SET007 Axioms: SET007+833.ax
%------------------------------------------------------------------------------
% File : SET007+833 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Fundamental Group
% 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 82 ( 2 unt; 0 def)
% Number of atoms : 822 ( 56 equ)
% Maximal formula atoms : 26 ( 10 avg)
% Number of connectives : 814 ( 74 ~; 0 |; 288 &)
% ( 10 <=>; 442 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 13 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-6 aty)
% Number of functors : 50 ( 50 usr; 6 con; 0-6 aty)
% Number of variables : 446 ( 443 !; 3 ?)
% 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_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ~ v1_xboole_0(k1_topalg_1(A,B)) ) ).
fof(fc2_topalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_relat_1(k2_topalg_1(A,B))
& ~ v1_xboole_0(k2_topalg_1(A,B))
& v1_relat_2(k2_topalg_1(A,B))
& v3_relat_2(k2_topalg_1(A,B))
& v8_relat_2(k2_topalg_1(A,B))
& v1_partfun1(k2_topalg_1(A,B),k1_topalg_1(A,B),k1_topalg_1(A,B)) ) ) ).
fof(fc3_topalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_topalg_1(A,B))
& v1_group_1(k3_topalg_1(A,B)) ) ) ).
fof(fc4_topalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k3_topalg_1(A,B))
& v1_group_1(k3_topalg_1(A,B))
& v2_group_1(k3_topalg_1(A,B))
& v3_group_1(k3_topalg_1(A,B))
& v4_group_1(k3_topalg_1(A,B)) ) ) ).
fof(fc5_topalg_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_borsuk_2(D,A,B,C) )
=> ( v1_relat_1(k4_topalg_1(A,B,C,D))
& v1_funct_1(k4_topalg_1(A,B,C,D))
& v2_funct_1(k4_topalg_1(A,B,C,D))
& v1_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
& v2_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) ).
fof(cc1_topalg_1,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A)))
& m1_borsuk_2(D,k15_euclid(A),B,C)
& m1_borsuk_2(E,k15_euclid(A),B,C) )
=> ! [F] :
( m1_borsuk_6(F,k15_euclid(A),B,C,D,E)
=> ( v1_relat_1(F)
& v5_pre_topc(F,k6_borsuk_1(k5_topmetr,k5_topmetr),k15_euclid(A)) ) ) ) ).
fof(fc6_topalg_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A))) )
=> ( ~ v3_struct_0(k3_topalg_1(k15_euclid(A),B))
& v1_group_1(k3_topalg_1(k15_euclid(A),B))
& v2_group_1(k3_topalg_1(k15_euclid(A),B))
& v3_group_1(k3_topalg_1(k15_euclid(A),B))
& v4_group_1(k3_topalg_1(k15_euclid(A),B))
& v3_realset2(k3_topalg_1(k15_euclid(A),B)) ) ) ).
fof(t1_topalg_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),k2_tops_2(A,B,C),C) = k7_grcat_1(B)
& k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,k2_tops_2(A,B,C)) = k7_grcat_1(A) )
=> v4_group_6(C,A,B) ) ) ) ) ).
fof(t2_topalg_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
=> ( A = k2_rcomp_2(B,np__1)
=> k3_subset_1(u1_struct_0(k22_borsuk_1),A) = k1_rcomp_1(np__0,B) ) ) ) ).
fof(t3_topalg_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
=> ( A = k1_rcomp_2(np__0,B)
=> k3_subset_1(u1_struct_0(k22_borsuk_1),A) = k1_rcomp_1(B,np__1) ) ) ) ).
fof(t4_topalg_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
=> ( A = k2_rcomp_2(B,np__1)
=> v3_pre_topc(A,k22_borsuk_1) ) ) ) ).
fof(t5_topalg_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k22_borsuk_1)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k22_borsuk_1))
=> ( A = k1_rcomp_2(np__0,B)
=> v3_pre_topc(A,k22_borsuk_1) ) ) ) ).
fof(t6_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_finseq_2(B,k1_numbers))
=> k10_rvsum_1(B,A,k6_rvsum_1(B,C)) = k6_rvsum_1(B,k10_rvsum_1(B,A,C)) ) ) ) ).
fof(t7_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k4_finseq_2(B,k1_numbers))
=> ! [D] :
( m1_subset_1(D,k4_finseq_2(B,k1_numbers))
=> k10_rvsum_1(B,A,k8_rvsum_1(B,C,D)) = k8_rvsum_1(B,k10_rvsum_1(B,A,C),k10_rvsum_1(B,A,D)) ) ) ) ) ).
