SET007 Axioms: SET007+593.ax
%------------------------------------------------------------------------------
% File : SET007+593 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Propositional 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_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 41 ( 1 unt; 0 def)
% Number of atoms : 209 ( 69 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 208 ( 40 ~; 0 |; 11 &)
% ( 2 <=>; 155 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 139 ( 139 !; 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_5,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))
=> ( ( B = k19_bvfunc_1(A)
& C = k19_bvfunc_1(A) )
<=> k6_valuat_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t2_bvfunc_5,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))
=> ( ( B = k19_bvfunc_1(A)
& k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) )
=> C = k19_bvfunc_1(A) ) ) ) ) ).
fof(t3_bvfunc_5,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))
=> ( B = k19_bvfunc_1(A)
=> k8_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t4_bvfunc_5,axiom,
$true ).
fof(t5_bvfunc_5,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))
=> ( C = k19_bvfunc_1(A)
=> k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t6_bvfunc_5,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,B) = k19_bvfunc_1(A)
=> k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t7_bvfunc_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k5_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ).
fof(t8_bvfunc_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,B) = k19_bvfunc_1(A) ) ) ).
fof(t9_bvfunc_5,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,C) = k19_bvfunc_1(A)
<=> k14_bvfunc_1(A,k5_valuat_1(A,C),k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t10_bvfunc_5,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,C) = k19_bvfunc_1(A)
& k14_bvfunc_1(A,C,D) = k19_bvfunc_1(A) )
=> k14_bvfunc_1(A,B,D) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t11_bvfunc_5,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,C) = k19_bvfunc_1(A)
& k14_bvfunc_1(A,B,k5_valuat_1(A,C)) = k19_bvfunc_1(A) )
=> k5_valuat_1(A,B) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t12_bvfunc_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,k14_bvfunc_1(A,k5_valuat_1(A,B),B),B) = k19_bvfunc_1(A) ) ) ).
fof(t13_bvfunc_5,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,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k5_valuat_1(A,k6_valuat_1(A,C,D)),k5_valuat_1(A,k6_valuat_1(A,B,D)))) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t14_bvfunc_5,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,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t15_bvfunc_5,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,C) = k19_bvfunc_1(A)
=> k14_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,B,D)) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t16_bvfunc_5,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,C,k14_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ).
fof(t17_bvfunc_5,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,k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),D),k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t18_bvfunc_5,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,C,k14_bvfunc_1(A,k14_bvfunc_1(A,C,B),B)) = k19_bvfunc_1(A) ) ) ) ).
fof(t19_bvfunc_5,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,k14_bvfunc_1(A,D,k14_bvfunc_1(A,C,B)),k14_bvfunc_1(A,C,k14_bvfunc_1(A,D,B))) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t20_bvfunc_5,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,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t21_bvfunc_5,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,k14_bvfunc_1(A,C,k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t22_bvfunc_5,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,k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t23_bvfunc_5,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))
=> ( B = k19_bvfunc_1(A)
=> k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),C) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t24_bvfunc_5,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,D,k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A)
=> k14_bvfunc_1(A,C,k14_bvfunc_1(A,D,B)) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t25_bvfunc_5,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,D,k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A)
& C = k19_bvfunc_1(A) )
=> k14_bvfunc_1(A,D,B) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t26_bvfunc_5,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,D,k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A)
& C = k19_bvfunc_1(A)
& D = k19_bvfunc_1(A) )
=> B = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t27_bvfunc_5,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,k14_bvfunc_1(A,B,C)) = k19_bvfunc_1(A)
=> k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ).
fof(t28_bvfunc_5,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,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
=> k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t29_bvfunc_5,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,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
& k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) )
=> k14_bvfunc_1(A,B,D) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t30_bvfunc_5,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,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
& k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
& B = k19_bvfunc_1(A) )
=> D = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t31_bvfunc_5,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))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( ( k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)) = k19_bvfunc_1(A)
& k14_bvfunc_1(A,B,k14_bvfunc_1(A,D,E)) = k19_bvfunc_1(A) )
=> k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,E)) = k19_bvfunc_1(A) ) ) ) ) ) ) ).
fof(t32_bvfunc_5,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,k14_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A) ) ) ) ).
fof(t33_bvfunc_5,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,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k5_valuat_1(A,C),k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ) ).
fof(t34_bvfunc_5,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,k14_bvfunc_1(A,B,k5_valuat_1(A,C)),k14_bvfunc_1(A,C,k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ) ).
fof(t35_bvfunc_5,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,k14_bvfunc_1(A,k5_valuat_1(A,B),C),k14_bvfunc_1(A,k5_valuat_1(A,C),B)) = k19_bvfunc_1(A) ) ) ) ).
fof(t36_bvfunc_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,k14_bvfunc_1(A,B,k5_valuat_1(A,B)),k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) ).
fof(t37_bvfunc_5,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,k5_valuat_1(A,B),k14_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ).
fof(t38_bvfunc_5,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))
=> k5_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) ).
fof(t39_bvfunc_5,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))
=> k5_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) = k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k5_valuat_1(A,D)) ) ) ) ) ).
fof(t40_bvfunc_5,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))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k8_bvfunc_1(A,B,k6_valuat_1(A,k6_valuat_1(A,C,D),E)) = k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,B,D)),k8_bvfunc_1(A,B,E)) ) ) ) ) ) ).
fof(t41_bvfunc_5,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))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,B,k8_bvfunc_1(A,k8_bvfunc_1(A,C,D),E)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,D)),k6_valuat_1(A,B,E)) ) ) ) ) ) ).
%------------------------------------------------------------------------------