% Mizar ND problem: t1_borsuk_2,borsuk_2,77,58 
fof(dh_c1_3__borsuk_2,definition,
    ( ( ( ~ v3_struct_0(c1_3__borsuk_2)
        & v2_pre_topc(c1_3__borsuk_2)
        & l1_pre_topc(c1_3__borsuk_2) )
     => ! [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(c1_3__borsuk_2),u1_struct_0(A))
                        & m2_relset_1(D,u1_struct_0(c1_3__borsuk_2),u1_struct_0(A)) )
                     => ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
                            & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
                         => ~ ( m1_pre_topc(c1_3__borsuk_2,C)
                              & m1_pre_topc(B,C)
                              & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(B)) = k2_pre_topc(C)
                              & v2_compts_1(c1_3__borsuk_2)
                              & v2_compts_1(B)
                              & v3_compts_1(C)
                              & v5_pre_topc(D,c1_3__borsuk_2,A)
                              & v5_pre_topc(E,B,A)
                              & ! [F] : 
                                  ( r2_hidden(F,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(B)))
                                 => k1_funct_1(D,F) = k1_funct_1(E,F) )
                              & ! [F] : 
                                  ( ( v1_funct_1(F)
                                    & v1_funct_2(F,u1_struct_0(C),u1_struct_0(A))
                                    & m2_relset_1(F,u1_struct_0(C),u1_struct_0(A)) )
                                 => ~ ( F = k1_funct_4(D,E)
                                      & v5_pre_topc(F,C,A) ) ) ) ) ) ) ) ) )
   => ! [G] : 
        ( ( ~ v3_struct_0(G)
          & v2_pre_topc(G)
          & l1_pre_topc(G) )
       => ! [H] : 
            ( ( ~ v3_struct_0(H)
              & v2_pre_topc(H)
              & l1_pre_topc(H) )
           => ! [I] : 
                ( ( ~ v3_struct_0(I)
                  & v2_pre_topc(I)
                  & l1_pre_topc(I) )
               => ! [J] : 
                    ( ( ~ v3_struct_0(J)
                      & v2_pre_topc(J)
                      & l1_pre_topc(J) )
                   => ! [K] : 
                        ( ( v1_funct_1(K)
                          & v1_funct_2(K,u1_struct_0(G),u1_struct_0(H))
                          & m2_relset_1(K,u1_struct_0(G),u1_struct_0(H)) )
                       => ! [L] : 
                            ( ( v1_funct_1(L)
                              & v1_funct_2(L,u1_struct_0(I),u1_struct_0(H))
                              & m2_relset_1(L,u1_struct_0(I),u1_struct_0(H)) )
                           => ~ ( m1_pre_topc(G,J)
                                & m1_pre_topc(I,J)
                                & k2_xboole_0(k2_pre_topc(G),k2_pre_topc(I)) = k2_pre_topc(J)
                                & v2_compts_1(G)
                                & v2_compts_1(I)
                                & v3_compts_1(J)
                                & v5_pre_topc(K,G,H)
                                & v5_pre_topc(L,I,H)
                                & ! [M] : 
                                    ( r2_hidden(M,k3_xboole_0(k2_pre_topc(G),k2_pre_topc(I)))
                                   => k1_funct_1(K,M) = k1_funct_1(L,M) )
                                & ! [M] : 
                                    ( ( v1_funct_1(M)
                                      & v1_funct_2(M,u1_struct_0(J),u1_struct_0(H))
                                      & m2_relset_1(M,u1_struct_0(J),u1_struct_0(H)) )
                                   => ~ ( M = k1_funct_4(K,L)
                                        & v5_pre_topc(M,J,H) ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__borsuk_2),file(borsuk_2,c1_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c1_3__borsuk_2)]).

fof(dh_c2_3__borsuk_2,definition,
    ( ( ( ~ v3_struct_0(c2_3__borsuk_2)
        & v2_pre_topc(c2_3__borsuk_2)
        & l1_pre_topc(c2_3__borsuk_2) )
     => ! [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(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                    & m2_relset_1(C,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
                 => ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2)) )
                     => ~ ( m1_pre_topc(c1_3__borsuk_2,B)
                          & m1_pre_topc(A,B)
                          & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(A)) = k2_pre_topc(B)
                          & v2_compts_1(c1_3__borsuk_2)
                          & v2_compts_1(A)
                          & v3_compts_1(B)
                          & v5_pre_topc(C,c1_3__borsuk_2,c2_3__borsuk_2)
                          & v5_pre_topc(D,A,c2_3__borsuk_2)
                          & ! [E] : 
                              ( r2_hidden(E,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(A)))
                             => k1_funct_1(C,E) = k1_funct_1(D,E) )
                          & ! [E] : 
                              ( ( v1_funct_1(E)
                                & v1_funct_2(E,u1_struct_0(B),u1_struct_0(c2_3__borsuk_2))
                                & m2_relset_1(E,u1_struct_0(B),u1_struct_0(c2_3__borsuk_2)) )
                             => ~ ( E = k1_funct_4(C,D)
                                  & v5_pre_topc(E,B,c2_3__borsuk_2) ) ) ) ) ) ) ) )
   => ! [F] : 
        ( ( ~ v3_struct_0(F)
          & v2_pre_topc(F)
          & l1_pre_topc(F) )
       => ! [G] : 
            ( ( ~ v3_struct_0(G)
              & v2_pre_topc(G)
              & l1_pre_topc(G) )
           => ! [H] : 
                ( ( ~ v3_struct_0(H)
                  & v2_pre_topc(H)
                  & l1_pre_topc(H) )
               => ! [I] : 
                    ( ( v1_funct_1(I)
                      & v1_funct_2(I,u1_struct_0(c1_3__borsuk_2),u1_struct_0(F))
                      & m2_relset_1(I,u1_struct_0(c1_3__borsuk_2),u1_struct_0(F)) )
                   => ! [J] : 
                        ( ( v1_funct_1(J)
                          & v1_funct_2(J,u1_struct_0(G),u1_struct_0(F))
                          & m2_relset_1(J,u1_struct_0(G),u1_struct_0(F)) )
                       => ~ ( m1_pre_topc(c1_3__borsuk_2,H)
                            & m1_pre_topc(G,H)
                            & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(G)) = k2_pre_topc(H)
                            & v2_compts_1(c1_3__borsuk_2)
                            & v2_compts_1(G)
                            & v3_compts_1(H)
                            & v5_pre_topc(I,c1_3__borsuk_2,F)
                            & v5_pre_topc(J,G,F)
                            & ! [K] : 
                                ( r2_hidden(K,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(G)))
                               => k1_funct_1(I,K) = k1_funct_1(J,K) )
                            & ! [K] : 
                                ( ( v1_funct_1(K)
                                  & v1_funct_2(K,u1_struct_0(H),u1_struct_0(F))
                                  & m2_relset_1(K,u1_struct_0(H),u1_struct_0(F)) )
                               => ~ ( K = k1_funct_4(I,J)
                                    & v5_pre_topc(K,H,F) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__borsuk_2),file(borsuk_2,c2_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c2_3__borsuk_2)]).

fof(dh_c3_3__borsuk_2,definition,
    ( ( ( ~ v3_struct_0(c3_3__borsuk_2)
        & v2_pre_topc(c3_3__borsuk_2)
        & l1_pre_topc(c3_3__borsuk_2) )
     => ! [A] : 
          ( ( ~ v3_struct_0(A)
            & v2_pre_topc(A)
            & l1_pre_topc(A) )
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                & m2_relset_1(B,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
             => ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                    & m2_relset_1(C,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
                 => ~ ( m1_pre_topc(c1_3__borsuk_2,A)
                      & m1_pre_topc(c3_3__borsuk_2,A)
                      & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(A)
                      & v2_compts_1(c1_3__borsuk_2)
                      & v2_compts_1(c3_3__borsuk_2)
                      & v3_compts_1(A)
                      & v5_pre_topc(B,c1_3__borsuk_2,c2_3__borsuk_2)
                      & v5_pre_topc(C,c3_3__borsuk_2,c2_3__borsuk_2)
                      & ! [D] : 
                          ( r2_hidden(D,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                         => k1_funct_1(B,D) = k1_funct_1(C,D) )
                      & ! [D] : 
                          ( ( v1_funct_1(D)
                            & v1_funct_2(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2))
                            & m2_relset_1(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2)) )
                         => ~ ( D = k1_funct_4(B,C)
                              & v5_pre_topc(D,A,c2_3__borsuk_2) ) ) ) ) ) ) )
   => ! [E] : 
        ( ( ~ v3_struct_0(E)
          & v2_pre_topc(E)
          & l1_pre_topc(E) )
       => ! [F] : 
            ( ( ~ v3_struct_0(F)
              & v2_pre_topc(F)
              & l1_pre_topc(F) )
           => ! [G] : 
                ( ( v1_funct_1(G)
                  & v1_funct_2(G,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                  & m2_relset_1(G,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
               => ! [H] : 
                    ( ( v1_funct_1(H)
                      & v1_funct_2(H,u1_struct_0(E),u1_struct_0(c2_3__borsuk_2))
                      & m2_relset_1(H,u1_struct_0(E),u1_struct_0(c2_3__borsuk_2)) )
                   => ~ ( m1_pre_topc(c1_3__borsuk_2,F)
                        & m1_pre_topc(E,F)
                        & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(E)) = k2_pre_topc(F)
                        & v2_compts_1(c1_3__borsuk_2)
                        & v2_compts_1(E)
                        & v3_compts_1(F)
                        & v5_pre_topc(G,c1_3__borsuk_2,c2_3__borsuk_2)
                        & v5_pre_topc(H,E,c2_3__borsuk_2)
                        & ! [I] : 
                            ( r2_hidden(I,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(E)))
                           => k1_funct_1(G,I) = k1_funct_1(H,I) )
                        & ! [I] : 
                            ( ( v1_funct_1(I)
                              & v1_funct_2(I,u1_struct_0(F),u1_struct_0(c2_3__borsuk_2))
                              & m2_relset_1(I,u1_struct_0(F),u1_struct_0(c2_3__borsuk_2)) )
                           => ~ ( I = k1_funct_4(G,H)
                                & v5_pre_topc(I,F,c2_3__borsuk_2) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_3__borsuk_2),file(borsuk_2,c3_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c3_3__borsuk_2)]).

fof(dh_c4_3__borsuk_2,definition,
    ( ( ( ~ v3_struct_0(c4_3__borsuk_2)
        & v2_pre_topc(c4_3__borsuk_2)
        & l1_pre_topc(c4_3__borsuk_2) )
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
            & m2_relset_1(A,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
         => ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                & m2_relset_1(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
             => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
                  & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
                  & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
                  & v2_compts_1(c1_3__borsuk_2)
                  & v2_compts_1(c3_3__borsuk_2)
                  & v3_compts_1(c4_3__borsuk_2)
                  & v5_pre_topc(A,c1_3__borsuk_2,c2_3__borsuk_2)
                  & v5_pre_topc(B,c3_3__borsuk_2,c2_3__borsuk_2)
                  & ! [C] : 
                      ( r2_hidden(C,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                     => k1_funct_1(A,C) = k1_funct_1(B,C) )
                  & ! [C] : 
                      ( ( v1_funct_1(C)
                        & v1_funct_2(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                        & m2_relset_1(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
                     => ~ ( C = k1_funct_4(A,B)
                          & v5_pre_topc(C,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) ) )
   => ! [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(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
              & m2_relset_1(E,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
           => ! [F] : 
                ( ( v1_funct_1(F)
                  & v1_funct_2(F,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                  & m2_relset_1(F,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
               => ~ ( m1_pre_topc(c1_3__borsuk_2,D)
                    & m1_pre_topc(c3_3__borsuk_2,D)
                    & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(D)
                    & v2_compts_1(c1_3__borsuk_2)
                    & v2_compts_1(c3_3__borsuk_2)
                    & v3_compts_1(D)
                    & v5_pre_topc(E,c1_3__borsuk_2,c2_3__borsuk_2)
                    & v5_pre_topc(F,c3_3__borsuk_2,c2_3__borsuk_2)
                    & ! [G] : 
                        ( r2_hidden(G,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                       => k1_funct_1(E,G) = k1_funct_1(F,G) )
                    & ! [G] : 
                        ( ( v1_funct_1(G)
                          & v1_funct_2(G,u1_struct_0(D),u1_struct_0(c2_3__borsuk_2))
                          & m2_relset_1(G,u1_struct_0(D),u1_struct_0(c2_3__borsuk_2)) )
                       => ~ ( G = k1_funct_4(E,F)
                            & v5_pre_topc(G,D,c2_3__borsuk_2) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_3__borsuk_2),file(borsuk_2,c4_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c4_3__borsuk_2)]).

