% Mizar problem: t54_transgeo,transgeo,674,23 
fof(t54_transgeo,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
            & v3_funct_2(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
            & m2_relset_1(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A))) )
         => ~ ( r3_transgeo(k2_diraf(A),B)
              & ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( B = C
                      & v4_transgeo(C,A) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_analoaf,antisymmetry_r2_hidden,cc1_funct_2,cc1_relset_1,cc2_funct_2,cc3_funct_2,cc5_funct_2,cc6_funct_2,d2_diraf,d4_transgeo,d8_transgeo,dt_g1_analoaf,dt_k1_diraf,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_diraf,dt_k2_zfmisc_1,dt_l1_analoaf,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_analoaf,dt_u1_struct_0,existence_l1_analoaf,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_diraf,fc1_struct_0,fc1_xboole_0,free_g1_analoaf,rc1_analoaf,rc1_funct_2,rc1_partfun1,rc1_xboole_0,rc2_analoaf,rc2_funct_2,rc2_partfun1,rc2_xboole_0,rc3_analoaf,rc3_struct_0,rc5_struct_0,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(transgeo,t54_transgeo)]).

fof(abstractness_v1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => ( v1_analoaf(A)
       => A = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ) ),
    file(analoaf,v1_analoaf),
    []).

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

fof(cc1_funct_2,axiom,(
    ! [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),
    []).

fof(cc1_relset_1,axiom,(
    ! [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),
    []).

fof(cc2_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc2_funct_2),
    []).

fof(cc3_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v2_funct_1(C)
          & v1_funct_2(C,A,B)
          & v2_funct_2(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B)
          & v3_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc3_funct_2),
    []).

fof(cc5_funct_2,axiom,(
    ! [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),
    []).

fof(cc6_funct_2,axiom,(
    ! [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),
    []).

fof(d2_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => k2_diraf(A) = g1_analoaf(u1_struct_0(A),k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ),
    file(diraf,d2_diraf),
    []).

fof(d4_transgeo,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r3_transgeo(A,B)
          <=> r1_transgeo(u1_struct_0(A),B,u1_analoaf(A)) ) ) ) ),
    file(transgeo,d4_transgeo),
    []).

fof(d8_transgeo,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(B,A)
          <=> r1_transgeo(u1_struct_0(A),B,k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ) ) ),
    file(transgeo,d8_transgeo),
    []).

fof(dt_g1_analoaf,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ( v1_analoaf(g1_analoaf(A,B))
        & l1_analoaf(g1_analoaf(A,B)) ) ) ),
    file(analoaf,g1_analoaf),
    []).

fof(dt_k1_diraf,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
     => m2_relset_1(k1_diraf(A,B),k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) ) ),
    file(diraf,k1_diraf),
    []).

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_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_analoaf(k2_diraf(A))
        & l1_analoaf(k2_diraf(A)) ) ) ),
    file(diraf,k2_diraf),
    []).

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

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_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => m2_relset_1(u1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ),
    file(analoaf,u1_analoaf),
    []).

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_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & v1_analoaf(k2_diraf(A)) ) ) ),
    file(diraf,fc1_diraf),
    []).

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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(free_g1_analoaf,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ! [C,D] : 
          ( g1_analoaf(A,B) = g1_analoaf(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(analoaf,g1_analoaf),
    []).

fof(rc1_analoaf,axiom,(
    ? [A] : 
      ( l1_analoaf(A)
      & v1_analoaf(A) ) ),
    file(analoaf,rc1_analoaf),
    []).

fof(rc1_funct_2,axiom,(
    ! [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),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_analoaf,axiom,(
    ? [A] : 
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_analoaf(A) ) ),
    file(analoaf,rc2_analoaf),
    []).

fof(rc2_funct_2,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v2_funct_1(B)
      & v1_funct_2(B,A,A)
      & v2_funct_2(B,A,A)
      & v3_funct_2(B,A,A) ) ),
    file(funct_2,rc2_funct_2),
    []).

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_analoaf,axiom,(
    ? [A] : 
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & ~ v3_realset2(A)
      & v1_analoaf(A)
      & v2_analoaf(A) ) ),
    file(analoaf,rc3_analoaf),
    []).

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_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),
    []).