SET007 Axioms: SET007+857.ax
%------------------------------------------------------------------------------
% File : SET007+857 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Fundamental Groups of Products of Topological Spaces
% 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 : topalg_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 60 ( 0 unt; 0 def)
% Number of atoms : 899 ( 50 equ)
% Maximal formula atoms : 28 ( 14 avg)
% Number of connectives : 982 ( 143 ~; 0 |; 545 &)
% ( 2 <=>; 292 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 18 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 0 prp; 1-6 aty)
% Number of functors : 37 ( 37 usr; 3 con; 0-8 aty)
% Number of variables : 387 ( 382 !; 5 ?)
% 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_topalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B) )
=> ( ~ v3_struct_0(k6_borsuk_1(A,B))
& v1_pre_topc(k6_borsuk_1(A,B))
& v2_pre_topc(k6_borsuk_1(A,B))
& v1_borsuk_2(k6_borsuk_1(A,B)) ) ) ).
fof(fc2_topalg_4,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)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( v1_relat_1(k12_topalg_4(A,B,C,D))
& v1_funct_1(k12_topalg_4(A,B,C,D))
& v2_funct_1(k12_topalg_4(A,B,C,D))
& v1_funct_2(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
& v2_funct_2(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) ) ) ).
fof(t1_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& C = k17_group_7(A,B,D,E) ) ) ) ) ) ).
fof(d1_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_group_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_group_1(D) )
=> ! [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)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))))
& m2_relset_1(G,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D)))) )
=> ( G = k1_topalg_4(A,B,C,D,E,F)
<=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))))
=> ? [I] :
( m1_subset_1(I,u1_struct_0(A))
& ? [J] :
( m1_subset_1(J,u1_struct_0(B))
& H = k17_group_7(A,B,I,J)
& k8_funct_2(u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))),G,H) = k17_group_7(C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(C),E,I),k8_funct_2(u1_struct_0(B),u1_struct_0(D),F,J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_group_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_group_1(D) )
=> ! [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)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))),k1_topalg_4(A,B,C,D,E,F),k17_group_7(A,B,G,H)) = k17_group_7(C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(C),E,G),k8_funct_2(u1_struct_0(B),u1_struct_0(D),F,H)) ) ) ) ) ) ) ) ) ).
fof(t3_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_group_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_group_1(D) )
=> ! [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)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( v2_funct_1(E)
& v2_funct_1(F) )
=> v2_funct_1(k1_topalg_4(A,B,C,D,E,F)) ) ) ) ) ) ) ) ).
fof(t4_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_group_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_group_1(D) )
=> ! [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)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( v2_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& v2_funct_2(F,u1_struct_0(B),u1_struct_0(D)) )
=> v2_funct_2(k1_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D)))) ) ) ) ) ) ) ) ).
fof(t5_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_group_1(D)
& v4_group_1(D)
& l1_group_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& v1_group_6(E,A,C)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& v1_group_6(F,B,D)
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( v4_group_6(E,A,C)
& v4_group_6(F,B,D) )
=> v4_group_6(k2_topalg_4(A,B,C,D,E,F),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D))) ) ) ) ) ) ) ) ).
fof(t6_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_group_1(D)
& v4_group_1(D)
& l1_group_1(D) )
=> ( ( r1_group_6(A,C)
& r1_group_6(B,D) )
=> r2_group_6(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D))) ) ) ) ) ) ).
fof(t7_topalg_4,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k1_relat_1(A) = k1_relat_1(B)
=> k15_mcart_1(k13_funct_3(A,B)) = A ) ) ) ).
fof(t8_topalg_4,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( k1_relat_1(A) = k1_relat_1(B)
=> k16_mcart_1(k13_funct_3(A,B)) = B ) ) ) ).
fof(t9_topalg_4,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C)))
& v5_pre_topc(D,A,k6_borsuk_1(B,C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) )
=> v5_pre_topc(k4_topalg_4(B,C,A,D),A,B) ) ) ) ) ).
fof(t10_topalg_4,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C)))
& v5_pre_topc(D,A,k6_borsuk_1(B,C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) )
=> v5_pre_topc(k5_topalg_4(B,C,A,D),A,C) ) ) ) ) ).
fof(t11_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> r1_borsuk_6(A,C,D) ) ) ) ) ) ) ) ).
fof(t12_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> r1_borsuk_6(B,E,F) ) ) ) ) ) ) ) ).
fof(t13_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> m1_borsuk_2(k4_topalg_4(A,B,k5_topmetr,G),A,C,D) ) ) ) ) ) ) ) ) ).
fof(t14_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> m1_borsuk_2(k5_topalg_4(A,B,k5_topmetr,G),B,E,F) ) ) ) ) ) ) ) ) ).
fof(t15_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_borsuk_6(A,C,D)
& r1_borsuk_6(B,E,F) )
=> r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) ) ) ) ) ) ) ) ).
