% Mizar ND problem: t1_amistd_3,amistd_3,70,46 
fof(dh_c1_3__amistd_3,definition,
    ( ! [A,B] : 
        ( v1_relat_1(B)
       => ( ( k1_relat_1(B) = k1_tarski(c1_3__amistd_3)
            & k2_relat_1(B) = k1_tarski(A) )
         => B = k3_cqc_lang(c1_3__amistd_3,A) ) )
   => ! [C,D,E] : 
        ( v1_relat_1(E)
       => ( ( k1_relat_1(E) = k1_tarski(C)
            & k2_relat_1(E) = k1_tarski(D) )
         => E = k3_cqc_lang(C,D) ) ) ),
    introduced(definition,[new_symbol(c1_3__amistd_3),file(amistd_3,c1_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c1_3__amistd_3)]).

fof(dh_c2_3__amistd_3,definition,
    ( ! [A] : 
        ( v1_relat_1(A)
       => ( ( k1_relat_1(A) = k1_tarski(c1_3__amistd_3)
            & k2_relat_1(A) = k1_tarski(c2_3__amistd_3) )
         => A = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ) )
   => ! [B,C] : 
        ( v1_relat_1(C)
       => ( ( k1_relat_1(C) = k1_tarski(c1_3__amistd_3)
            & k2_relat_1(C) = k1_tarski(B) )
         => C = k3_cqc_lang(c1_3__amistd_3,B) ) ) ),
    introduced(definition,[new_symbol(c2_3__amistd_3),file(amistd_3,c2_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c2_3__amistd_3)]).

fof(dh_c3_3__amistd_3,definition,
    ( ( v1_relat_1(c3_3__amistd_3)
     => ( ( k1_relat_1(c3_3__amistd_3) = k1_tarski(c1_3__amistd_3)
          & k2_relat_1(c3_3__amistd_3) = k1_tarski(c2_3__amistd_3) )
       => c3_3__amistd_3 = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ) )
   => ! [A] : 
        ( v1_relat_1(A)
       => ( ( k1_relat_1(A) = k1_tarski(c1_3__amistd_3)
            & k2_relat_1(A) = k1_tarski(c2_3__amistd_3) )
         => A = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ) ) ),
    introduced(definition,[new_symbol(c3_3__amistd_3),file(amistd_3,c3_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c3_3__amistd_3)]).

fof(e1_3__amistd_3,assumption,(
    k1_relat_1(c3_3__amistd_3) = k1_tarski(c1_3__amistd_3) ),
    introduced(assumption,[file(amistd_3,e1_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,e1_3__amistd_3)]).

fof(e2_3__amistd_3,assumption,(
    k2_relat_1(c3_3__amistd_3) = k1_tarski(c2_3__amistd_3) ),
    introduced(assumption,[file(amistd_3,e2_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,e2_3__amistd_3)]).

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(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(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(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(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_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(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(fc10_membered,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc12_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    [interesting(0.9),axiom,file(membered,fc12_membered)]).

fof(fc13_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    [interesting(0.9),axiom,file(membered,fc13_membered)]).

fof(fc14_membered,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    [interesting(0.9),axiom,file(membered,fc14_membered)]).

fof(fc15_membered,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    [interesting(0.9),axiom,file(membered,fc15_membered)]).

fof(fc16_membered,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    [interesting(0.9),axiom,file(membered,fc16_membered)]).

fof(fc7_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

fof(rc1_amistd_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & ~ v1_realset1(A) ) ),
    file(amistd_1,rc1_amistd_1),
    [interesting(0.9),axiom,file(amistd_1,rc1_amistd_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_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(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(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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_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(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_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(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_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(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_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(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_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(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(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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

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(cc2_necklace,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_realset1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A)
        & v1_setfam_1(A) ) ) ),
    file(necklace,cc2_necklace),
    [interesting(0.9),axiom,file(necklace,cc2_necklace)]).

