SET007 Axioms: SET007+509.ax
%------------------------------------------------------------------------------
% File : SET007+509 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Algebraic and Arithmetic Lattices. 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 : waybel13 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 38 ( 0 unt; 0 def)
% Number of atoms : 502 ( 13 equ)
% Maximal formula atoms : 26 ( 13 avg)
% Number of connectives : 518 ( 54 ~; 0 |; 344 &)
% ( 9 <=>; 111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 52 ( 51 usr; 0 prp; 1-3 aty)
% Number of functors : 20 ( 20 usr; 0 con; 1-4 aty)
% Number of variables : 108 ( 99 !; 9 ?)
% 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(rc1_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& v14_waybel_0(B,A) ) ) ).
fof(cc1_waybel13,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v23_waybel_0(C,A,B) )
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& v18_waybel_0(C,A,B)
& v19_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v21_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ) ) ).
fof(t1_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> r1_tarski(k2_waybel_8(A,B),k2_waybel_8(A,C)) ) ) ) ) ).
fof(t2_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> m1_subset_1(k2_waybel_8(A,B),k1_zfmisc_1(u1_struct_0(k1_waybel_8(A)))) ) ) ).
fof(t3_waybel13,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_0(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t4_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(u1_struct_0(A))
& v1_waybel_0(u1_struct_0(A),A)
& v12_waybel_0(u1_struct_0(A),A)
& m1_subset_1(u1_struct_0(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(t5_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& v24_waybel_0(A) )
=> u1_struct_0(k1_waybel_8(A)) = u1_struct_0(k1_waybel_8(B)) ) ) ) ).
fof(t6_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> v2_waybel_8(B) ) ) ).
fof(t8_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(A)))
& v4_yellow_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A)))
& v7_yellow_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A)))
& v4_waybel_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A)))
& m1_yellow_0(k2_yellow_1(k8_waybel_0(A)),k3_yellow_1(u1_struct_0(A))) ) ) ).
fof(t9_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k2_yellow_1(k8_waybel_0(A)))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) )
=> k1_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) = k3_tarski(B) ) ) ).
fof(t10_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> v2_waybel_8(k2_yellow_1(k8_waybel_0(A))) ) ).
fof(t11_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
=> ( v1_waybel_3(B,k2_yellow_1(k8_waybel_0(A)))
<=> ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& v14_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ).
fof(t12_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
=> ( v1_waybel_3(B,k2_yellow_1(k8_waybel_0(A)))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& B = k6_waybel_0(A,C) ) ) ) ) ).
fof(t13_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_waybel_8(k2_yellow_1(k8_waybel_0(A)))))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_waybel_8(k2_yellow_1(k8_waybel_0(A))))) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_waybel_0(A,k1_waybel_8(k2_yellow_1(k8_waybel_0(A))),B,C) = k6_waybel_0(A,C) )
=> v23_waybel_0(B,A,k1_waybel_8(k2_yellow_1(k8_waybel_0(A)))) ) ) ) ).
fof(t14_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> v3_waybel_8(k2_yellow_1(k8_waybel_0(A))) ) ).
fof(t15_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( v2_orders_2(k1_waybel_8(A))
& v3_orders_2(k1_waybel_8(A))
& v4_orders_2(k1_waybel_8(A))
& v1_lattice3(k1_waybel_8(A))
& v1_yellow_0(k1_waybel_8(A))
& l1_orders_2(k1_waybel_8(A)) ) ) ).
fof(t16_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A)))))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))))) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_waybel_0(A,k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),B,C) = k2_waybel_8(A,C) )
=> v23_waybel_0(B,A,k2_yellow_1(k8_waybel_0(k1_waybel_8(A)))) ) ) ) ).
fof(t17_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ( ~ v1_xboole_0(k2_waybel_8(A,B))
& v1_waybel_0(k2_waybel_8(A,B),k1_waybel_8(A))
& v12_waybel_0(k2_waybel_8(A,B),k1_waybel_8(A))
& v14_waybel_0(k2_waybel_8(A,B),k1_waybel_8(A))
& m1_subset_1(k2_waybel_8(A,B),k1_zfmisc_1(u1_struct_0(k1_waybel_8(A)))) )
<=> v1_waybel_3(B,A) ) ) ) ).
fof(t18_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(E,A,B)
=> ( r1_lattice3(A,C,D)
<=> r1_lattice3(B,k4_pre_topc(A,B,E,C),k1_waybel_0(A,B,E,D)) ) ) ) ) ) ) ) ).
fof(t19_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(E,A,B)
=> ( r2_lattice3(A,C,D)
<=> r2_lattice3(B,k4_pre_topc(A,B,E,C),k1_waybel_0(A,B,E,D)) ) ) ) ) ) ) ) ).
fof(t20_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(C,A,B)
=> ( v17_waybel_0(C,A,B)
& v18_waybel_0(C,A,B) ) ) ) ) ) ).
fof(t21_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ~ ( v17_waybel_0(D,A,B)
& v4_yellow_0(B,C)
& v7_yellow_0(B,C)
& m1_yellow_0(B,C)
& v3_lattice3(C)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ~ ( D = E
& v17_waybel_0(E,A,C) ) ) ) ) ) ) ) ).
