% Mizar problem: t32_midsp_2,midsp_2,733,75 
fof(t32_midsp_2,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => r1_midsp_2(g1_midsp_1(A,k6_midsp_2(A,B,C)),B,k7_midsp_2(A,B,C)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_midsp_1,antisymmetry_r2_hidden,cc1_midsp_2,cc1_relset_1,d10_midsp_2,d1_binop_1,d2_midsp_2,dt_g1_midsp_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_midsp_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_k6_midsp_2,dt_k7_midsp_2,dt_l1_midsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_midsp_1,dt_u1_struct_0,existence_l1_midsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc3_midsp_2,fc4_subset_1,free_g1_midsp_1,l40_midsp_2,rc14_vectsp_1,rc1_midsp_1,rc1_subset_1,rc1_xboole_0,rc2_midsp_1,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc4_struct_0,rc5_struct_0,redefinition_k2_binop_1,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(midsp_2,t32_midsp_2)]).

fof(abstractness_v1_midsp_1,axiom,(
    ! [A] : 
      ( l1_midsp_1(A)
     => ( v1_midsp_1(A)
       => A = g1_midsp_1(u1_struct_0(A),u1_midsp_1(A)) ) ) ),
    file(midsp_1,v1_midsp_1),
    []).

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

fof(cc1_midsp_2,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_midsp_2(A) )
       => ( ~ v3_struct_0(A)
          & v13_vectsp_1(A) ) ) ) ),
    file(midsp_2,cc1_midsp_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(d10_midsp_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => k7_midsp_2(A,B,C) = C ) ) ) ),
    file(midsp_2,d10_midsp_2),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d2_midsp_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(B)) )
             => ( r1_midsp_2(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k1_midsp_1(A,D,E) = F
                            <=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,D,F) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),C,F,E) ) ) ) ) ) ) ) ) ),
    file(midsp_2,d2_midsp_2),
    []).

fof(dt_g1_midsp_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_midsp_1(g1_midsp_1(A,B))
        & l1_midsp_1(g1_midsp_1(A,B)) ) ) ),
    file(midsp_1,g1_midsp_1),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

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

fof(dt_k1_midsp_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_midsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_midsp_1(A,B,C),u1_struct_0(A)) ) ),
    file(midsp_1,k1_midsp_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_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

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_k6_midsp_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v1_midsp_2(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ( v1_funct_1(k6_midsp_2(A,B,C))
        & v1_funct_2(k6_midsp_2(A,B,C),k2_zfmisc_1(A,A),A)
        & m2_relset_1(k6_midsp_2(A,B,C),k2_zfmisc_1(A,A),A) ) ) ),
    file(midsp_2,k6_midsp_2),
    []).

fof(dt_k7_midsp_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v1_midsp_2(B)
        & l1_rlvect_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
        & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
     => ( v1_funct_1(k7_midsp_2(A,B,C))
        & v1_funct_2(k7_midsp_2(A,B,C),k2_zfmisc_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C)))),u1_struct_0(B))
        & m2_relset_1(k7_midsp_2(A,B,C),k2_zfmisc_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C)))),u1_struct_0(B)) ) ) ),
    file(midsp_2,k7_midsp_2),
    []).

fof(dt_l1_midsp_1,axiom,(
    ! [A] : 
      ( l1_midsp_1(A)
     => l1_struct_0(A) ) ),
    file(midsp_1,l1_midsp_1),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

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

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_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_midsp_1,axiom,(
    ! [A] : 
      ( l1_midsp_1(A)
     => ( v1_funct_1(u1_midsp_1(A))
        & v1_funct_2(u1_midsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_midsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(midsp_1,u1_midsp_1),
    []).

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

fof(existence_l1_midsp_1,axiom,(
    ? [A] : l1_midsp_1(A) ),
    file(midsp_1,l1_midsp_1),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

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

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_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(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc3_midsp_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( ~ v3_struct_0(g1_midsp_1(A,B))
        & v1_midsp_1(g1_midsp_1(A,B)) ) ) ),
    file(midsp_2,fc3_midsp_2),
    []).

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(free_g1_midsp_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] : 
          ( g1_midsp_1(A,B) = g1_midsp_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(midsp_1,g1_midsp_1),
    []).

fof(l40_midsp_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v1_midsp_2(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B))
                & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) )
             => ( r2_midsp_2(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))))
                           => ( k1_midsp_1(g1_midsp_1(A,k6_midsp_2(A,B,C)),D,E) = F
                            <=> k2_binop_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(B),k7_midsp_2(A,B,C),D,F) = k2_binop_1(u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(g1_midsp_1(A,k6_midsp_2(A,B,C))),u1_struct_0(B),k7_midsp_2(A,B,C),F,E) ) ) ) ) ) ) ) ) ),
    file(midsp_2,l40_midsp_2),
    []).

fof(rc14_vectsp_1,axiom,(
    ? [A] : 
      ( l1_rlvect_1(A)
      & ~ v3_struct_0(A)
      & v13_vectsp_1(A) ) ),
    file(vectsp_1,rc14_vectsp_1),
    []).

fof(rc1_midsp_1,axiom,(
    ? [A] : 
      ( l1_midsp_1(A)
      & v1_midsp_1(A) ) ),
    file(midsp_1,rc1_midsp_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(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_midsp_1,axiom,(
    ? [A] : 
      ( l1_midsp_1(A)
      & ~ v3_struct_0(A) ) ),
    file(midsp_1,rc2_midsp_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(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_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_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

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),
    []).