(E,F,G,H,A,B,C,D))
& ~ r1_tarski(A,k2_mcart_5(F,G,H,A,B,C,D,E))
& ~ r1_tarski(A,k2_mcart_5(G,H,A,B,C,D,E,F))
& ~ r1_tarski(A,k2_mcart_5(H,A,B,C,D,E,F,G)) )
=> A = k1_xboole_0 ) ).
fof(t28_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( ~ r1_xboole_0(k2_mcart_5(A,B,C,D,E,F,G,H),k2_mcart_5(I,J,K,L,M,N,O,P))
=> ( ~ r1_xboole_0(A,I)
& ~ r1_xboole_0(B,J)
& ~ r1_xboole_0(C,K)
& ~ r1_xboole_0(D,L)
& ~ r1_xboole_0(E,M)
& ~ r1_xboole_0(F,N)
& ~ r1_xboole_0(G,O)
& ~ r1_xboole_0(H,P) ) ) ).
fof(t29_mcart_5,axiom,
! [A,B,C,D,E,F,G,H] : k2_mcart_5(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(k1_mcart_5(A,B,C,D,E,F,G,H)) ).
fof(t30_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ~ ( 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
& ? [J,K,L,M,N,O,P,Q] :
( I = k1_mcart_5(J,K,L,M,N,O,P,Q)
& ~ ( k3_mcart_5(A,B,C,D,E,F,G,H,I) = J
& k4_mcart_5(A,B,C,D,E,F,G,H,I) = K
& k5_mcart_5(A,B,C,D,E,F,G,H,I) = L
& k6_mcart_5(A,B,C,D,E,F,G,H,I) = M
& k7_mcart_5(A,B,C,D,E,F,G,H,I) = N
& k8_mcart_5(A,B,C,D,E,F,G,H,I) = O
& k9_mcart_5(A,B,C,D,E,F,G,H,I) = P
& k10_mcart_5(A,B,C,D,E,F,G,H,I) = Q ) ) ) ) ).
fof(t31_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> 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
| I = k1_xboole_0
| A = k3_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t32_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> 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
| I = k1_xboole_0
| A = k4_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t33_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> 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
| I = k1_xboole_0
| A = k5_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t34_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> 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
| I = k1_xboole_0
| A = k6_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t35_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> 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
| I = k1_xboole_0
| A = k7_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t36_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> 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
| I = k1_xboole_0
| A = k8_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t37_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> A = Q ) ) ) ) ) ) ) ) )
=> ( 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 = k9_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t38_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( m1_subset_1(J,k2_mcart_5(B,C,D,E,F,G,H,I))
=> ( ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,C)
=> ! [M] :
( m1_subset_1(M,D)
=> ! [N] :
( m1_subset_1(N,E)
=> ! [O] :
( m1_subset_1(O,F)
=> ! [P] :
( m1_subset_1(P,G)
=> ! [Q] :
( m1_subset_1(Q,H)
=> ! [R] :
( m1_subset_1(R,I)
=> ( J = k1_mcart_5(K,L,M,N,O,P,Q,R)
=> A = R ) ) ) ) ) ) ) ) )
=> ( 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 = k10_mcart_5(B,C,D,E,F,G,H,I,J) ) ) ) ).
fof(t39_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
~ ( r2_hidden(A,k2_mcart_5(B,C,D,E,F,G,H,I))
& ! [J,K,L,M,N,O,P,Q] :
~ ( r2_hidden(J,B)
& r2_hidden(K,C)
& r2_hidden(L,D)
& r2_hidden(M,E)
& r2_hidden(N,F)
& r2_hidden(O,G)
& r2_hidden(P,H)
& r2_hidden(Q,I)
& A = k1_mcart_5(J,K,L,M,N,O,P,Q) ) ) ).
fof(t40_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( r2_hidden(k1_mcart_5(A,B,C,D,E,F,G,H),k2_mcart_5(I,J,K,L,M,N,O,P))
<=> ( r2_hidden(A,I)
& r2_hidden(B,J)
& r2_hidden(C,K)
& r2_hidden(D,L)
& r2_hidden(E,M)
& r2_hidden(F,N)
& r2_hidden(G,O)
& r2_hidden(H,P) ) ) ).
fof(t41_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ! [J] :
( r2_hidden(J,I)
<=> ? [K,L,M,N,O,P,Q,R] :
( r2_hidden(K,A)
& 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)
& J = k1_mcart_5(K,L,M,N,O,P,Q,R) ) )
=> I = k2_mcart_5(A,B,C,D,E,F,G,H) ) ).