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_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc1_heyting2,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k1_tarski(k4_tarski(A,B)))
      & v1_relat_1(k1_tarski(k4_tarski(A,B)))
      & v1_funct_1(k1_tarski(k4_tarski(A,B))) ) ),
    file(heyting2,fc1_heyting2),
    [interesting(0.9),axiom,file(heyting2,fc1_heyting2)]).

fof(fc2_finset_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k2_tarski(A,B))
      & v1_finset_1(k2_tarski(A,B)) ) ),
    file(finset_1,fc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc2_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(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(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(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    [interesting(0.9),axiom,file(cqc_lang,k3_cqc_lang)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(dt_c1_3__amistd_3,assumption,(
    $true ),
    introduced(assumption,[file(amistd_3,c1_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c1_3__amistd_3)]).

fof(dt_c2_3__amistd_3,assumption,(
    $true ),
    introduced(assumption,[file(amistd_3,c2_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c2_3__amistd_3)]).

fof(dt_c3_3__amistd_3,assumption,(
    v1_relat_1(c3_3__amistd_3) ),
    introduced(assumption,[file(amistd_3,c3_3__amistd_3)]),
    [interesting(0.8),axiom,file(amistd_3,c3_3__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(fc2_amistd_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(k3_cqc_lang(A,B))
      & v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B))
      & v1_realset1(k3_cqc_lang(A,B))
      & v1_setfam_1(k3_cqc_lang(A,B)) ) ),
    file(amistd_1,fc2_amistd_1),
    [interesting(0.9),axiom,file(amistd_1,fc2_amistd_1)]).

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(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(dh_c1_3_1__amistd_3,definition,
    ( ! [A] : 
        ( r2_hidden(k4_tarski(c1_3_1__amistd_3,A),c3_3__amistd_3)
      <=> r2_hidden(k4_tarski(c1_3_1__amistd_3,A),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) )
   => ! [B,C] : 
        ( r2_hidden(k4_tarski(B,C),c3_3__amistd_3)
      <=> r2_hidden(k4_tarski(B,C),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ) ),
    introduced(definition,[new_symbol(c1_3_1__amistd_3),file(amistd_3,c1_3_1__amistd_3)]),
    [interesting(0.65),axiom,file(amistd_3,c1_3_1__amistd_3)]).

fof(dh_c2_3_1__amistd_3,definition,
    ( ( r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3)
    <=> r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) )
   => ! [A] : 
        ( r2_hidden(k4_tarski(c1_3_1__amistd_3,A),c3_3__amistd_3)
      <=> r2_hidden(k4_tarski(c1_3_1__amistd_3,A),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ) ),
    introduced(definition,[new_symbol(c2_3_1__amistd_3),file(amistd_3,c2_3_1__amistd_3)]),
    [interesting(0.65),axiom,file(amistd_3,c2_3_1__amistd_3)]).

fof(e1_3_1_1__amistd_3,assumption,(
    r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3) ),
    introduced(assumption,[file(amistd_3,e1_3_1_1__amistd_3)]),
    [interesting(0.5),axiom,file(amistd_3,e1_3_1_1__amistd_3)]).

fof(dt_c1_3_1__amistd_3,assumption,(
    $true ),
    introduced(assumption,[file(amistd_3,c1_3_1__amistd_3)]),
    [interesting(0.65),axiom,file(amistd_3,c1_3_1__amistd_3)]).

fof(dt_c2_3_1__amistd_3,assumption,(
    $true ),
    introduced(assumption,[file(amistd_3,c2_3_1__amistd_3)]),
    [interesting(0.65),axiom,file(amistd_3,c2_3_1__amistd_3)]).

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(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(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(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(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(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(t20_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k2_relat_1(C)) ) ) ) ),
    file(relat_1,t20_relat_1),
    [interesting(0.9),axiom,file(relat_1,t20_relat_1)]).