fof(t22_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ~ ( v5_orders_3(D,A,B)
& v22_waybel_0(D,A,B)
& v4_yellow_0(B,C)
& v4_waybel_0(B,C)
& m1_yellow_0(B,C)
& v3_lattice3(C)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ~ ( D = E
& v22_waybel_0(E,A,C) ) ) ) ) ) ) ) ).
fof(t23_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))))
& v4_yellow_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
& v7_yellow_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
& v4_waybel_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
& m1_yellow_0(k2_yellow_1(k8_waybel_0(k1_waybel_8(A))),k3_yellow_1(u1_struct_0(k1_waybel_8(A)))) ) ) ).
fof(t24_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_waybel_8(A)
& l1_orders_2(A) )
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_yellow_1(u1_struct_0(k1_waybel_8(A)))))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_yellow_1(u1_struct_0(k1_waybel_8(A)))))
& v17_waybel_0(B,A,k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
& v22_waybel_0(B,A,k3_yellow_1(u1_struct_0(k1_waybel_8(A))))
& v2_funct_1(B)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_waybel_0(A,k3_yellow_1(u1_struct_0(k1_waybel_8(A))),B,C) = k2_waybel_8(A,C) ) ) ) ).
fof(t25_waybel13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& v5_waybel_3(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v2_orders_2(k6_waybel_3(A,B,C))
& v3_orders_2(k6_waybel_3(A,B,C))
& v4_orders_2(k6_waybel_3(A,B,C))
& v1_lattice3(k6_waybel_3(A,B,C))
& v2_lattice3(k6_waybel_3(A,B,C))
& v1_yellow_0(k6_waybel_3(A,B,C))
& v2_waybel_8(k6_waybel_3(A,B,C))
& l1_orders_2(k6_waybel_3(A,B,C)) ) )
=> ( v2_orders_2(k5_yellow_1(A,B))
& v3_orders_2(k5_yellow_1(A,B))
& v4_orders_2(k5_yellow_1(A,B))
& v1_lattice3(k5_yellow_1(A,B))
& v2_lattice3(k5_yellow_1(A,B))
& v1_yellow_0(k5_yellow_1(A,B))
& v2_waybel_8(k5_yellow_1(A,B))
& l1_orders_2(k5_yellow_1(A,B)) ) ) ) ) ).
fof(t26_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> r5_waybel_1(A,B) ) ) ) ).
fof(t27_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_waybel_3(A,D,E)
<=> r1_waybel_3(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ) ).
fof(t28_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( v1_waybel_3(D,A)
<=> v1_waybel_3(k1_waybel_0(A,B,C,D),B) ) ) ) ) ) ) ).
fof(t29_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k4_pre_topc(A,B,C,k2_waybel_8(A,D)) = k2_waybel_8(B,k1_waybel_0(A,B,C,D)) ) ) ) ) ) ).
fof(t30_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v24_waybel_0(A) )
=> v24_waybel_0(B) ) ) ) ).
fof(t31_waybel13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v3_lattice3(A)
& v1_waybel_8(A) )
=> v1_waybel_8(B) ) ) ) ).
fof(t32_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v1_yellow_0(A)
& v2_waybel_8(A) )
=> v2_waybel_8(B) ) ) ) ).
fof(t33_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ( v17_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v18_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ).
fof(t34_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ ( v2_waybel_8(A)
& ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v4_yellow_0(C,k3_yellow_1(B))
& m1_yellow_0(C,k3_yellow_1(B)) )
=> ~ ( v7_yellow_0(C,k3_yellow_1(B))
& v4_waybel_0(C,k3_yellow_1(B))
& r5_waybel_1(A,C) ) ) ) )
& ( ? [B,C] :
( v4_yellow_0(C,k3_yellow_1(B))
& m1_yellow_0(C,k3_yellow_1(B))
& v7_yellow_0(C,k3_yellow_1(B))
& v4_waybel_0(C,k3_yellow_1(B))
& r5_waybel_1(A,C) )
=> v2_waybel_8(A) ) ) ) ).
fof(t35_waybel13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ ( v2_waybel_8(A)
& ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
& v7_waybel_1(C,k3_yellow_1(B))
& m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B))) )
=> ~ ( v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B))
& r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) ) ) ) )
& ( ? [B,C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
& v7_waybel_1(C,k3_yellow_1(B))
& m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B)))
& v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B))
& r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) )
=> v2_waybel_8(A) ) ) ) ).
fof(t7_waybel13,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,k3_yellow_1(A))
& v7_yellow_0(C,k3_yellow_1(A))
& v4_waybel_0(C,k3_yellow_1(A))
& m1_yellow_0(C,k3_yellow_1(A)) )
=> ( r2_hidden(B,u1_struct_0(k1_waybel_8(C)))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k3_yellow_1(A)))
& v1_finset_1(D)
& B = k1_setfam_1(a_3_0_waybel13(A,C,D))
& r1_tarski(D,B) ) ) ) ).
fof(fraenkel_a_3_0_waybel13,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,k3_yellow_1(B))
& v7_yellow_0(C,k3_yellow_1(B))
& v4_waybel_0(C,k3_yellow_1(B))
& m1_yellow_0(C,k3_yellow_1(B))
& m1_subset_1(D,u1_struct_0(k3_yellow_1(B))) )
=> ( r2_hidden(A,a_3_0_waybel13(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = E
& r1_tarski(D,E) ) ) ) ).
%------------------------------------------------------------------------------