%------------------------------------------------------------------------------
% File : SET007+633 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : 6 Variable Predicate Calculus for Boolean Valued Functions. Part I
% 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 : bvfunc23 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 11 ( 0 unt; 0 def)
% Number of atoms : 263 ( 176 equ)
% Maximal formula atoms : 31 ( 23 avg)
% Number of connectives : 292 ( 40 ~; 120 |; 50 &)
% ( 0 <=>; 82 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 33 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 0 prp; 1-2 aty)
% Number of functors : 11 ( 11 usr; 0 con; 1-6 aty)
% Number of variables : 109 ( 109 !; 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_bvfunc23,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)
=> ( B = k4_enumset1(C,D,E,F,G,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
| k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_bvfunc23,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)
=> ( ( v2_bvfunc_2(B,A)
& B = k4_enumset1(C,D,E,F,G,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
| k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,E),F),G),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_bvfunc23,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)
=> ( ( v2_bvfunc_2(B,A)
& B = k4_enumset1(C,D,E,F,G,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
| k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),F),G),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_bvfunc23,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)
=> ( ( v2_bvfunc_2(B,A)
& B = k4_enumset1(C,D,E,F,G,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
| k5_bvfunc_2(A,F,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),G),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_bvfunc23,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)
=> ( ( v2_bvfunc_2(B,A)
& B = k4_enumset1(C,D,E,F,G,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
| k5_bvfunc_2(A,G,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),H) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_bvfunc23,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)
=> ( ( v2_bvfunc_2(B,A)
& B = k4_enumset1(C,D,E,F,G,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
| k5_bvfunc_2(A,H,B) = k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,C,D),E),F),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_bvfunc23,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ! [H,I,J,K,L,M] :
( G = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,I),k3_cqc_lang(C,J)),k3_cqc_lang(D,K)),k3_cqc_lang(E,L)),k3_cqc_lang(F,M)),k3_cqc_lang(A,H))
=> ( A = B
| A = C
| A = D
| A = E
| A = F
| B = C
| B = D
| B = E
| B = F
| C = D
| C = E
| C = F
| D = E
| D = F
| E = F
| ( k1_funct_1(G,A) = H
& k1_funct_1(G,B) = I
& k1_funct_1(G,C) = J
& k1_funct_1(G,D) = K
& k1_funct_1(G,E) = L
& k1_funct_1(G,F) = M ) ) ) ) ).
fof(t8_bvfunc23,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ! [H,I,J,K,L,M] :
( G = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,I),k3_cqc_lang(C,J)),k3_cqc_lang(D,K)),k3_cqc_lang(E,L)),k3_cqc_lang(F,M)),k3_cqc_lang(A,H))
=> k1_relat_1(G) = k4_enumset1(A,B,C,D,E,F) ) ) ).
fof(t9_bvfunc23,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ! [H,I,J,K,L,M] :
( G = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k3_cqc_lang(B,I),k3_cqc_lang(C,J)),k3_cqc_lang(D,K)),k3_cqc_lang(E,L)),k3_cqc_lang(F,M)),k3_cqc_lang(A,H))
=> ( A = B
| A = C
| A = D
| A = E
| A = F
| B = C
| B = D
| B = E
| B = F
| C = D
| C = E
| C = F
| D = E
| D = F
| E = F
| k2_relat_1(G) = k4_enumset1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C),k1_funct_1(G,D),k1_funct_1(G,E),k1_funct_1(G,F)) ) ) ) ).
fof(t10_bvfunc23,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_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,A)
=> ! [K] :
( ( v1_relat_1(K)
& v1_funct_1(K) )
=> ~ ( v2_bvfunc_2(B,A)
& B = k4_enumset1(C,D,E,F,G,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
& r1_xboole_0(k22_bvfunc_1(A,J,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,D,E),F),G),H)),k22_bvfunc_1(A,I,C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_bvfunc23,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_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,A)
=> ! [K] :
( ( v1_relat_1(K)
& v1_funct_1(K) )
=> ~ ( v2_bvfunc_2(B,A)
& B = k4_enumset1(C,D,E,F,G,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
& k22_bvfunc_1(A,I,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H)) = k22_bvfunc_1(A,J,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H))
& r1_xboole_0(k22_bvfunc_1(A,J,k5_bvfunc_2(A,C,B)),k22_bvfunc_1(A,I,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------