fof(e2_3_1_1__amistd_3,plain,
    ( r2_hidden(c1_3_1__amistd_3,k1_relat_1(c3_3__amistd_3))
    & r2_hidden(c2_3_1__amistd_3,k2_relat_1(c3_3__amistd_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,e1_3_1_1__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_card_5,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc11_finseq_1,fc12_relat_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc4_relat_1,fc5_trees_2,fc6_membered,rc1_card_5,rc1_finset_1,rc1_membered,rc1_ordinal1,rc3_ordinal1,rc7_finseq_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc1_finset_1,fc1_heyting2,fc2_finset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k4_tarski,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,cc1_amistd_1,t1_subset,t7_boole,d5_tarski,e1_3_1_1__amistd_3,t20_relat_1]),
    [interesting(0.5),file(amistd_3,e2_3_1_1__amistd_3),[file(amistd_3,e2_3_1_1__amistd_3)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e3_3_1_1__amistd_3,plain,
    ( c1_3_1__amistd_3 = c1_3__amistd_3
    & c2_3_1__amistd_3 = c2_3__amistd_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__amistd_3,dt_c2_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,e1_3_1_1__amistd_3,e1_3__amistd_3,e2_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,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,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_amistd_1,cc1_card_5,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc11_finseq_1,fc5_relat_1,fc5_trees_2,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k1_tarski,dt_k2_relat_1,dt_c1_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,fc1_finset_1,t1_subset,t7_boole,e2_3_1_1__amistd_3,e1_3__amistd_3,e2_3__amistd_3,d1_tarski]),
    [interesting(0.5),file(amistd_3,e3_3_1_1__amistd_3),[file(amistd_3,e3_3_1_1__amistd_3)]]).

fof(t19_ami_1,theorem,(
    ! [A,B] : k3_cqc_lang(A,B) = k1_tarski(k4_tarski(A,B)) ),
    file(ami_1,t19_ami_1),
    [interesting(0.9),axiom,file(ami_1,t19_ami_1)]).

fof(e3_3__amistd_3,plain,(
    k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) = k1_tarski(k4_tarski(c1_3__amistd_3,c2_3__amistd_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__amistd_3,dt_c2_3__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,fc10_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc7_membered,fc8_membered,fc9_membered,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,fc11_membered,fc16_membered,rc1_amistd_1,rc1_arytm_3,rc1_finseq_1,rc3_finseq_1,rc3_relat_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,rc2_ordinal1,rc3_ordinal1,rc6_finseq_1,t1_subset,commutativity_k2_tarski,dt_k2_tarski,cc15_membered,cc1_amistd_1,cc1_card_5,cc1_finset_1,cc1_relat_1,cc2_necklace,cc3_ordinal1,fc2_finset_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,dt_k1_tarski,dt_k3_cqc_lang,dt_k4_tarski,dt_c1_3__amistd_3,dt_c2_3__amistd_3,fc1_finset_1,fc1_heyting2,fc2_amistd_1,d5_tarski,t19_ami_1]),
    [interesting(0.8),file(amistd_3,e3_3__amistd_3),[file(amistd_3,e3_3__amistd_3)]]).

fof(e4_3_1_1__amistd_3,plain,(
    r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,e1_3_1_1__amistd_3,e1_3__amistd_3,e2_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_amistd_1,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc3_finseq_1,rc3_relat_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,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,rc2_ordinal1,rc3_ordinal1,rc6_finseq_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_amistd_1,cc1_card_5,cc1_finset_1,cc1_relat_1,cc2_necklace,cc3_ordinal1,fc2_finset_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k3_cqc_lang,dt_k4_tarski,dt_c1_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3__amistd_3,dt_c2_3_1__amistd_3,fc1_finset_1,fc1_heyting2,fc2_amistd_1,t1_subset,t7_boole,d5_tarski,e3_3_1_1__amistd_3,e3_3__amistd_3,d1_tarski]),
    [interesting(0.5),file(amistd_3,e4_3_1_1__amistd_3),[file(amistd_3,e4_3_1_1__amistd_3)]]).

fof(i2_3_1_1__amistd_3,theorem,(
    $true ),
    introduced(tautology,[file(amistd_3,i2_3_1_1__amistd_3)]),
    [interesting(0.5),trivial,file(amistd_3,i2_3_1_1__amistd_3)]).

fof(i1_3_1_1__amistd_3,plain,(
    r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,e1_3_1_1__amistd_3,e1_3__amistd_3,e2_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3])],[e4_3_1_1__amistd_3,i2_3_1_1__amistd_3]),
    [interesting(0.5),file(amistd_3,i1_3_1_1__amistd_3),[file(amistd_3,i1_3_1_1__amistd_3)]]).

fof(e1_3_1__amistd_3,plain,
    ( r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3)
   => r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,e1_3__amistd_3,e2_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3]),discharge_asm(discharge,[e1_3_1_1__amistd_3])],[e1_3_1_1__amistd_3,i1_3_1_1__amistd_3]),
    [interesting(0.65),file(amistd_3,e1_3_1__amistd_3),[file(amistd_3,e1_3_1__amistd_3)]]).

