SET007 Axioms: SET007+866.ax
%------------------------------------------------------------------------------
% File : SET007+866 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Propositional Calculus for Boolean Valued Functions. Part VIII
% 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 : bvfunc26 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 95 ( 0 unt; 0 def)
% Number of atoms : 446 ( 105 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 438 ( 87 ~; 0 |; 84 &)
% ( 4 <=>; 263 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 0 prp; 1-4 aty)
% Number of functors : 22 ( 22 usr; 1 con; 0-3 aty)
% Number of variables : 293 ( 293 !; 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(fc1_bvfunc26,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ( v1_relat_1(k1_bvfunc26(A,B))
& v1_funct_1(k1_bvfunc26(A,B))
& v1_valuat_1(k1_bvfunc26(A,B)) ) ) ).
fof(fc2_bvfunc26,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ( v1_relat_1(k2_bvfunc26(A,B))
& v1_funct_1(k2_bvfunc26(A,B))
& v1_valuat_1(k2_bvfunc26(A,B)) ) ) ).
fof(d1_bvfunc26,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( C = k1_bvfunc26(A,B)
<=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
& ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> k1_funct_1(C,D) = k1_binari_5(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(d2_bvfunc26,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( C = k2_bvfunc26(A,B)
<=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
& ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> k1_funct_1(C,D) = k3_binari_5(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(d3_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( D = k3_bvfunc26(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> k1_funct_1(D,E) = k1_binari_5(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ).
fof(d4_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( D = k4_bvfunc26(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> k1_funct_1(D,E) = k3_binari_5(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ).
fof(t1_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,C) = k5_valuat_1(A,k6_valuat_1(A,B,C)) ) ) ) ).
fof(t2_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,C) = k5_valuat_1(A,k8_bvfunc_1(A,B,C)) ) ) ) ).
fof(t3_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,k19_bvfunc_1(A),B) = k5_valuat_1(A,B) ) ) ).
fof(t4_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,k18_bvfunc_1(A),B) = k19_bvfunc_1(A) ) ) ).
fof(t5_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( k3_bvfunc26(A,k18_bvfunc_1(A),k18_bvfunc_1(A)) = k19_bvfunc_1(A)
& k3_bvfunc26(A,k18_bvfunc_1(A),k19_bvfunc_1(A)) = k19_bvfunc_1(A)
& k3_bvfunc26(A,k19_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A) ) ) ).
fof(t6_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k3_bvfunc26(A,B,B) = k5_valuat_1(A,B)
& k5_valuat_1(A,k3_bvfunc26(A,B,B)) = B ) ) ) ).
fof(t7_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k5_valuat_1(A,k3_bvfunc26(A,B,C)) = k6_valuat_1(A,B,C) ) ) ) ).
fof(t8_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k3_bvfunc26(A,B,k5_valuat_1(A,B)) = k19_bvfunc_1(A)
& k5_valuat_1(A,k3_bvfunc26(A,B,k5_valuat_1(A,B))) = k18_bvfunc_1(A) ) ) ) ).
fof(t9_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k6_valuat_1(A,C,D)) = k5_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D)) ) ) ) ) ).
fof(t10_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k6_valuat_1(A,C,D)) = k3_bvfunc26(A,k6_valuat_1(A,B,C),D) ) ) ) ) ).
fof(t11_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k8_bvfunc_1(A,C,D)) = k6_valuat_1(A,k5_valuat_1(A,k6_valuat_1(A,B,C)),k5_valuat_1(A,k6_valuat_1(A,B,D))) ) ) ) ) ).
fof(t12_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k9_bvfunc_1(A,C,D)) = k15_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,D)) ) ) ) ) ).
fof(t13_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k3_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k5_valuat_1(A,B),k6_valuat_1(A,C,D))
& k3_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k14_bvfunc_1(A,B,k6_valuat_1(A,C,D)) ) ) ) ) ) ).
fof(t14_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k3_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),D)
& k3_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,D)) ) ) ) ) ) ).
fof(t15_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k15_bvfunc_1(A,C,D)) = k14_bvfunc_1(A,B,k9_bvfunc_1(A,C,D)) ) ) ) ) ).
fof(t16_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k6_valuat_1(A,B,C)) = k3_bvfunc26(A,B,C) ) ) ) ).
fof(t17_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k8_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,k6_valuat_1(A,B,C))) ) ) ) ).
fof(t18_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k15_bvfunc_1(A,B,C)) = k14_bvfunc_1(A,B,k9_bvfunc_1(A,B,C)) ) ) ) ).
fof(t19_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k3_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),C)
& k3_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k14_bvfunc_1(A,B,C) ) ) ) ) ).
fof(t20_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k4_bvfunc26(A,B,C)) = k19_bvfunc_1(A) ) ) ) ).
fof(t21_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k15_bvfunc_1(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) ).
