SET007 Axioms: SET007+601.ax
%------------------------------------------------------------------------------
% File : SET007+601 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Propositional Calculus for Boolean Valued Functions. Part V
% 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_9 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 40 ( 0 unt; 0 def)
% Number of atoms : 227 ( 1 equ)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 227 ( 40 ~; 0 |; 7 &)
% ( 0 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-4 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-3 aty)
% Number of variables : 177 ( 177 !; 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_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k8_bvfunc_1(A,B,D)) ) ) ) ) ).
fof(t2_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,B,k14_bvfunc_1(A,B,C)),C) ) ) ) ).
fof(t3_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k5_valuat_1(A,C)),k5_valuat_1(A,B)) ) ) ) ).
fof(t4_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k5_valuat_1(A,B)),C) ) ) ) ).
fof(t5_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k5_valuat_1(A,B),C)),C) ) ) ) ).
fof(t6_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,k5_valuat_1(A,C))),k5_valuat_1(A,B)) ) ) ) ).
fof(t7_bvfunc_9,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))
=> r1_bvfunc_1(A,k14_bvfunc_1(A,B,k6_valuat_1(A,C,D)),k14_bvfunc_1(A,B,C)) ) ) ) ) ).
fof(t8_bvfunc_9,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))
=> r1_bvfunc_1(A,k14_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),k14_bvfunc_1(A,B,D)) ) ) ) ) ).
fof(t9_bvfunc_9,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))
=> r1_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k6_valuat_1(A,B,D),C)) ) ) ) ) ).
fof(t10_bvfunc_9,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))
=> r1_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,D))) ) ) ) ) ).
fof(t11_bvfunc_9,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))
=> r1_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,D))) ) ) ) ) ).
fof(t12_bvfunc_9,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))
=> r1_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,D))) ) ) ) ) ).
fof(t13_bvfunc_9,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))
=> r1_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,B,C),D),k8_bvfunc_1(A,B,D)) ) ) ) ) ).
fof(t14_bvfunc_9,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))
=> r1_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,D,E)),k8_bvfunc_1(A,B,D)) ) ) ) ) ) ).
fof(t15_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k8_bvfunc_1(A,B,D)) ) ) ) ) ).
fof(t16_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k5_valuat_1(A,B),D)),k8_bvfunc_1(A,C,D)) ) ) ) ) ).
fof(t17_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,D,k5_valuat_1(A,C))),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,D))) ) ) ) ) ).
fof(t18_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,k5_valuat_1(A,B),D)),k8_bvfunc_1(A,C,D)) ) ) ) ) ).
fof(t19_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,D,E)),k14_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,E))) ) ) ) ) ) ).
fof(t20_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)),k14_bvfunc_1(A,B,k6_valuat_1(A,C,D))) ) ) ) ) ).
fof(t21_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,D,C)),k14_bvfunc_1(A,k8_bvfunc_1(A,B,D),C)) ) ) ) ) ).
fof(t22_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,D,E)),k14_bvfunc_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,E))) ) ) ) ) ) ).
fof(t23_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)),k14_bvfunc_1(A,B,k8_bvfunc_1(A,C,D))) ) ) ) ) ).
fof(t24_bvfunc_9,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))
=> ! [F] :
( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [G] :
( m2_fraenkel(G,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,C,F),k14_bvfunc_1(A,D,G)),k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)),k5_valuat_1(A,k6_valuat_1(A,E,F))),k5_valuat_1(A,k6_valuat_1(A,E,G))),k14_bvfunc_1(A,E,B)) ) ) ) ) ) ) ) ).
fof(t25_bvfunc_9,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))
=> ! [F] :
( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [G] :
( m2_fraenkel(G,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,E),k14_bvfunc_1(A,C,F)),k14_bvfunc_1(A,D,G)),k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)),k5_valuat_1(A,k6_valuat_1(A,E,F))),k5_valuat_1(A,k6_valuat_1(A,E,G))),k5_valuat_1(A,k6_valuat_1(A,F,G))),k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,E,B),k14_bvfunc_1(A,F,C)),k14_bvfunc_1(A,G,D))) ) ) ) ) ) ) ) ).
fof(t26_bvfunc_9,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,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,C,E)),k5_valuat_1(A,k6_valuat_1(A,D,E))),k5_valuat_1(A,k6_valuat_1(A,B,C))) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t27_bvfunc_9,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))
=> ! [F] :
( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [G] :
( m2_fraenkel(G,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,E),k14_bvfunc_1(A,C,F)),k14_bvfunc_1(A,D,G)),k5_valuat_1(A,k6_valuat_1(A,E,F))),k5_valuat_1(A,k6_valuat_1(A,E,G))),k5_valuat_1(A,k6_valuat_1(A,F,G))),k6_valuat_1(A,k6_valuat_1(A,k5_valuat_1(A,k6_valuat_1(A,B,C)),k5_valuat_1(A,k6_valuat_1(A,B,D))),k5_valuat_1(A,k6_valuat_1(A,C,D)))) ) ) ) ) ) ) ) ).
fof(t28_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,B,C),B) ) ) ) ).
fof(t29_bvfunc_9,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))
=> ( r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),B)
& r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),C) ) ) ) ) ) ).
fof(t30_bvfunc_9,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))
=> ( r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),B)
& r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),C) ) ) ) ) ) ) ).
fof(t31_bvfunc_9,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))
=> ! [F] :
( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),F),B)
& r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),F),C) ) ) ) ) ) ) ) ).
fof(t32_bvfunc_9,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))
=> ! [F] :
( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [G] :
( m2_fraenkel(G,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),F),G),B)
& r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),F),G),C) ) ) ) ) ) ) ) ) ).
fof(t33_bvfunc_9,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))
=> ! [F] :
( m2_fraenkel(F,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [G] :
( m2_fraenkel(G,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [H] :
( m2_fraenkel(H,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),F),G),H),B)
& r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E),F),G),H),C) ) ) ) ) ) ) ) ) ) ).
fof(t34_bvfunc_9,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))
=> ( ( r1_bvfunc_1(A,B,C)
& r1_bvfunc_1(A,D,E) )
=> r1_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,E)) ) ) ) ) ) ) ).
fof(t35_bvfunc_9,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))
=> ( r1_bvfunc_1(A,k6_valuat_1(A,B,C),D)
=> r1_bvfunc_1(A,k6_valuat_1(A,B,k5_valuat_1(A,D)),k5_valuat_1(A,C)) ) ) ) ) ) ).
fof(t36_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,D,C)),k8_bvfunc_1(A,B,D)),C) ) ) ) ) ).
fof(t37_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,k8_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,D,C)),k6_valuat_1(A,B,D)),C) ) ) ) ) ).
fof(t38_bvfunc_9,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))
=> ( ( r1_bvfunc_1(A,B,C)
& r1_bvfunc_1(A,D,E) )
=> r1_bvfunc_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,E)) ) ) ) ) ) ) ).
fof(t39_bvfunc_9,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))
=> r1_bvfunc_1(A,B,k8_bvfunc_1(A,B,C)) ) ) ) ).
fof(t40_bvfunc_9,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))
=> r1_bvfunc_1(A,k6_valuat_1(A,B,C),k8_bvfunc_1(A,B,C)) ) ) ) ).
%------------------------------------------------------------------------------