% Mizar ND problem: t2_alg_1,alg_1,51,25 
fof(dh_c1_2__alg_1,definition,
    ( ( ( ~ v3_struct_0(c1_2__alg_1)
        & v6_unialg_1(c1_2__alg_1)
        & v7_unialg_1(c1_2__alg_1)
        & v8_unialg_1(c1_2__alg_1)
        & l1_unialg_1(c1_2__alg_1) )
     => ! [A] : 
          ( ( ~ v1_xboole_0(A)
            & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_2__alg_1))) )
         => ( A = u1_struct_0(c1_2__alg_1)
           => k3_unialg_2(c1_2__alg_1,A) = u1_unialg_1(c1_2__alg_1) ) ) )
   => ! [B] : 
        ( ( ~ v3_struct_0(B)
          & v6_unialg_1(B)
          & v7_unialg_1(B)
          & v8_unialg_1(B)
          & l1_unialg_1(B) )
       => ! [C] : 
            ( ( ~ v1_xboole_0(C)
              & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
           => ( C = u1_struct_0(B)
             => k3_unialg_2(B,C) = u1_unialg_1(B) ) ) ) ),
    introduced(definition,[new_symbol(c1_2__alg_1),file(alg_1,c1_2__alg_1)]),
    [interesting(0.8),axiom,file(alg_1,c1_2__alg_1)]).

fof(dh_c2_2__alg_1,definition,
    ( ( ( ~ v1_xboole_0(c2_2__alg_1)
        & m1_subset_1(c2_2__alg_1,k1_zfmisc_1(u1_struct_0(c1_2__alg_1))) )
     => ( c2_2__alg_1 = u1_struct_0(c1_2__alg_1)
       => k3_unialg_2(c1_2__alg_1,c2_2__alg_1) = u1_unialg_1(c1_2__alg_1) ) )
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_2__alg_1))) )
       => ( A = u1_struct_0(c1_2__alg_1)
         => k3_unialg_2(c1_2__alg_1,A) = u1_unialg_1(c1_2__alg_1) ) ) ),
    introduced(definition,[new_symbol(c2_2__alg_1),file(alg_1,c2_2__alg_1)]),
    [interesting(0.8),axiom,file(alg_1,c2_2__alg_1)]).

fof(e1_2__alg_1,assumption,(
    c2_2__alg_1 = u1_struct_0(c1_2__alg_1) ),
    introduced(assumption,[file(alg_1,e1_2__alg_1)]),
    [interesting(0.8),axiom,file(alg_1,e1_2__alg_1)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(cc1_relset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_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),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_membered)]).

fof(cc1_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

fof(cc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(rc4_unialg_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v1_finseq_1(B)
          & v4_unialg_1(B,A)
          & v5_unialg_1(B,A) ) ) ),
    file(unialg_1,rc4_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,rc4_unialg_1)]).

fof(rc5_struct_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(existence_l1_unialg_1,axiom,(
    ? [A] : l1_unialg_1(A) ),
    file(unialg_1,l1_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,l1_unialg_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(redefinition_m2_finseq_1,definition,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k13_finseq_1)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k4_partfun1,axiom,(
    $true ),
    file(partfun1,k4_partfun1),
    [interesting(0.9),axiom,file(partfun1,k4_partfun1)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(dt_l1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => l1_struct_0(A) ) ),
    file(unialg_1,l1_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,l1_unialg_1)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc3_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc1_partfun1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ),
    file(partfun1,fc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,fc1_partfun1)]).

fof(fc2_unialg_1,theorem,(
    ! [A] : 
      ( ( v6_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A))
        & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,fc2_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,fc2_unialg_1)]).

fof(fc3_unialg_1,theorem,(
    ! [A] : 
      ( ( v7_unialg_1(A)
        & l1_unialg_1(A) )
     => ( v1_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A))
        & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,fc3_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,fc3_unialg_1)]).

fof(fc4_unialg_1,theorem,(
    ! [A] : 
      ( ( v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ( ~ v1_xboole_0(u1_unialg_1(A))
        & v1_relat_1(u1_unialg_1(A))
        & v2_relat_1(u1_unialg_1(A))
        & v1_funct_1(u1_unialg_1(A))
        & v1_finseq_1(u1_unialg_1(A)) ) ) ),
    file(unialg_1,fc4_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,fc4_unialg_1)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k4_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k3_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m2_finseq_1(k3_unialg_2(A,B),k4_partfun1(k13_finseq_1(B),B)) ) ),
    file(unialg_2,k3_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,k3_unialg_2)]).