fof(e2_3_1__amistd_3,assumption,(
    r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ),
    introduced(assumption,[file(amistd_3,e2_3_1__amistd_3)]),
    [interesting(0.65),axiom,file(amistd_3,e2_3_1__amistd_3)]).

fof(dh_c3_3_1__amistd_3,definition,
    ( ? [A] : r2_hidden(k4_tarski(c1_3_1__amistd_3,A),c3_3__amistd_3)
   => r2_hidden(k4_tarski(c1_3_1__amistd_3,c3_3_1__amistd_3),c3_3__amistd_3) ),
    introduced(definition,[new_symbol(c3_3_1__amistd_3),file(amistd_3,c3_3_1__amistd_3)]),
    [interesting(0.65),axiom,file(amistd_3,c3_3_1__amistd_3)]).

fof(e3_3_1__amistd_3,plain,(
    k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3) = k4_tarski(c1_3__amistd_3,c2_3__amistd_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_amistd_1,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc3_finseq_1,rc3_relat_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,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,rc2_ordinal1,rc3_ordinal1,rc6_finseq_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_amistd_1,cc1_card_5,cc1_finset_1,cc1_relat_1,cc2_necklace,cc3_ordinal1,fc2_finset_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k3_cqc_lang,dt_k4_tarski,dt_c1_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3__amistd_3,dt_c2_3_1__amistd_3,fc1_finset_1,fc1_heyting2,fc2_amistd_1,t1_subset,t7_boole,d5_tarski,e2_3_1__amistd_3,e3_3__amistd_3,d1_tarski]),
    [interesting(0.65),file(amistd_3,e3_3_1__amistd_3),[file(amistd_3,e3_3_1__amistd_3)]]).

fof(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t33_zfmisc_1)]).

fof(e4_3_1__amistd_3,plain,
    ( c1_3_1__amistd_3 = c1_3__amistd_3
    & c2_3_1__amistd_3 = c2_3__amistd_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__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,fc10_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc7_membered,fc8_membered,fc9_membered,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,fc11_membered,fc16_membered,rc1_arytm_3,rc1_finseq_1,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_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,cc15_membered,cc1_amistd_1,cc1_card_5,cc1_finset_1,cc1_relat_1,cc3_ordinal1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,dt_k1_tarski,dt_k2_tarski,fc1_finset_1,fc1_heyting2,fc2_finset_1,dt_k4_tarski,dt_c1_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3__amistd_3,dt_c2_3_1__amistd_3,d5_tarski,e3_3_1__amistd_3,t33_zfmisc_1]),
    [interesting(0.65),file(amistd_3,e4_3_1__amistd_3),[file(amistd_3,e4_3_1__amistd_3)]]).

fof(e5_3_1__amistd_3,plain,(
    r2_hidden(c1_3_1__amistd_3,k1_relat_1(c3_3__amistd_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc17_finseq_1,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,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,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_amistd_1,cc1_card_5,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc5_relat_1,fc5_trees_2,fc7_relat_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k1_tarski,dt_c1_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,fc1_finset_1,t1_subset,t7_boole,e4_3_1__amistd_3,e1_3__amistd_3,d1_tarski]),
    [interesting(0.65),file(amistd_3,e5_3_1__amistd_3),[file(amistd_3,e5_3_1__amistd_3)]]).

fof(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    [interesting(0.9),axiom,file(relat_1,d4_relat_1)]).

fof(e6_3_1__amistd_3,plain,(
    ? [A] : r2_hidden(k4_tarski(c1_3_1__amistd_3,A),c3_3__amistd_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_card_5,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc12_relat_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc4_relat_1,fc5_trees_2,fc6_membered,rc1_card_5,rc1_finset_1,rc1_membered,rc1_ordinal1,rc3_ordinal1,rc7_finseq_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc1_finset_1,fc1_heyting2,fc2_finset_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k4_tarski,dt_c1_3_1__amistd_3,dt_c3_3__amistd_3,cc1_amistd_1,t1_subset,t7_boole,d5_tarski,e5_3_1__amistd_3,d4_relat_1]),
    [interesting(0.65),file(amistd_3,e6_3_1__amistd_3),[file(amistd_3,e6_3_1__amistd_3)]]).