fof(dh_c5_3__borsuk_2,definition,
    ( ( ( v1_funct_1(c5_3__borsuk_2)
        & v1_funct_2(c5_3__borsuk_2,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
        & m2_relset_1(c5_3__borsuk_2,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
     => ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
            & m2_relset_1(A,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
         => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
              & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
              & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
              & v2_compts_1(c1_3__borsuk_2)
              & v2_compts_1(c3_3__borsuk_2)
              & v3_compts_1(c4_3__borsuk_2)
              & v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2)
              & v5_pre_topc(A,c3_3__borsuk_2,c2_3__borsuk_2)
              & ! [B] : 
                  ( r2_hidden(B,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                 => k1_funct_1(c5_3__borsuk_2,B) = k1_funct_1(A,B) )
              & ! [B] : 
                  ( ( v1_funct_1(B)
                    & v1_funct_2(B,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                    & m2_relset_1(B,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
                 => ~ ( B = k1_funct_4(c5_3__borsuk_2,A)
                      & v5_pre_topc(B,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) )
   => ! [C] : 
        ( ( v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
          & m2_relset_1(C,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
       => ! [D] : 
            ( ( v1_funct_1(D)
              & v1_funct_2(D,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
              & m2_relset_1(D,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
           => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
                & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
                & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
                & v2_compts_1(c1_3__borsuk_2)
                & v2_compts_1(c3_3__borsuk_2)
                & v3_compts_1(c4_3__borsuk_2)
                & v5_pre_topc(C,c1_3__borsuk_2,c2_3__borsuk_2)
                & v5_pre_topc(D,c3_3__borsuk_2,c2_3__borsuk_2)
                & ! [E] : 
                    ( r2_hidden(E,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                   => k1_funct_1(C,E) = k1_funct_1(D,E) )
                & ! [E] : 
                    ( ( v1_funct_1(E)
                      & v1_funct_2(E,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                      & m2_relset_1(E,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
                   => ~ ( E = k1_funct_4(C,D)
                        & v5_pre_topc(E,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c5_3__borsuk_2),file(borsuk_2,c5_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c5_3__borsuk_2)]).

fof(dh_c6_3__borsuk_2,definition,
    ( ( ( v1_funct_1(c6_3__borsuk_2)
        & v1_funct_2(c6_3__borsuk_2,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
        & m2_relset_1(c6_3__borsuk_2,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
     => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
          & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
          & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
          & v2_compts_1(c1_3__borsuk_2)
          & v2_compts_1(c3_3__borsuk_2)
          & v3_compts_1(c4_3__borsuk_2)
          & v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2)
          & v5_pre_topc(c6_3__borsuk_2,c3_3__borsuk_2,c2_3__borsuk_2)
          & ! [A] : 
              ( r2_hidden(A,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
             => k1_funct_1(c5_3__borsuk_2,A) = k1_funct_1(c6_3__borsuk_2,A) )
          & ! [A] : 
              ( ( v1_funct_1(A)
                & v1_funct_2(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                & m2_relset_1(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
             => ~ ( A = k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)
                  & v5_pre_topc(A,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) )
   => ! [B] : 
        ( ( v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
          & m2_relset_1(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
       => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
            & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
            & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
            & v2_compts_1(c1_3__borsuk_2)
            & v2_compts_1(c3_3__borsuk_2)
            & v3_compts_1(c4_3__borsuk_2)
            & v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2)
            & v5_pre_topc(B,c3_3__borsuk_2,c2_3__borsuk_2)
            & ! [C] : 
                ( r2_hidden(C,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
               => k1_funct_1(c5_3__borsuk_2,C) = k1_funct_1(B,C) )
            & ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                  & m2_relset_1(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
               => ~ ( C = k1_funct_4(c5_3__borsuk_2,B)
                    & v5_pre_topc(C,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) ),
    introduced(definition,[new_symbol(c6_3__borsuk_2),file(borsuk_2,c6_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c6_3__borsuk_2)]).

fof(e1_3__borsuk_2,assumption,
    ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
    & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e1_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e1_3__borsuk_2)]).

fof(e2_3__borsuk_2,assumption,(
    k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e2_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e2_3__borsuk_2)]).

fof(e3_3__borsuk_2,assumption,(
    v2_compts_1(c1_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e3_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e3_3__borsuk_2)]).

fof(e4_3__borsuk_2,assumption,(
    v2_compts_1(c3_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e4_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e4_3__borsuk_2)]).

fof(e5_3__borsuk_2,assumption,(
    v3_compts_1(c4_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e5_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e5_3__borsuk_2)]).

fof(e6_3__borsuk_2,assumption,(
    v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e6_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e6_3__borsuk_2)]).

fof(e7_3__borsuk_2,assumption,(
    v5_pre_topc(c6_3__borsuk_2,c3_3__borsuk_2,c2_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e7_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e7_3__borsuk_2)]).

fof(e8_3__borsuk_2,assumption,(
    ! [A] : 
      ( r2_hidden(A,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
     => k1_funct_1(c5_3__borsuk_2,A) = k1_funct_1(c6_3__borsuk_2,A) ) ),
    introduced(assumption,[file(borsuk_2,e8_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,e8_3__borsuk_2)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_funct_2,theorem,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc1_funct_2)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc2_borsuk_1,theorem,(
    ! [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(A),u1_struct_0(B))
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
          & v5_pre_topc(C,A,B)
          & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ),
    file(borsuk_1,rc2_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,rc2_borsuk_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc5_funct_2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc5_funct_2)]).

fof(cc6_funct_2,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    [interesting(0.9),axiom,file(funct_2,cc6_funct_2)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc5_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_c1_3__borsuk_2,assumption,
    ( ~ v3_struct_0(c1_3__borsuk_2)
    & v2_pre_topc(c1_3__borsuk_2)
    & l1_pre_topc(c1_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,c1_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c1_3__borsuk_2)]).

fof(dt_c3_3__borsuk_2,assumption,
    ( ~ v3_struct_0(c3_3__borsuk_2)
    & v2_pre_topc(c3_3__borsuk_2)
    & l1_pre_topc(c3_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,c3_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c3_3__borsuk_2)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_funct_2,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    [interesting(0.9),axiom,file(funct_2,rc1_funct_2)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(idempotence_k1_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c2_3__borsuk_2,assumption,
    ( ~ v3_struct_0(c2_3__borsuk_2)
    & v2_pre_topc(c2_3__borsuk_2)
    & l1_pre_topc(c2_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,c2_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c2_3__borsuk_2)]).

fof(dt_c4_3__borsuk_2,assumption,
    ( ~ v3_struct_0(c4_3__borsuk_2)
    & v2_pre_topc(c4_3__borsuk_2)
    & l1_pre_topc(c4_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,c4_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c4_3__borsuk_2)]).

fof(dt_c5_3__borsuk_2,assumption,
    ( v1_funct_1(c5_3__borsuk_2)
    & v1_funct_2(c5_3__borsuk_2,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
    & m2_relset_1(c5_3__borsuk_2,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,c5_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c5_3__borsuk_2)]).

fof(dt_c6_3__borsuk_2,assumption,
    ( v1_funct_1(c6_3__borsuk_2)
    & v1_funct_2(c6_3__borsuk_2,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
    & m2_relset_1(c6_3__borsuk_2,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,c6_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c6_3__borsuk_2)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,l1_pre_topc)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(de_c8_3__borsuk_2,definition,(
    c8_3__borsuk_2 = k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2) ),
    introduced(definition,[new_symbol(c8_3__borsuk_2),file(borsuk_2,c8_3__borsuk_2)]),
    [interesting(0.8),axiom,file(borsuk_2,c8_3__borsuk_2)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(fc22_membered,theorem,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    [interesting(0.9),axiom,file(membered,fc22_membered)]).

fof(fc23_membered,theorem,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    [interesting(0.9),axiom,file(membered,fc23_membered)]).

fof(fc24_membered,theorem,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    [interesting(0.9),axiom,file(membered,fc24_membered)]).

fof(fc25_membered,theorem,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    [interesting(0.9),axiom,file(membered,fc25_membered)]).

fof(fc26_membered,theorem,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    [interesting(0.9),axiom,file(membered,fc26_membered)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.9),axiom,file(relset_1,t12_relset_1)]).

fof(e12_3__borsuk_2,plain,
    ( r1_tarski(k2_relat_1(c5_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
    & r1_tarski(k2_relat_1(c6_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,t8_boole,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,cc1_relset_1,fc1_struct_0,fc1_subset_1,rc1_funct_1,rc1_funct_2,rc3_struct_0,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k2_relat_1,dt_m2_relset_1,dt_u1_struct_0,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,t3_subset,t12_relset_1]),
    [interesting(0.8),file(borsuk_2,e12_3__borsuk_2),[file(borsuk_2,e12_3__borsuk_2)]]).

fof(t18_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(funct_4,t18_funct_4),
    [interesting(0.9),axiom,file(funct_4,t18_funct_4)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t8_xboole_1)]).

fof(e13_3__borsuk_2,plain,
    ( r1_tarski(k2_xboole_0(k2_relat_1(c5_3__borsuk_2),k2_relat_1(c6_3__borsuk_2)),u1_struct_0(c2_3__borsuk_2))
    & r1_tarski(k2_relat_1(k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)),k2_xboole_0(k2_relat_1(c5_3__borsuk_2),k2_relat_1(c6_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,fc1_struct_0,fc1_subset_1,rc3_struct_0,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_funct_4,dt_k2_relat_1,dt_k2_xboole_0,dt_u1_struct_0,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,rc1_funct_1,t3_subset,e12_3__borsuk_2,t18_funct_4,t8_xboole_1]),
    [interesting(0.8),file(borsuk_2,e13_3__borsuk_2),[file(borsuk_2,e13_3__borsuk_2)]]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e14_3__borsuk_2,plain,(
    r1_tarski(k2_relat_1(k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)),u1_struct_0(c2_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,fc1_struct_0,fc1_subset_1,rc1_funct_1,rc3_struct_0,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_funct_4,dt_k2_relat_1,dt_k2_xboole_0,dt_u1_struct_0,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,t3_subset,e13_3__borsuk_2,t1_xboole_1]),
    [interesting(0.8),file(borsuk_2,e14_3__borsuk_2),[file(borsuk_2,e14_3__borsuk_2)]]).

fof(rc6_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc6_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc6_pre_topc)]).

fof(rc7_pre_topc,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B)
          & v4_pre_topc(B,A) ) ) ),
    file(pre_topc,rc7_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,rc7_pre_topc)]).

fof(fc2_pre_topc,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(k2_pre_topc(A)) ) ),
    file(pre_topc,fc2_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,fc2_pre_topc)]).

fof(fc5_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => v4_pre_topc(k2_pre_topc(A),A) ) ),
    file(pre_topc,fc5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,fc5_pre_topc)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k2_pre_topc,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k2_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k2_pre_topc)]).

fof(d3_pre_topc,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_pre_topc(A) = u1_struct_0(A) ) ),
    file(pre_topc,d3_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,d3_pre_topc)]).

fof(redefinition_k4_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.9),axiom,file(funct_2,d1_funct_2)]).

fof(e1_3_2__borsuk_2,plain,(
    k1_relat_1(c6_3__borsuk_2) = u1_struct_0(c3_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_c2_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,fc6_membered,t6_boole,d1_funct_2]),
    [interesting(0.65),file(borsuk_2,e1_3_2__borsuk_2),[file(borsuk_2,e1_3_2__borsuk_2)]]).

fof(e2_3_2__borsuk_2,plain,(
    u1_struct_0(c3_3__borsuk_2) = k2_pre_topc(c3_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,t3_subset,dt_k2_pre_topc,dt_u1_struct_0,dt_c3_3__borsuk_2,d3_pre_topc]),
    [interesting(0.65),file(borsuk_2,e2_3_2__borsuk_2),[file(borsuk_2,e2_3_2__borsuk_2)]]).

fof(e10_3__borsuk_2,plain,(
    k1_relat_1(c6_3__borsuk_2) = k2_pre_topc(c3_3__borsuk_2) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e1_3_2__borsuk_2,e2_3_2__borsuk_2]),
    [interesting(0.8),file(borsuk_2,e10_3__borsuk_2),[file(borsuk_2,e10_3__borsuk_2)]]).

fof(e1_3_1__borsuk_2,plain,(
    k1_relat_1(c5_3__borsuk_2) = u1_struct_0(c1_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__borsuk_2,dt_c1_3__borsuk_2,dt_c5_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_c2_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_1,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_membered,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c5_3__borsuk_2,fc6_membered,t6_boole,d1_funct_2]),
    [interesting(0.65),file(borsuk_2,e1_3_1__borsuk_2),[file(borsuk_2,e1_3_1__borsuk_2)]]).

fof(e2_3_1__borsuk_2,plain,(
    u1_struct_0(c1_3__borsuk_2) = k2_pre_topc(c1_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,t3_subset,dt_k2_pre_topc,dt_u1_struct_0,dt_c1_3__borsuk_2,d3_pre_topc]),
    [interesting(0.65),file(borsuk_2,e2_3_1__borsuk_2),[file(borsuk_2,e2_3_1__borsuk_2)]]).

fof(e9_3__borsuk_2,plain,(
    k1_relat_1(c5_3__borsuk_2) = k2_pre_topc(c1_3__borsuk_2) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2])],[e1_3_1__borsuk_2,e2_3_1__borsuk_2]),
    [interesting(0.8),file(borsuk_2,e9_3__borsuk_2),[file(borsuk_2,e9_3__borsuk_2)]]).

fof(d1_funct_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.9),axiom,file(funct_4,d1_funct_4)]).

