SET007 Axioms: SET007+578.ax
%------------------------------------------------------------------------------
% File : SET007+578 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : 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 : bvfunc_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 41 ( 0 unt; 0 def)
% Number of atoms : 258 ( 5 equ)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 258 ( 41 ~; 0 |; 0 &)
% ( 0 <=>; 217 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 12 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-4 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-4 aty)
% Number of variables : 215 ( 215 !; 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_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t2_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k6_valuat_1(A,C,D)) ) ) ) ) ) ).
fof(t3_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,C,D),k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t4_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> k5_valuat_1(A,k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E))) = k8_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,C),B,E),k7_bvfunc_2(A,k5_valuat_1(A,D),B,E)) ) ) ) ) ) ).
fof(t5_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> k5_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) = k8_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,C),B,E),k6_bvfunc_2(A,k5_valuat_1(A,D),B,E)) ) ) ) ) ) ).
fof(t6_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k8_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k8_bvfunc_1(A,C,D)) ) ) ) ) ) ).
fof(t7_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k8_bvfunc_1(A,C,D),k8_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t8_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k9_bvfunc_1(A,C,D),k8_bvfunc_1(A,k5_valuat_1(A,k9_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,C),B,E),k7_bvfunc_2(A,D,B,E))),k5_valuat_1(A,k9_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,k5_valuat_1(A,D),B,E))))) ) ) ) ) ) ).
fof(t9_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E),k8_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t10_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E),k8_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t11_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E),k8_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t12_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)) ) ) ) ) ) ).
fof(t13_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)) ) ) ) ) ) ).
fof(t14_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t15_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t16_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ).
fof(t17_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,C,k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t18_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ).
fof(t19_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t20_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k14_bvfunc_1(A,k7_bvfunc_2(A,D,B,E),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E))) ) ) ) ) ) ).
fof(t21_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( r3_bvfunc_2(A,C,B,E)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,C,k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ) ).
fof(t22_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( r3_bvfunc_2(A,C,B,E)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k14_bvfunc_1(A,D,C),B,E),k14_bvfunc_1(A,k6_bvfunc_2(A,D,B,E),C)) ) ) ) ) ) ) ).
fof(t23_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)) = k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E) ) ) ) ) ) ).
fof(t24_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t25_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) ).
fof(t26_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E) = k6_bvfunc_2(A,k8_bvfunc_1(A,k5_valuat_1(A,C),D),B,E) ) ) ) ) ) ).
fof(t27_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E) = k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,k5_valuat_1(A,D)),B,E)) ) ) ) ) ) ).
fof(t28_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k5_valuat_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k6_bvfunc_2(A,k14_bvfunc_1(A,C,k5_valuat_1(A,D)),B,E)))) ) ) ) ) ) ).
fof(t29_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k5_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)),k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,k5_valuat_1(A,D)),B,E))))) ) ) ) ) ) ).
fof(t30_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E)),k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E)) ) ) ) ) ) ).
fof(t31_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E))),k5_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E))) ) ) ) ) ) ).
fof(t32_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,D,E),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,E),B,F)) ) ) ) ) ) ) ).
fof(t33_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k7_bvfunc_2(A,k6_valuat_1(A,E,C),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,D),B,F)) ) ) ) ) ) ) ).
fof(t34_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,k5_valuat_1(A,D)),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,E,D),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) ).
fof(t35_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,D)),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) ).
fof(t36_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,k5_valuat_1(A,D)),B,F),k7_bvfunc_2(A,k6_valuat_1(A,E,D),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) ).
fof(t37_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,D)),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) ).
fof(t38_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,E),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,D),B,F)) ) ) ) ) ) ) ).
fof(t39_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,D,k5_valuat_1(A,E)),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,E,k5_valuat_1(A,C)),B,F)) ) ) ) ) ) ) ).
fof(t40_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,D,E),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,C),B,F)) ) ) ) ) ) ) ).
fof(t41_bvfunc_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [F] :
( m1_eqrel_1(F,A)
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k7_bvfunc_2(A,C,B,F),k6_bvfunc_2(A,k14_bvfunc_1(A,D,k5_valuat_1(A,C)),B,F)),k6_bvfunc_2(A,k14_bvfunc_1(A,C,E),B,F)),k7_bvfunc_2(A,k6_valuat_1(A,E,k5_valuat_1(A,D)),B,F)) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------