fof(t16_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( r1_borsuk_6(A,C,D)
& r1_borsuk_6(B,E,F) )
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,B,E,F)
=> m1_borsuk_2(k3_topalg_4(A,B,k5_topmetr,G,H),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) ) ) ) ) ) ) ) ) ) ).
fof(t17_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [H] :
( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [I] :
( m1_borsuk_6(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H)
=> ! [J] :
( m1_borsuk_2(J,A,C,D)
=> ! [K] :
( m1_borsuk_2(K,A,C,D)
=> ( ( J = k4_topalg_4(A,B,k5_topmetr,G)
& K = k4_topalg_4(A,B,k5_topmetr,H)
& r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
=> m1_borsuk_6(k4_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),I),A,C,D,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [H] :
( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [I] :
( m1_borsuk_6(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H)
=> ! [J] :
( m1_borsuk_2(J,B,E,F)
=> ! [K] :
( m1_borsuk_2(K,B,E,F)
=> ( ( J = k5_topalg_4(A,B,k5_topmetr,G)
& K = k5_topalg_4(A,B,k5_topmetr,H)
& r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
=> m1_borsuk_6(k5_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),I),B,E,F,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [H] :
( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [I] :
( m1_borsuk_2(I,A,C,D)
=> ! [J] :
( m1_borsuk_2(J,A,C,D)
=> ( ( I = k4_topalg_4(A,B,k5_topmetr,G)
& J = k4_topalg_4(A,B,k5_topmetr,H)
& r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
=> r3_borsuk_2(A,C,D,I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [H] :
( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [I] :
( m1_borsuk_2(I,B,E,F)
=> ! [J] :
( m1_borsuk_2(J,B,E,F)
=> ( ( I = k5_topalg_4(A,B,k5_topmetr,G)
& J = k5_topalg_4(A,B,k5_topmetr,H)
& r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) )
=> r3_borsuk_2(B,E,F,I,J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [H] :
( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [I] :
( m1_borsuk_2(I,A,C,D)
=> ! [J] :
( m1_borsuk_2(J,A,C,D)
=> ! [K] :
( m1_borsuk_2(K,B,E,F)
=> ! [L] :
( m1_borsuk_2(L,B,E,F)
=> ! [M] :
( m1_borsuk_6(M,A,C,D,I,J)
=> ! [N] :
( m1_borsuk_6(N,B,E,F,K,L)
=> ( ( I = k4_topalg_4(A,B,k5_topmetr,G)
& J = k4_topalg_4(A,B,k5_topmetr,H)
& K = k5_topalg_4(A,B,k5_topmetr,G)
& L = k5_topalg_4(A,B,k5_topmetr,H)
& r3_borsuk_2(A,C,D,I,J)
& r3_borsuk_2(B,E,F,K,L) )
=> m1_borsuk_6(k3_topalg_4(A,B,k6_borsuk_1(k5_topmetr,k5_topmetr),M,N),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [H] :
( m1_borsuk_2(H,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F))
=> ! [I] :
( m1_borsuk_2(I,A,C,D)
=> ! [J] :
( m1_borsuk_2(J,A,C,D)
=> ! [K] :
( m1_borsuk_2(K,B,E,F)
=> ! [L] :
( m1_borsuk_2(L,B,E,F)
=> ( ( I = k4_topalg_4(A,B,k5_topmetr,G)
& J = k4_topalg_4(A,B,k5_topmetr,H)
& K = k5_topalg_4(A,B,k5_topmetr,G)
& L = k5_topalg_4(A,B,k5_topmetr,H)
& r3_borsuk_2(A,C,D,I,J)
& r3_borsuk_2(B,E,F,K,L) )
=> r3_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F),G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
=> ! [J] :
( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
=> ! [K] :
( m1_borsuk_2(K,A,C,D)
=> ! [L] :
( m1_borsuk_2(L,A,D,E)
=> ( ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
& r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
& K = k4_topalg_4(A,B,k5_topmetr,I)
& L = k4_topalg_4(A,B,k5_topmetr,J) )
=> k4_topalg_4(A,B,k5_topmetr,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(A,C,D,E,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
=> ! [J] :
( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
=> k8_topalg_4(A,B,C,E,F,H,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(A,C,D,E,k8_topalg_4(A,B,C,D,F,G,I),k8_topalg_4(A,B,D,E,G,H,J)) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
=> ! [J] :
( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
=> ! [K] :
( m1_borsuk_2(K,B,F,G)
=> ! [L] :
( m1_borsuk_2(L,B,G,H)
=> ( ( r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
& r1_borsuk_6(k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
& K = k5_topalg_4(A,B,k5_topmetr,I)
& L = k5_topalg_4(A,B,k5_topmetr,J) )
=> k5_topalg_4(A,B,k5_topmetr,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(B,F,G,H,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_borsuk_2(I,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G))
=> ! [J] :
( m1_borsuk_2(J,k6_borsuk_1(A,B),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H))
=> k9_topalg_4(A,B,C,E,F,H,k1_borsuk_2(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,F),k8_borsuk_1(A,B,D,G),k8_borsuk_1(A,B,E,H),I,J)) = k1_borsuk_2(B,F,G,H,k9_topalg_4(A,B,C,D,F,G,I),k9_topalg_4(A,B,D,E,G,H,J)) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
& m2_relset_1(E,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) )
=> ( E = k12_topalg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))))
=> ? [G] :
( m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D))
& F = k6_eqrel_1(k1_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),G)
& k8_funct_2(u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))),E,F) = k10_finseq_1(k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),k10_topalg_4(A,B,C,D,G)),k6_eqrel_1(k1_topalg_1(B,D),k2_topalg_1(B,D),k11_topalg_4(A,B,C,D,G))) ) ) ) ) ) ) ) ) ).
