% Mizar problem: t15_msualg_9,msualg_9,535,11 
fof(t15_msualg_9,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m2_pralg_2(D,B,A)
                 => ! [E] : 
                      ( m1_pralg_2(E,k4_card_3(k10_pralg_2(B,A,C,D)))
                     => ! [F] : 
                          ( m1_pralg_2(F,k4_card_3(k10_pralg_2(B,A,C,D)))
                         => ( ! [G] : 
                                ( m1_subset_1(G,B)
                               => k1_funct_1(k3_pralg_3(k10_pralg_2(B,A,C,D),G),E) = k1_funct_1(k3_pralg_3(k10_pralg_2(B,A,C,D),G),F) )
                           => r6_pboole(k1_pralg_2(k4_card_3(k10_pralg_2(B,A,C,D))),E,F) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_closure2,cc1_finset_1,cc1_fraenkel,cc1_mssubfam,cc1_pboole,cc2_pboole,d2_pralg_3,d3_pboole,dt_k10_pralg_2,dt_k1_funct_1,dt_k1_pralg_2,dt_k1_relat_1,dt_k1_xboole_0,dt_k3_pralg_3,dt_k4_card_3,dt_l1_msualg_1,dt_l1_struct_0,dt_m1_pboole,dt_m1_pralg_2,dt_m1_subset_1,dt_m2_pralg_2,dt_u1_struct_0,existence_l1_msualg_1,existence_l1_struct_0,existence_m1_pboole,existence_m1_pralg_2,existence_m1_subset_1,existence_m2_pralg_2,fc1_pralg_2,fc1_struct_0,fc1_xboole_0,fc2_pboole,fc6_pralg_2,rc1_finset_1,rc1_fraenkel,rc1_pboole,rc1_pralg_2,rc1_xboole_0,rc2_pboole,rc2_pre_circ,rc2_xboole_0,rc3_pboole,rc3_struct_0,redefinition_m1_pralg_2,redefinition_r6_pboole,reflexivity_r6_pboole,symmetry_r6_pboole,t18_card_3,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole,t9_funct_1]),
    [file(msualg_9,t15_msualg_9)]).

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

fof(cc1_closure2,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_fraenkel(A) ) ),
    file(closure2,cc1_closure2),
    []).

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

fof(cc1_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v3_relat_1(B)
       => v1_pre_circ(B,A) ) ) ),
    file(mssubfam,cc1_mssubfam),
    []).

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(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(d2_pralg_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( C = k3_pralg_3(A,B)
          <=> ( k1_relat_1(C) = k4_card_3(A)
              & ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r2_hidden(D,k1_relat_1(C))
                   => k1_funct_1(C,D) = k1_funct_1(D,B) ) ) ) ) ) ) ),
    file(pralg_3,d2_pralg_3),
    []).

fof(d3_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    []).

fof(dt_k10_pralg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m2_pralg_2(D,A,B) )
     => m1_pboole(k10_pralg_2(A,B,C,D),A) ) ),
    file(pralg_2,k10_pralg_2),
    []).

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

fof(dt_k1_pralg_2,axiom,(
    $true ),
    file(pralg_2,k1_pralg_2),
    []).

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

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

fof(dt_k3_pralg_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_pralg_3(A,B))
        & v1_funct_1(k3_pralg_3(A,B)) ) ) ),
    file(pralg_3,k3_pralg_3),
    []).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

fof(dt_l1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) ),
    file(msualg_1,l1_msualg_1),
    []).

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

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_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_pralg_2(A) )
     => ! [B] : 
          ( m1_pralg_2(B,A)
         => m1_pboole(B,k1_pralg_2(A)) ) ) ),
    file(pralg_2,m1_pralg_2),
    []).

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

fof(dt_m2_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ! [C] : 
          ( m2_pralg_2(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pralg_2,m2_pralg_2),
    []).

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

fof(existence_l1_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_1),
    []).

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

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

fof(existence_m1_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_pralg_2(A) )
     => ? [B] : m1_pralg_2(B,A) ) ),
    file(pralg_2,m1_pralg_2),
    []).

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

fof(existence_m2_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ? [C] : m2_pralg_2(C,A,B) ) ),
    file(pralg_2,m2_pralg_2),
    []).

fof(fc1_pralg_2,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( ~ v1_xboole_0(k4_card_3(B))
        & v1_fraenkel(k4_card_3(B))
        & v1_pralg_2(k4_card_3(B)) ) ) ),
    file(pralg_2,fc1_pralg_2),
    []).

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(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(fc6_pralg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m2_pralg_2(D,A,B) )
     => ( v1_relat_1(k10_pralg_2(A,B,C,D))
        & v2_relat_1(k10_pralg_2(A,B,C,D))
        & v1_funct_1(k10_pralg_2(A,B,C,D)) ) ) ),
    file(pralg_2,fc6_pralg_2),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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

fof(rc1_pralg_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A)
      & v1_pralg_2(A) ) ),
    file(pralg_2,rc1_pralg_2),
    []).

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

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_pre_circ,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B)
      & v1_pre_circ(B,A) ) ),
    file(pre_circ,rc2_pre_circ),
    []).

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

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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(redefinition_m1_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A)
        & v1_pralg_2(A) )
     => ! [B] : 
          ( m1_pralg_2(B,A)
        <=> m1_subset_1(B,A) ) ) ),
    file(pralg_2,m1_pralg_2),
    []).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t18_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    []).

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(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),
    []).

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).