fof(dt_c3_3_1__amistd_3,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[dh_c3_3_1__amistd_3,e6_3_1__amistd_3]),
    [interesting(0.65),file(amistd_3,c3_3_1__amistd_3),[file(amistd_3,c3_3_1__amistd_3)]]).

fof(e7_3_1__amistd_3,plain,(
    r2_hidden(k4_tarski(c1_3_1__amistd_3,c3_3_1__amistd_3),c3_3__amistd_3) ),
    inference(consider,[status(thm),assumptions([dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[dh_c3_3_1__amistd_3,e6_3_1__amistd_3]),
    [interesting(0.65),file(amistd_3,e7_3_1__amistd_3),[file(amistd_3,e7_3_1__amistd_3)]]).

fof(e8_3_1__amistd_3,plain,(
    r2_hidden(c3_3_1__amistd_3,k2_relat_1(c3_3__amistd_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_card_5,cc1_membered,cc1_ordinal1,cc2_arytm_3,cc2_membered,cc2_ordinal1,cc3_membered,cc4_membered,fc11_finseq_1,fc12_relat_1,fc17_finseq_1,fc2_finseq_1,fc2_ordinal1,fc4_relat_1,fc5_trees_2,fc6_membered,rc1_card_5,rc1_finset_1,rc1_membered,rc1_ordinal1,rc3_ordinal1,rc7_finseq_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc1_finset_1,fc1_heyting2,fc2_finset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k4_tarski,dt_c1_3_1__amistd_3,dt_c3_3__amistd_3,dt_c3_3_1__amistd_3,cc1_amistd_1,t1_subset,t7_boole,d5_tarski,e7_3_1__amistd_3,t20_relat_1]),
    [interesting(0.65),file(amistd_3,e8_3_1__amistd_3),[file(amistd_3,e8_3_1__amistd_3)]]).

fof(e9_3_1__amistd_3,plain,(
    r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3) ),
    inference(mizar_by,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc2_ordinal1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,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,commutativity_k2_tarski,existence_m1_subset_1,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_amistd_1,cc1_card_5,cc1_finset_1,cc1_relat_1,cc3_ordinal1,fc11_finseq_1,fc2_finset_1,fc6_relat_1,fc8_relat_1,rc1_card_5,rc1_finset_1,rc1_relat_1,rc2_relat_1,rc7_finseq_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_relat_1,dt_k4_tarski,dt_c1_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3__amistd_3,dt_c2_3_1__amistd_3,dt_c3_3__amistd_3,dt_c3_3_1__amistd_3,fc1_finset_1,fc1_heyting2,t1_subset,t7_boole,d5_tarski,e8_3_1__amistd_3,e2_3__amistd_3,e4_3_1__amistd_3,e7_3_1__amistd_3,d1_tarski]),
    [interesting(0.65),file(amistd_3,e9_3_1__amistd_3),[file(amistd_3,e9_3_1__amistd_3)]]).

fof(i4_3_1__amistd_3,theorem,(
    $true ),
    introduced(tautology,[file(amistd_3,i4_3_1__amistd_3)]),
    [interesting(0.65),trivial,file(amistd_3,i4_3_1__amistd_3)]).

fof(i3_3_1__amistd_3,plain,(
    r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3) ),
    inference(conclusion,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,e2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[e9_3_1__amistd_3,i4_3_1__amistd_3]),
    [interesting(0.65),file(amistd_3,i3_3_1__amistd_3),[file(amistd_3,i3_3_1__amistd_3)]]).

fof(i2_3_1__amistd_3,plain,
    ( r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3))
   => r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3) ),
    inference(discharge_asm,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3]),discharge_asm(discharge,[e2_3_1__amistd_3])],[e2_3_1__amistd_3,i3_3_1__amistd_3]),
    [interesting(0.65),file(amistd_3,i2_3_1__amistd_3),[file(amistd_3,i2_3_1__amistd_3)]]).

fof(i1_3_1__amistd_3,plain,
    ( r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3)
  <=> r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ),
    inference(conclusion,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[e1_3_1__amistd_3,i2_3_1__amistd_3]),
    [interesting(0.65),file(amistd_3,i1_3_1__amistd_3),[file(amistd_3,i1_3_1__amistd_3)]]).