fof(t8_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k4_finseq_2(C,k1_numbers))
=> k10_rvsum_1(C,k6_xcmplx_0(A,B),D) = k8_rvsum_1(C,k10_rvsum_1(C,A,D),k10_rvsum_1(C,B,D)) ) ) ) ) ).
fof(t9_topalg_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k4_finseq_2(A,k1_numbers))
=> ! [C] :
( m1_subset_1(C,k4_finseq_2(A,k1_numbers))
=> ! [D] :
( m1_subset_1(D,k4_finseq_2(A,k1_numbers))
=> ! [E] :
( m1_subset_1(E,k4_finseq_2(A,k1_numbers))
=> k8_rvsum_1(A,k4_rvsum_1(A,B,C),k4_rvsum_1(A,D,E)) = k4_rvsum_1(A,k8_rvsum_1(A,B,D),k8_rvsum_1(A,C,E)) ) ) ) ) ) ).
fof(t10_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k1_numbers,k1_euclid(B))
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,np__1) )
=> r1_xreal_0(k12_euclid(k9_euclid(B,A,C)),k12_euclid(C)) ) ) ) ) ).
fof(t11_topalg_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k1_euclid(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k22_borsuk_1))
=> r1_xreal_0(k12_euclid(k9_euclid(A,C,B)),k12_euclid(B)) ) ) ) ).
fof(t12_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k14_euclid(C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k14_euclid(C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k14_euclid(C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k14_euclid(C)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k14_euclid(C)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k14_euclid(C)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(C)))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(k15_euclid(C)))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(k15_euclid(C)))
=> ! [M] :
( m1_subset_1(M,u1_struct_0(k15_euclid(C)))
=> ~ ( D = J
& E = K
& F = L
& G = M
& H = k17_euclid(C,J,L)
& I = k17_euclid(C,K,M)
& ~ r1_xreal_0(A,k4_metric_1(k14_euclid(C),D,E))
& ~ r1_xreal_0(B,k4_metric_1(k14_euclid(C),F,G))
& r1_xreal_0(k2_xcmplx_0(A,B),k4_metric_1(k14_euclid(C),H,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k14_euclid(C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k14_euclid(C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k14_euclid(C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k14_euclid(C)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(C)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(C)))
=> ~ ( D = H
& E = I
& F = k18_euclid(A,C,H)
& G = k18_euclid(A,C,I)
& ~ r1_xreal_0(B,k4_metric_1(k14_euclid(C),D,E))
& A != np__0
& r1_xreal_0(k3_xcmplx_0(k18_complex1(A),B),k4_metric_1(k14_euclid(C),F,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k14_euclid(E)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k14_euclid(E)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k14_euclid(E)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k14_euclid(E)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k14_euclid(E)))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(k14_euclid(E)))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(k15_euclid(E)))
=> ! [M] :
( m1_subset_1(M,u1_struct_0(k15_euclid(E)))
=> ! [N] :
( m1_subset_1(N,u1_struct_0(k15_euclid(E)))
=> ! [O] :
( m1_subset_1(O,u1_struct_0(k15_euclid(E)))
=> ~ ( F = L
& G = M
& H = N
& I = O
& J = k17_euclid(E,k18_euclid(A,E,L),k18_euclid(B,E,N))
& K = k17_euclid(E,k18_euclid(A,E,M),k18_euclid(B,E,O))
& ~ r1_xreal_0(C,k4_metric_1(k14_euclid(E),F,G))
& ~ r1_xreal_0(D,k4_metric_1(k14_euclid(E),H,I))
& A != np__0
& B != np__0
& r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k18_complex1(A),C),k3_xcmplx_0(k18_complex1(B),D)),k4_metric_1(k14_euclid(E),J,K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_topalg_1,axiom,
$true ).
fof(t16_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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(C),u1_struct_0(k15_euclid(B)))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(k15_euclid(B))) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(k15_euclid(B)))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(k15_euclid(B))) )
=> ( ( v5_pre_topc(D,C,k15_euclid(B))
& ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k7_yellow_2(u1_struct_0(C),k15_euclid(B),E,F) = k18_euclid(A,B,k7_yellow_2(u1_struct_0(C),k15_euclid(B),D,F)) ) )
=> v5_pre_topc(E,C,k15_euclid(B)) ) ) ) ) ) ) ).