fof(dt_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_u1_unialg_1,axiom,(
    ! [A] : 
      ( l1_unialg_1(A)
     => m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))) ) ),
    file(unialg_1,u1_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,u1_unialg_1)]).

fof(dt_c1_2__alg_1,assumption,
    ( ~ v3_struct_0(c1_2__alg_1)
    & v6_unialg_1(c1_2__alg_1)
    & v7_unialg_1(c1_2__alg_1)
    & v8_unialg_1(c1_2__alg_1)
    & l1_unialg_1(c1_2__alg_1) ),
    introduced(assumption,[file(alg_1,c1_2__alg_1)]),
    [interesting(0.8),axiom,file(alg_1,c1_2__alg_1)]).

fof(dt_c2_2__alg_1,assumption,
    ( ~ v1_xboole_0(c2_2__alg_1)
    & m1_subset_1(c2_2__alg_1,k1_zfmisc_1(u1_struct_0(c1_2__alg_1))) ),
    introduced(assumption,[file(alg_1,c2_2__alg_1)]),
    [interesting(0.8),axiom,file(alg_1,c2_2__alg_1)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(dh_c1_2_1__alg_1,definition,
    ( ( m2_subset_1(c1_2_1__alg_1,k1_numbers,k5_numbers)
     => ( r2_hidden(c1_2_1__alg_1,k4_finseq_1(u1_unialg_1(c1_2__alg_1)))
       => k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),c1_2_1__alg_1) = k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r2_hidden(A,k4_finseq_1(u1_unialg_1(c1_2__alg_1)))
         => k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),A) = k1_funct_1(u1_unialg_1(c1_2__alg_1),A) ) ) ),
    introduced(definition,[new_symbol(c1_2_1__alg_1),file(alg_1,c1_2_1__alg_1)]),
    [interesting(0.65),axiom,file(alg_1,c1_2_1__alg_1)]).

fof(e1_2_1__alg_1,assumption,(
    r2_hidden(c1_2_1__alg_1,k4_finseq_1(u1_unialg_1(c1_2__alg_1))) ),
    introduced(assumption,[file(alg_1,e1_2_1__alg_1)]),
    [interesting(0.65),axiom,file(alg_1,e1_2_1__alg_1)]).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

fof(rc1_finseq_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_finseq_2(B,A)
      & ~ v1_xboole_0(B) ) ),
    file(finseq_2,rc1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,rc1_finseq_2)]).

fof(rc1_unialg_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_relset_1(B,k13_finseq_1(A),A)
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_unialg_1(B,A)
          & v2_unialg_1(B,A) ) ) ),
    file(unialg_1,rc1_unialg_1),
    [interesting(0.9),axiom,file(unialg_1,rc1_unialg_1)]).

fof(existence_m1_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_unialg_2(B,A) ) ),
    file(unialg_2,m1_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,m1_unialg_2)]).

fof(redefinition_k3_finseq_2,definition,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ),
    file(finseq_2,k3_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k3_finseq_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) ),
    file(finseq_2,k3_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]).

fof(dt_m1_unialg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_unialg_2(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(unialg_2,m1_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,m1_unialg_2)]).

fof(existence_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ? [C] : m2_unialg_2(C,A,B) ) ),
    file(unialg_2,m2_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,m2_unialg_2)]).

fof(redefinition_m2_unialg_2,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] : 
          ( m2_unialg_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(unialg_2,m2_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,m2_unialg_2)]).

fof(dt_k1_unialg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m1_unialg_2(k1_unialg_2(A),u1_struct_0(A)) ) ),
    file(unialg_2,k1_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,k1_unialg_2)]).

fof(dt_k2_unialg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        & m1_subset_1(C,k1_unialg_2(A)) )
     => ( ~ v1_xboole_0(k2_unialg_2(A,B,C))
        & v1_funct_1(k2_unialg_2(A,B,C))
        & v1_unialg_1(k2_unialg_2(A,B,C),B)
        & v2_unialg_1(k2_unialg_2(A,B,C),B)
        & m2_relset_1(k2_unialg_2(A,B,C),k3_finseq_2(B),B) ) ) ),
    file(unialg_2,k2_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,k2_unialg_2)]).