fof(t22_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,B,C) = k3_bvfunc26(A,k3_bvfunc26(A,B,C),k3_bvfunc26(A,B,C)) ) ) ) ).
fof(t23_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,k3_bvfunc26(A,B,C),k3_bvfunc26(A,B,D)) = k6_valuat_1(A,B,k8_bvfunc_1(A,C,D)) ) ) ) ) ).
fof(t24_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k14_bvfunc_1(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),k5_valuat_1(A,k6_valuat_1(A,B,D))) ) ) ) ) ).
fof(t25_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k14_bvfunc_1(A,B,C)) = k5_valuat_1(A,k6_valuat_1(A,B,C)) ) ) ) ).
fof(t26_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,k19_bvfunc_1(A),B) = k18_bvfunc_1(A) ) ) ).
fof(t27_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,k18_bvfunc_1(A),B) = k5_valuat_1(A,B) ) ) ).
fof(t28_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( k4_bvfunc26(A,k18_bvfunc_1(A),k18_bvfunc_1(A)) = k19_bvfunc_1(A)
& k4_bvfunc26(A,k18_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A)
& k4_bvfunc26(A,k19_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A) ) ) ).
fof(t29_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k4_bvfunc26(A,B,B) = k5_valuat_1(A,B)
& k5_valuat_1(A,k4_bvfunc26(A,B,B)) = B ) ) ) ).
fof(t30_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k5_valuat_1(A,k4_bvfunc26(A,B,C)) = k8_bvfunc_1(A,B,C) ) ) ) ).
fof(t31_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k4_bvfunc26(A,B,k5_valuat_1(A,B)) = k18_bvfunc_1(A)
& k5_valuat_1(A,k4_bvfunc26(A,B,k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ) ).
fof(t32_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,k5_valuat_1(A,B),k9_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) ).
fof(t33_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k6_valuat_1(A,C,D)) = k8_bvfunc_1(A,k5_valuat_1(A,k8_bvfunc_1(A,B,C)),k5_valuat_1(A,k8_bvfunc_1(A,B,D))) ) ) ) ) ).
fof(t34_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k8_bvfunc_1(A,C,D)) = k5_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) ) ) ) ) ).
fof(t35_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k15_bvfunc_1(A,C,D)) = k6_valuat_1(A,k5_valuat_1(A,B),k9_bvfunc_1(A,C,D)) ) ) ) ) ).
fof(t36_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k14_bvfunc_1(A,C,D)) = k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),C),k5_valuat_1(A,D)) ) ) ) ) ).
fof(t37_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),C),D) ) ) ) ) ).
fof(t38_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k5_valuat_1(A,B),k8_bvfunc_1(A,C,D)) ) ) ) ) ).
fof(t39_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k6_valuat_1(A,B,C)) = k5_valuat_1(A,k6_valuat_1(A,B,k8_bvfunc_1(A,B,C))) ) ) ) ).
fof(t40_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k8_bvfunc_1(A,B,C)) = k5_valuat_1(A,k8_bvfunc_1(A,B,C)) ) ) ) ).
fof(t41_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k15_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) ).
fof(t42_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k14_bvfunc_1(A,B,C)) = k18_bvfunc_1(A) ) ) ) ).
fof(t43_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k18_bvfunc_1(A) ) ) ) ).
fof(t44_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k4_bvfunc26(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) ).
fof(t45_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k15_bvfunc_1(A,k18_bvfunc_1(A),k18_bvfunc_1(A)) = k19_bvfunc_1(A) ) ).
fof(t46_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k15_bvfunc_1(A,k18_bvfunc_1(A),k19_bvfunc_1(A)) = k18_bvfunc_1(A) ) ).
fof(t47_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k15_bvfunc_1(A,k19_bvfunc_1(A),k19_bvfunc_1(A)) = k19_bvfunc_1(A) ) ).
fof(t48_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( k15_bvfunc_1(A,B,B) = k19_bvfunc_1(A)
& k5_valuat_1(A,k15_bvfunc_1(A,B,B)) = k18_bvfunc_1(A) ) ) ) ).
fof(t49_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,k8_bvfunc_1(A,B,C)) = k8_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) ).
fof(t50_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),k6_valuat_1(A,B,k5_valuat_1(A,D))) ) ) ) ) ).
fof(t51_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k8_bvfunc_1(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) ).
fof(t52_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,k6_valuat_1(A,C,D))),k6_valuat_1(A,k6_valuat_1(A,B,C),D)) ) ) ) ) ).
fof(t53_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,k3_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k6_valuat_1(A,B,k5_valuat_1(A,k6_valuat_1(A,C,D))),k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),C),D)) ) ) ) ) ).
fof(t54_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,k3_bvfunc26(A,C,D)) = k5_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D)) ) ) ) ) ).
fof(t55_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k3_bvfunc26(A,C,D)) = k5_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D))) ) ) ) ) ).
