SET007 Axioms: SET007+617.ax
%------------------------------------------------------------------------------
% File : SET007+617 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Injective Spaces. Part II
% 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 : waybel25 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 77 ( 0 unt; 0 def)
% Number of atoms : 868 ( 24 equ)
% Maximal formula atoms : 27 ( 11 avg)
% Number of connectives : 915 ( 124 ~; 0 |; 598 &)
% ( 5 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 71 ( 70 usr; 0 prp; 1-6 aty)
% Number of functors : 32 ( 32 usr; 3 con; 0-5 aty)
% Number of variables : 176 ( 170 !; 6 ?)
% 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_waybel25,axiom,
( ~ v3_struct_0(k9_waybel18)
& v1_pre_topc(k9_waybel18)
& v2_pre_topc(k9_waybel18)
& v2_t_0topsp(k9_waybel18)
& ~ v1_urysohn1(k9_waybel18)
& v2_waybel18(k9_waybel18) ) ).
fof(cc1_waybel25,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(rc1_waybel25,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_waybel18(A) ) ).
fof(rc2_waybel25,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_waybel_9(A)
& v4_waybel11(A) ) ).
fof(cc2_waybel25,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( v4_waybel11(B)
=> ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& ~ v1_yellow_3(B)
& v2_waybel_3(B)
& v3_waybel_3(B)
& v2_waybel18(B) ) ) ) ) ).
fof(fc2_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_waybel18(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
& v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
& v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))
& v2_waybel18(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ).
fof(fc3_waybel25,axiom,
! [A] :
( ( v3_struct_0(A)
& l1_pre_topc(A) )
=> ( v3_struct_0(k1_waybel25(A))
& v1_yellow_0(k1_waybel25(A))
& v2_yellow_0(k1_waybel25(A))
& v3_yellow_0(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(fc4_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(fc5_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v2_pre_topc(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(fc6_waybel25,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v2_orders_2(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(fc7_waybel25,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v2_orders_2(k1_waybel25(A))
& v3_orders_2(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(fc8_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k1_waybel25(A))
& v2_pre_topc(k1_waybel25(A))
& v2_orders_2(k1_waybel25(A))
& v3_orders_2(k1_waybel25(A))
& v4_orders_2(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(fc9_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> ( ~ v3_struct_0(k1_waybel25(A))
& v2_pre_topc(k1_waybel25(A))
& v2_orders_2(k1_waybel25(A))
& v3_orders_2(k1_waybel25(A))
& v4_orders_2(k1_waybel25(A))
& v1_lattice3(k1_waybel25(A))
& v2_lattice3(k1_waybel25(A))
& v3_lattice3(k1_waybel25(A))
& v1_yellow_0(k1_waybel25(A))
& v2_yellow_0(k1_waybel25(A))
& v3_yellow_0(k1_waybel25(A))
& v24_waybel_0(k1_waybel25(A))
& v25_waybel_0(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(fc10_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_waybel18(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k1_waybel25(A))
& v2_pre_topc(k1_waybel25(A))
& v2_orders_2(k1_waybel25(A))
& v3_orders_2(k1_waybel25(A))
& v4_orders_2(k1_waybel25(A))
& v1_lattice3(k1_waybel25(A))
& v2_lattice3(k1_waybel25(A))
& v3_lattice3(k1_waybel25(A))
& v1_yellow_0(k1_waybel25(A))
& v2_yellow_0(k1_waybel25(A))
& v3_yellow_0(k1_waybel25(A))
& v24_waybel_0(k1_waybel25(A))
& v25_waybel_0(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A))
& v3_waybel_3(k1_waybel25(A)) ) ) ).
fof(cc3_waybel25,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B)) )
=> ( v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v1_partfun1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v5_orders_3(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) ).
fof(fc11_waybel25,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(k1_waybel25(A))) )
=> ( ~ v1_xboole_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)))
& v4_pre_topc(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A))
& v1_waybel_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A))
& v12_waybel_0(k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)),k1_waybel25(A)) ) ) ).
fof(fc12_waybel25,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(k1_waybel25(A))) )
=> ( ~ v1_xboole_0(k6_waybel_0(k1_waybel25(A),B))
& v4_pre_topc(k6_waybel_0(k1_waybel25(A),B),k1_waybel25(A))
& v1_waybel_0(k6_waybel_0(k1_waybel25(A),B),k1_waybel25(A))
& v12_waybel_0(k6_waybel_0(k1_waybel25(A),B),k1_waybel25(A)) ) ) ).