fof(t17_topalg_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(k15_euclid(C)))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(k15_euclid(C))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(k15_euclid(C)))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(k15_euclid(C))) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(D),u1_struct_0(k15_euclid(C)))
& m2_relset_1(G,u1_struct_0(D),u1_struct_0(k15_euclid(C))) )
=> ( ( v5_pre_topc(E,D,k15_euclid(C))
& v5_pre_topc(F,D,k15_euclid(C))
& ! [H] :
( m1_subset_1(H,u1_struct_0(D))
=> k7_yellow_2(u1_struct_0(D),k15_euclid(C),G,H) = k17_euclid(C,k18_euclid(A,C,k7_yellow_2(u1_struct_0(D),k15_euclid(C),E,H)),k18_euclid(B,C,k7_yellow_2(u1_struct_0(D),k15_euclid(C),F,H))) ) )
=> v5_pre_topc(G,D,k15_euclid(C)) ) ) ) ) ) ) ) ) ).
fof(t18_topalg_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A))) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k22_borsuk_1))
=> k1_binop_1(B,C,D) = k18_euclid(k6_xcmplx_0(np__1,D),A,C) ) )
=> v5_pre_topc(B,k6_borsuk_1(k15_euclid(A),k22_borsuk_1),k15_euclid(A)) ) ) ) ).
fof(t19_topalg_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(A),k22_borsuk_1)),u1_struct_0(k15_euclid(A))) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k22_borsuk_1))
=> k1_binop_1(B,C,D) = k18_euclid(D,A,C) ) )
=> v5_pre_topc(B,k6_borsuk_1(k15_euclid(A),k22_borsuk_1),k15_euclid(A)) ) ) ) ).
fof(t20_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D) )
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,C,D)
=> r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,F),k2_borsuk_2(A,C,D,F))) ) ) ) ) ) ) ) ).
fof(t21_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,C,D)
=> r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,F),k2_borsuk_2(A,C,D,F))) ) ) ) ) ) ) ).
fof(t22_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,D,C) )
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,D,C)
=> r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,k2_borsuk_2(A,D,C,F)),F)) ) ) ) ) ) ) ) ).
fof(t23_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,D,C)
=> r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,E,k2_borsuk_2(A,D,C,F)),F)) ) ) ) ) ) ) ).
fof(t24_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,D,B) )
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,D,B)
=> r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,k2_borsuk_2(A,D,B,F),F),E)) ) ) ) ) ) ) ) ).
fof(t25_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,D,B)
=> r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,k2_borsuk_2(A,D,B,F),F),E)) ) ) ) ) ) ) ).
fof(t26_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,B,D) )
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,D)
=> r3_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,F,k2_borsuk_2(A,B,D,F)),E)) ) ) ) ) ) ) ) ).
fof(t27_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,D)
=> r4_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,B,C,k1_borsuk_2(A,B,D,B,F,k2_borsuk_2(A,B,D,F)),E)) ) ) ) ) ) ) ).
fof(t28_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,D,C) )
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ( r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,G))
=> r3_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t29_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ( r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,G))
=> r4_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) ).
fof(t30_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,B,D) )
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,D,B)
=> ( r3_borsuk_2(A,D,C,k1_borsuk_2(A,D,B,C,G,E),k1_borsuk_2(A,D,B,C,G,F))
=> r3_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t31_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,D,B)
=> ( r4_borsuk_2(A,D,C,k1_borsuk_2(A,D,B,C,G,E),k1_borsuk_2(A,D,B,C,G,F))
=> r4_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) ).