fof(e1_3_3__borsuk_2,plain,(
    k1_relat_1(k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_subset_1,fc6_membered,rc1_funct_2,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,t1_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c2_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_pre_topc,dt_k2_xboole_0,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,d3_pre_topc,e10_3__borsuk_2,e2_3__borsuk_2,e9_3__borsuk_2,d1_funct_4]),
    [interesting(0.65),file(borsuk_2,e1_3_3__borsuk_2),[file(borsuk_2,e1_3_3__borsuk_2)]]).

fof(e2_3_3__borsuk_2,plain,(
    k2_pre_topc(c4_3__borsuk_2) = u1_struct_0(c4_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,rc1_subset_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,t3_subset,dt_k2_pre_topc,dt_u1_struct_0,dt_c4_3__borsuk_2,d3_pre_topc]),
    [interesting(0.65),file(borsuk_2,e2_3_3__borsuk_2),[file(borsuk_2,e2_3_3__borsuk_2)]]).

fof(e11_3__borsuk_2,plain,(
    k1_relat_1(k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)) = u1_struct_0(c4_3__borsuk_2) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[e1_3_3__borsuk_2,e2_3_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,e11_3__borsuk_2),[file(borsuk_2,e11_3__borsuk_2)]]).

fof(t4_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k2_relat_1(B),A)
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_relat_1(B),A)
          & m2_relset_1(B,k1_relat_1(B),A) ) ) ) ),
    file(funct_2,t4_funct_2),
    [interesting(0.9),axiom,file(funct_2,t4_funct_2)]).

fof(e15_3__borsuk_2,plain,
    ( v1_funct_1(k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2))
    & v1_funct_2(k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2),u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
    & m2_relset_1(k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2),u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,cc1_relset_1,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc3_struct_0,idempotence_k1_funct_4,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_relat_1,dt_m2_relset_1,dt_u1_struct_0,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,rc1_funct_1,t3_subset,e14_3__borsuk_2,e11_3__borsuk_2,t4_funct_2]),
    [interesting(0.8),file(borsuk_2,e15_3__borsuk_2),[file(borsuk_2,e15_3__borsuk_2)]]).

fof(dt_c8_3__borsuk_2,plain,
    ( v1_funct_1(c8_3__borsuk_2)
    & v1_funct_2(c8_3__borsuk_2,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
    & m2_relset_1(c8_3__borsuk_2,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,cc1_relset_1,fc1_struct_0,fc1_subset_1,rc1_funct_1,rc1_funct_2,rc3_struct_0,t3_subset,idempotence_k1_funct_4,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_m2_relset_1,dt_u1_struct_0,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,de_c8_3__borsuk_2,e15_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,c8_3__borsuk_2),[file(borsuk_2,c8_3__borsuk_2)]]).

fof(e16_3__borsuk_2,plain,(
    c8_3__borsuk_2 = k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,cc1_relset_1,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc3_struct_0,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,rc1_funct_1,idempotence_k1_funct_4,dt_k1_funct_4,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,e16_3__borsuk_2),[file(borsuk_2,e16_3__borsuk_2)]]).

fof(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_relat_1)]).

fof(redefinition_k5_pre_topc,definition,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => k5_pre_topc(A,B,C,D) = k10_relat_1(C,D) ) ),
    file(pre_topc,k5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k5_pre_topc)]).

fof(dt_k5_pre_topc,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
        & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
     => m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k5_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,k5_pre_topc)]).

fof(dh_c1_3_4__borsuk_2,definition,
    ( ( m1_subset_1(c1_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c2_3__borsuk_2)))
     => ( v4_pre_topc(c1_3_4__borsuk_2,c2_3__borsuk_2)
       => v4_pre_topc(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),c4_3__borsuk_2) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_3__borsuk_2)))
       => ( v4_pre_topc(A,c2_3__borsuk_2)
         => v4_pre_topc(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,A),c4_3__borsuk_2) ) ) ),
    introduced(definition,[new_symbol(c1_3_4__borsuk_2),file(borsuk_2,c1_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,c1_3_4__borsuk_2)]).

fof(e1_3_4__borsuk_2,assumption,(
    v4_pre_topc(c1_3_4__borsuk_2,c2_3__borsuk_2) ),
    introduced(assumption,[file(borsuk_2,e1_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,e1_3_4__borsuk_2)]).

fof(cc5_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & v2_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v2_t_0topsp(A) ) ) ) ),
    file(tsp_1,cc5_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc5_tsp_1)]).

fof(cc6_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_tdlat_3(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & v3_realset2(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v2_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A)
          & v2_t_0topsp(A) ) ) ) ),
    file(tsp_1,cc6_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc6_tsp_1)]).

fof(cc8_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_tdlat_3(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A)
          & v3_tdlat_3(A)
          & v4_tdlat_3(A)
          & v5_tdlat_3(A)
          & v2_t_0topsp(A) ) ) ) ),
    file(tsp_1,cc8_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc8_tsp_1)]).

fof(cc9_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & v3_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & ~ v2_t_0topsp(A) ) ) ) ),
    file(tsp_1,cc9_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc9_tsp_1)]).

fof(cc10_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A)
          & ~ v2_tdlat_3(A)
          & ~ v3_tdlat_3(A) ) ) ) ),
    file(tsp_1,cc10_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc10_tsp_1)]).

fof(cc1_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v2_t_0topsp(A) ) ) ) ),
    file(tsp_1,cc1_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc1_tsp_1)]).

fof(cc3_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v1_tdlat_3(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A) ) ) ) ),
    file(tsp_1,cc3_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc3_tsp_1)]).

fof(cc7_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v2_tdlat_3(A) ) ) ) ),
    file(tsp_1,cc7_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc7_tsp_1)]).

fof(cc2_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & ~ v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A) ) ) ) ),
    file(tsp_1,cc2_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc2_tsp_1)]).

fof(cc4_tsp_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & ~ v2_t_0topsp(A) )
       => ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_pre_topc(A)
          & ~ v1_tdlat_3(A) ) ) ) ),
    file(tsp_1,cc4_tsp_1),
    [interesting(0.9),axiom,file(tsp_1,cc4_tsp_1)]).

fof(cc4_yellow_8,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_yellow_8(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v2_t_0topsp(A) ) ) ) ),
    file(yellow_8,cc4_yellow_8),
    [interesting(0.9),axiom,file(yellow_8,cc4_yellow_8)]).

fof(rc2_yellow_8,theorem,(
    ? [A] : 
      ( l1_pre_topc(A)
      & ~ v3_struct_0(A)
      & v2_pre_topc(A)
      & v3_yellow_8(A) ) ),
    file(yellow_8,rc2_yellow_8),
    [interesting(0.9),axiom,file(yellow_8,rc2_yellow_8)]).

fof(commutativity_k4_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(idempotence_k4_subset_1,theorem,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(redefinition_k4_subset_1,definition,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    [interesting(0.9),axiom,file(subset_1,k4_subset_1)]).

fof(dt_c1_3_4__borsuk_2,assumption,(
    m1_subset_1(c1_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c2_3__borsuk_2))) ),
    introduced(assumption,[file(borsuk_2,c1_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,c1_3_4__borsuk_2)]).

fof(de_c2_3_4__borsuk_2,definition,(
    c2_3_4__borsuk_2 = k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2) ),
    introduced(definition,[new_symbol(c2_3_4__borsuk_2),file(borsuk_2,c2_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,c2_3_4__borsuk_2)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t7_xboole_1)]).

fof(e9_3_4__borsuk_2,plain,
    ( r1_tarski(k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))
    & r1_tarski(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c4_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,dt_k2_zfmisc_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k2_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,t3_subset,d3_pre_topc,e2_3__borsuk_2,t7_xboole_1]),
    [interesting(0.65),file(borsuk_2,e9_3_4__borsuk_2),[file(borsuk_2,e9_3_4__borsuk_2)]]).

fof(e10_3_4__borsuk_2,plain,(
    r1_tarski(k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c4_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,dt_k2_zfmisc_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,reflexivity_r1_tarski,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,t3_subset,d3_pre_topc,e9_3_4__borsuk_2,t1_xboole_1]),
    [interesting(0.65),file(borsuk_2,e10_3_4__borsuk_2),[file(borsuk_2,e10_3_4__borsuk_2)]]).

fof(e11_3_4__borsuk_2,plain,(
    m1_subset_1(k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2),k1_zfmisc_1(u1_struct_0(c4_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc6_pre_topc,rc7_pre_topc,t1_subset,t4_subset,t5_subset,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,fc1_subset_1,t3_subset,d3_pre_topc,e10_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,e11_3_4__borsuk_2),[file(borsuk_2,e11_3_4__borsuk_2)]]).

fof(dt_c2_3_4__borsuk_2,plain,(
    m1_subset_1(c2_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c4_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,fc1_subset_1,t3_subset,de_c2_3_4__borsuk_2,e11_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,c2_3_4__borsuk_2),[file(borsuk_2,c2_3_4__borsuk_2)]]).

fof(de_c3_3_4__borsuk_2,definition,(
    c3_3_4__borsuk_2 = k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2) ),
    introduced(definition,[new_symbol(c3_3_4__borsuk_2),file(borsuk_2,c3_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,c3_3_4__borsuk_2)]).

fof(e12_3_4__borsuk_2,plain,
    ( r1_tarski(k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))
    & r1_tarski(k2_pre_topc(c3_3__borsuk_2),k2_pre_topc(c4_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_boole,t1_subset,t4_subset,t5_subset,dt_k2_zfmisc_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k2_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,t3_subset,d3_pre_topc,e2_3__borsuk_2,t7_xboole_1]),
    [interesting(0.65),file(borsuk_2,e12_3_4__borsuk_2),[file(borsuk_2,e12_3_4__borsuk_2)]]).

fof(e13_3_4__borsuk_2,plain,(
    r1_tarski(k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c4_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,dt_k2_zfmisc_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,reflexivity_r1_tarski,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,t3_subset,d3_pre_topc,e12_3_4__borsuk_2,t1_xboole_1]),
    [interesting(0.65),file(borsuk_2,e13_3_4__borsuk_2),[file(borsuk_2,e13_3_4__borsuk_2)]]).

fof(e14_3_4__borsuk_2,plain,(
    m1_subset_1(k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2),k1_zfmisc_1(u1_struct_0(c4_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc6_pre_topc,rc7_pre_topc,t1_subset,t4_subset,t5_subset,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k2_pre_topc,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,fc1_subset_1,t3_subset,d3_pre_topc,e13_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,e14_3_4__borsuk_2),[file(borsuk_2,e14_3_4__borsuk_2)]]).

fof(dt_c3_3_4__borsuk_2,plain,(
    m1_subset_1(c3_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c4_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,e2_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,fc1_subset_1,t3_subset,de_c3_3_4__borsuk_2,e14_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,c3_3_4__borsuk_2),[file(borsuk_2,c3_3_4__borsuk_2)]]).

fof(cc3_yellow_8,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_compts_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & v3_yellow_8(A) ) ) ) ),
    file(yellow_8,cc3_yellow_8),
    [interesting(0.9),axiom,file(yellow_8,cc3_yellow_8)]).

fof(de_c4_3_4__borsuk_2,definition,(
    c4_3_4__borsuk_2 = k4_subset_1(u1_struct_0(c4_3__borsuk_2),c2_3_4__borsuk_2,c3_3_4__borsuk_2) ),
    introduced(definition,[new_symbol(c4_3_4__borsuk_2),file(borsuk_2,c4_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,c4_3_4__borsuk_2)]).

fof(e15_3_4__borsuk_2,plain,(
    m1_subset_1(k4_subset_1(u1_struct_0(c4_3__borsuk_2),c2_3_4__borsuk_2,c3_3_4__borsuk_2),k1_zfmisc_1(u1_struct_0(c4_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,e2_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc1_funct_2,cc1_relset_1,cc1_xreal_0,cc2_funct_1,cc2_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_xreal_0,rc2_funct_1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_xboole_0,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,redefinition_k5_pre_topc,dt_k2_xboole_0,dt_k5_pre_topc,dt_l1_pre_topc,dt_l1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_subset_1,idempotence_k4_subset_1,existence_m1_subset_1,redefinition_k4_subset_1,dt_k1_zfmisc_1,dt_k4_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c2_3_4__borsuk_2,dt_c3_3_4__borsuk_2,dt_c4_3__borsuk_2,de_c2_3_4__borsuk_2,de_c3_3_4__borsuk_2,fc1_subset_1,t3_subset]),
    [interesting(0.65),file(borsuk_2,e15_3_4__borsuk_2),[file(borsuk_2,e15_3_4__borsuk_2)]]).

fof(dt_c4_3_4__borsuk_2,plain,(
    m1_subset_1(c4_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c4_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,e2_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc1_funct_2,cc1_relset_1,cc1_xreal_0,cc2_funct_1,cc2_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_xreal_0,rc2_funct_1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_xboole_0,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,redefinition_k5_pre_topc,dt_k2_xboole_0,dt_k5_pre_topc,dt_l1_pre_topc,dt_l1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_subset_1,idempotence_k4_subset_1,existence_m1_subset_1,redefinition_k4_subset_1,dt_k1_zfmisc_1,dt_k4_subset_1,dt_m1_subset_1,dt_u1_struct_0,dt_c2_3_4__borsuk_2,dt_c3_3_4__borsuk_2,dt_c4_3__borsuk_2,de_c2_3_4__borsuk_2,de_c3_3_4__borsuk_2,fc1_subset_1,t3_subset,de_c4_3_4__borsuk_2,e15_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,c4_3_4__borsuk_2),[file(borsuk_2,c4_3_4__borsuk_2)]]).