fof(cc4_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A))))
=> ( v3_pre_topc(B,k1_waybel25(A))
=> v13_waybel_0(B,k1_waybel25(A)) ) ) ) ).
fof(fc13_waybel25,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v10_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
& l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D))
& v3_orders_2(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D))
& v6_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B))
& v7_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D))
& v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) ) ) ).
fof(cc5_waybel25,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
=> ( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C) )
=> ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v1_yellow14(C,k3_waybel24(A,k1_waybel25(B))) ) ) ) ) ).
fof(cc6_waybel25,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v1_waybel25(A) ) ) ) ).
fof(rc3_waybel25,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v3_realset2(A)
& v1_waybel25(A) ) ).
fof(cc7_waybel25,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( v4_waybel11(B)
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v4_waybel11(B)
& v1_waybel25(B) ) ) ) ) ).
fof(fc14_waybel25,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A)
& v4_waybel11(B)
& m1_yellow_9(B,A) )
=> ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))
& v1_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))
& v2_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))
& v1_waybel25(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) ) ) ).
fof(fc15_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ( ~ v3_struct_0(k1_waybel25(A))
& v2_pre_topc(k1_waybel25(A))
& v2_orders_2(k1_waybel25(A))
& v3_orders_2(k1_waybel25(A))
& v4_orders_2(k1_waybel25(A))
& v24_waybel_0(k1_waybel25(A))
& v1_waybel_9(k1_waybel25(A)) ) ) ).
fof(cc8_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ! [B] :
( l1_waybel_0(B,k1_waybel25(A))
=> ( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v10_waybel_0(B,k1_waybel25(A)) )
=> ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v10_waybel_0(B,k1_waybel25(A))
& v3_yellow_6(B,k1_waybel25(A)) ) ) ) ) ).
fof(cc9_waybel25,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_waybel25(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B)) )
=> ( v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v1_partfun1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v22_waybel_0(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) ).
fof(cc10_waybel25,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_waybel18(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v1_waybel25(A) ) ) ) ).
fof(t1_waybel25,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k9_waybel18))
=> ( A = np__0
=> v4_pre_topc(k1_struct_0(k9_waybel18,A),k9_waybel18) ) ) ).
fof(t2_waybel25,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k9_waybel18))
=> ~ ( A = np__1
& v4_pre_topc(k1_struct_0(k9_waybel18,A),k9_waybel18) ) ) ).
fof(t3_waybel25,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(np__1)))) )
=> u1_struct_0(B) = u1_struct_0(k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ) ).
fof(t4_waybel25,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v4_waybel11(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( ( v4_waybel11(D)
& m1_yellow_9(D,B) )
=> ! [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)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( r4_nattra_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),E,F)
& v23_waybel_0(E,A,B) )
=> v3_tops_2(F,C,D) ) ) ) ) ) ) ) ).
fof(t5_waybel25,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v4_waybel11(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( ( v4_waybel11(D)
& m1_yellow_9(D,B) )
=> ( r5_waybel_1(A,B)
=> r1_borsuk_3(C,D) ) ) ) ) ) ).
fof(t6_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( ( v2_waybel18(A)
& r1_borsuk_3(A,B) )
=> v2_waybel18(B) ) ) ) ).
fof(t7_waybel25,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v4_waybel11(C)
& m1_yellow_9(C,A) )
=> ! [D] :
( ( v4_waybel11(D)
& m1_yellow_9(D,B) )
=> ( ( r5_waybel_1(A,B)
& v2_waybel18(C) )
=> v2_waybel18(D) ) ) ) ) ) ).
fof(d1_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r1_waybel18(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v5_pre_topc(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& r4_nattra_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_borsuk_1(A,B,A,C,D),k7_grcat_1(A)) ) ) ) ) ) ).
fof(t8_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D))
& r1_waybel18(A,C) )
=> r1_waybel18(B,D) ) ) ) ) ) ).
fof(t9_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_pre_topc(C) )
=> ( ( r1_borsuk_3(B,C)
& r1_waybel18(B,A) )
=> r1_waybel18(C,A) ) ) ) ) ).
fof(t10_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( ( v2_waybel18(B)
& r1_waybel18(A,B) )
=> v2_waybel18(A) ) ) ) ).
fof(t11_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_waybel18(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( m1_pre_topc(A,B)
=> r1_waybel18(A,B) ) ) ) ).
fof(t12_waybel25,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> v2_waybel18(B) ) ) ).
fof(d2_waybel25,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v1_waybel_9(B)
& l1_waybel_9(B) )
=> ( B = k1_waybel25(A)
<=> ( g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_orders_2(B,C,D)
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
& E = k1_tarski(D)
& r2_hidden(C,k6_pre_topc(A,E)) ) ) ) ) ) ) ) ) ).