fof(t56_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,B,k3_bvfunc26(A,B,C)) = k6_valuat_1(A,B,k5_valuat_1(A,C)) ) ) ) ).
fof(t57_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k8_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k19_bvfunc_1(A) ) ) ) ).
fof(t58_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),C) ) ) ) ).
fof(t59_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k6_valuat_1(A,B,k5_valuat_1(A,C)) ) ) ) ).
fof(t60_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,k3_bvfunc26(A,B,C)) = k5_valuat_1(A,k6_valuat_1(A,B,C)) ) ) ) ).
fof(t61_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k4_bvfunc26(A,B,k3_bvfunc26(A,B,C)) = k18_bvfunc_1(A) ) ) ) ).
fof(t62_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) ).
fof(t63_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k8_bvfunc_1(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k8_bvfunc_1(A,B,k5_valuat_1(A,D))) ) ) ) ) ).
fof(t64_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,k8_bvfunc_1(A,C,D))),k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),D)) ) ) ) ) ).
fof(t65_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,k4_bvfunc26(A,C,D)) = k6_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,k8_bvfunc_1(A,C,D)))) ) ) ) ) ).
fof(t66_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,k4_bvfunc26(A,C,D)) = k5_valuat_1(A,k6_valuat_1(A,B,k8_bvfunc_1(A,C,D))) ) ) ) ) ).
fof(t67_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k4_bvfunc26(A,C,D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),C),D) ) ) ) ) ).
fof(t68_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,B,k4_bvfunc26(A,B,C)) = k18_bvfunc_1(A) ) ) ) ).
fof(t69_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k8_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k8_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) ).
fof(t70_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k8_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) ).
fof(t71_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),C) ) ) ) ).
fof(t72_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,k4_bvfunc26(A,B,C)) = k5_valuat_1(A,k8_bvfunc_1(A,B,k6_valuat_1(A,B,C))) ) ) ) ).
fof(t73_bvfunc26,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k3_bvfunc26(A,B,k4_bvfunc26(A,B,C)) = k19_bvfunc_1(A) ) ) ) ).
fof(dt_k1_bvfunc26,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ( v1_relat_1(k1_bvfunc26(A,B))
& v1_funct_1(k1_bvfunc26(A,B)) ) ) ).
fof(commutativity_k1_bvfunc26,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> k1_bvfunc26(A,B) = k1_bvfunc26(B,A) ) ).
fof(dt_k2_bvfunc26,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ( v1_relat_1(k2_bvfunc26(A,B))
& v1_funct_1(k2_bvfunc26(A,B)) ) ) ).
fof(commutativity_k2_bvfunc26,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> k2_bvfunc26(A,B) = k2_bvfunc26(B,A) ) ).
fof(dt_k3_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> m2_fraenkel(k3_bvfunc26(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ).
fof(commutativity_k3_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> k3_bvfunc26(A,B,C) = k3_bvfunc26(A,C,B) ) ).
fof(redefinition_k3_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> k3_bvfunc26(A,B,C) = k1_bvfunc26(B,C) ) ).
fof(dt_k4_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> m2_fraenkel(k4_bvfunc26(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ).
fof(commutativity_k4_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> k4_bvfunc26(A,B,C) = k4_bvfunc26(A,C,B) ) ).
fof(redefinition_k4_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> k4_bvfunc26(A,B,C) = k2_bvfunc26(B,C) ) ).
fof(dt_k5_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k3_bvfunc_1(A))
& m1_subset_1(C,k3_bvfunc_1(A)) )
=> m1_subset_1(k5_bvfunc26(A,B,C),k3_bvfunc_1(A)) ) ).
fof(commutativity_k5_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k3_bvfunc_1(A))
& m1_subset_1(C,k3_bvfunc_1(A)) )
=> k5_bvfunc26(A,B,C) = k5_bvfunc26(A,C,B) ) ).
fof(redefinition_k5_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k3_bvfunc_1(A))
& m1_subset_1(C,k3_bvfunc_1(A)) )
=> k5_bvfunc26(A,B,C) = k1_bvfunc26(B,C) ) ).
fof(dt_k6_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k3_bvfunc_1(A))
& m1_subset_1(C,k3_bvfunc_1(A)) )
=> m1_subset_1(k6_bvfunc26(A,B,C),k3_bvfunc_1(A)) ) ).
fof(commutativity_k6_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k3_bvfunc_1(A))
& m1_subset_1(C,k3_bvfunc_1(A)) )
=> k6_bvfunc26(A,B,C) = k6_bvfunc26(A,C,B) ) ).
fof(redefinition_k6_bvfunc26,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k3_bvfunc_1(A))
& m1_subset_1(C,k3_bvfunc_1(A)) )
=> k6_bvfunc26(A,B,C) = k2_bvfunc26(B,C) ) ).
%------------------------------------------------------------------------------