fof(cc1_pre_topc,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => v2_pre_topc(B) ) ) ),
    file(pre_topc,cc1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,cc1_pre_topc)]).

fof(existence_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ? [B] : m1_pre_topc(B,A) ) ),
    file(pre_topc,m1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]).

fof(dt_m1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => l1_pre_topc(B) ) ) ),
    file(pre_topc,m1_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,m1_pre_topc)]).

fof(de_c5_3_4__borsuk_2,definition,(
    c5_3_4__borsuk_2 = k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2) ),
    introduced(definition,[new_symbol(c5_3_4__borsuk_2),file(borsuk_2,c5_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,c5_3_4__borsuk_2)]).

fof(e16_3_4__borsuk_2,plain,(
    m1_subset_1(k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2),k1_zfmisc_1(u1_struct_0(c1_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,fc1_subset_1,t3_subset]),
    [interesting(0.65),file(borsuk_2,e16_3_4__borsuk_2),[file(borsuk_2,e16_3_4__borsuk_2)]]).

fof(dt_c5_3_4__borsuk_2,plain,(
    m1_subset_1(c5_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c1_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,fc1_subset_1,t3_subset,de_c5_3_4__borsuk_2,e16_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,c5_3_4__borsuk_2),[file(borsuk_2,c5_3_4__borsuk_2)]]).

fof(de_c6_3_4__borsuk_2,definition,(
    c6_3_4__borsuk_2 = k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2) ),
    introduced(definition,[new_symbol(c6_3_4__borsuk_2),file(borsuk_2,c6_3_4__borsuk_2)]),
    [interesting(0.65),axiom,file(borsuk_2,c6_3_4__borsuk_2)]).

fof(e17_3_4__borsuk_2,plain,(
    m1_subset_1(k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2),k1_zfmisc_1(u1_struct_0(c3_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,fc1_subset_1,t3_subset]),
    [interesting(0.65),file(borsuk_2,e17_3_4__borsuk_2),[file(borsuk_2,e17_3_4__borsuk_2)]]).

fof(dt_c6_3_4__borsuk_2,plain,(
    m1_subset_1(c6_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c3_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,fc1_subset_1,t3_subset,de_c6_3_4__borsuk_2,e17_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,c6_3_4__borsuk_2),[file(borsuk_2,c6_3_4__borsuk_2)]]).

fof(d12_pre_topc,definition,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [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)) )
             => ( v5_pre_topc(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( v4_pre_topc(D,B)
                     => v4_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ),
    file(pre_topc,d12_pre_topc),
    [interesting(0.9),axiom,file(pre_topc,d12_pre_topc)]).

fof(e18_3_4__borsuk_2,plain,
    ( v4_pre_topc(c5_3_4__borsuk_2,c1_3__borsuk_2)
    & v4_pre_topc(c6_3_4__borsuk_2,c3_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,e6_3__borsuk_2,e7_3__borsuk_2,e1_3_4__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_borsuk_1,rc2_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_relset_1,dt_k10_relat_1,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_pre_topc,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_l1_pre_topc,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3__borsuk_2,dt_c5_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c6_3_4__borsuk_2,de_c5_3_4__borsuk_2,de_c6_3_4__borsuk_2,fc1_subset_1,t3_subset,e6_3__borsuk_2,e7_3__borsuk_2,e1_3_4__borsuk_2,d12_pre_topc]),
    [interesting(0.65),file(borsuk_2,e18_3_4__borsuk_2),[file(borsuk_2,e18_3_4__borsuk_2)]]).

fof(t17_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v2_compts_1(A)
              & v4_pre_topc(B,A) )
           => v6_compts_1(B,A) ) ) ) ),
    file(compts_1,t17_compts_1),
    [interesting(0.9),axiom,file(compts_1,t17_compts_1)]).

fof(e19_3_4__borsuk_2,plain,
    ( v6_compts_1(c5_3_4__borsuk_2,c1_3__borsuk_2)
    & v6_compts_1(c6_3_4__borsuk_2,c3_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,e6_3__borsuk_2,e7_3__borsuk_2,e1_3_4__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc1_funct_2,cc1_relset_1,cc1_xreal_0,cc2_funct_1,cc2_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_xreal_0,rc2_funct_1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_xboole_0,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,redefinition_k5_pre_topc,dt_k5_pre_topc,dt_l1_struct_0,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3_4__borsuk_2,dt_c6_3_4__borsuk_2,de_c5_3_4__borsuk_2,de_c6_3_4__borsuk_2,fc1_subset_1,t3_subset,e18_3_4__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,t17_compts_1]),
    [interesting(0.65),file(borsuk_2,e19_3_4__borsuk_2),[file(borsuk_2,e19_3_4__borsuk_2)]]).

fof(t42_borsuk_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_pre_topc(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( C = D
                   => ( v6_compts_1(C,A)
                    <=> v6_compts_1(D,B) ) ) ) ) ) ) ),
    file(borsuk_1,t42_borsuk_1),
    [interesting(0.9),axiom,file(borsuk_1,t42_borsuk_1)]).

fof(e20_3_4__borsuk_2,plain,
    ( v6_compts_1(c2_3_4__borsuk_2,c4_3__borsuk_2)
    & v6_compts_1(c3_3_4__borsuk_2,c4_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([e2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c1_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,e6_3__borsuk_2,e7_3__borsuk_2,e1_3_4__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc1_funct_2,cc1_relset_1,cc1_xreal_0,cc2_funct_1,cc2_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_xreal_0,rc2_funct_1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_xboole_0,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_l1_struct_0,redefinition_k5_pre_topc,dt_k5_pre_topc,dt_l1_struct_0,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc1_pre_topc,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_m1_pre_topc,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_m1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c2_3_4__borsuk_2,dt_c3_3__borsuk_2,dt_c3_3_4__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3_4__borsuk_2,dt_c6_3_4__borsuk_2,de_c2_3_4__borsuk_2,de_c3_3_4__borsuk_2,de_c5_3_4__borsuk_2,de_c6_3_4__borsuk_2,fc1_subset_1,t3_subset,e19_3_4__borsuk_2,e1_3__borsuk_2,t42_borsuk_1]),
    [interesting(0.65),file(borsuk_2,e20_3_4__borsuk_2),[file(borsuk_2,e20_3_4__borsuk_2)]]).

fof(t19_compts_1,theorem,(
    ! [A] : 
      ( l1_pre_topc(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v6_compts_1(B,A)
                  & v6_compts_1(C,A) )
               => v6_compts_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ),
    file(compts_1,t19_compts_1),
    [interesting(0.9),axiom,file(compts_1,t19_compts_1)]).

fof(e21_3_4__borsuk_2,plain,(
    v6_compts_1(c4_3_4__borsuk_2,c4_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([e2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c1_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,e6_3__borsuk_2,e7_3__borsuk_2,e1_3_4__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,dt_k2_zfmisc_1,cc1_funct_2,cc1_relset_1,cc1_xreal_0,cc2_funct_1,cc2_xreal_0,cc7_xreal_0,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_xreal_0,rc2_funct_1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_xboole_0,dt_m1_relset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,t1_boole,t1_subset,t4_subset,t5_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,existence_l1_struct_0,redefinition_k5_pre_topc,dt_k2_xboole_0,dt_k5_pre_topc,dt_l1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_subset_1,idempotence_k4_subset_1,existence_l1_pre_topc,existence_m1_subset_1,redefinition_k4_subset_1,dt_k1_zfmisc_1,dt_k4_subset_1,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c2_3_4__borsuk_2,dt_c3_3_4__borsuk_2,dt_c4_3__borsuk_2,dt_c4_3_4__borsuk_2,de_c2_3_4__borsuk_2,de_c3_3_4__borsuk_2,de_c4_3_4__borsuk_2,fc1_subset_1,t3_subset,e20_3_4__borsuk_2,t19_compts_1]),
    [interesting(0.65),file(borsuk_2,e21_3_4__borsuk_2),[file(borsuk_2,e21_3_4__borsuk_2)]]).

fof(fc27_membered,theorem,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(A,B)) ) ),
    file(membered,fc27_membered),
    [interesting(0.9),axiom,file(membered,fc27_membered)]).

fof(fc28_membered,theorem,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k3_xboole_0(B,A)) ) ),
    file(membered,fc28_membered),
    [interesting(0.9),axiom,file(membered,fc28_membered)]).

fof(fc29_membered,theorem,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc29_membered),
    [interesting(0.9),axiom,file(membered,fc29_membered)]).

fof(fc30_membered,theorem,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc30_membered),
    [interesting(0.9),axiom,file(membered,fc30_membered)]).

fof(fc31_membered,theorem,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc31_membered),
    [interesting(0.9),axiom,file(membered,fc31_membered)]).

fof(fc32_membered,theorem,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc32_membered),
    [interesting(0.9),axiom,file(membered,fc32_membered)]).

fof(fc33_membered,theorem,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc33_membered),
    [interesting(0.9),axiom,file(membered,fc33_membered)]).

fof(fc34_membered,theorem,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc34_membered),
    [interesting(0.9),axiom,file(membered,fc34_membered)]).

fof(fc35_membered,theorem,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(A,B))
        & v2_membered(k3_xboole_0(A,B))
        & v3_membered(k3_xboole_0(A,B))
        & v4_membered(k3_xboole_0(A,B))
        & v5_membered(k3_xboole_0(A,B)) ) ) ),
    file(membered,fc35_membered),
    [interesting(0.9),axiom,file(membered,fc35_membered)]).

fof(fc36_membered,theorem,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k3_xboole_0(B,A))
        & v2_membered(k3_xboole_0(B,A))
        & v3_membered(k3_xboole_0(B,A))
        & v4_membered(k3_xboole_0(B,A))
        & v5_membered(k3_xboole_0(B,A)) ) ) ),
    file(membered,fc36_membered),
    [interesting(0.9),axiom,file(membered,fc36_membered)]).

fof(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

fof(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dh_c1_3_4_4__borsuk_2,definition,
    ( ( ( r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
       => r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) )
      & ( r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2))
       => r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ) )
   => ! [A] : 
        ( ( r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
         => r2_hidden(A,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) )
        & ( r2_hidden(A,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2))
         => r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ) ) ),
    introduced(definition,[new_symbol(c1_3_4_4__borsuk_2),file(borsuk_2,c1_3_4_4__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,c1_3_4_4__borsuk_2)]).

fof(e1_3_4_4_1__borsuk_2,assumption,(
    r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    introduced(assumption,[file(borsuk_2,e1_3_4_4_1__borsuk_2)]),
    [interesting(0.35),axiom,file(borsuk_2,e1_3_4_4_1__borsuk_2)]).

fof(dt_c1_3_4_4__borsuk_2,assumption,(
    $true ),
    introduced(assumption,[file(borsuk_2,c1_3_4_4__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,c1_3_4_4__borsuk_2)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d3_xboole_0)]).

fof(e2_3_4_4_1__borsuk_2,plain,
    ( r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2))
    & r2_hidden(c1_3_4_4__borsuk_2,k1_relat_1(c6_3__borsuk_2))
    & r2_hidden(c1_3_4_4__borsuk_2,k2_pre_topc(c3_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,e1_3_4_4_1__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c1_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,t2_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c5_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k1_relat_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e1_3_4_4_1__borsuk_2,e10_3__borsuk_2,d3_xboole_0]),
    [interesting(0.35),file(borsuk_2,e2_3_4_4_1__borsuk_2),[file(borsuk_2,e2_3_4_4_1__borsuk_2)]]).

fof(d13_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( r2_hidden(D,k1_relat_1(A))
                & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ),
    file(funct_1,d13_funct_1),
    [interesting(0.9),axiom,file(funct_1,d13_funct_1)]).

fof(t14_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.9),axiom,file(funct_4,t14_funct_4)]).

fof(e3_3_4_4_1__borsuk_2,plain,
    ( r2_hidden(k1_funct_1(c8_3__borsuk_2,c1_3_4_4__borsuk_2),c1_3_4__borsuk_2)
    & r2_hidden(c1_3_4_4__borsuk_2,k1_relat_1(c6_3__borsuk_2))
    & k1_funct_1(c6_3__borsuk_2,c1_3_4_4__borsuk_2) = k1_funct_1(c8_3__borsuk_2,c1_3_4_4__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,e1_3_4_4_1__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c1_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c5_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_pre_topc,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,d3_pre_topc,e2_3_4_4_1__borsuk_2,d13_funct_1,t14_funct_4]),
    [interesting(0.35),file(borsuk_2,e3_3_4_4_1__borsuk_2),[file(borsuk_2,e3_3_4_4_1__borsuk_2)]]).

fof(e4_3_4_4_1__borsuk_2,plain,(
    r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,e1_3_4_4_1__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c1_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,e3_3_4_4_1__borsuk_2,d13_funct_1]),
    [interesting(0.35),file(borsuk_2,e4_3_4_4_1__borsuk_2),[file(borsuk_2,e4_3_4_4_1__borsuk_2)]]).

fof(i2_3_4_4_1__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i2_3_4_4_1__borsuk_2)]),
    [interesting(0.35),trivial,file(borsuk_2,i2_3_4_4_1__borsuk_2)]).