fof(t27_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))))
=> ! [F] :
( m1_borsuk_2(F,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D))
=> ( E = k6_eqrel_1(k1_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),F)
=> k8_funct_2(u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))),k12_topalg_4(A,B,C,D),E) = k10_finseq_1(k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),k10_topalg_4(A,B,C,D,F)),k6_eqrel_1(k1_topalg_1(B,D),k2_topalg_1(B,D),k11_topalg_4(A,B,C,D,F))) ) ) ) ) ) ) ) ).
fof(t28_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D))
=> k1_funct_1(k12_topalg_4(A,B,C,D),k6_eqrel_1(k1_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),E)) = k10_finseq_1(k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),k10_topalg_4(A,B,C,D,E)),k6_eqrel_1(k1_topalg_1(B,D),k2_topalg_1(B,D),k11_topalg_4(A,B,C,D,E))) ) ) ) ) ) ).
fof(t29_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> v4_group_6(k13_topalg_4(A,B,C,D),k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))) ) ) ) ) ).
fof(t30_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> r2_group_6(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))) ) ) ) ) ).
fof(t31_topalg_4,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,D)))
& v1_group_6(G,k3_topalg_1(A,C),k3_topalg_1(A,D))
& m2_relset_1(G,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,D))) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k3_topalg_1(B,E)),u1_struct_0(k3_topalg_1(B,F)))
& v1_group_6(H,k3_topalg_1(B,E),k3_topalg_1(B,F))
& m2_relset_1(H,u1_struct_0(k3_topalg_1(B,E)),u1_struct_0(k3_topalg_1(B,F))) )
=> ( ( v4_group_6(G,k3_topalg_1(A,C),k3_topalg_1(A,D))
& v4_group_6(H,k3_topalg_1(B,E),k3_topalg_1(B,F)) )
=> v4_group_6(k8_group_6(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,E))),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,D),k3_topalg_1(B,F))),k13_topalg_4(A,B,C,E),k2_topalg_4(k3_topalg_1(A,C),k3_topalg_1(B,E),k3_topalg_1(A,D),k3_topalg_1(B,F),G,H)),k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,D),k3_topalg_1(B,F)))) ) ) ) ) ) ) ) ) ) ).
fof(t32_topalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> r2_group_6(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,D),k3_topalg_1(B,F)))) ) ) ) ) ) ) ).
fof(dt_k1_topalg_4,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& l1_group_1(C)
& ~ v3_struct_0(D)
& l1_group_1(D)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
& v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( v1_funct_1(k1_topalg_4(A,B,C,D,E,F))
& v1_funct_2(k1_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D))))
& m2_relset_1(k1_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(C,D)))) ) ) ).
fof(dt_k2_topalg_4,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C)
& ~ v3_struct_0(D)
& v3_group_1(D)
& v4_group_1(D)
& l1_group_1(D)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& v1_group_6(E,A,C)
& m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
& v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& v1_group_6(F,B,D)
& m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( v1_funct_1(k2_topalg_4(A,B,C,D,E,F))
& v1_funct_2(k2_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D))))
& v1_group_6(k2_topalg_4(A,B,C,D,E,F),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D)))
& m2_relset_1(k2_topalg_4(A,B,C,D,E,F),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(C,D)))) ) ) ).
fof(redefinition_k2_topalg_4,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C)
& ~ v3_struct_0(D)
& v3_group_1(D)
& v4_group_1(D)
& l1_group_1(D)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& v1_group_6(E,A,C)
& m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
& v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& v1_group_6(F,B,D)
& m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> k2_topalg_4(A,B,C,D,E,F) = k1_topalg_4(A,B,C,D,E,F) ) ).
