% Mizar ND problem: t7_afinsq_1,afinsq_1,106,45 
fof(dh_c1_6__afinsq_1,definition,
    ( ( ( v1_relat_1(c1_6__afinsq_1)
        & v1_funct_1(c1_6__afinsq_1) )
     => ( ( v1_finset_1(c1_6__afinsq_1)
          & v5_ordinal1(c1_6__afinsq_1) )
      <=> ? [A] : 
            ( m2_subset_1(A,k1_numbers,k5_numbers)
            & k1_relat_1(c1_6__afinsq_1) = A ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ( ( v1_finset_1(B)
            & v5_ordinal1(B) )
        <=> ? [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
              & k1_relat_1(B) = C ) ) ) ),
    introduced(definition,[new_symbol(c1_6__afinsq_1),file(afinsq_1,c1_6__afinsq_1)]),
    [interesting(0.8),axiom,file(afinsq_1,c1_6__afinsq_1)]).

fof(e1_6_1__afinsq_1,assumption,
    ( v1_finset_1(c1_6__afinsq_1)
    & v5_ordinal1(c1_6__afinsq_1) ),
    introduced(assumption,[file(afinsq_1,e1_6_1__afinsq_1)]),
    [interesting(0.65),axiom,file(afinsq_1,e1_6_1__afinsq_1)]).

fof(cc1_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_funct_7(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A)
        & v1_funcop_1(A) ) ) ),
    file(funct_7,cc1_funct_7),
    [interesting(0.9),axiom,file(funct_7,cc1_funct_7)]).

fof(cc2_funct_7,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A)
        & v1_funcop_1(A)
        & v1_funct_7(A) ) ) ),
    file(funct_7,cc2_funct_7),
    [interesting(0.9),axiom,file(funct_7,cc2_funct_7)]).

fof(cc3_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(rc1_funcop_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,rc1_funcop_1)]).

fof(rc2_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc3_xreal_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(rc4_xreal_0,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

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

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

fof(cc1_card_1,theorem,(
    ! [A] : 
      ( v1_card_1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(card_1,cc1_card_1),
    [interesting(0.9),axiom,file(card_1,cc1_card_1)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(cc4_xreal_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc2_ordinal1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(fc3_funct_7,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0) ),
    file(funct_7,fc3_funct_7),
    [interesting(0.9),axiom,file(funct_7,fc3_funct_7)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

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_card_1,theorem,(
    ? [A] : v1_card_1(A) ),
    file(card_1,rc1_card_1),
    [interesting(0.9),axiom,file(card_1,rc1_card_1)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(rc2_card_1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_1,rc2_card_1),
    [interesting(0.9),axiom,file(card_1,rc2_card_1)]).

fof(rc2_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_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(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_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

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_card_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc2_card_1),
    [interesting(0.9),axiom,file(card_1,cc2_card_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

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(cc3_card_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_finset_1(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A)
        & v1_card_1(A) ) ) ),
    file(card_1,cc3_card_1),
    [interesting(0.9),axiom,file(card_1,cc3_card_1)]).

fof(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

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_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_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

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_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_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

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_c1_6__afinsq_1,assumption,
    ( v1_relat_1(c1_6__afinsq_1)
    & v1_funct_1(c1_6__afinsq_1) ),
    introduced(assumption,[file(afinsq_1,c1_6__afinsq_1)]),
    [interesting(0.8),axiom,file(afinsq_1,c1_6__afinsq_1)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

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(fc5_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( v1_ordinal1(k1_relat_1(A))
        & v2_ordinal1(k1_relat_1(A))
        & v3_ordinal1(k1_relat_1(A)) ) ) ),
    file(ordinal1,fc5_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc5_ordinal1)]).

fof(rc4_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A) ) ),
    file(ordinal1,rc4_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc4_ordinal1)]).

fof(t29_finset_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_finset_1(k1_relat_1(A))
      <=> v1_finset_1(A) ) ) ),
    file(finset_1,t29_finset_1),
    [interesting(0.9),axiom,file(finset_1,t29_finset_1)]).

fof(d7_ordinal1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v5_ordinal1(A)
      <=> v3_ordinal1(k1_relat_1(A)) ) ) ),
    file(ordinal1,d7_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,d7_ordinal1)]).

