% Mizar problem: t3_homothet,homothet,674,59 
fof(t3_homothet,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( B != C
                        & B != D
                        & r1_aff_1(A,B,C,D)
                        & ! [E] : 
                            ( ( v1_funct_1(E)
                              & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                              & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                              & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                           => ~ ( v6_transgeo(E,A)
                                & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
                                & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) = D ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k8_funct_2,dt_l1_analoaf,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,existence_l1_analoaf,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,l15_homothet,l19_homothet,rc3_struct_0,rc5_struct_0,redefinition_k8_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(homothet,t3_homothet)]).

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

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

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

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

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

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    []).

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

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

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

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),
    []).

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

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    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),
    []).

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

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

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

fof(l15_homothet,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( v4_aff_2(A)
                      & B != C
                      & B != D
                      & r1_aff_1(A,B,C,D)
                      & ! [E] : 
                          ( ( v1_funct_1(E)
                            & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                            & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                            & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                         => ~ ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ! [G] : 
                                    ( m1_subset_1(G,u1_struct_0(A))
                                   => ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,F) = G
                                    <=> ( ( ~ r1_aff_1(A,B,C,F)
                                          & r1_aff_1(A,B,F,G)
                                          & r2_analoaf(A,C,F,D,G) )
                                        | ( r1_aff_1(A,B,C,F)
                                          & ? [H] : 
                                              ( m1_subset_1(H,u1_struct_0(A))
                                              & ? [I] : 
                                                  ( m1_subset_1(I,u1_struct_0(A))
                                                  & ~ r1_aff_1(A,B,C,H)
                                                  & r1_aff_1(A,B,H,I)
                                                  & r2_analoaf(A,C,H,D,I)
                                                  & r2_analoaf(A,H,F,I,G)
                                                  & r1_aff_1(A,B,C,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(homothet,l15_homothet),
    []).

fof(l19_homothet,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( r1_aff_1(A,B,C,D)
                          & v4_aff_2(A)
                          & ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,F) = G
                                  <=> ( ( ~ r1_aff_1(A,B,C,F)
                                        & r1_aff_1(A,B,F,G)
                                        & r2_analoaf(A,C,F,D,G) )
                                      | ( r1_aff_1(A,B,C,F)
                                        & ? [H] : 
                                            ( m1_subset_1(H,u1_struct_0(A))
                                            & ? [I] : 
                                                ( m1_subset_1(I,u1_struct_0(A))
                                                & ~ r1_aff_1(A,B,C,H)
                                                & r1_aff_1(A,B,H,I)
                                                & r2_analoaf(A,C,H,D,I)
                                                & r2_analoaf(A,H,F,I,G)
                                                & r1_aff_1(A,B,C,G) ) ) ) ) ) ) ) )
                       => ( B = C
                          | B = D
                          | ( v6_transgeo(E,A)
                            & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
                            & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) = D ) ) ) ) ) ) ) ) ),
    file(homothet,l19_homothet),
    []).

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

fof(rc5_struct_0,axiom,(
    ! [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),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

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

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

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

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

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

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

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

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

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

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