fof(t13_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> k1_waybel25(A) = k1_waybel25(B) ) ) ) ).
fof(t14_waybel25,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> g1_orders_2(u1_struct_0(k1_waybel25(k3_waybel18(A,k2_pre_circ(A,B)))),u1_orders_2(k1_waybel25(k3_waybel18(A,k2_pre_circ(A,B))))) = g1_orders_2(u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k1_waybel25(B)))),u1_orders_2(k5_yellow_1(A,k2_pre_circ(A,k1_waybel25(B))))) ) ) ).
fof(t15_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> k1_waybel25(A) = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ).
fof(t16_waybel25,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,A) )
=> g1_orders_2(u1_struct_0(k1_waybel25(B)),u1_orders_2(k1_waybel25(B))) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ).
fof(t17_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( v4_yellow_0(k1_waybel25(B),k1_waybel25(A))
& m1_yellow_0(k1_waybel25(B),k1_waybel25(A)) ) ) ) ).
fof(t18_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(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)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& m2_relset_1(D,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) )
=> ( ( C = D
& v3_tops_2(C,A,B) )
=> v23_waybel_0(D,k1_waybel25(A),k1_waybel25(B)) ) ) ) ) ) ).
fof(t19_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r1_t_0topsp(A,B)
=> r5_waybel_1(k1_waybel25(A),k1_waybel25(B)) ) ) ) ).
fof(t20_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_waybel18(A)
& l1_pre_topc(A) )
=> ( v2_orders_2(k1_waybel25(A))
& v3_orders_2(k1_waybel25(A))
& v4_orders_2(k1_waybel25(A))
& v1_lattice3(k1_waybel25(A))
& v2_lattice3(k1_waybel25(A))
& v3_lattice3(k1_waybel25(A))
& v3_waybel_3(k1_waybel25(A))
& l1_orders_2(k1_waybel25(A)) ) ) ).
fof(t21_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B))
& m2_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) )
=> v5_orders_3(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ).
fof(t22_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_waybel25(A)))
=> k6_pre_topc(k1_waybel25(A),k1_struct_0(k1_waybel25(A),B)) = k6_waybel_0(k1_waybel25(A),B) ) ) ).
fof(t23_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v3_pre_topc(B,k1_waybel25(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) )
=> v13_waybel_0(B,k1_waybel25(A)) ) ) ).
fof(d3_waybel25,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,C) )
=> ! [E] :
( m1_subset_1(E,A)
=> ( r1_tarski(u1_struct_0(C),u1_struct_0(k6_yellow_1(A,B)))
=> ! [F] :
( ( ~ v3_struct_0(F)
& v3_orders_2(F)
& v6_waybel_0(F,B)
& v7_waybel_0(F)
& l1_waybel_0(F,B) )
=> ( F = k2_waybel25(A,B,C,D,E)
<=> ( g1_orders_2(u1_struct_0(F),u1_orders_2(F)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D))
& u1_waybel_0(B,F) = k1_funct_1(k10_funct_6(u1_waybel_0(C,D)),E) ) ) ) ) ) ) ) ) ) ).
fof(t24_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_funct_1(u1_waybel_0(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,E)),D) = k1_funct_1(k3_yellow_6(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C),D),E) ) ) ) ) ) ).
fof(t25_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& v10_waybel_0(C,k3_waybel24(A,k1_waybel25(B)))
& l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) ) ) ) ) ).
fof(t26_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_waybel_9(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) )
=> r1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) ) ) ) ) ).
fof(d4_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_waybel25(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,k1_waybel25(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_waybel25(A)))) )
=> ( r1_yellow_0(k1_waybel25(A),B)
& ! [C] :
( ( v3_pre_topc(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(k1_yellow_0(k1_waybel25(A),B),C)
& r1_xboole_0(B,C) ) ) ) ) ) ) ).
fof(t27_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v1_waybel25(A) )
=> v1_waybel25(B) ) ) ) ).
fof(t28_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ( r1_borsuk_3(A,B)
=> v1_waybel25(B) ) ) ) ).
fof(t29_waybel25,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v4_waybel11(A)
& l1_waybel_9(A) )
=> v1_waybel25(A) ) ).
fof(t30_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> v24_waybel_0(k1_waybel25(A)) ) ).
fof(t31_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v7_waybel_0(B)
& v10_waybel_0(B,k1_waybel25(A))
& l1_waybel_0(B,k1_waybel25(A)) )
=> r1_waybel_9(k1_waybel25(A),B) ) ) ).