fof(dt_m2_unialg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_unialg_2(B,A) )
     => ! [C] : 
          ( m2_unialg_2(C,A,B)
         => ( ~ v1_xboole_0(C)
            & v1_funct_1(C)
            & v1_unialg_1(C,A)
            & v2_unialg_1(C,A)
            & m2_relset_1(C,k3_finseq_2(A),A) ) ) ) ),
    file(unialg_2,m2_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,m2_unialg_2)]).

fof(dt_c1_2_1__alg_1,assumption,(
    m2_subset_1(c1_2_1__alg_1,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(alg_1,c1_2_1__alg_1)]),
    [interesting(0.65),axiom,file(alg_1,c1_2_1__alg_1)]).

fof(d3_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k1_unialg_2(A) = k2_relat_1(u1_unialg_1(A)) ) ),
    file(unialg_2,d3_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,d3_unialg_2)]).

fof(de_c2_2_1__alg_1,definition,(
    c2_2_1__alg_1 = k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1) ),
    introduced(definition,[new_symbol(c2_2_1__alg_1),file(alg_1,c2_2_1__alg_1)]),
    [interesting(0.65),axiom,file(alg_1,c2_2_1__alg_1)]).

fof(t6_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k4_finseq_1(u1_unialg_1(A)))
         => m2_unialg_2(k1_funct_1(u1_unialg_1(A),B),u1_struct_0(A),k1_unialg_2(A)) ) ) ),
    file(unialg_2,t6_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,t6_unialg_2)]).

fof(e2_2_1__alg_1,plain,(
    m2_unialg_2(k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1),u1_struct_0(c1_2__alg_1),k1_unialg_2(c1_2__alg_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__alg_1,dt_c1_2_1__alg_1,e1_2_1__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc5_membered,fc6_membered,rc1_finseq_2,rc1_membered,rc1_unialg_1,rc2_partfun1,rc4_unialg_1,existence_l1_struct_0,existence_m1_subset_1,existence_m1_unialg_2,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k3_finseq_2,dt_k4_partfun1,dt_k5_numbers,dt_l1_struct_0,dt_m1_subset_1,dt_m1_unialg_2,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,cc6_membered,cc9_membered,fc1_partfun1,fc1_struct_0,fc2_membered,rc3_struct_0,rc5_struct_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_l1_unialg_1,existence_m2_unialg_2,redefinition_k4_finseq_1,redefinition_m2_unialg_2,dt_k1_funct_1,dt_k1_unialg_2,dt_k4_finseq_1,dt_l1_unialg_1,dt_m2_unialg_2,dt_u1_struct_0,dt_u1_unialg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,fc2_unialg_1,fc3_unialg_1,fc4_unialg_1,t1_subset,t7_boole,d3_unialg_2,e1_2_1__alg_1,t6_unialg_2]),
    [interesting(0.65),file(alg_1,e2_2_1__alg_1),[file(alg_1,e2_2_1__alg_1)]]).

fof(dt_c2_2_1__alg_1,plain,(
    m2_unialg_2(c2_2_1__alg_1,u1_struct_0(c1_2__alg_1),k1_unialg_2(c1_2__alg_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__alg_1,dt_c1_2_1__alg_1,e1_2_1__alg_1])],[reflexivity_r1_tarski,cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc5_membered,fc6_membered,rc1_finseq_2,rc1_membered,rc1_unialg_1,rc2_partfun1,rc4_unialg_1,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_l1_unialg_1,existence_m1_subset_1,existence_m1_unialg_2,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k1_numbers,dt_k2_relat_1,dt_k3_finseq_2,dt_k4_partfun1,dt_k5_numbers,dt_l1_struct_0,dt_l1_unialg_1,dt_m1_subset_1,dt_m1_unialg_2,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,fc1_partfun1,fc1_struct_0,fc2_membered,fc2_unialg_1,fc3_unialg_1,fc4_unialg_1,rc3_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m2_unialg_2,redefinition_m2_unialg_2,dt_k1_funct_1,dt_k1_unialg_2,dt_m2_unialg_2,dt_u1_struct_0,dt_u1_unialg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,d3_unialg_2,de_c2_2_1__alg_1,e2_2_1__alg_1]),
    [interesting(0.65),file(alg_1,c2_2_1__alg_1),[file(alg_1,c2_2_1__alg_1)]]).

