% Mizar ND problem: t4_amistd_3,amistd_3,152,56 
fof(dh_c1_10__amistd_3,definition,
    ( ( v1_relat_1(c1_10__amistd_3)
     => ( ( v1_finset_1(k1_relat_1(c1_10__amistd_3))
          & v1_finset_1(k2_relat_1(c1_10__amistd_3)) )
       => v1_finset_1(c1_10__amistd_3) ) )
   => ! [A] : 
        ( v1_relat_1(A)
       => ( ( v1_finset_1(k1_relat_1(A))
            & v1_finset_1(k2_relat_1(A)) )
         => v1_finset_1(A) ) ) ),
    introduced(definition,[new_symbol(c1_10__amistd_3),file(amistd_3,c1_10__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c1_10__amistd_3)]).

fof(e1_10__amistd_3,assumption,
    ( v1_finset_1(k1_relat_1(c1_10__amistd_3))
    & v1_finset_1(k2_relat_1(c1_10__amistd_3)) ),
    introduced(assumption,[file(amistd_3,e1_10__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,e1_10__amistd_3)]).

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(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(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(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_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_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(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(cc2_card_5,theorem,(
    ! [A] : 
      ( ( ~ v1_finset_1(A)
        & v1_card_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(card_5,cc2_card_5),
    [interesting(0.9),axiom,file(card_5,cc2_card_5)]).

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(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(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_card_5,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & ~ v1_finset_1(A)
      & v1_card_1(A) ) ),
    file(card_5,rc2_card_5),
    [interesting(0.9),axiom,file(card_5,rc2_card_5)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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(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(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_finseq_1,theorem,(
    ! [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) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(cc1_necklace,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_card_1(A) ) ),
    file(necklace,cc1_necklace),
    [interesting(0.9),axiom,file(necklace,cc1_necklace)]).

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(rc1_amistd_3,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & ~ v1_finset_1(A)
      & v1_setfam_1(A) ) ),
    file(amistd_3,rc1_amistd_3),
    [interesting(0.9),axiom,file(amistd_3,rc1_amistd_3)]).

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_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_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_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

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(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

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

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

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

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

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_finseq_1,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) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_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(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(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_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(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(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(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(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(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(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

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(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(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

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(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(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(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(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    [interesting(0.9),axiom,file(relat_1,k3_relat_1)]).

fof(dt_c1_10__amistd_3,assumption,(
    v1_relat_1(c1_10__amistd_3) ),
    introduced(assumption,[file(amistd_3,c1_10__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c1_10__amistd_3)]).

fof(cc1_amistd_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_1(A)
        & v1_setfam_1(A) ) ) ),
    file(amistd_1,cc1_amistd_1),
    [interesting(0.9),axiom,file(amistd_1,cc1_amistd_1)]).

fof(cc1_card_5,theorem,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ~ v1_xboole_0(A) ) ),
    file(card_5,cc1_card_5),
    [interesting(0.9),axiom,file(card_5,cc1_card_5)]).

fof(fc4_amistd_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k3_relat_1(A)) ) ),
    file(amistd_3,fc4_amistd_3),
    [interesting(0.9),axiom,file(amistd_3,fc4_amistd_3)]).

fof(fc5_amistd_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & ~ v1_finset_1(A) )
     => ( ~ v1_xboole_0(k3_relat_1(A))
        & ~ v1_finset_1(k3_relat_1(A)) ) ) ),
    file(amistd_3,fc5_amistd_3),
    [interesting(0.9),axiom,file(amistd_3,fc5_amistd_3)]).

fof(rc1_card_5,theorem,(
    ? [A] : ~ v1_finset_1(A) ),
    file(card_5,rc1_card_5),
    [interesting(0.9),axiom,file(card_5,rc1_card_5)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(fc22_membered,theorem,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    [interesting(0.9),axiom,file(membered,fc22_membered)]).

fof(fc23_membered,theorem,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    [interesting(0.9),axiom,file(membered,fc23_membered)]).

fof(fc24_membered,theorem,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    [interesting(0.9),axiom,file(membered,fc24_membered)]).

fof(fc25_membered,theorem,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    [interesting(0.9),axiom,file(membered,fc25_membered)]).

fof(fc26_membered,theorem,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    [interesting(0.9),axiom,file(membered,fc26_membered)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

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(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_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(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(fc2_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc2_relat_1)]).

fof(fc5_trees_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(trees_2,fc5_trees_2),
    [interesting(0.9),axiom,file(trees_2,fc5_trees_2)]).

fof(fc9_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]).

fof(t14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,t14_finset_1),
    [interesting(0.9),axiom,file(finset_1,t14_finset_1)]).

fof(e2_10__amistd_3,plain,(
    v1_finset_1(k2_xboole_0(k1_relat_1(c1_10__amistd_3),k2_relat_1(c1_10__amistd_3))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__amistd_3,e1_10__amistd_3])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_card_1,cc2_card_5,cc2_xreal_0,cc7_xreal_0,rc1_card_1,rc1_xreal_0,rc2_card_1,rc2_card_5,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_finseq_1,cc1_necklace,cc1_xreal_0,fc17_finseq_1,rc1_amistd_3,rc1_arytm_3,rc1_finseq_1,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc12_relat_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_ordinal1,fc4_relat_1,fc6_membered,rc1_membered,rc1_ordinal1,rc3_ordinal1,t1_boole,t1_subset,cc15_membered,cc1_amistd_1,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc11_finseq_1,fc2_relat_1,fc5_relat_1,fc5_trees_2,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finset_1,rc1_relat_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_c1_10__amistd_3,cc1_card_5,fc9_finset_1,rc1_card_5,e1_10__amistd_3,t14_finset_1]),
    [interesting(0.8),file(amistd_3,e2_10__amistd_3),[file(amistd_3,e2_10__amistd_3)]]).