fof(t32_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v10_waybel_0(B,k1_waybel25(A))
& l1_waybel_0(B,k1_waybel25(A)) )
=> r2_hidden(k1_waybel_2(k1_waybel25(A),B),k11_yellow_6(k1_waybel25(A),B)) ) ) ).
fof(t33_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v10_waybel_0(B,k1_waybel25(A))
& l1_waybel_0(B,k1_waybel25(A)) )
=> v3_yellow_6(B,k1_waybel25(A)) ) ) ).
fof(t34_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v7_waybel_0(B)
& v10_waybel_0(B,k1_waybel25(A))
& l1_waybel_0(B,k1_waybel25(A)) )
=> ( r1_waybel_9(k1_waybel25(A),B)
& r2_hidden(k1_waybel_2(k1_waybel25(A),B),k11_yellow_6(k1_waybel25(A),B)) ) )
=> v1_waybel25(A) ) ) ).
fof(t35_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B)))
& v5_pre_topc(C,k1_waybel25(A),k1_waybel25(B))
& m2_relset_1(C,u1_struct_0(k1_waybel25(A)),u1_struct_0(k1_waybel25(B))) )
=> v22_waybel_0(C,k1_waybel25(A),k1_waybel25(B)) ) ) ) ).
fof(t36_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v1_waybel25(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& l1_pre_topc(B) )
=> ( r1_waybel18(B,A)
=> v1_waybel25(B) ) ) ) ).
fof(t37_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_waybel18(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v4_waybel11(B)
& m1_yellow_9(B,k1_waybel25(A)) )
=> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ).
fof(t38_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_waybel18(A)
& l1_pre_topc(A) )
=> ( v2_compts_1(A)
& v6_waybel_3(A)
& v3_yellow_8(A) ) ) ).
fof(t39_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_t_0topsp(A)
& v2_waybel18(A)
& l1_pre_topc(A) )
=> v1_waybel25(A) ) ).
fof(t40_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& v1_waybel25(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k1_waybel25(B)))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B)))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) )
=> ( ( D = k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C)))
& r1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C)))
& r2_hidden(E,k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) )
=> r1_yellow_2(u1_struct_0(A),k1_waybel25(B),E,D) ) ) ) ) ) ) ).
fof(t41_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& v1_waybel25(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
=> ! [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(k1_waybel25(B)))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_waybel25(B))) )
=> ( ( ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,F),k1_waybel25(B)) )
& E = k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))) )
=> k3_yellow_6(u1_struct_0(A),k1_waybel25(B),E,D) = k1_waybel_2(k1_waybel25(B),k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D)) ) ) ) ) ) ) ).
fof(t42_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& v1_waybel25(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_orders_2(C)
& v7_waybel_0(C)
& l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> v10_waybel_0(k2_waybel25(u1_struct_0(A),k1_waybel25(B),k3_waybel24(A,k1_waybel25(B)),C,D),k1_waybel25(B)) )
=> ( v1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))))
& v1_funct_2(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),A,B)
& m2_relset_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),k1_waybel25(B)),k8_yellow_2(u1_struct_0(C),k3_waybel24(A,k1_waybel25(B)),u1_waybel_0(k3_waybel24(A,k1_waybel25(B)),C))),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ).
fof(t43_waybel25,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_t_0topsp(B)
& v1_waybel25(B)
& l1_pre_topc(B) )
=> ( v4_waybel_0(k3_waybel24(A,k1_waybel25(B)),k6_yellow_1(u1_struct_0(A),k1_waybel25(B)))
& m1_yellow_0(k3_waybel24(A,k1_waybel25(B)),k6_yellow_1(u1_struct_0(A),k1_waybel25(B))) ) ) ) ).
fof(dt_k1_waybel25,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_waybel_9(k1_waybel25(A))
& l1_waybel_9(k1_waybel25(A)) ) ) ).
fof(dt_k2_waybel25,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& l1_orders_2(C)
& ~ v3_struct_0(D)
& v3_orders_2(D)
& v7_waybel_0(D)
& l1_waybel_0(D,C)
& m1_subset_1(E,A) )
=> ( ~ v3_struct_0(k2_waybel25(A,B,C,D,E))
& v3_orders_2(k2_waybel25(A,B,C,D,E))
& v6_waybel_0(k2_waybel25(A,B,C,D,E),B)
& v7_waybel_0(k2_waybel25(A,B,C,D,E))
& l1_waybel_0(k2_waybel25(A,B,C,D,E),B) ) ) ).
%------------------------------------------------------------------------------