fof(i1_3_4_4_1__borsuk_2,plain,(
    r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,e1_3_4_4_1__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e4_3_4_4_1__borsuk_2,i2_3_4_4_1__borsuk_2]),
    [interesting(0.35),file(borsuk_2,i1_3_4_4_1__borsuk_2),[file(borsuk_2,i1_3_4_4_1__borsuk_2)]]).

fof(e1_3_4_4__borsuk_2,plain,
    ( r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
   => r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e1_3_4_4_1__borsuk_2])],[e1_3_4_4_1__borsuk_2,i1_3_4_4_1__borsuk_2]),
    [interesting(0.5),file(borsuk_2,e1_3_4_4__borsuk_2),[file(borsuk_2,e1_3_4_4__borsuk_2)]]).

fof(e2_3_4_4__borsuk_2,assumption,(
    r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,e2_3_4_4__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,e2_3_4_4__borsuk_2)]).

fof(e3_3_4_4__borsuk_2,plain,
    ( r2_hidden(c1_3_4_4__borsuk_2,k1_relat_1(c6_3__borsuk_2))
    & r2_hidden(k1_funct_1(c6_3__borsuk_2,c1_3_4_4__borsuk_2),c1_3_4__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,e2_3_4_4__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c6_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,e2_3_4_4__borsuk_2,d13_funct_1]),
    [interesting(0.5),file(borsuk_2,e3_3_4_4__borsuk_2),[file(borsuk_2,e3_3_4_4__borsuk_2)]]).

fof(t167_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k10_relat_1(B,A),k1_relat_1(B)) ) ),
    file(relat_1,t167_relat_1),
    [interesting(0.9),axiom,file(relat_1,t167_relat_1)]).

fof(e2_3_4__borsuk_2,plain,
    ( r1_tarski(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k1_relat_1(c8_3__borsuk_2))
    & k1_relat_1(c8_3__borsuk_2) = k2_xboole_0(k1_relat_1(c5_3__borsuk_2),k1_relat_1(c6_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,t1_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_xboole_0,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t3_subset,t7_boole,d1_funct_4,t167_relat_1]),
    [interesting(0.65),file(borsuk_2,e2_3_4__borsuk_2),[file(borsuk_2,e2_3_4__borsuk_2)]]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d2_xboole_0)]).

fof(e4_3_4_4__borsuk_2,plain,
    ( r2_hidden(c1_3_4_4__borsuk_2,k1_relat_1(c8_3__borsuk_2))
    & r2_hidden(c1_3_4_4__borsuk_2,k2_pre_topc(c3_3__borsuk_2))
    & r2_hidden(k1_funct_1(c8_3__borsuk_2,c1_3_4_4__borsuk_2),c1_3_4__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_4__borsuk_2,e2_3_4_4__borsuk_2,dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,t1_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_pre_topc,dt_k2_xboole_0,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t3_subset,t7_boole,d3_pre_topc,e3_3_4_4__borsuk_2,e10_3__borsuk_2,e2_3_4__borsuk_2,t14_funct_4,d2_xboole_0]),
    [interesting(0.5),file(borsuk_2,e4_3_4_4__borsuk_2),[file(borsuk_2,e4_3_4_4__borsuk_2)]]).

fof(e5_3_4_4__borsuk_2,plain,
    ( r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2))
    & r2_hidden(c1_3_4_4__borsuk_2,k2_pre_topc(c3_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_4__borsuk_2,e2_3_4_4__borsuk_2,dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c1_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_pre_topc,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,d3_pre_topc,e4_3_4_4__borsuk_2,d13_funct_1]),
    [interesting(0.5),file(borsuk_2,e5_3_4_4__borsuk_2),[file(borsuk_2,e5_3_4_4__borsuk_2)]]).

fof(e6_3_4_4__borsuk_2,plain,(
    r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_4__borsuk_2,e2_3_4_4__borsuk_2,dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c1_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc6_pre_topc,rc7_pre_topc,t2_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3_4__borsuk_2,dt_c1_3_4_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e5_3_4_4__borsuk_2,d3_xboole_0]),
    [interesting(0.5),file(borsuk_2,e6_3_4_4__borsuk_2),[file(borsuk_2,e6_3_4_4__borsuk_2)]]).

fof(i4_3_4_4__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i4_3_4_4__borsuk_2)]),
    [interesting(0.5),trivial,file(borsuk_2,i4_3_4_4__borsuk_2)]).

fof(i3_3_4_4__borsuk_2,plain,(
    r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4_4__borsuk_2,e2_3_4_4__borsuk_2,dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[e6_3_4_4__borsuk_2,i4_3_4_4__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i3_3_4_4__borsuk_2),[file(borsuk_2,i3_3_4_4__borsuk_2)]]).

fof(i2_3_4_4__borsuk_2,plain,
    ( r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2))
   => r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4_4__borsuk_2,dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2]),discharge_asm(discharge,[e2_3_4_4__borsuk_2])],[e2_3_4_4__borsuk_2,i3_3_4_4__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i2_3_4_4__borsuk_2),[file(borsuk_2,i2_3_4_4__borsuk_2)]]).

fof(i1_3_4_4__borsuk_2,plain,
    ( ( r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
     => r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) )
    & ( r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2))
     => r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4_4__borsuk_2,dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[e1_3_4_4__borsuk_2,i2_3_4_4__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i1_3_4_4__borsuk_2),[file(borsuk_2,i1_3_4_4__borsuk_2)]]).

fof(i1_3_4_4_tmp__borsuk_2,plain,
    ( ( r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
     => r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) )
    & ( r2_hidden(c1_3_4_4__borsuk_2,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2))
     => r2_hidden(c1_3_4_4__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2]),discharge_asm(discharge,[dt_c1_3_4_4__borsuk_2])],[dt_c1_3_4_4__borsuk_2,i1_3_4_4__borsuk_2]),
    [interesting(0.65),e7_3_4__borsuk_2]).

fof(e7_3_4__borsuk_2,plain,(
    ! [A] : 
      ( ( r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
       => r2_hidden(A,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) )
      & ( r2_hidden(A,k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2))
       => r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[i1_3_4_4_tmp__borsuk_2,dh_c1_3_4_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,e7_3_4__borsuk_2),[file(borsuk_2,e7_3_4__borsuk_2)]]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t28_xboole_1)]).

fof(e1_3_4_1__borsuk_2,plain,(
    k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2) = k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,e2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_boole,t1_subset,t2_boole,t4_subset,t5_subset,dt_k2_zfmisc_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_1,rc1_funct_2,rc3_struct_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,redefinition_k5_pre_topc,dt_k1_relat_1,dt_k2_pre_topc,dt_k2_xboole_0,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t3_subset,d3_pre_topc,e2_3_4__borsuk_2,e9_3__borsuk_2,e10_3__borsuk_2,t28_xboole_1]),
    [interesting(0.5),file(borsuk_2,e1_3_4_1__borsuk_2),[file(borsuk_2,e1_3_4_1__borsuk_2)]]).

fof(t23_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t23_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t23_xboole_1)]).

fof(e2_3_4_1__borsuk_2,plain,(
    k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) = k2_xboole_0(k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)),k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_boole,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,dt_k2_zfmisc_1,cc15_membered,cc1_funct_1,cc1_relset_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc3_struct_0,t3_subset,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k2_xboole_0,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,d3_pre_topc,t23_xboole_1]),
    [interesting(0.5),file(borsuk_2,e2_3_4_1__borsuk_2),[file(borsuk_2,e2_3_4_1__borsuk_2)]]).

fof(e3_3_4__borsuk_2,plain,(
    k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2) = k2_xboole_0(k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)),k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2])],[e1_3_4_1__borsuk_2,e2_3_4_1__borsuk_2]),
    [interesting(0.65),file(borsuk_2,e3_3_4__borsuk_2),[file(borsuk_2,e3_3_4__borsuk_2)]]).

fof(dh_c1_3_4_3__borsuk_2,definition,
    ( ( ( r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)))
       => r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) )
      & ( r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2))
       => r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ) )
   => ! [A] : 
        ( ( r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)))
         => r2_hidden(A,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) )
        & ( r2_hidden(A,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2))
         => r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ) ) ),
    introduced(definition,[new_symbol(c1_3_4_3__borsuk_2),file(borsuk_2,c1_3_4_3__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,c1_3_4_3__borsuk_2)]).

fof(e1_3_4_3_1__borsuk_2,assumption,(
    r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ),
    introduced(assumption,[file(borsuk_2,e1_3_4_3_1__borsuk_2)]),
    [interesting(0.35),axiom,file(borsuk_2,e1_3_4_3_1__borsuk_2)]).

fof(dt_c1_3_4_3__borsuk_2,assumption,(
    $true ),
    introduced(assumption,[file(borsuk_2,c1_3_4_3__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,c1_3_4_3__borsuk_2)]).

fof(e2_3_4_3_1__borsuk_2,plain,
    ( r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2))
    & r2_hidden(c1_3_4_3__borsuk_2,k1_relat_1(c5_3__borsuk_2))
    & r2_hidden(c1_3_4_3__borsuk_2,k2_pre_topc(c1_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e2_3__borsuk_2,dt_c4_3__borsuk_2,e1_3_4_3_1__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c3_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,t2_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k1_relat_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e1_3_4_3_1__borsuk_2,e9_3__borsuk_2,d3_xboole_0]),
    [interesting(0.35),file(borsuk_2,e2_3_4_3_1__borsuk_2),[file(borsuk_2,e2_3_4_3_1__borsuk_2)]]).

fof(dh_c1_3_4_2__borsuk_2,definition,
    ( ( r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c1_3__borsuk_2))
     => k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) )
   => ! [A] : 
        ( r2_hidden(A,k2_pre_topc(c1_3__borsuk_2))
       => k1_funct_1(c8_3__borsuk_2,A) = k1_funct_1(c5_3__borsuk_2,A) ) ),
    introduced(definition,[new_symbol(c1_3_4_2__borsuk_2),file(borsuk_2,c1_3_4_2__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,c1_3_4_2__borsuk_2)]).

fof(e1_3_4_2__borsuk_2,assumption,(
    r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c1_3__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,e1_3_4_2__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,e1_3_4_2__borsuk_2)]).

fof(dt_c1_3_4_2__borsuk_2,assumption,(
    $true ),
    introduced(assumption,[file(borsuk_2,c1_3_4_2__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,c1_3_4_2__borsuk_2)]).

fof(e1_3_4_2_1_1_1__borsuk_2,assumption,(
    r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c3_3__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,e1_3_4_2_1_1_1__borsuk_2)]),
    [interesting(0.05),axiom,file(borsuk_2,e1_3_4_2_1_1_1__borsuk_2)]).

fof(e2_3_4_2_1_1_1__borsuk_2,plain,(
    r2_hidden(c1_3_4_2__borsuk_2,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2,e1_3_4_2_1_1_1__borsuk_2,e1_3_4_2__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc6_membered,rc1_membered,rc6_pre_topc,rc7_pre_topc,t2_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,cc15_membered,cc1_funct_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k2_pre_topc,dt_k3_xboole_0,dt_c1_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e1_3_4_2_1_1_1__borsuk_2,e1_3_4_2__borsuk_2,d3_xboole_0]),
    [interesting(0.05),file(borsuk_2,e2_3_4_2_1_1_1__borsuk_2),[file(borsuk_2,e2_3_4_2_1_1_1__borsuk_2)]]).

fof(e3_3_4_2_1_1_1__borsuk_2,plain,(
    k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c6_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c1_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2,e1_3_4_2_1_1_1__borsuk_2,e1_3_4_2__borsuk_2,e8_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc4_subset_1,fc6_membered,rc1_funct_2,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,t2_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c2_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_pre_topc,dt_k3_xboole_0,dt_c1_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e2_3_4_2_1_1_1__borsuk_2,e8_3__borsuk_2]),
    [interesting(0.05),file(borsuk_2,e3_3_4_2_1_1_1__borsuk_2),[file(borsuk_2,e3_3_4_2_1_1_1__borsuk_2)]]).

fof(e4_3_4_2_1_1_1__borsuk_2,plain,(
    k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([e2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c1_3_4_2__borsuk_2,e1_3_4_2__borsuk_2,e8_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e1_3_4_2_1_1_1__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc4_subset_1,fc6_membered,rc1_funct_2,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_pre_topc,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,d3_pre_topc,e3_3_4_2_1_1_1__borsuk_2,e10_3__borsuk_2,e1_3_4_2_1_1_1__borsuk_2,t14_funct_4]),
    [interesting(0.05),file(borsuk_2,e4_3_4_2_1_1_1__borsuk_2),[file(borsuk_2,e4_3_4_2_1_1_1__borsuk_2)]]).

fof(i2_3_4_2_1_1_1__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i2_3_4_2_1_1_1__borsuk_2)]),
    [interesting(0.05),trivial,file(borsuk_2,i2_3_4_2_1_1_1__borsuk_2)]).

fof(i1_3_4_2_1_1_1__borsuk_2,plain,(
    k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(conclusion,[status(thm),assumptions([e2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c1_3_4_2__borsuk_2,e1_3_4_2__borsuk_2,e8_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2,e1_3_4_2_1_1_1__borsuk_2])],[e4_3_4_2_1_1_1__borsuk_2,i2_3_4_2_1_1_1__borsuk_2]),
    [interesting(0.05),file(borsuk_2,i1_3_4_2_1_1_1__borsuk_2),[file(borsuk_2,i1_3_4_2_1_1_1__borsuk_2)]]).