fof(d6_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_relat_1),
    [interesting(0.9),axiom,file(relat_1,d6_relat_1)]).

fof(e3_10__amistd_3,plain,(
    v1_finset_1(k3_relat_1(c1_10__amistd_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__amistd_3,e1_10__amistd_3])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_card_1,cc2_card_5,cc2_xreal_0,cc7_xreal_0,rc1_card_1,rc1_xreal_0,rc2_card_1,rc2_card_5,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_finseq_1,cc1_necklace,cc1_xreal_0,fc17_finseq_1,rc1_amistd_3,rc1_arytm_3,rc1_finseq_1,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc12_relat_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_ordinal1,fc4_relat_1,fc6_membered,rc1_membered,rc1_ordinal1,rc3_ordinal1,t1_boole,t1_subset,cc15_membered,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_finset_1,rc1_relat_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_relat_1,dt_c1_10__amistd_3,cc1_amistd_1,cc1_card_5,fc11_finseq_1,fc2_relat_1,fc4_amistd_3,fc5_amistd_3,fc5_trees_2,fc9_finset_1,rc1_card_5,e2_10__amistd_3,d6_relat_1]),
    [interesting(0.8),file(amistd_3,e3_10__amistd_3),[file(amistd_3,e3_10__amistd_3)]]).

fof(t3_amistd_3,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finset_1(k3_relat_1(A))
       => v1_finset_1(A) ) ) ),
    file(amistd_3,t3_amistd_3),
    [interesting(0.9),axiom,file(amistd_3,t3_amistd_3)]).

fof(e4_10__amistd_3,plain,(
    v1_finset_1(c1_10__amistd_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_10__amistd_3,e1_10__amistd_3])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_card_1,cc2_card_5,cc2_xreal_0,cc7_xreal_0,rc1_card_1,rc1_xreal_0,rc2_card_1,rc2_card_5,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_finseq_1,cc1_necklace,cc1_xreal_0,rc1_amistd_3,rc1_arytm_3,rc1_finseq_1,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc12_relat_1,fc2_finseq_1,fc2_ordinal1,fc4_relat_1,fc6_membered,rc1_membered,rc1_ordinal1,rc3_ordinal1,t1_subset,t8_boole,cc15_membered,cc1_finset_1,cc1_relat_1,cc3_ordinal1,rc1_finset_1,rc1_relat_1,rc2_relat_1,t6_boole,t7_boole,dt_k3_relat_1,dt_c1_10__amistd_3,cc1_amistd_1,cc1_card_5,fc4_amistd_3,fc5_amistd_3,rc1_card_5,e3_10__amistd_3,t3_amistd_3]),
    [interesting(0.8),file(amistd_3,e4_10__amistd_3),[file(amistd_3,e4_10__amistd_3)]]).

fof(i3_10__amistd_3,theorem,(
    $true ),
    introduced(tautology,[file(amistd_3,i3_10__amistd_3)]),
    [interesting(0.8),trivial,file(amistd_3,i3_10__amistd_3)]).

fof(i2_10__amistd_3,plain,(
    v1_finset_1(c1_10__amistd_3) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_10__amistd_3,e1_10__amistd_3])],[e4_10__amistd_3,i3_10__amistd_3]),
    [interesting(0.8),file(amistd_3,i2_10__amistd_3),[file(amistd_3,i2_10__amistd_3)]]).

fof(i1_10__amistd_3,plain,
    ( ( v1_finset_1(k1_relat_1(c1_10__amistd_3))
      & v1_finset_1(k2_relat_1(c1_10__amistd_3)) )
   => v1_finset_1(c1_10__amistd_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_10__amistd_3]),discharge_asm(discharge,[e1_10__amistd_3])],[e1_10__amistd_3,i2_10__amistd_3]),
    [interesting(0.8),file(amistd_3,i1_10__amistd_3),[file(amistd_3,i1_10__amistd_3)]]).

fof(i1_10_tmp__amistd_3,plain,
    ( v1_relat_1(c1_10__amistd_3)
   => ( ( v1_finset_1(k1_relat_1(c1_10__amistd_3))
        & v1_finset_1(k2_relat_1(c1_10__amistd_3)) )
     => v1_finset_1(c1_10__amistd_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_10__amistd_3])],[dt_c1_10__amistd_3,i1_10__amistd_3]),
    [interesting(1),t4_amistd_3]).

fof(t4_amistd_3,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( v1_finset_1(k1_relat_1(A))
          & v1_finset_1(k2_relat_1(A)) )
       => v1_finset_1(A) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_10_tmp__amistd_3,dh_c1_10__amistd_3]),
    [interesting(1),file(amistd_3,t4_amistd_3),[file(amistd_3,t4_amistd_3)]]).