fof(d7_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(B),B))
             => ( C = k3_unialg_2(A,B)
              <=> ( k4_finseq_1(C) = k4_finseq_1(u1_unialg_1(A))
                  & ! [D,E] : 
                      ( m2_unialg_2(E,u1_struct_0(A),k1_unialg_2(A))
                     => ( ( r2_hidden(D,k4_finseq_1(C))
                          & E = k1_funct_1(u1_unialg_1(A),D) )
                       => k1_funct_1(C,D) = k2_unialg_2(A,B,E) ) ) ) ) ) ) ) ),
    file(unialg_2,d7_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,d7_unialg_2)]).

fof(e2_2__alg_1,plain,(
    k4_finseq_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1)) = k4_finseq_1(u1_unialg_1(c1_2__alg_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2__alg_1,dt_c2_2__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,existence_m1_finseq_2,existence_m1_relset_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m1_relset_1,cc1_relset_1,cc3_arytm_3,cc6_membered,fc2_membered,fc5_membered,rc1_finseq_2,rc1_unialg_1,rc2_partfun1,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_finseq_1,existence_m1_unialg_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k3_finseq_2,dt_k5_numbers,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_unialg_2,dt_m2_relset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc9_membered,fc1_struct_0,fc6_membered,rc1_membered,rc3_struct_0,rc4_unialg_1,rc5_struct_0,antisymmetry_r2_hidden,existence_l1_unialg_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_unialg_2,redefinition_k4_finseq_1,redefinition_m2_finseq_1,redefinition_m2_unialg_2,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_unialg_2,dt_k1_zfmisc_1,dt_k2_unialg_2,dt_k3_unialg_2,dt_k4_finseq_1,dt_k4_partfun1,dt_l1_unialg_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_unialg_2,dt_u1_struct_0,dt_u1_unialg_1,dt_c1_2__alg_1,dt_c2_2__alg_1,cc15_membered,fc1_partfun1,fc2_unialg_1,fc3_unialg_1,fc4_unialg_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d3_unialg_2,d7_unialg_2]),
    [interesting(0.8),file(alg_1,e2_2__alg_1),[file(alg_1,e2_2__alg_1)]]).

fof(e1_2_1_1__alg_1,plain,(
    k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),c1_2_1__alg_1) = k2_unialg_2(c1_2__alg_1,c2_2__alg_1,c2_2_1__alg_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_2_1__alg_1,dt_c1_2__alg_1,dt_c2_2__alg_1,e1_2_1__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,existence_m1_finseq_2,existence_m1_relset_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m1_relset_1,cc1_relset_1,cc3_arytm_3,fc5_membered,rc1_finseq_2,rc1_unialg_1,rc2_partfun1,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_finseq_1,existence_m1_unialg_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k3_finseq_2,dt_k5_numbers,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_unialg_2,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_struct_0,fc2_membered,fc6_membered,rc1_membered,rc3_struct_0,rc4_unialg_1,rc5_struct_0,antisymmetry_r2_hidden,existence_l1_unialg_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_unialg_2,redefinition_k4_finseq_1,redefinition_m2_finseq_1,redefinition_m2_unialg_2,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_unialg_2,dt_k1_zfmisc_1,dt_k2_unialg_2,dt_k3_unialg_2,dt_k4_finseq_1,dt_k4_partfun1,dt_l1_unialg_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_unialg_2,dt_u1_struct_0,dt_u1_unialg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,dt_c2_2__alg_1,dt_c2_2_1__alg_1,de_c2_2_1__alg_1,cc15_membered,fc1_partfun1,fc2_unialg_1,fc3_unialg_1,fc4_unialg_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d3_unialg_2,e2_2__alg_1,e1_2_1__alg_1,d7_unialg_2]),
    [interesting(0.5),file(alg_1,e1_2_1_1__alg_1),[file(alg_1,e1_2_1_1__alg_1)]]).

fof(t7_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = u1_struct_0(A)
           => ( v1_unialg_2(B,A)
              & ! [C] : 
                  ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
                 => k2_unialg_2(A,B,C) = C ) ) ) ) ) ),
    file(unialg_2,t7_unialg_2),
    [interesting(0.9),axiom,file(unialg_2,t7_unialg_2)]).