fof(t32_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,D,E)
& r1_borsuk_6(A,E,F) )
=> ! [G] :
( m1_borsuk_2(G,A,B,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ! [I] :
( m1_borsuk_2(I,A,D,E)
=> ! [J] :
( m1_borsuk_2(J,A,E,F)
=> r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ! [G] :
( m1_borsuk_2(G,A,B,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ! [I] :
( m1_borsuk_2(I,A,D,E)
=> ! [J] :
( m1_borsuk_2(J,A,E,F)
=> r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J)) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,D,E)
& r1_borsuk_6(A,E,F) )
=> ! [G] :
( m1_borsuk_2(G,A,B,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ! [I] :
( m1_borsuk_2(I,A,D,E)
=> ! [J] :
( m1_borsuk_2(J,A,E,F)
=> r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,C,F,G,k1_borsuk_2(A,C,E,F,k1_borsuk_2(A,C,D,E,H,I),J))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ! [G] :
( m1_borsuk_2(G,A,B,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ! [I] :
( m1_borsuk_2(I,A,D,E)
=> ! [J] :
( m1_borsuk_2(J,A,E,F)
=> r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,G,H),I),J),k1_borsuk_2(A,B,C,F,G,k1_borsuk_2(A,C,E,F,k1_borsuk_2(A,C,D,E,H,I),J))) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,D,E)
& r1_borsuk_6(A,E,F) )
=> ! [G] :
( m1_borsuk_2(G,A,B,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ! [I] :
( m1_borsuk_2(I,A,D,E)
=> ! [J] :
( m1_borsuk_2(J,A,E,F)
=> r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J),k1_borsuk_2(A,B,D,F,k1_borsuk_2(A,B,C,D,G,H),k1_borsuk_2(A,D,E,F,I,J))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ! [G] :
( m1_borsuk_2(G,A,B,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> ! [I] :
( m1_borsuk_2(I,A,D,E)
=> ! [J] :
( m1_borsuk_2(J,A,E,F)
=> r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,G,k1_borsuk_2(A,C,D,E,H,I)),J),k1_borsuk_2(A,B,D,F,k1_borsuk_2(A,B,C,D,G,H),k1_borsuk_2(A,D,E,F,I,J))) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,C,E) )
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,E,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,D)
=> r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,k1_borsuk_2(A,B,E,C,k1_borsuk_2(A,B,C,E,F,k2_borsuk_2(A,E,C,G)),G),H),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t39_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,D,C)
=> ! [H] :
( m1_borsuk_2(H,A,C,E)
=> r4_borsuk_2(A,B,E,k1_borsuk_2(A,B,C,E,k1_borsuk_2(A,B,D,C,k1_borsuk_2(A,B,C,D,F,k2_borsuk_2(A,D,C,G)),G),H),k1_borsuk_2(A,B,C,E,F,H)) ) ) ) ) ) ) ) ) ).
fof(t40_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,B,D)
& r1_borsuk_6(A,D,E) )
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,D,E)
=> ! [H] :
( m1_borsuk_2(H,A,B,D)
=> r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,B,D,k1_borsuk_2(A,B,C,B,F,k2_borsuk_2(A,B,C,F)),H),G),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) ) ).
fof(t41_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,D,E)
=> ! [H] :
( m1_borsuk_2(H,A,B,D)
=> r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,B,D,k1_borsuk_2(A,B,C,B,F,k2_borsuk_2(A,B,C,F)),H),G),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) ).
fof(t42_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,B,D)
& r1_borsuk_6(A,E,D) )
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,D,E)
=> ! [H] :
( m1_borsuk_2(H,A,B,D)
=> r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,k1_borsuk_2(A,C,B,D,k2_borsuk_2(A,B,C,F),H),G)),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) ) ).
fof(t43_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,D,E)
=> ! [H] :
( m1_borsuk_2(H,A,B,D)
=> r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,E,D,k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,k1_borsuk_2(A,C,B,D,k2_borsuk_2(A,B,C,F),H),G)),k2_borsuk_2(A,D,E,G)),H) ) ) ) ) ) ) ) ) ).
fof(t44_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,D,E)
& r1_borsuk_6(A,E,F)
& r1_borsuk_6(A,B,G) )
=> ! [H] :
( m1_borsuk_2(H,A,B,C)
=> ! [I] :
( m1_borsuk_2(I,A,C,D)
=> ! [J] :
( m1_borsuk_2(J,A,D,E)
=> ! [K] :
( m1_borsuk_2(K,A,E,F)
=> ! [L] :
( m1_borsuk_2(L,A,G,D)
=> r3_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,H,k1_borsuk_2(A,C,D,E,I,J)),K),k1_borsuk_2(A,B,G,F,k1_borsuk_2(A,B,D,G,k1_borsuk_2(A,B,C,D,H,I),k2_borsuk_2(A,G,D,L)),k1_borsuk_2(A,G,E,F,k1_borsuk_2(A,G,D,E,L,J),K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [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(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_borsuk_2(H,A,B,C)
=> ! [I] :
( m1_borsuk_2(I,A,C,D)
=> ! [J] :
( m1_borsuk_2(J,A,D,E)
=> ! [K] :
( m1_borsuk_2(K,A,E,F)
=> ! [L] :
( m1_borsuk_2(L,A,G,D)
=> r4_borsuk_2(A,B,F,k1_borsuk_2(A,B,E,F,k1_borsuk_2(A,B,C,E,H,k1_borsuk_2(A,C,D,E,I,J)),K),k1_borsuk_2(A,B,G,F,k1_borsuk_2(A,B,D,G,k1_borsuk_2(A,B,C,D,H,I),k2_borsuk_2(A,G,D,L)),k1_borsuk_2(A,G,E,F,k1_borsuk_2(A,G,D,E,L,J),K))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( C = k1_topalg_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> m1_borsuk_2(D,A,B,B) ) ) ) ) ).