fof(i1_3_4_2_1_1__borsuk_2,plain,
    ( r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c3_3__borsuk_2))
   => k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(discharge_asm,[status(thm),assumptions([e2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c1_3_4_2__borsuk_2,e1_3_4_2__borsuk_2,e8_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e1_3_4_2_1_1_1__borsuk_2])],[e1_3_4_2_1_1_1__borsuk_2,i1_3_4_2_1_1_1__borsuk_2]),
    [interesting(0.2),file(borsuk_2,i1_3_4_2_1_1__borsuk_2),[file(borsuk_2,i1_3_4_2_1_1__borsuk_2)]]).

fof(e1_3_4_2_1_1_2__borsuk_2,assumption,(
    ~ r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c3_3__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,e1_3_4_2_1_1_2__borsuk_2)]),
    [interesting(0.05),axiom,file(borsuk_2,e1_3_4_2_1_1_2__borsuk_2)]).

fof(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.9),axiom,file(funct_4,t12_funct_4)]).

fof(e2_3_4_2_1_1_2__borsuk_2,plain,(
    k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_2__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,e1_3_4_2_1_1_2__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_funct_2,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,fc4_subset_1,fc6_membered,rc1_funct_2,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_pre_topc,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,d3_pre_topc,e1_3_4_2_1_1_2__borsuk_2,e10_3__borsuk_2,t12_funct_4]),
    [interesting(0.05),file(borsuk_2,e2_3_4_2_1_1_2__borsuk_2),[file(borsuk_2,e2_3_4_2_1_1_2__borsuk_2)]]).

fof(i2_3_4_2_1_1_2__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i2_3_4_2_1_1_2__borsuk_2)]),
    [interesting(0.05),trivial,file(borsuk_2,i2_3_4_2_1_1_2__borsuk_2)]).

fof(i1_3_4_2_1_1_2__borsuk_2,plain,(
    k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4_2__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,e1_3_4_2_1_1_2__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e2_3_4_2_1_1_2__borsuk_2,i2_3_4_2_1_1_2__borsuk_2]),
    [interesting(0.05),file(borsuk_2,i1_3_4_2_1_1_2__borsuk_2),[file(borsuk_2,i1_3_4_2_1_1_2__borsuk_2)]]).

fof(i2_3_4_2_1_1__borsuk_2,plain,
    ( ~ r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c3_3__borsuk_2))
   => k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4_2__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e1_3_4_2_1_1_2__borsuk_2])],[e1_3_4_2_1_1_2__borsuk_2,i1_3_4_2_1_1_2__borsuk_2]),
    [interesting(0.2),file(borsuk_2,i2_3_4_2_1_1__borsuk_2),[file(borsuk_2,i2_3_4_2_1_1__borsuk_2)]]).

fof(e1_3_4_2_1_1__borsuk_2,plain,(
    ~ ( ~ r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c3_3__borsuk_2))
      & r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c3_3__borsuk_2)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc6_pre_topc,rc7_pre_topc,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,cc15_membered,cc1_funct_1,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_pre_topc,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc]),
    [interesting(0.2),file(borsuk_2,e1_3_4_2_1_1__borsuk_2),[file(borsuk_2,e1_3_4_2_1_1__borsuk_2)]]).

fof(e2_3_4_2__borsuk_2,plain,(
    k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(percases,[status(thm),assumptions([e1_3_4_2__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2])],[i1_3_4_2_1_1__borsuk_2,i2_3_4_2_1_1__borsuk_2,e1_3_4_2_1_1__borsuk_2]),
    [interesting(0.5),file(borsuk_2,e2_3_4_2__borsuk_2),[file(borsuk_2,e2_3_4_2__borsuk_2)]]).

fof(e3_3_4_2__borsuk_2,plain,(
    k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([e1_3_4_2__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,rc3_funct_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_c3_3__borsuk_2,cc1_relset_1,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc3_struct_0,t3_subset,idempotence_k1_funct_4,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_m2_relset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,rc1_funct_1,dt_k1_funct_1,dt_c1_3_4_2__borsuk_2,dt_c5_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,e2_3_4_2__borsuk_2]),
    [interesting(0.5),file(borsuk_2,e3_3_4_2__borsuk_2),[file(borsuk_2,e3_3_4_2__borsuk_2)]]).

fof(i3_3_4_2__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i3_3_4_2__borsuk_2)]),
    [interesting(0.5),trivial,file(borsuk_2,i3_3_4_2__borsuk_2)]).

fof(i2_3_4_2__borsuk_2,plain,(
    k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(conclusion,[status(thm),assumptions([e1_3_4_2__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2])],[e3_3_4_2__borsuk_2,i3_3_4_2__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i2_3_4_2__borsuk_2),[file(borsuk_2,i2_3_4_2__borsuk_2)]]).

fof(i1_3_4_2__borsuk_2,plain,
    ( r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c1_3__borsuk_2))
   => k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(discharge_asm,[status(thm),assumptions([e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c1_3_4_2__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e1_3_4_2__borsuk_2])],[e1_3_4_2__borsuk_2,i2_3_4_2__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i1_3_4_2__borsuk_2),[file(borsuk_2,i1_3_4_2__borsuk_2)]]).

fof(i1_3_4_2_tmp__borsuk_2,plain,
    ( r2_hidden(c1_3_4_2__borsuk_2,k2_pre_topc(c1_3__borsuk_2))
   => k1_funct_1(c8_3__borsuk_2,c1_3_4_2__borsuk_2) = k1_funct_1(c5_3__borsuk_2,c1_3_4_2__borsuk_2) ),
    inference(discharge_asm,[status(thm),assumptions([e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[dt_c1_3_4_2__borsuk_2])],[dt_c1_3_4_2__borsuk_2,i1_3_4_2__borsuk_2]),
    [interesting(0.65),e4_3_4__borsuk_2]).

fof(e4_3_4__borsuk_2,plain,(
    ! [A] : 
      ( r2_hidden(A,k2_pre_topc(c1_3__borsuk_2))
     => k1_funct_1(c8_3__borsuk_2,A) = k1_funct_1(c5_3__borsuk_2,A) ) ),
    inference(let,[status(thm),assumptions([e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[i1_3_4_2_tmp__borsuk_2,dh_c1_3_4_2__borsuk_2]),
    [interesting(0.65),file(borsuk_2,e4_3_4__borsuk_2),[file(borsuk_2,e4_3_4__borsuk_2)]]).

fof(e3_3_4_3_1__borsuk_2,plain,
    ( r2_hidden(k1_funct_1(c8_3__borsuk_2,c1_3_4_3__borsuk_2),c1_3_4__borsuk_2)
    & r2_hidden(c1_3_4_3__borsuk_2,k1_relat_1(c5_3__borsuk_2))
    & k1_funct_1(c5_3__borsuk_2,c1_3_4_3__borsuk_2) = k1_funct_1(c8_3__borsuk_2,c1_3_4_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,e1_3_4_3_1__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c3_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_pre_topc,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,d3_pre_topc,e2_3_4_3_1__borsuk_2,e4_3_4__borsuk_2,d13_funct_1]),
    [interesting(0.35),file(borsuk_2,e3_3_4_3_1__borsuk_2),[file(borsuk_2,e3_3_4_3_1__borsuk_2)]]).

fof(e4_3_4_3_1__borsuk_2,plain,(
    r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,e1_3_4_3_1__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c3_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c4_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,e3_3_4_3_1__borsuk_2,d13_funct_1]),
    [interesting(0.35),file(borsuk_2,e4_3_4_3_1__borsuk_2),[file(borsuk_2,e4_3_4_3_1__borsuk_2)]]).

fof(i2_3_4_3_1__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i2_3_4_3_1__borsuk_2)]),
    [interesting(0.35),trivial,file(borsuk_2,i2_3_4_3_1__borsuk_2)]).

fof(i1_3_4_3_1__borsuk_2,plain,(
    r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,e1_3_4_3_1__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e4_3_4_3_1__borsuk_2,i2_3_4_3_1__borsuk_2]),
    [interesting(0.35),file(borsuk_2,i1_3_4_3_1__borsuk_2),[file(borsuk_2,i1_3_4_3_1__borsuk_2)]]).

fof(e1_3_4_3__borsuk_2,plain,
    ( r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)))
   => r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e1_3_4_3_1__borsuk_2])],[e1_3_4_3_1__borsuk_2,i1_3_4_3_1__borsuk_2]),
    [interesting(0.5),file(borsuk_2,e1_3_4_3__borsuk_2),[file(borsuk_2,e1_3_4_3__borsuk_2)]]).

fof(e2_3_4_3__borsuk_2,assumption,(
    r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) ),
    introduced(assumption,[file(borsuk_2,e2_3_4_3__borsuk_2)]),
    [interesting(0.5),axiom,file(borsuk_2,e2_3_4_3__borsuk_2)]).

fof(e3_3_4_3__borsuk_2,plain,
    ( r2_hidden(c1_3_4_3__borsuk_2,k1_relat_1(c5_3__borsuk_2))
    & r2_hidden(k1_funct_1(c5_3__borsuk_2,c1_3_4_3__borsuk_2),c1_3_4__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,e2_3_4_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c5_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,e2_3_4_3__borsuk_2,d13_funct_1]),
    [interesting(0.5),file(borsuk_2,e3_3_4_3__borsuk_2),[file(borsuk_2,e3_3_4_3__borsuk_2)]]).

fof(e4_3_4_3__borsuk_2,plain,
    ( r2_hidden(c1_3_4_3__borsuk_2,k1_relat_1(c8_3__borsuk_2))
    & r2_hidden(c1_3_4_3__borsuk_2,k2_pre_topc(c1_3__borsuk_2))
    & r2_hidden(k1_funct_1(c8_3__borsuk_2,c1_3_4_3__borsuk_2),c1_3_4__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_3__borsuk_2,e2_3_4_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,t1_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c3_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k1_funct_1,dt_k1_relat_1,dt_k2_pre_topc,dt_k2_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t1_subset,t3_subset,t7_boole,d3_pre_topc,e3_3_4_3__borsuk_2,e9_3__borsuk_2,e2_3_4__borsuk_2,e4_3_4__borsuk_2,d2_xboole_0]),
    [interesting(0.5),file(borsuk_2,e4_3_4_3__borsuk_2),[file(borsuk_2,e4_3_4_3__borsuk_2)]]).

fof(e5_3_4_3__borsuk_2,plain,
    ( r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2))
    & r2_hidden(c1_3_4_3__borsuk_2,k2_pre_topc(c1_3__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_3__borsuk_2,e2_3_4_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c3_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc4_subset_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_pre_topc,rc7_pre_topc,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_funct_2,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_pre_topc,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,rc1_funct_1,t1_subset,t7_boole,d3_pre_topc,e4_3_4_3__borsuk_2,d13_funct_1]),
    [interesting(0.5),file(borsuk_2,e5_3_4_3__borsuk_2),[file(borsuk_2,e5_3_4_3__borsuk_2)]]).

fof(e6_3_4_3__borsuk_2,plain,(
    r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4_3__borsuk_2,e2_3_4_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c3_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc6_pre_topc,rc7_pre_topc,t2_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c1_3_4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e5_3_4_3__borsuk_2,d3_xboole_0]),
    [interesting(0.5),file(borsuk_2,e6_3_4_3__borsuk_2),[file(borsuk_2,e6_3_4_3__borsuk_2)]]).

fof(i4_3_4_3__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i4_3_4_3__borsuk_2)]),
    [interesting(0.5),trivial,file(borsuk_2,i4_3_4_3__borsuk_2)]).

fof(i3_3_4_3__borsuk_2,plain,(
    r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4_3__borsuk_2,e2_3_4_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e6_3_4_3__borsuk_2,i4_3_4_3__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i3_3_4_3__borsuk_2),[file(borsuk_2,i3_3_4_3__borsuk_2)]]).

fof(i2_3_4_3__borsuk_2,plain,
    ( r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2))
   => r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e2_3_4_3__borsuk_2])],[e2_3_4_3__borsuk_2,i3_3_4_3__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i2_3_4_3__borsuk_2),[file(borsuk_2,i2_3_4_3__borsuk_2)]]).

fof(i1_3_4_3__borsuk_2,plain,
    ( ( r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)))
     => r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) )
    & ( r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2))
     => r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_4_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e1_3_4_3__borsuk_2,i2_3_4_3__borsuk_2]),
    [interesting(0.5),file(borsuk_2,i1_3_4_3__borsuk_2),[file(borsuk_2,i1_3_4_3__borsuk_2)]]).

fof(i1_3_4_3_tmp__borsuk_2,plain,
    ( ( r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)))
     => r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) )
    & ( r2_hidden(c1_3_4_3__borsuk_2,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2))
     => r2_hidden(c1_3_4_3__borsuk_2,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[dt_c1_3_4_3__borsuk_2])],[dt_c1_3_4_3__borsuk_2,i1_3_4_3__borsuk_2]),
    [interesting(0.65),e5_3_4__borsuk_2]).