fof(e2_2_1_1__alg_1,plain,(
    k2_unialg_2(c1_2__alg_1,c2_2__alg_1,c2_2_1__alg_1) = k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_2__alg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,e1_2_1__alg_1,e1_2__alg_1])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,cc1_relset_1,cc3_arytm_3,fc5_membered,rc1_finseq_2,rc1_unialg_1,rc2_partfun1,rc4_unialg_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_m1_unialg_2,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k13_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_relat_1,dt_k3_finseq_2,dt_k4_partfun1,dt_k5_numbers,dt_l1_struct_0,dt_m1_unialg_2,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_partfun1,fc1_struct_0,fc2_membered,fc6_membered,rc1_membered,rc3_struct_0,rc5_struct_0,t1_subset,t4_subset,t5_subset,existence_l1_unialg_1,existence_m1_subset_1,existence_m2_unialg_2,redefinition_m2_unialg_2,dt_k1_funct_1,dt_k1_unialg_2,dt_k1_zfmisc_1,dt_k2_unialg_2,dt_l1_unialg_1,dt_m1_subset_1,dt_m2_unialg_2,dt_u1_struct_0,dt_u1_unialg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,dt_c2_2__alg_1,dt_c2_2_1__alg_1,de_c2_2_1__alg_1,cc15_membered,fc2_unialg_1,fc3_unialg_1,fc4_unialg_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d3_unialg_2,e1_2__alg_1,t7_unialg_2]),
    [interesting(0.5),file(alg_1,e2_2_1_1__alg_1),[file(alg_1,e2_2_1_1__alg_1)]]).

fof(e3_2_1__alg_1,plain,(
    k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),c1_2_1__alg_1) = k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_2__alg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,e1_2_1__alg_1,e1_2__alg_1])],[e1_2_1_1__alg_1,e2_2_1_1__alg_1]),
    [interesting(0.65),file(alg_1,e3_2_1__alg_1),[file(alg_1,e3_2_1__alg_1)]]).

fof(i3_2_1__alg_1,theorem,(
    $true ),
    introduced(tautology,[file(alg_1,i3_2_1__alg_1)]),
    [interesting(0.65),trivial,file(alg_1,i3_2_1__alg_1)]).

fof(i2_2_1__alg_1,plain,(
    k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),c1_2_1__alg_1) = k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c2_2__alg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,e1_2_1__alg_1,e1_2__alg_1])],[e3_2_1__alg_1,i3_2_1__alg_1]),
    [interesting(0.65),file(alg_1,i2_2_1__alg_1),[file(alg_1,i2_2_1__alg_1)]]).

fof(i1_2_1__alg_1,plain,
    ( r2_hidden(c1_2_1__alg_1,k4_finseq_1(u1_unialg_1(c1_2__alg_1)))
   => k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),c1_2_1__alg_1) = k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__alg_1,dt_c1_2__alg_1,dt_c1_2_1__alg_1,e1_2__alg_1]),discharge_asm(discharge,[e1_2_1__alg_1])],[e1_2_1__alg_1,i2_2_1__alg_1]),
    [interesting(0.65),file(alg_1,i1_2_1__alg_1),[file(alg_1,i1_2_1__alg_1)]]).

fof(i1_2_1_tmp__alg_1,plain,
    ( m2_subset_1(c1_2_1__alg_1,k1_numbers,k5_numbers)
   => ( r2_hidden(c1_2_1__alg_1,k4_finseq_1(u1_unialg_1(c1_2__alg_1)))
     => k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),c1_2_1__alg_1) = k1_funct_1(u1_unialg_1(c1_2__alg_1),c1_2_1__alg_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_2__alg_1,dt_c1_2__alg_1,e1_2__alg_1]),discharge_asm(discharge,[dt_c1_2_1__alg_1])],[dt_c1_2_1__alg_1,i1_2_1__alg_1]),
    [interesting(0.8),e3_2__alg_1]).

fof(e3_2__alg_1,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r2_hidden(A,k4_finseq_1(u1_unialg_1(c1_2__alg_1)))
       => k1_funct_1(k3_unialg_2(c1_2__alg_1,c2_2__alg_1),A) = k1_funct_1(u1_unialg_1(c1_2__alg_1),A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c2_2__alg_1,dt_c1_2__alg_1,e1_2__alg_1])],[i1_2_1_tmp__alg_1,dh_c1_2_1__alg_1]),
    [interesting(0.8),file(alg_1,e3_2__alg_1),[file(alg_1,e3_2__alg_1)]]).

fof(t17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k4_finseq_1(A) = k4_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t17_finseq_1)]).