fof(dt_k3_topalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& v2_pre_topc(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(C),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ( v1_funct_1(k3_topalg_4(A,B,C,D,E))
& v1_funct_2(k3_topalg_4(A,B,C,D,E),u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
& m2_relset_1(k3_topalg_4(A,B,C,D,E),u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) ) ) ).
fof(redefinition_k3_topalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& v2_pre_topc(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(C),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> k3_topalg_4(A,B,C,D,E) = k13_funct_3(D,E) ) ).
fof(dt_k4_topalg_4,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)
& v2_pre_topc(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
& m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
=> ( v1_funct_1(k4_topalg_4(A,B,C,D))
& v1_funct_2(k4_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(k4_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(A)) ) ) ).
fof(redefinition_k4_topalg_4,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)
& v2_pre_topc(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
& m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
=> k4_topalg_4(A,B,C,D) = k15_mcart_1(D) ) ).
fof(dt_k5_topalg_4,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)
& v2_pre_topc(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
& m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
=> ( v1_funct_1(k5_topalg_4(A,B,C,D))
& v1_funct_2(k5_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(k5_topalg_4(A,B,C,D),u1_struct_0(C),u1_struct_0(B)) ) ) ).
fof(redefinition_k5_topalg_4,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)
& v2_pre_topc(C)
& l1_pre_topc(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B)))
& m1_relset_1(D,u1_struct_0(C),u1_struct_0(k6_borsuk_1(A,B))) )
=> k5_topalg_4(A,B,C,D) = k16_mcart_1(D) ) ).
fof(dt_k6_topalg_4,axiom,
! [A,B,C,D,E,F,G,H] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& m1_borsuk_2(G,A,C,D)
& m1_borsuk_2(H,B,E,F) )
=> m1_borsuk_2(k6_topalg_4(A,B,C,D,E,F,G,H),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) ) ).
fof(redefinition_k6_topalg_4,axiom,
! [A,B,C,D,E,F,G,H] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& m1_borsuk_2(G,A,C,D)
& m1_borsuk_2(H,B,E,F) )
=> k6_topalg_4(A,B,C,D,E,F,G,H) = k13_funct_3(G,H) ) ).
fof(dt_k7_topalg_4,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B))
& m1_borsuk_2(E,A,C,C)
& m1_borsuk_2(F,B,D,D) )
=> m1_borsuk_2(k7_topalg_4(A,B,C,D,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) ) ).
fof(redefinition_k7_topalg_4,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B))
& m1_borsuk_2(E,A,C,C)
& m1_borsuk_2(F,B,D,D) )
=> k7_topalg_4(A,B,C,D,E,F) = k13_funct_3(E,F) ) ).
fof(dt_k8_topalg_4,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
=> m1_borsuk_2(k8_topalg_4(A,B,C,D,E,F,G),A,C,D) ) ).
fof(redefinition_k8_topalg_4,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
=> k8_topalg_4(A,B,C,D,E,F,G) = k15_mcart_1(G) ) ).
fof(dt_k9_topalg_4,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
=> m1_borsuk_2(k9_topalg_4(A,B,C,D,E,F,G),B,E,F) ) ).
fof(redefinition_k9_topalg_4,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& v1_borsuk_2(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& m1_borsuk_2(G,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,E),k8_borsuk_1(A,B,D,F)) )
=> k9_topalg_4(A,B,C,D,E,F,G) = k16_mcart_1(G) ) ).
fof(dt_k10_topalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B))
& m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
=> m1_borsuk_2(k10_topalg_4(A,B,C,D,E),A,C,C) ) ).
fof(redefinition_k10_topalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B))
& m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
=> k10_topalg_4(A,B,C,D,E) = k15_mcart_1(E) ) ).
fof(dt_k11_topalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B))
& m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
=> m1_borsuk_2(k11_topalg_4(A,B,C,D,E),B,D,D) ) ).
fof(redefinition_k11_topalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B))
& m1_borsuk_2(E,k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D),k8_borsuk_1(A,B,C,D)) )
=> k11_topalg_4(A,B,C,D,E) = k16_mcart_1(E) ) ).
fof(dt_k12_topalg_4,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)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( v1_funct_1(k12_topalg_4(A,B,C,D))
& v1_funct_2(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
& m2_relset_1(k12_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) ) ) ).
fof(dt_k13_topalg_4,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)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( v1_funct_1(k13_topalg_4(A,B,C,D))
& v1_funct_2(k13_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D)))))
& v1_group_6(k13_topalg_4(A,B,C,D),k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)),k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))
& m2_relset_1(k13_topalg_4(A,B,C,D),u1_struct_0(k3_topalg_1(k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D))),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(k3_topalg_1(A,C),k3_topalg_1(B,D))))) ) ) ).
fof(redefinition_k13_topalg_4,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)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> k13_topalg_4(A,B,C,D) = k12_topalg_4(A,B,C,D) ) ).
%------------------------------------------------------------------------------