fof(e5_3_4__borsuk_2,plain,(
    ! [A] : 
      ( ( r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)))
       => r2_hidden(A,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2)) )
      & ( r2_hidden(A,k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2))
       => r2_hidden(A,k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2))) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[i1_3_4_3_tmp__borsuk_2,dh_c1_3_4_3__borsuk_2]),
    [interesting(0.65),file(borsuk_2,e5_3_4__borsuk_2),[file(borsuk_2,e5_3_4__borsuk_2)]]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(e6_3_4__borsuk_2,plain,(
    k3_xboole_0(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),k2_pre_topc(c1_3__borsuk_2)) = k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_c3_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc6_pre_topc,rc7_pre_topc,t2_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e5_3_4__borsuk_2,t2_tarski]),
    [interesting(0.65),file(borsuk_2,e6_3_4__borsuk_2),[file(borsuk_2,e6_3_4__borsuk_2)]]).

fof(e8_3_4__borsuk_2,plain,(
    k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2) = k2_xboole_0(k5_pre_topc(c1_3__borsuk_2,c2_3__borsuk_2,c5_3__borsuk_2,c1_3_4__borsuk_2),k5_pre_topc(c3_3__borsuk_2,c2_3__borsuk_2,c6_3__borsuk_2,c1_3_4__borsuk_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc6_pre_topc,rc7_pre_topc,t1_boole,t2_boole,idempotence_k1_funct_4,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k1_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,cc15_membered,cc1_funct_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc1_subset_1,fc2_pre_topc,fc5_pre_topc,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k5_pre_topc,dt_k2_pre_topc,dt_k2_xboole_0,dt_k3_xboole_0,dt_k5_pre_topc,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,t1_subset,t7_boole,d3_pre_topc,e7_3_4__borsuk_2,e3_3_4__borsuk_2,e6_3_4__borsuk_2,t2_tarski]),
    [interesting(0.65),file(borsuk_2,e8_3_4__borsuk_2),[file(borsuk_2,e8_3_4__borsuk_2)]]).

fof(t16_compts_1,theorem,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_compts_1(A)
              & v6_compts_1(B,A) )
           => v4_pre_topc(B,A) ) ) ) ),
    file(compts_1,t16_compts_1),
    [interesting(0.9),axiom,file(compts_1,t16_compts_1)]).

fof(e22_3_4__borsuk_2,plain,(
    v4_pre_topc(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),c4_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e1_3_4__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc5_tsp_1,cc6_tsp_1,cc8_tsp_1,cc9_tsp_1,cc10_tsp_1,cc1_tsp_1,cc3_tsp_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_tsp_1,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_tsp_1,cc2_xreal_0,cc4_tsp_1,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_zfmisc_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,cc4_yellow_8,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc4_subset_1,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_funct_1,rc2_yellow_8,t1_boole,t1_subset,t4_subset,t5_subset,idempotence_k1_funct_4,commutativity_k4_subset_1,idempotence_k4_subset_1,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_k4_subset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k4_subset_1,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_c2_3_4__borsuk_2,dt_c3_3_4__borsuk_2,de_c2_3_4__borsuk_2,de_c3_3_4__borsuk_2,cc15_membered,cc1_funct_1,cc3_yellow_8,cc5_funct_2,cc6_funct_2,fc1_struct_0,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,existence_l1_pre_topc,existence_m1_subset_1,redefinition_k5_pre_topc,dt_k1_zfmisc_1,dt_k2_xboole_0,dt_k5_pre_topc,dt_l1_pre_topc,dt_m1_subset_1,dt_u1_struct_0,dt_c1_3__borsuk_2,dt_c1_3_4__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2,dt_c4_3__borsuk_2,dt_c4_3_4__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,de_c4_3_4__borsuk_2,de_c8_3__borsuk_2,fc1_subset_1,rc6_pre_topc,t3_subset,e21_3_4__borsuk_2,e5_3__borsuk_2,e8_3_4__borsuk_2,t16_compts_1]),
    [interesting(0.65),file(borsuk_2,e22_3_4__borsuk_2),[file(borsuk_2,e22_3_4__borsuk_2)]]).

fof(i3_3_4__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i3_3_4__borsuk_2)]),
    [interesting(0.65),trivial,file(borsuk_2,i3_3_4__borsuk_2)]).

fof(i2_3_4__borsuk_2,plain,(
    v4_pre_topc(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),c4_3__borsuk_2) ),
    inference(conclusion,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e1_3_4__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e22_3_4__borsuk_2,i3_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,i2_3_4__borsuk_2),[file(borsuk_2,i2_3_4__borsuk_2)]]).

fof(i1_3_4__borsuk_2,plain,
    ( v4_pre_topc(c1_3_4__borsuk_2,c2_3__borsuk_2)
   => v4_pre_topc(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),c4_3__borsuk_2) ),
    inference(discharge_asm,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,dt_c1_3_4__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e1_3_4__borsuk_2])],[e1_3_4__borsuk_2,i2_3_4__borsuk_2]),
    [interesting(0.65),file(borsuk_2,i1_3_4__borsuk_2),[file(borsuk_2,i1_3_4__borsuk_2)]]).

fof(i1_3_4_tmp__borsuk_2,plain,
    ( m1_subset_1(c1_3_4__borsuk_2,k1_zfmisc_1(u1_struct_0(c2_3__borsuk_2)))
   => ( v4_pre_topc(c1_3_4__borsuk_2,c2_3__borsuk_2)
     => v4_pre_topc(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,c1_3_4__borsuk_2),c4_3__borsuk_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[dt_c1_3_4__borsuk_2])],[dt_c1_3_4__borsuk_2,i1_3_4__borsuk_2]),
    [interesting(0.8),e17_3__borsuk_2]).

fof(e17_3__borsuk_2,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c2_3__borsuk_2)))
     => ( v4_pre_topc(A,c2_3__borsuk_2)
       => v4_pre_topc(k5_pre_topc(c4_3__borsuk_2,c2_3__borsuk_2,c8_3__borsuk_2,A),c4_3__borsuk_2) ) ) ),
    inference(let,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[i1_3_4_tmp__borsuk_2,dh_c1_3_4__borsuk_2]),
    [interesting(0.8),file(borsuk_2,e17_3__borsuk_2),[file(borsuk_2,e17_3__borsuk_2)]]).

fof(e18_3__borsuk_2,plain,(
    v5_pre_topc(c8_3__borsuk_2,c4_3__borsuk_2,c2_3__borsuk_2) ),
    inference(mizar_by,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,rc3_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_funct_1,rc1_funct_2,rc1_membered,rc2_borsuk_1,rc2_funct_1,t1_subset,t4_subset,t5_subset,idempotence_k1_funct_4,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_relset_1,dt_k10_relat_1,dt_k1_funct_4,dt_k2_zfmisc_1,dt_l1_struct_0,dt_m1_relset_1,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,cc15_membered,cc1_funct_1,cc1_relset_1,cc5_funct_2,cc6_funct_2,fc1_struct_0,fc4_subset_1,rc1_subset_1,rc2_subset_1,rc3_struct_0,rc5_struct_0,rc6_pre_topc,rc7_pre_topc,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_pre_topc,existence_m1_subset_1,existence_m2_relset_1,redefinition_k5_pre_topc,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_pre_topc,dt_l1_pre_topc,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c8_3__borsuk_2,de_c8_3__borsuk_2,fc1_subset_1,t3_subset,e17_3__borsuk_2,d12_pre_topc]),
    [interesting(0.8),file(borsuk_2,e18_3__borsuk_2),[file(borsuk_2,e18_3__borsuk_2)]]).

fof(i10_3__borsuk_2,theorem,(
    $true ),
    introduced(tautology,[file(borsuk_2,i10_3__borsuk_2)]),
    [interesting(0.8),trivial,file(borsuk_2,i10_3__borsuk_2)]).

fof(i9_3__borsuk_2,plain,(
    v5_pre_topc(c8_3__borsuk_2,c4_3__borsuk_2,c2_3__borsuk_2) ),
    inference(conclusion,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e18_3__borsuk_2,i10_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i9_3__borsuk_2),[file(borsuk_2,i9_3__borsuk_2)]]).

fof(i8_3__borsuk_2,plain,
    ( c8_3__borsuk_2 = k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)
    & v5_pre_topc(c8_3__borsuk_2,c4_3__borsuk_2,c2_3__borsuk_2) ),
    inference(conclusion,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[e16_3__borsuk_2,i9_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i8_3__borsuk_2),[file(borsuk_2,i8_3__borsuk_2)]]).

fof(i7_3__borsuk_2,plain,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
      & m2_relset_1(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
      & A = k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)
      & v5_pre_topc(A,c4_3__borsuk_2,c2_3__borsuk_2) ) ),
    inference(take,[status(thm),assumptions([e6_3__borsuk_2,e7_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e1_3__borsuk_2,e5_3__borsuk_2,e8_3__borsuk_2,e2_3__borsuk_2,dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,rc1_xreal_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_funct_2,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,rc1_membered,rc2_borsuk_1,rc3_funct_1,cc15_membered,cc1_funct_1,cc2_funct_1,cc5_funct_2,cc6_funct_2,fc4_subset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc5_struct_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_c1_3__borsuk_2,dt_c3_3__borsuk_2,cc1_relset_1,fc1_struct_0,fc1_subset_1,rc1_funct_1,rc1_funct_2,rc3_struct_0,idempotence_k1_funct_4,redefinition_m2_relset_1,dt_k1_funct_4,dt_m2_relset_1,dt_u1_struct_0,dt_c2_3__borsuk_2,dt_c4_3__borsuk_2,dt_c5_3__borsuk_2,dt_c6_3__borsuk_2,dt_c8_3__borsuk_2,i8_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i7_3__borsuk_2),[file(borsuk_2,i7_3__borsuk_2)]]).

fof(i6_3__borsuk_2,plain,(
    ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
      & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
      & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
      & v2_compts_1(c1_3__borsuk_2)
      & v2_compts_1(c3_3__borsuk_2)
      & v3_compts_1(c4_3__borsuk_2)
      & v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2)
      & v5_pre_topc(c6_3__borsuk_2,c3_3__borsuk_2,c2_3__borsuk_2)
      & ! [A] : 
          ( r2_hidden(A,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
         => k1_funct_1(c5_3__borsuk_2,A) = k1_funct_1(c6_3__borsuk_2,A) )
      & ! [A] : 
          ( ( v1_funct_1(A)
            & v1_funct_2(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
            & m2_relset_1(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
         => ~ ( A = k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)
              & v5_pre_topc(A,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c6_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[e1_3__borsuk_2,e2_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e5_3__borsuk_2,e6_3__borsuk_2,e7_3__borsuk_2,e8_3__borsuk_2])],[e1_3__borsuk_2,e2_3__borsuk_2,e3_3__borsuk_2,e4_3__borsuk_2,e5_3__borsuk_2,e6_3__borsuk_2,e7_3__borsuk_2,e8_3__borsuk_2,i7_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i6_3__borsuk_2),[file(borsuk_2,i6_3__borsuk_2)]]).

fof(i6_3_tmp__borsuk_2,plain,
    ( ( v1_funct_1(c6_3__borsuk_2)
      & v1_funct_2(c6_3__borsuk_2,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
      & m2_relset_1(c6_3__borsuk_2,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
   => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
        & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
        & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
        & v2_compts_1(c1_3__borsuk_2)
        & v2_compts_1(c3_3__borsuk_2)
        & v3_compts_1(c4_3__borsuk_2)
        & v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2)
        & v5_pre_topc(c6_3__borsuk_2,c3_3__borsuk_2,c2_3__borsuk_2)
        & ! [A] : 
            ( r2_hidden(A,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
           => k1_funct_1(c5_3__borsuk_2,A) = k1_funct_1(c6_3__borsuk_2,A) )
        & ! [A] : 
            ( ( v1_funct_1(A)
              & v1_funct_2(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
              & m2_relset_1(A,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
           => ~ ( A = k1_funct_4(c5_3__borsuk_2,c6_3__borsuk_2)
                & v5_pre_topc(A,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[dt_c6_3__borsuk_2])],[dt_c6_3__borsuk_2,i6_3__borsuk_2]),
    [interesting(0.8),i5_3__borsuk_2]).

fof(i5_3__borsuk_2,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
        & m2_relset_1(A,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
     => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
          & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
          & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
          & v2_compts_1(c1_3__borsuk_2)
          & v2_compts_1(c3_3__borsuk_2)
          & v3_compts_1(c4_3__borsuk_2)
          & v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2)
          & v5_pre_topc(A,c3_3__borsuk_2,c2_3__borsuk_2)
          & ! [B] : 
              ( r2_hidden(B,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
             => k1_funct_1(c5_3__borsuk_2,B) = k1_funct_1(A,B) )
          & ! [B] : 
              ( ( v1_funct_1(B)
                & v1_funct_2(B,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                & m2_relset_1(B,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
             => ~ ( B = k1_funct_4(c5_3__borsuk_2,A)
                  & v5_pre_topc(B,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c5_3__borsuk_2,dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2])],[i6_3_tmp__borsuk_2,dh_c6_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i5_3__borsuk_2),[file(borsuk_2,i5_3__borsuk_2)]]).

