%------------------------------------------------------------------------------
% File : SET007+635 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Predicate Calculus for Boolean Valued Functions. Part XII
% 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 : bvfunc24 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 50 ( 10 unt; 0 def)
% Number of atoms : 1409 (1064 equ)
% Maximal formula atoms : 53 ( 28 avg)
% Number of connectives : 1575 ( 216 ~; 780 |; 221 &)
% ( 2 <=>; 356 =>; 0 <=; 0 <~>)
% Maximal formula depth : 67 ( 39 avg)
% Maximal term depth : 10 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 1 con; 0-9 aty)
% Number of variables : 550 ( 550 !; 0 ?)
% 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_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ( B = k5_enumset1(C,D,E,F,G,H,I)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ( B = k5_enumset1(C,D,E,F,G,H,I)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,E),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ( B = k5_enumset1(C,D,E,F,G,H,I)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ( B = k5_enumset1(C,D,E,F,G,H,I)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| k5_bvfunc_2(A,F,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),G),H),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ( B = k5_enumset1(C,D,E,F,G,H,I)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| k5_bvfunc_2(A,G,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),H),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ( B = k5_enumset1(C,D,E,F,G,H,I)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| k5_bvfunc_2(A,H,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ( B = k5_enumset1(C,D,E,F,G,H,I)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| k5_bvfunc_2(A,I,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ! [I,J,K,L,M,N,O] :
( H = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,J),k3_cqc_lang(C,K)),k3_cqc_lang(D,L)),k3_cqc_lang(E,M)),k3_cqc_lang(F,N)),k3_cqc_lang(G,O)),k3_cqc_lang(A,I))
=> ( A = B
| A = C
| A = D
| A = E
| A = F
| A = G
| B = C
| B = D
| B = E
| B = F
| B = G
| C = D
| C = E
| C = F
| C = G
| D = E
| D = F
| D = G
| E = F
| E = G
| F = G
| ( k1_funct_1(H,A) = I
& k1_funct_1(H,B) = J
& k1_funct_1(H,C) = K
& k1_funct_1(H,D) = L
& k1_funct_1(H,E) = M
& k1_funct_1(H,F) = N
& k1_funct_1(H,G) = O ) ) ) ) ).
fof(t9_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ! [I,J,K,L,M,N,O] :
( H = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,J),k3_cqc_lang(C,K)),k3_cqc_lang(D,L)),k3_cqc_lang(E,M)),k3_cqc_lang(F,N)),k3_cqc_lang(G,O)),k3_cqc_lang(A,I))
=> k1_relat_1(H) = k5_enumset1(A,B,C,D,E,F,G) ) ) ).
fof(t10_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ! [I,J,K,L,M,N,O] :
( H = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,J),k3_cqc_lang(C,K)),k3_cqc_lang(D,L)),k3_cqc_lang(E,M)),k3_cqc_lang(F,N)),k3_cqc_lang(G,O)),k3_cqc_lang(A,I))
=> k2_relat_1(H) = k5_enumset1(k1_funct_1(H,A),k1_funct_1(H,B),k1_funct_1(H,C),k1_funct_1(H,D),k1_funct_1(H,E),k1_funct_1(H,F),k1_funct_1(H,G)) ) ) ).
fof(t11_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_subset_1(J,A)
=> ! [K] :
( m1_subset_1(K,A)
=> ~ ( v2_bvfunc_2(B,A)
& B = k5_enumset1(C,D,E,F,G,H,I)
& C != D
& C != E
& C != F
& C != G
& C != H
& C != I
& D != E
& D != F
& D != G
& D != H
& D != I
& E != F
& E != G
& E != H
& E != I
& F != G
& F != H
& F != I
& G != H
& G != I
& H != I
& r1_xboole_0(k22_bvfunc_1(A,K,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I)),k22_bvfunc_1(A,J,C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_subset_1(J,A)
=> ! [K] :
( m1_subset_1(K,A)
=> ~ ( v2_bvfunc_2(B,A)
& B = k5_enumset1(C,D,E,F,G,H,I)
& C != D
& C != E
& C != F
& C != G
& C != H
& C != I
& D != E
& D != F
& D != G
& D != H
& D != I
& E != F
& E != G
& E != H
& E != I
& F != G
& F != H
& F != I
& G != H
& G != I
& H != I
& k22_bvfunc_1(A,J,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I)) = k22_bvfunc_1(A,K,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I))
& r1_xboole_0(k22_bvfunc_1(A,K,k5_bvfunc_2(A,C,B)),k22_bvfunc_1(A,J,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,E),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,F,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,G,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,H,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,I,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ( B = k6_enumset1(C,D,E,F,G,H,I,J)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| E = F
| E = G
| E = H
| E = I
| E = J
| F = G
| F = H
| F = I
| F = J
| G = H
| G = I
| G = J
| H = I
| H = J
| I = J
| k5_bvfunc_2(A,J,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( v1_relat_1(I)
& v1_funct_1(I) )
=> ! [J,K,L,M,N,O,P,Q] :
( I = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,K),k3_cqc_lang(C,L)),k3_cqc_lang(D,M)),k3_cqc_lang(E,N)),k3_cqc_lang(F,O)),k3_cqc_lang(G,P)),k3_cqc_lang(H,Q)),k3_cqc_lang(A,J))
=> ( A = B
| A = C
| A = D
| A = E
| A = F
| A = G
| A = H
| B = C
| B = D
| B = E
| B = F
| B = G
| B = H
| C = D
| C = E
| C = F
| C = G
| C = H
| D = E
| D = F
| D = G
| D = H
| E = F
| E = G
| E = H
| F = G
| F = H
| G = H
| ( k1_funct_1(I,B) = K
& k1_funct_1(I,C) = L
& k1_funct_1(I,D) = M
& k1_funct_1(I,E) = N
& k1_funct_1(I,F) = O
& k1_funct_1(I,G) = P ) ) ) ) ).
