% Mizar problem: t1_osalg_4,osalg_4,115,54 
fof(t1_osalg_4,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_pboole(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_msualg_4(D,u1_struct_0(A),B,C)
                 => ( v1_osalg_4(D,A,B,C)
                   => ( v11_osalg_1(D,A)
                      & m1_pboole(D,u1_struct_0(A)) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finseq_5,cc1_msualg_4,cc1_orders_3,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_pboole,commutativity_k2_tarski,d18_osalg_1,d1_osalg_4,d3_relat_1,d5_tarski,dt_k1_funct_1,dt_k1_msualg_4,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_l1_orders_2,dt_l1_struct_0,dt_m1_msualg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_msualg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc12_relat_1,fc1_struct_0,fc1_subset_1,fc2_pboole,fc2_subset_1,fc3_subset_1,fc4_relat_1,fc4_subset_1,rc10_osalg_1,rc11_osalg_1,rc1_msualg_4,rc1_osalg_4,rc1_pboole,rc1_relat_1,rc1_subset_1,rc2_osalg_4,rc2_partfun1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_pboole,rc3_relat_1,rc3_struct_0,rc5_struct_0,redefinition_k1_msualg_4,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t106_zfmisc_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(osalg_4,t1_osalg_4)]).

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

fof(cc1_finseq_5,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_realset1(A) ) ),
    file(finseq_5,cc1_finseq_5),
    []).

fof(cc1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m1_msualg_4(D,A,B,C)
         => v1_msualg_4(D) ) ) ),
    file(msualg_4,cc1_msualg_4),
    []).

fof(cc1_orders_3,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
       => v1_orders_3(A) ) ) ),
    file(orders_3,cc1_orders_3),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d18_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => ( v11_osalg_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r3_orders_2(A,C,D)
                     => r1_tarski(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(osalg_1,d18_osalg_1),
    []).

fof(d1_osalg_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_pboole(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_msualg_4(D,u1_struct_0(A),B,C)
                 => ( v1_osalg_4(D,A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( r3_orders_2(A,E,F)
                             => ! [G,H] : 
                                  ( ( r2_hidden(G,k1_funct_1(B,E))
                                    & r2_hidden(H,k1_funct_1(C,E)) )
                                 => ( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),B,C,D,E))
                                  <=> r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),B,C,D,F)) ) ) ) ) ) ) ) ) ) ) ),
    file(osalg_4,d1_osalg_4),
    []).

fof(d3_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_1),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

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

fof(dt_k1_msualg_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_msualg_4(D,A,B,C)
        & m1_subset_1(E,A) )
     => m2_relset_1(k1_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ),
    file(msualg_4,k1_msualg_4),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

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

fof(dt_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m1_msualg_4(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(msualg_4,m1_msualg_4),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

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

fof(existence_m1_msualg_4,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m1_msualg_4(D,A,B,C) ) ),
    file(msualg_4,m1_msualg_4),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_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(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

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

fof(rc10_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A) ) ) ),
    file(osalg_1,rc10_osalg_1),
    []).

fof(rc11_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A) ) ) ),
    file(osalg_1,rc11_osalg_1),
    []).

fof(rc1_msualg_4,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_msualg_4(B) ) ),
    file(msualg_4,rc1_msualg_4),
    []).

fof(rc1_osalg_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A)
          & v1_msualg_4(B) ) ) ),
    file(osalg_4,rc1_osalg_4),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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

fof(rc2_osalg_4,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A)
        & m1_pboole(B,u1_struct_0(A))
        & m1_pboole(C,u1_struct_0(A)) )
     => ? [D] : 
          ( m1_msualg_4(D,u1_struct_0(A),B,C)
          & v1_relat_1(D)
          & v1_funct_1(D)
          & v1_msualg_4(D)
          & v1_osalg_4(D,A,B,C) ) ) ),
    file(osalg_4,rc2_osalg_4),
    []).

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_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

fof(rc2_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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

fof(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc3_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

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_k1_msualg_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m1_msualg_4(D,A,B,C)
        & m1_subset_1(E,A) )
     => k1_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ),
    file(msualg_4,k1_msualg_4),
    []).

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(redefinition_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_orders_2(A,B,C)
      <=> r1_orders_2(A,B,C) ) ) ),
    file(orders_2,r3_orders_2),
    []).

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

fof(reflexivity_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_orders_2(A,B,B) ) ),
    file(orders_2,r3_orders_2),
    []).

fof(t106_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    []).

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),
    []).