fof(i5_3_tmp__borsuk_2,plain,
    ( ( v1_funct_1(c5_3__borsuk_2)
      & v1_funct_2(c5_3__borsuk_2,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
      & m2_relset_1(c5_3__borsuk_2,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
          & m2_relset_1(A,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
       => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
            & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
            & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
            & v2_compts_1(c1_3__borsuk_2)
            & v2_compts_1(c3_3__borsuk_2)
            & v3_compts_1(c4_3__borsuk_2)
            & v5_pre_topc(c5_3__borsuk_2,c1_3__borsuk_2,c2_3__borsuk_2)
            & v5_pre_topc(A,c3_3__borsuk_2,c2_3__borsuk_2)
            & ! [B] : 
                ( r2_hidden(B,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
               => k1_funct_1(c5_3__borsuk_2,B) = k1_funct_1(A,B) )
            & ! [B] : 
                ( ( v1_funct_1(B)
                  & v1_funct_2(B,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                  & m2_relset_1(B,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
               => ~ ( B = k1_funct_4(c5_3__borsuk_2,A)
                    & v5_pre_topc(B,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[dt_c5_3__borsuk_2])],[dt_c5_3__borsuk_2,i5_3__borsuk_2]),
    [interesting(0.8),i4_3__borsuk_2]).

fof(i4_3__borsuk_2,plain,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
        & m2_relset_1(A,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
            & m2_relset_1(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
         => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
              & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
              & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
              & v2_compts_1(c1_3__borsuk_2)
              & v2_compts_1(c3_3__borsuk_2)
              & v3_compts_1(c4_3__borsuk_2)
              & v5_pre_topc(A,c1_3__borsuk_2,c2_3__borsuk_2)
              & v5_pre_topc(B,c3_3__borsuk_2,c2_3__borsuk_2)
              & ! [C] : 
                  ( r2_hidden(C,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) )
              & ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                    & m2_relset_1(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
                 => ~ ( C = k1_funct_4(A,B)
                      & v5_pre_topc(C,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c4_3__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2])],[i5_3_tmp__borsuk_2,dh_c5_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i4_3__borsuk_2),[file(borsuk_2,i4_3__borsuk_2)]]).

fof(i4_3_tmp__borsuk_2,plain,
    ( ( ~ v3_struct_0(c4_3__borsuk_2)
      & v2_pre_topc(c4_3__borsuk_2)
      & l1_pre_topc(c4_3__borsuk_2) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v1_funct_2(A,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
          & m2_relset_1(A,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
       => ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
              & m2_relset_1(B,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
           => ~ ( m1_pre_topc(c1_3__borsuk_2,c4_3__borsuk_2)
                & m1_pre_topc(c3_3__borsuk_2,c4_3__borsuk_2)
                & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(c4_3__borsuk_2)
                & v2_compts_1(c1_3__borsuk_2)
                & v2_compts_1(c3_3__borsuk_2)
                & v3_compts_1(c4_3__borsuk_2)
                & v5_pre_topc(A,c1_3__borsuk_2,c2_3__borsuk_2)
                & v5_pre_topc(B,c3_3__borsuk_2,c2_3__borsuk_2)
                & ! [C] : 
                    ( r2_hidden(C,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) )
                & ! [C] : 
                    ( ( v1_funct_1(C)
                      & v1_funct_2(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                      & m2_relset_1(C,u1_struct_0(c4_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
                   => ~ ( C = k1_funct_4(A,B)
                        & v5_pre_topc(C,c4_3__borsuk_2,c2_3__borsuk_2) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2]),discharge_asm(discharge,[dt_c4_3__borsuk_2])],[dt_c4_3__borsuk_2,i4_3__borsuk_2]),
    [interesting(0.8),i3_3__borsuk_2]).

fof(i3_3__borsuk_2,plain,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
            & m2_relset_1(B,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                & m2_relset_1(C,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
             => ~ ( m1_pre_topc(c1_3__borsuk_2,A)
                  & m1_pre_topc(c3_3__borsuk_2,A)
                  & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(A)
                  & v2_compts_1(c1_3__borsuk_2)
                  & v2_compts_1(c3_3__borsuk_2)
                  & v3_compts_1(A)
                  & v5_pre_topc(B,c1_3__borsuk_2,c2_3__borsuk_2)
                  & v5_pre_topc(C,c3_3__borsuk_2,c2_3__borsuk_2)
                  & ! [D] : 
                      ( r2_hidden(D,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                     => k1_funct_1(B,D) = k1_funct_1(C,D) )
                  & ! [D] : 
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2))
                        & m2_relset_1(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2)) )
                     => ~ ( D = k1_funct_4(B,C)
                          & v5_pre_topc(D,A,c2_3__borsuk_2) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c2_3__borsuk_2,dt_c3_3__borsuk_2])],[i4_3_tmp__borsuk_2,dh_c4_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i3_3__borsuk_2),[file(borsuk_2,i3_3__borsuk_2)]]).

fof(i3_3_tmp__borsuk_2,plain,
    ( ( ~ v3_struct_0(c3_3__borsuk_2)
      & v2_pre_topc(c3_3__borsuk_2)
      & l1_pre_topc(c3_3__borsuk_2) )
   => ! [A] : 
        ( ( ~ v3_struct_0(A)
          & v2_pre_topc(A)
          & l1_pre_topc(A) )
       => ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
              & m2_relset_1(B,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
           => ! [C] : 
                ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                  & m2_relset_1(C,u1_struct_0(c3_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
               => ~ ( m1_pre_topc(c1_3__borsuk_2,A)
                    & m1_pre_topc(c3_3__borsuk_2,A)
                    & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)) = k2_pre_topc(A)
                    & v2_compts_1(c1_3__borsuk_2)
                    & v2_compts_1(c3_3__borsuk_2)
                    & v3_compts_1(A)
                    & v5_pre_topc(B,c1_3__borsuk_2,c2_3__borsuk_2)
                    & v5_pre_topc(C,c3_3__borsuk_2,c2_3__borsuk_2)
                    & ! [D] : 
                        ( r2_hidden(D,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(c3_3__borsuk_2)))
                       => k1_funct_1(B,D) = k1_funct_1(C,D) )
                    & ! [D] : 
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2))
                          & m2_relset_1(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2)) )
                       => ~ ( D = k1_funct_4(B,C)
                            & v5_pre_topc(D,A,c2_3__borsuk_2) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c2_3__borsuk_2]),discharge_asm(discharge,[dt_c3_3__borsuk_2])],[dt_c3_3__borsuk_2,i3_3__borsuk_2]),
    [interesting(0.8),i2_3__borsuk_2]).

fof(i2_3__borsuk_2,plain,(
    ! [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(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                & m2_relset_1(C,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2)) )
                 => ~ ( m1_pre_topc(c1_3__borsuk_2,B)
                      & m1_pre_topc(A,B)
                      & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(A)) = k2_pre_topc(B)
                      & v2_compts_1(c1_3__borsuk_2)
                      & v2_compts_1(A)
                      & v3_compts_1(B)
                      & v5_pre_topc(C,c1_3__borsuk_2,c2_3__borsuk_2)
                      & v5_pre_topc(D,A,c2_3__borsuk_2)
                      & ! [E] : 
                          ( r2_hidden(E,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(A)))
                         => k1_funct_1(C,E) = k1_funct_1(D,E) )
                      & ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(B),u1_struct_0(c2_3__borsuk_2))
                            & m2_relset_1(E,u1_struct_0(B),u1_struct_0(c2_3__borsuk_2)) )
                         => ~ ( E = k1_funct_4(C,D)
                              & v5_pre_topc(E,B,c2_3__borsuk_2) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__borsuk_2,dt_c2_3__borsuk_2])],[i3_3_tmp__borsuk_2,dh_c3_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i2_3__borsuk_2),[file(borsuk_2,i2_3__borsuk_2)]]).

fof(i2_3_tmp__borsuk_2,plain,
    ( ( ~ v3_struct_0(c2_3__borsuk_2)
      & v2_pre_topc(c2_3__borsuk_2)
      & l1_pre_topc(c2_3__borsuk_2) )
   => ! [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(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2))
                  & m2_relset_1(C,u1_struct_0(c1_3__borsuk_2),u1_struct_0(c2_3__borsuk_2)) )
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2))
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(c2_3__borsuk_2)) )
                   => ~ ( m1_pre_topc(c1_3__borsuk_2,B)
                        & m1_pre_topc(A,B)
                        & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(A)) = k2_pre_topc(B)
                        & v2_compts_1(c1_3__borsuk_2)
                        & v2_compts_1(A)
                        & v3_compts_1(B)
                        & v5_pre_topc(C,c1_3__borsuk_2,c2_3__borsuk_2)
                        & v5_pre_topc(D,A,c2_3__borsuk_2)
                        & ! [E] : 
                            ( r2_hidden(E,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(A)))
                           => k1_funct_1(C,E) = k1_funct_1(D,E) )
                        & ! [E] : 
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(B),u1_struct_0(c2_3__borsuk_2))
                              & m2_relset_1(E,u1_struct_0(B),u1_struct_0(c2_3__borsuk_2)) )
                           => ~ ( E = k1_funct_4(C,D)
                                & v5_pre_topc(E,B,c2_3__borsuk_2) ) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__borsuk_2]),discharge_asm(discharge,[dt_c2_3__borsuk_2])],[dt_c2_3__borsuk_2,i2_3__borsuk_2]),
    [interesting(0.8),i1_3__borsuk_2]).

fof(i1_3__borsuk_2,plain,(
    ! [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(c1_3__borsuk_2),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(c1_3__borsuk_2),u1_struct_0(A)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
                     => ~ ( m1_pre_topc(c1_3__borsuk_2,C)
                          & m1_pre_topc(B,C)
                          & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(B)) = k2_pre_topc(C)
                          & v2_compts_1(c1_3__borsuk_2)
                          & v2_compts_1(B)
                          & v3_compts_1(C)
                          & v5_pre_topc(D,c1_3__borsuk_2,A)
                          & v5_pre_topc(E,B,A)
                          & ! [F] : 
                              ( r2_hidden(F,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(B)))
                             => k1_funct_1(D,F) = k1_funct_1(E,F) )
                          & ! [F] : 
                              ( ( v1_funct_1(F)
                                & v1_funct_2(F,u1_struct_0(C),u1_struct_0(A))
                                & m2_relset_1(F,u1_struct_0(C),u1_struct_0(A)) )
                             => ~ ( F = k1_funct_4(D,E)
                                  & v5_pre_topc(F,C,A) ) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__borsuk_2])],[i2_3_tmp__borsuk_2,dh_c2_3__borsuk_2]),
    [interesting(0.8),file(borsuk_2,i1_3__borsuk_2),[file(borsuk_2,i1_3__borsuk_2)]]).

fof(i1_3_tmp__borsuk_2,plain,
    ( ( ~ v3_struct_0(c1_3__borsuk_2)
      & v2_pre_topc(c1_3__borsuk_2)
      & l1_pre_topc(c1_3__borsuk_2) )
   => ! [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(c1_3__borsuk_2),u1_struct_0(A))
                      & m2_relset_1(D,u1_struct_0(c1_3__borsuk_2),u1_struct_0(A)) )
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
                          & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
                       => ~ ( m1_pre_topc(c1_3__borsuk_2,C)
                            & m1_pre_topc(B,C)
                            & k2_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(B)) = k2_pre_topc(C)
                            & v2_compts_1(c1_3__borsuk_2)
                            & v2_compts_1(B)
                            & v3_compts_1(C)
                            & v5_pre_topc(D,c1_3__borsuk_2,A)
                            & v5_pre_topc(E,B,A)
                            & ! [F] : 
                                ( r2_hidden(F,k3_xboole_0(k2_pre_topc(c1_3__borsuk_2),k2_pre_topc(B)))
                               => k1_funct_1(D,F) = k1_funct_1(E,F) )
                            & ! [F] : 
                                ( ( v1_funct_1(F)
                                  & v1_funct_2(F,u1_struct_0(C),u1_struct_0(A))
                                  & m2_relset_1(F,u1_struct_0(C),u1_struct_0(A)) )
                               => ~ ( F = k1_funct_4(D,E)
                                    & v5_pre_topc(F,C,A) ) ) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__borsuk_2])],[dt_c1_3__borsuk_2,i1_3__borsuk_2]),
    [interesting(1),t1_borsuk_2]).

fof(t1_borsuk_2,theorem,(
    ! [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) )
                 => ! [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(B))
                            & m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
                         => ~ ( m1_pre_topc(A,D)
                              & m1_pre_topc(C,D)
                              & k2_xboole_0(k2_pre_topc(A),k2_pre_topc(C)) = k2_pre_topc(D)
                              & v2_compts_1(A)
                              & v2_compts_1(C)
                              & v3_compts_1(D)
                              & v5_pre_topc(E,A,B)
                              & v5_pre_topc(F,C,B)
                              & ! [G] : 
                                  ( r2_hidden(G,k3_xboole_0(k2_pre_topc(A),k2_pre_topc(C)))
                                 => k1_funct_1(E,G) = k1_funct_1(F,G) )
                              & ! [G] : 
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,u1_struct_0(D),u1_struct_0(B))
                                    & m2_relset_1(G,u1_struct_0(D),u1_struct_0(B)) )
                                 => ~ ( G = k1_funct_4(E,F)
                                      & v5_pre_topc(G,D,B) ) ) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__borsuk_2,dh_c1_3__borsuk_2]),
    [interesting(1),file(borsuk_2,t1_borsuk_2),[file(borsuk_2,t1_borsuk_2)]]).