fof(t42_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,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 != 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] :
( m1_subset_1(Q,k2_mcart_5(A,B,C,D,E,F,G,H))
& ? [R] :
( m1_subset_1(R,k2_mcart_5(I,J,K,L,M,N,O,P))
& Q = R
& ~ ( k3_mcart_5(A,B,C,D,E,F,G,H,Q) = k3_mcart_5(I,J,K,L,M,N,O,P,R)
& k4_mcart_5(A,B,C,D,E,F,G,H,Q) = k4_mcart_5(I,J,K,L,M,N,O,P,R)
& k5_mcart_5(A,B,C,D,E,F,G,H,Q) = k5_mcart_5(I,J,K,L,M,N,O,P,R)
& k6_mcart_5(A,B,C,D,E,F,G,H,Q) = k6_mcart_5(I,J,K,L,M,N,O,P,R)
& k7_mcart_5(A,B,C,D,E,F,G,H,Q) = k7_mcart_5(I,J,K,L,M,N,O,P,R)
& k8_mcart_5(A,B,C,D,E,F,G,H,Q) = k8_mcart_5(I,J,K,L,M,N,O,P,R)
& k9_mcart_5(A,B,C,D,E,F,G,H,Q) = k9_mcart_5(I,J,K,L,M,N,O,P,R)
& k10_mcart_5(A,B,C,D,E,F,G,H,Q) = k10_mcart_5(I,J,K,L,M,N,O,P,R) ) ) ) ) ).
fof(t43_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k1_zfmisc_1(A))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(B))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(C))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(D))
=> ! [M] :
( m1_subset_1(M,k1_zfmisc_1(E))
=> ! [N] :
( m1_subset_1(N,k1_zfmisc_1(F))
=> ! [O] :
( m1_subset_1(O,k1_zfmisc_1(G))
=> ! [P] :
( m1_subset_1(P,k1_zfmisc_1(H))
=> ! [Q] :
( m1_subset_1(Q,k2_mcart_5(A,B,C,D,E,F,G,H))
=> ( r2_hidden(Q,k2_mcart_5(I,J,K,L,M,N,O,P))
=> ( r2_hidden(k3_mcart_5(A,B,C,D,E,F,G,H,Q),I)
& r2_hidden(k4_mcart_5(A,B,C,D,E,F,G,H,Q),J)
& r2_hidden(k5_mcart_5(A,B,C,D,E,F,G,H,Q),K)
& r2_hidden(k6_mcart_5(A,B,C,D,E,F,G,H,Q),L)
& r2_hidden(k7_mcart_5(A,B,C,D,E,F,G,H,Q),M)
& r2_hidden(k8_mcart_5(A,B,C,D,E,F,G,H,Q),N)
& r2_hidden(k9_mcart_5(A,B,C,D,E,F,G,H,Q),O)
& r2_hidden(k10_mcart_5(A,B,C,D,E,F,G,H,Q),P) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P] :
( ( r1_tarski(A,I)
& r1_tarski(B,J)
& r1_tarski(C,K)
& r1_tarski(D,L)
& r1_tarski(E,M)
& r1_tarski(F,N)
& r1_tarski(G,O)
& r1_tarski(H,P) )
=> r1_tarski(k2_mcart_5(A,B,C,D,E,F,G,H),k2_mcart_5(I,J,K,L,M,N,O,P)) ) ).
fof(t45_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k1_zfmisc_1(A))
=> ! [J] :
( m1_subset_1(J,k1_zfmisc_1(B))
=> ! [K] :
( m1_subset_1(K,k1_zfmisc_1(C))
=> ! [L] :
( m1_subset_1(L,k1_zfmisc_1(D))
=> ! [M] :
( m1_subset_1(M,k1_zfmisc_1(E))
=> ! [N] :
( m1_subset_1(N,k1_zfmisc_1(F))
=> ! [O] :
( m1_subset_1(O,k1_zfmisc_1(G))
=> ! [P] :
( m1_subset_1(P,k1_zfmisc_1(H))
=> m1_subset_1(k2_mcart_5(I,J,K,L,M,N,O,P),k1_zfmisc_1(k2_mcart_5(A,B,C,D,E,F,G,H))) ) ) ) ) ) ) ) ) ).
fof(dt_k1_mcart_5,axiom,
$true ).
fof(dt_k2_mcart_5,axiom,
$true ).
fof(dt_k3_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k3_mcart_5(A,B,C,D,E,F,G,H,I),A) ) ).
fof(dt_k4_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k4_mcart_5(A,B,C,D,E,F,G,H,I),B) ) ).
fof(dt_k5_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k5_mcart_5(A,B,C,D,E,F,G,H,I),C) ) ).
fof(dt_k6_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k6_mcart_5(A,B,C,D,E,F,G,H,I),D) ) ).
fof(dt_k7_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k7_mcart_5(A,B,C,D,E,F,G,H,I),E) ) ).
fof(dt_k8_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k8_mcart_5(A,B,C,D,E,F,G,H,I),F) ) ).
fof(dt_k9_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k9_mcart_5(A,B,C,D,E,F,G,H,I),G) ) ).
fof(dt_k10_mcart_5,axiom,
! [A,B,C,D,E,F,G,H,I] :
( m1_subset_1(I,k2_mcart_5(A,B,C,D,E,F,G,H))
=> m1_subset_1(k10_mcart_5(A,B,C,D,E,F,G,H,I),H) ) ).
%------------------------------------------------------------------------------