SET007 Axioms: SET007+621.ax
%------------------------------------------------------------------------------
% File : SET007+621 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Predicate 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 : bvfunc13 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 5 unt; 0 def)
% Number of atoms : 386 ( 7 equ)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 381 ( 57 ~; 0 |; 0 &)
% ( 0 <=>; 324 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 11 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 285 ( 285 !; 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_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t2_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ).
fof(t3_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ).
fof(t4_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t5_bvfunc13,axiom,
$true ).
fof(t6_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t7_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t8_bvfunc13,axiom,
$true ).
fof(t9_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t10_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t11_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ).
fof(t12_bvfunc13,axiom,
$true ).
fof(t13_bvfunc13,axiom,
$true ).
fof(t14_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t15_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t16_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k5_valuat_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ).
fof(t17_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t18_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t19_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ).
fof(t20_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t21_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t22_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ).
fof(t23_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)) = k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) ).
fof(t24_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) ).
fof(t25_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ).
fof(t26_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) ).
fof(t27_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) ).
fof(t28_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)),k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ).
fof(t29_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,D),C,E)) = k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D) ) ) ) ) ) ) ).
fof(t30_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t31_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ).
fof(t32_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ).
fof(t33_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E) = k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D)) ) ) ) ) ) ) ).
fof(t34_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,D)),C,E) = k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) ).
fof(t35_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t36_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t37_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ).
fof(t38_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t39_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t40_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ).
fof(t41_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E) = k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) ).
fof(t42_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) ).
fof(t43_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ).
fof(t44_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) ).
fof(t45_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) ).
fof(t46_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E),k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ).
fof(t47_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,D)),C,E) = k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D) ) ) ) ) ) ) ).
fof(t48_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t49_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t50_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ).
fof(t51_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k5_valuat_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) ).
fof(t52_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t53_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t54_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t55_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ).
fof(t56_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t57_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k6_bvfunc_2(A,k5_valuat_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) ).
fof(t58_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ).
fof(t59_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> k6_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E) = k6_bvfunc_2(A,k5_valuat_1(A,k7_bvfunc_2(A,B,C,E)),C,D) ) ) ) ) ) ) ).
fof(t60_bvfunc13,axiom,
$true ).
fof(t61_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> r1_bvfunc_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ).
fof(t62_bvfunc13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
=> ! [D] :
( m1_eqrel_1(D,A)
=> ! [E] :
( m1_eqrel_1(E,A)
=> ( v2_bvfunc_2(C,A)
=> r1_bvfunc_1(A,k7_bvfunc_2(A,k6_bvfunc_2(A,k5_valuat_1(A,B),C,D),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k5_valuat_1(A,B),C,E),C,D)) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------