fof(t22_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( v1_relat_1(I)
& v1_funct_1(I) )
=> ! [J,K,L,M,N,O,P,Q] :
( I = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,K),k3_cqc_lang(C,L)),k3_cqc_lang(D,M)),k3_cqc_lang(E,N)),k3_cqc_lang(F,O)),k3_cqc_lang(G,P)),k3_cqc_lang(H,Q)),k3_cqc_lang(A,J))
=> k1_relat_1(I) = k6_enumset1(A,B,C,D,E,F,G,H) ) ) ).
fof(t23_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( v1_relat_1(I)
& v1_funct_1(I) )
=> ! [J,K,L,M,N,O,P,Q] :
( I = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,K),k3_cqc_lang(C,L)),k3_cqc_lang(D,M)),k3_cqc_lang(E,N)),k3_cqc_lang(F,O)),k3_cqc_lang(G,P)),k3_cqc_lang(H,Q)),k3_cqc_lang(A,J))
=> k2_relat_1(I) = k6_enumset1(k1_funct_1(I,A),k1_funct_1(I,B),k1_funct_1(I,C),k1_funct_1(I,D),k1_funct_1(I,E),k1_funct_1(I,F),k1_funct_1(I,G),k1_funct_1(I,H)) ) ) ).
fof(t24_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_subset_1(K,A)
=> ! [L] :
( m1_subset_1(L,A)
=> ~ ( v2_bvfunc_2(B,A)
& B = k6_enumset1(C,D,E,F,G,H,I,J)
& C != D
& C != E
& C != F
& C != G
& C != H
& C != I
& C != J
& D != E
& D != F
& D != G
& D != H
& D != I
& D != J
& E != F
& E != G
& E != H
& E != I
& E != J
& F != G
& F != H
& F != I
& F != J
& G != H
& G != I
& G != J
& H != I
& H != J
& I != J
& k5_subset_1(A,k22_bvfunc_1(A,L,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J)),k22_bvfunc_1(A,K,C)) = k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_subset_1(K,A)
=> ! [L] :
( m1_subset_1(L,A)
=> ~ ( v2_bvfunc_2(B,A)
& B = k6_enumset1(C,D,E,F,G,H,I,J)
& C != D
& C != E
& C != F
& C != G
& C != H
& C != I
& C != J
& D != E
& D != F
& D != G
& D != H
& D != I
& D != J
& E != F
& E != G
& E != H
& E != I
& E != J
& F != G
& F != H
& F != I
& F != J
& G != H
& G != I
& G != J
& H != I
& H != J
& I != J
& k22_bvfunc_1(A,K,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J)) = k22_bvfunc_1(A,L,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J))
& r1_xboole_0(k22_bvfunc_1(A,L,k5_bvfunc_2(A,C,B)),k22_bvfunc_1(A,K,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( J = k1_bvfunc24(A,B,C,D,E,F,G,H,I)
<=> ! [K] :
( r2_hidden(K,J)
<=> ~ ( K != A
& K != B
& K != C
& K != D
& K != E
& K != F
& K != G
& K != H
& K != I ) ) ) ).
fof(t26_bvfunc24,axiom,
$true ).
fof(t27_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k1_tarski(A),k6_enumset1(B,C,D,E,F,G,H,I)) ).
fof(t28_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k2_tarski(A,B),k5_enumset1(C,D,E,F,G,H,I)) ).
fof(t29_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k1_enumset1(A,B,C),k4_enumset1(D,E,F,G,H,I)) ).
fof(t30_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k2_enumset1(A,B,C,D),k3_enumset1(E,F,G,H,I)) ).
fof(t31_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_enumset1(F,G,H,I)) ).
fof(t32_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_enumset1(G,H,I)) ).
fof(t33_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k2_tarski(H,I)) ).
fof(t34_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I] : k1_bvfunc24(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k6_enumset1(A,B,C,D,E,F,G,H),k1_tarski(I)) ).