fof(e4_2__alg_1,plain,(
    k3_unialg_2(c1_2__alg_1,c2_2__alg_1) = u1_unialg_1(c1_2__alg_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_2__alg_1,dt_c1_2__alg_1,dt_c2_2__alg_1])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,rc2_partfun1,reflexivity_r1_tarski,existence_l1_struct_0,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_l1_struct_0,dt_m1_finseq_1,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,fc1_struct_0,fc6_membered,rc1_arytm_3,rc1_membered,rc3_struct_0,rc4_unialg_1,rc5_struct_0,existence_l1_unialg_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_partfun1,dt_k5_ordinal2,dt_l1_unialg_1,dt_m1_subset_1,dt_m2_finseq_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_partfun1,fc2_unialg_1,fc3_unialg_1,fc4_unialg_1,fc5_membered,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_unialg_2,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_u1_unialg_1,dt_c1_2__alg_1,dt_c2_2__alg_1,fc2_membered,t1_subset,t7_boole,e3_2__alg_1,e2_2__alg_1,t17_finseq_1]),
    [interesting(0.8),file(alg_1,e4_2__alg_1),[file(alg_1,e4_2__alg_1)]]).

fof(i4_2__alg_1,theorem,(
    $true ),
    introduced(tautology,[file(alg_1,i4_2__alg_1)]),
    [interesting(0.8),trivial,file(alg_1,i4_2__alg_1)]).

fof(i3_2__alg_1,plain,(
    k3_unialg_2(c1_2__alg_1,c2_2__alg_1) = u1_unialg_1(c1_2__alg_1) ),
    inference(conclusion,[status(thm),assumptions([e1_2__alg_1,dt_c1_2__alg_1,dt_c2_2__alg_1])],[e4_2__alg_1,i4_2__alg_1]),
    [interesting(0.8),file(alg_1,i3_2__alg_1),[file(alg_1,i3_2__alg_1)]]).

fof(i2_2__alg_1,plain,
    ( c2_2__alg_1 = u1_struct_0(c1_2__alg_1)
   => k3_unialg_2(c1_2__alg_1,c2_2__alg_1) = u1_unialg_1(c1_2__alg_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__alg_1,dt_c2_2__alg_1]),discharge_asm(discharge,[e1_2__alg_1])],[e1_2__alg_1,i3_2__alg_1]),
    [interesting(0.8),file(alg_1,i2_2__alg_1),[file(alg_1,i2_2__alg_1)]]).

fof(i2_2_tmp__alg_1,plain,
    ( ( ~ v1_xboole_0(c2_2__alg_1)
      & m1_subset_1(c2_2__alg_1,k1_zfmisc_1(u1_struct_0(c1_2__alg_1))) )
   => ( c2_2__alg_1 = u1_struct_0(c1_2__alg_1)
     => k3_unialg_2(c1_2__alg_1,c2_2__alg_1) = u1_unialg_1(c1_2__alg_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_2__alg_1]),discharge_asm(discharge,[dt_c2_2__alg_1])],[dt_c2_2__alg_1,i2_2__alg_1]),
    [interesting(0.8),i1_2__alg_1]).

fof(i1_2__alg_1,plain,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_2__alg_1))) )
     => ( A = u1_struct_0(c1_2__alg_1)
       => k3_unialg_2(c1_2__alg_1,A) = u1_unialg_1(c1_2__alg_1) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_2__alg_1])],[i2_2_tmp__alg_1,dh_c2_2__alg_1]),
    [interesting(0.8),file(alg_1,i1_2__alg_1),[file(alg_1,i1_2__alg_1)]]).

fof(i1_2_tmp__alg_1,plain,
    ( ( ~ v3_struct_0(c1_2__alg_1)
      & v6_unialg_1(c1_2__alg_1)
      & v7_unialg_1(c1_2__alg_1)
      & v8_unialg_1(c1_2__alg_1)
      & l1_unialg_1(c1_2__alg_1) )
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_2__alg_1))) )
       => ( A = u1_struct_0(c1_2__alg_1)
         => k3_unialg_2(c1_2__alg_1,A) = u1_unialg_1(c1_2__alg_1) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__alg_1])],[dt_c1_2__alg_1,i1_2__alg_1]),
    [interesting(1),t2_alg_1]).

fof(t2_alg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = u1_struct_0(A)
           => k3_unialg_2(A,B) = u1_unialg_1(A) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_2_tmp__alg_1,dh_c1_2__alg_1]),
    [interesting(1),file(alg_1,t2_alg_1),[file(alg_1,t2_alg_1)]]).