fof(e2_6_1__afinsq_1,plain,
    ( v1_finset_1(k1_relat_1(c1_6__afinsq_1))
    & v3_ordinal1(k1_relat_1(c1_6__afinsq_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__afinsq_1,e1_6_1__afinsq_1])],[cc2_ordinal1,rc1_ordinal1,dt_k1_relat_1,dt_c1_6__afinsq_1,cc1_ordinal1,fc5_ordinal1,rc1_funct_1,rc4_ordinal1,e1_6_1__afinsq_1,t29_finset_1,d7_ordinal1]),
    [interesting(0.65),file(afinsq_1,e2_6_1__afinsq_1),[file(afinsq_1,e2_6_1__afinsq_1)]]).

fof(t7_card_4,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_finset_1(A)
      <=> r2_hidden(A,k5_ordinal2) ) ) ),
    file(card_4,t7_card_4),
    [interesting(0.9),axiom,file(card_4,t7_card_4)]).

fof(e3_6_1__afinsq_1,plain,(
    r2_hidden(k1_relat_1(c1_6__afinsq_1),k5_ordinal2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__afinsq_1,e1_6_1__afinsq_1])],[cc1_funct_7,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_funct_7,cc2_xreal_0,cc7_xreal_0,rc1_funcop_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_xreal_0,fc12_relat_1,fc2_ordinal1,fc3_funct_7,fc4_relat_1,rc1_arytm_3,rc2_ordinal1,rc3_funct_1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_arytm_3,cc1_funct_1,cc1_relat_1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_arytm_3,cc3_ordinal1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc3_ordinal1,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k5_ordinal2,dt_c1_6__afinsq_1,cc1_ordinal1,fc1_ordinal2,t1_subset,t7_boole,e2_6_1__afinsq_1,t7_card_4]),
    [interesting(0.65),file(afinsq_1,e3_6_1__afinsq_1),[file(afinsq_1,e3_6_1__afinsq_1)]]).

fof(e4_6_1__afinsq_1,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & k1_relat_1(c1_6__afinsq_1) = A ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__afinsq_1,e1_6_1__afinsq_1])],[cc1_funct_7,cc2_funct_7,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_funcop_1,rc2_xreal_0,rc3_relat_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_card_1,cc1_xreal_0,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc2_ordinal1,fc3_funct_7,fc4_relat_1,rc1_arytm_3,rc1_card_1,rc1_xreal_0,rc2_card_1,rc2_ordinal1,rc3_funct_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_arytm_3,cc1_funct_1,cc1_ordinal1,cc1_relat_1,cc2_arytm_3,cc2_card_1,cc2_funct_1,cc2_ordinal1,cc3_arytm_3,cc3_card_1,cc3_ordinal1,fc1_subset_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_ordinal1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_ordinal1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k5_numbers,dt_k5_ordinal2,dt_m2_subset_1,dt_c1_6__afinsq_1,fc1_ordinal2,t1_subset,t7_boole,e3_6_1__afinsq_1]),
    [interesting(0.65),file(afinsq_1,e4_6_1__afinsq_1),[file(afinsq_1,e4_6_1__afinsq_1)]]).

fof(i2_6_1__afinsq_1,theorem,(
    $true ),
    introduced(tautology,[file(afinsq_1,i2_6_1__afinsq_1)]),
    [interesting(0.65),trivial,file(afinsq_1,i2_6_1__afinsq_1)]).

fof(i1_6_1__afinsq_1,plain,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & k1_relat_1(c1_6__afinsq_1) = A ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__afinsq_1,e1_6_1__afinsq_1])],[e4_6_1__afinsq_1,i2_6_1__afinsq_1]),
    [interesting(0.65),file(afinsq_1,i1_6_1__afinsq_1),[file(afinsq_1,i1_6_1__afinsq_1)]]).

fof(e1_6__afinsq_1,plain,(
    ~ ( v1_finset_1(c1_6__afinsq_1)
      & v5_ordinal1(c1_6__afinsq_1)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => k1_relat_1(c1_6__afinsq_1) != A ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__afinsq_1]),discharge_asm(discharge,[e1_6_1__afinsq_1])],[e1_6_1__afinsq_1,i1_6_1__afinsq_1]),
    [interesting(0.8),file(afinsq_1,e1_6__afinsq_1),[file(afinsq_1,e1_6__afinsq_1)]]).