fof(d2_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_relset_1(C,k1_topalg_1(A,B),k1_topalg_1(A,B))
=> ( C = k2_topalg_1(A,B)
<=> ! [D] :
( m1_borsuk_2(D,A,B,B)
=> ! [E] :
( m1_borsuk_2(E,A,B,B)
=> ( r2_hidden(k4_tarski(D,E),C)
<=> r3_borsuk_2(A,B,B,D,E) ) ) ) ) ) ) ) ).
fof(t46_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_borsuk_2(C,A,B,B)
=> ! [D] :
( m1_borsuk_2(D,A,B,B)
=> ( r2_hidden(D,k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),C))
<=> r3_borsuk_2(A,B,B,C,D) ) ) ) ) ) ).
fof(t47_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_borsuk_2(C,A,B,B)
=> ! [D] :
( m1_borsuk_2(D,A,B,B)
=> ( k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),C) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),D)
<=> r3_borsuk_2(A,B,B,C,D) ) ) ) ) ) ).
fof(d3_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_group_1(C)
& l1_group_1(C) )
=> ( C = k3_topalg_1(A,B)
<=> ( u1_struct_0(C) = k8_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ? [F] :
( m1_borsuk_2(F,A,B,B)
& ? [G] :
( m1_borsuk_2(G,A,B,B)
& D = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),F)
& E = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),G)
& k1_binop_1(u1_group_1(C),D,E) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),k1_borsuk_2(A,B,B,B,F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t48_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( r2_hidden(C,u1_struct_0(k3_topalg_1(A,B)))
<=> ? [D] :
( m1_borsuk_2(D,A,B,B)
& C = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),D) ) ) ) ) ).
fof(d4_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
& m2_relset_1(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) )
=> ( E = k4_topalg_1(A,B,C,D)
<=> ! [F] :
( m1_borsuk_2(F,A,C,C)
=> k1_funct_1(E,k6_eqrel_1(k1_topalg_1(A,C),k2_topalg_1(A,C),F)) = k6_eqrel_1(k1_topalg_1(A,B),k2_topalg_1(A,B),k1_borsuk_2(A,B,C,B,k1_borsuk_2(A,B,C,C,D,F),k2_borsuk_2(A,B,C,D))) ) ) ) ) ) ) ) ) ).
fof(t49_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ( ( r1_borsuk_6(A,B,C)
& r3_borsuk_2(A,B,C,D,E) )
=> k4_topalg_1(A,B,C,D) = k4_topalg_1(A,B,C,E) ) ) ) ) ) ) ).
fof(t50_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ( r4_borsuk_2(A,B,C,D,E)
=> k4_topalg_1(A,B,C,D) = k4_topalg_1(A,B,C,E) ) ) ) ) ) ) ).
fof(t51_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> ( v1_funct_1(k4_topalg_1(A,B,C,D))
& v1_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
& v1_group_6(k4_topalg_1(A,B,C,D),k3_topalg_1(A,C),k3_topalg_1(A,B))
& m2_relset_1(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) ) ) ) ) ).
fof(t52_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> v2_funct_1(k4_topalg_1(A,B,C,D)) ) ) ) ) ) ).
fof(t53_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> v2_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) ) ) ) ).
fof(t54_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> k2_tops_2(k3_topalg_1(A,C),k3_topalg_1(A,B),k4_topalg_1(A,B,C,D)) = k4_topalg_1(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) ) ).
fof(t55_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> k2_tops_2(k3_topalg_1(A,C),k3_topalg_1(A,B),k5_topalg_1(A,B,C,D)) = k5_topalg_1(A,C,B,k2_borsuk_2(A,B,C,D)) ) ) ) ) ).
fof(t56_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
& v1_group_6(E,k3_topalg_1(A,C),k3_topalg_1(A,B))
& m2_relset_1(E,u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) )
=> ( E = k4_topalg_1(A,B,C,D)
=> v4_group_6(E,k3_topalg_1(A,C),k3_topalg_1(A,B)) ) ) ) ) ) ) ) ).