fof(t35_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,E),F),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),F),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,F,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),G),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,G,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,H,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,I,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),J),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,J,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),I),K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ( B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
=> ( C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| C = J
| C = K
| D = E
| D = F
| D = G
| D = H
| D = I
| D = J
| D = K
| E = F
| E = G
| E = H
| E = I
| E = J
| E = K
| F = G
| F = H
| F = I
| F = J
| F = K
| G = H
| G = I
| G = J
| G = K
| H = I
| H = J
| H = K
| I = J
| I = K
| J = K
| k5_bvfunc_2(A,K,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G),H),I),J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( v1_relat_1(J)
& v1_funct_1(J) )
=> ! [K,L,M,N,O,P,Q,R,S] :
( J = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,L),k3_cqc_lang(C,M)),k3_cqc_lang(D,N)),k3_cqc_lang(E,O)),k3_cqc_lang(F,P)),k3_cqc_lang(G,Q)),k3_cqc_lang(H,R)),k3_cqc_lang(I,S)),k3_cqc_lang(A,K))
=> ( A = B
| A = C
| A = D
| A = E
| A = F
| A = G
| A = H
| A = I
| B = C
| B = D
| B = E
| B = F
| B = G
| B = H
| B = I
| C = D
| C = E
| C = F
| C = G
| C = H
| C = I
| D = E
| D = F
| D = G
| D = H
| D = I
| E = F
| E = G
| E = H
| E = I
| F = G
| F = H
| F = I
| G = H
| G = I
| H = I
| ( k1_funct_1(J,A) = K
& k1_funct_1(J,B) = L
& k1_funct_1(J,C) = M
& k1_funct_1(J,D) = N
& k1_funct_1(J,E) = O
& k1_funct_1(J,F) = P
& k1_funct_1(J,G) = Q
& k1_funct_1(J,H) = R
& k1_funct_1(J,I) = S ) ) ) ) ).
fof(t45_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( v1_relat_1(J)
& v1_funct_1(J) )
=> ! [K,L,M,N,O,P,Q,R,S] :
( J = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,L),k3_cqc_lang(C,M)),k3_cqc_lang(D,N)),k3_cqc_lang(E,O)),k3_cqc_lang(F,P)),k3_cqc_lang(G,Q)),k3_cqc_lang(H,R)),k3_cqc_lang(I,S)),k3_cqc_lang(A,K))
=> k1_relat_1(J) = k1_bvfunc24(A,B,C,D,E,F,G,H,I) ) ) ).
fof(t46_bvfunc24,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( v1_relat_1(J)
& v1_funct_1(J) )
=> ! [K,L,M,N,O,P,Q,R,S] :
( J = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,L),k3_cqc_lang(C,M)),k3_cqc_lang(D,N)),k3_cqc_lang(E,O)),k3_cqc_lang(F,P)),k3_cqc_lang(G,Q)),k3_cqc_lang(H,R)),k3_cqc_lang(I,S)),k3_cqc_lang(A,K))
=> k2_relat_1(J) = k1_bvfunc24(k1_funct_1(J,A),k1_funct_1(J,B),k1_funct_1(J,C),k1_funct_1(J,D),k1_funct_1(J,E),k1_funct_1(J,F),k1_funct_1(J,G),k1_funct_1(J,H),k1_funct_1(J,I)) ) ) ).
fof(t47_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,A)
=> ~ ( v2_bvfunc_2(B,A)
& B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
& C != D
& C != E
& C != F
& C != G
& C != H
& C != I
& C != J
& C != K
& D != E
& D != F
& D != G
& D != H
& D != I
& D != J
& D != K
& E != F
& E != G
& E != H
& E != I
& E != J
& E != K
& F != G
& F != H
& F != I
& F != J
& F != K
& G != H
& G != I
& G != J
& G != K
& H != I
& H != J
& H != K
& I != J
& I != K
& J != K
& k5_subset_1(A,k22_bvfunc_1(A,M,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H),I),J),K)),k22_bvfunc_1(A,L,C)) = k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t48_bvfunc24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ! [F] :
( m1_eqrel_1(F,A)
=> ! [G] :
( m1_eqrel_1(G,A)
=> ! [H] :
( m1_eqrel_1(H,A)
=> ! [I] :
( m1_eqrel_1(I,A)
=> ! [J] :
( m1_eqrel_1(J,A)
=> ! [K] :
( m1_eqrel_1(K,A)
=> ! [L] :
( m1_subset_1(L,A)
=> ! [M] :
( m1_subset_1(M,A)
=> ~ ( v2_bvfunc_2(B,A)
& B = k1_bvfunc24(C,D,E,F,G,H,I,J,K)
& C != D
& C != E
& C != F
& C != G
& C != H
& C != I
& C != J
& C != K
& D != E
& D != F
& D != G
& D != H
& D != I
& D != J
& D != K
& E != F
& E != G
& E != H
& E != I
& E != J
& E != K
& F != G
& F != H
& F != I
& F != J
& F != K
& G != H
& G != I
& G != J
& G != K
& H != I
& H != J
& H != K
& I != J
& I != K
& J != K
& k22_bvfunc_1(A,L,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J),K)) = k22_bvfunc_1(A,M,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J),K))
& r1_xboole_0(k22_bvfunc_1(A,M,k5_bvfunc_2(A,C,B)),k22_bvfunc_1(A,L,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_bvfunc24,axiom,
$true ).
%------------------------------------------------------------------------------