fof(e2_6__afinsq_1,assumption,(
    ? [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
      & k1_relat_1(c1_6__afinsq_1) = A ) ),
    introduced(assumption,[file(afinsq_1,e2_6__afinsq_1)]),
    [interesting(0.8),axiom,file(afinsq_1,e2_6__afinsq_1)]).

fof(e3_6__afinsq_1,plain,
    ( v1_finset_1(c1_6__afinsq_1)
    & v5_ordinal1(c1_6__afinsq_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__afinsq_1,e2_6__afinsq_1])],[cc1_funct_7,cc2_funct_7,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_funcop_1,rc2_xreal_0,rc3_relat_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_card_1,cc1_xreal_0,cc2_xreal_0,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc12_relat_1,fc2_ordinal1,fc3_funct_7,fc4_relat_1,rc1_arytm_3,rc1_card_1,rc1_xreal_0,rc2_card_1,rc2_ordinal1,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc1_arytm_3,cc1_funct_1,cc1_relat_1,cc2_arytm_3,cc2_card_1,cc2_funct_1,cc2_ordinal1,cc3_arytm_3,cc3_card_1,cc3_ordinal1,fc1_ordinal2,fc1_subset_1,fc5_relat_1,fc7_relat_1,rc1_ordinal1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_ordinal1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_6__afinsq_1,cc1_ordinal1,fc5_ordinal1,rc1_funct_1,rc4_ordinal1,e2_6__afinsq_1,t29_finset_1,d7_ordinal1]),
    [interesting(0.8),file(afinsq_1,e3_6__afinsq_1),[file(afinsq_1,e3_6__afinsq_1)]]).

fof(i4_6__afinsq_1,theorem,(
    $true ),
    introduced(tautology,[file(afinsq_1,i4_6__afinsq_1)]),
    [interesting(0.8),trivial,file(afinsq_1,i4_6__afinsq_1)]).

fof(i3_6__afinsq_1,plain,
    ( v1_finset_1(c1_6__afinsq_1)
    & v5_ordinal1(c1_6__afinsq_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__afinsq_1,e2_6__afinsq_1])],[e3_6__afinsq_1,i4_6__afinsq_1]),
    [interesting(0.8),file(afinsq_1,i3_6__afinsq_1),[file(afinsq_1,i3_6__afinsq_1)]]).

fof(i2_6__afinsq_1,plain,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & k1_relat_1(c1_6__afinsq_1) = A )
   => ( v1_finset_1(c1_6__afinsq_1)
      & v5_ordinal1(c1_6__afinsq_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__afinsq_1]),discharge_asm(discharge,[e2_6__afinsq_1])],[e2_6__afinsq_1,i3_6__afinsq_1]),
    [interesting(0.8),file(afinsq_1,i2_6__afinsq_1),[file(afinsq_1,i2_6__afinsq_1)]]).

fof(i1_6__afinsq_1,plain,
    ( ( v1_finset_1(c1_6__afinsq_1)
      & v5_ordinal1(c1_6__afinsq_1) )
  <=> ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & k1_relat_1(c1_6__afinsq_1) = A ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__afinsq_1])],[e1_6__afinsq_1,i2_6__afinsq_1]),
    [interesting(0.8),file(afinsq_1,i1_6__afinsq_1),[file(afinsq_1,i1_6__afinsq_1)]]).

fof(i1_6_tmp__afinsq_1,plain,
    ( ( v1_relat_1(c1_6__afinsq_1)
      & v1_funct_1(c1_6__afinsq_1) )
   => ( ( v1_finset_1(c1_6__afinsq_1)
        & v5_ordinal1(c1_6__afinsq_1) )
    <=> ? [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
          & k1_relat_1(c1_6__afinsq_1) = A ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__afinsq_1])],[dt_c1_6__afinsq_1,i1_6__afinsq_1]),
    [interesting(1),t7_afinsq_1]).

fof(t7_afinsq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ( v1_finset_1(A)
          & v5_ordinal1(A) )
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k1_relat_1(A) = B ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__afinsq_1,dh_c1_6__afinsq_1]),
    [interesting(1),file(afinsq_1,t7_afinsq_1),[file(afinsq_1,t7_afinsq_1)]]).