fof(t57_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> v4_group_6(k5_topalg_1(A,B,C,D),k3_topalg_1(A,C),k3_topalg_1(A,B)) ) ) ) ) ).
fof(t58_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_borsuk_6(A,B,C)
=> r2_group_6(k3_topalg_1(A,B),k3_topalg_1(A,C)) ) ) ) ) ).
fof(t59_topalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_group_6(k3_topalg_1(A,B),k3_topalg_1(A,C)) ) ) ) ).
fof(d5_topalg_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_borsuk_2(D,k15_euclid(A),B,C)
=> ! [E] :
( m1_borsuk_2(E,k15_euclid(A),B,C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
& m2_relset_1(F,u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A))) )
=> ( F = k6_topalg_1(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(k22_borsuk_1))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k22_borsuk_1))
=> k1_binop_1(F,G,H) = k17_euclid(A,k18_euclid(k6_xcmplx_0(np__1,H),A,k7_yellow_2(u1_struct_0(k22_borsuk_1),k15_euclid(A),D,G)),k18_euclid(H,A,k7_yellow_2(u1_struct_0(k22_borsuk_1),k15_euclid(A),E,G))) ) ) ) ) ) ) ) ) ) ).
fof(t60_topalg_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_borsuk_2(D,k15_euclid(A),B,C)
=> ! [E] :
( m1_borsuk_2(E,k15_euclid(A),B,C)
=> r4_borsuk_2(k15_euclid(A),B,C,D,E) ) ) ) ) ) ).
fof(t61_topalg_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_borsuk_2(C,k15_euclid(A),B,B)
=> u1_struct_0(k3_topalg_1(k15_euclid(A),B)) = k1_tarski(k6_eqrel_1(k1_topalg_1(k15_euclid(A),B),k2_topalg_1(k15_euclid(A),B),C)) ) ) ) ).
fof(dt_k1_topalg_1,axiom,
$true ).
fof(dt_k2_topalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m2_relset_1(k2_topalg_1(A,B),k1_topalg_1(A,B),k1_topalg_1(A,B)) ) ).
fof(dt_k3_topalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_group_1(k3_topalg_1(A,B))
& l1_group_1(k3_topalg_1(A,B)) ) ) ).
fof(dt_k4_topalg_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_borsuk_2(D,A,B,C) )
=> ( v1_funct_1(k4_topalg_1(A,B,C,D))
& v1_funct_2(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
& m2_relset_1(k4_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) ).
fof(dt_k5_topalg_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_borsuk_2(D,A,B,C) )
=> ( v1_funct_1(k5_topalg_1(A,B,C,D))
& v1_funct_2(k5_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B)))
& v1_group_6(k5_topalg_1(A,B,C,D),k3_topalg_1(A,C),k3_topalg_1(A,B))
& m2_relset_1(k5_topalg_1(A,B,C,D),u1_struct_0(k3_topalg_1(A,C)),u1_struct_0(k3_topalg_1(A,B))) ) ) ).
fof(redefinition_k5_topalg_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_borsuk_2(D,A,B,C) )
=> k5_topalg_1(A,B,C,D) = k4_topalg_1(A,B,C,D) ) ).
fof(dt_k6_topalg_1,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A)))
& m1_borsuk_2(D,k15_euclid(A),B,C)
& m1_borsuk_2(E,k15_euclid(A),B,C) )
=> ( v1_funct_1(k6_topalg_1(A,B,C,D,E))
& v1_funct_2(k6_topalg_1(A,B,C,D,E),u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A)))
& m2_relset_1(k6_topalg_1(A,B,C,D,E),u1_struct_0(k6_borsuk_1(k22_borsuk_1,k22_borsuk_1)),u1_struct_0(k15_euclid(A))) ) ) ).
fof(dt_k7_topalg_1,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A)))
& m1_borsuk_2(D,k15_euclid(A),B,C)
& m1_borsuk_2(E,k15_euclid(A),B,C) )
=> m1_borsuk_6(k7_topalg_1(A,B,C,D,E),k15_euclid(A),B,C,D,E) ) ).
fof(redefinition_k7_topalg_1,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A)))
& m1_borsuk_2(D,k15_euclid(A),B,C)
& m1_borsuk_2(E,k15_euclid(A),B,C) )
=> k7_topalg_1(A,B,C,D,E) = k6_topalg_1(A,B,C,D,E) ) ).
%------------------------------------------------------------------------------