fof(i1_3_1_tmp__amistd_3,plain,
    ( r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),c3_3__amistd_3)
  <=> r2_hidden(k4_tarski(c1_3_1__amistd_3,c2_3_1__amistd_3),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ),
    inference(discharge_asm,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3]),discharge_asm(discharge,[dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3])],[dt_c1_3_1__amistd_3,dt_c2_3_1__amistd_3,i1_3_1__amistd_3]),
    [interesting(0.8),e4_3__amistd_3]).

fof(e4_3__amistd_3,plain,(
    ! [A,B] : 
      ( r2_hidden(k4_tarski(A,B),c3_3__amistd_3)
    <=> r2_hidden(k4_tarski(A,B),k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3)) ) ),
    inference(let,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[i1_3_1_tmp__amistd_3,dh_c1_3_1__amistd_3,dh_c2_3_1__amistd_3]),
    [interesting(0.8),file(amistd_3,e4_3__amistd_3),[file(amistd_3,e4_3__amistd_3)]]).

fof(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_1),
    [interesting(0.9),axiom,file(relat_1,d2_relat_1)]).

fof(e5_3__amistd_3,plain,(
    c3_3__amistd_3 = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ),
    inference(mizar_by,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[cc1_card_1,cc2_card_5,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_card_1,rc2_card_1,rc2_card_5,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_finseq_1,cc1_necklace,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_amistd_1,rc1_arytm_3,rc1_finseq_1,rc1_xreal_0,rc3_finseq_1,rc3_relat_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_arytm_3,cc1_card_5,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_card_5,rc1_finset_1,rc1_membered,rc1_ordinal1,rc2_ordinal1,rc3_ordinal1,rc6_finseq_1,rc7_finseq_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_relat_1,cc2_necklace,cc3_ordinal1,fc1_finset_1,fc1_heyting2,fc2_finset_1,rc1_relat_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k3_cqc_lang,dt_k4_tarski,dt_c1_3__amistd_3,dt_c2_3__amistd_3,dt_c3_3__amistd_3,cc1_amistd_1,fc2_amistd_1,t1_subset,t7_boole,d5_tarski,e4_3__amistd_3,d2_relat_1]),
    [interesting(0.8),file(amistd_3,e5_3__amistd_3),[file(amistd_3,e5_3__amistd_3)]]).

fof(i5_3__amistd_3,theorem,(
    $true ),
    introduced(tautology,[file(amistd_3,i5_3__amistd_3)]),
    [interesting(0.8),trivial,file(amistd_3,i5_3__amistd_3)]).

fof(i4_3__amistd_3,plain,(
    c3_3__amistd_3 = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ),
    inference(conclusion,[status(thm),assumptions([e2_3__amistd_3,dt_c3_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3,e1_3__amistd_3])],[e5_3__amistd_3,i5_3__amistd_3]),
    [interesting(0.8),file(amistd_3,i4_3__amistd_3),[file(amistd_3,i4_3__amistd_3)]]).

fof(i3_3__amistd_3,plain,
    ( ( k1_relat_1(c3_3__amistd_3) = k1_tarski(c1_3__amistd_3)
      & k2_relat_1(c3_3__amistd_3) = k1_tarski(c2_3__amistd_3) )
   => c3_3__amistd_3 = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__amistd_3,dt_c1_3__amistd_3,dt_c2_3__amistd_3]),discharge_asm(discharge,[e1_3__amistd_3,e2_3__amistd_3])],[e1_3__amistd_3,e2_3__amistd_3,i4_3__amistd_3]),
    [interesting(0.8),file(amistd_3,i3_3__amistd_3),[file(amistd_3,i3_3__amistd_3)]]).

fof(i3_3_tmp__amistd_3,plain,
    ( v1_relat_1(c3_3__amistd_3)
   => ( ( k1_relat_1(c3_3__amistd_3) = k1_tarski(c1_3__amistd_3)
        & k2_relat_1(c3_3__amistd_3) = k1_tarski(c2_3__amistd_3) )
     => c3_3__amistd_3 = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__amistd_3,dt_c2_3__amistd_3]),discharge_asm(discharge,[dt_c3_3__amistd_3])],[dt_c3_3__amistd_3,i3_3__amistd_3]),
    [interesting(0.8),i2_3__amistd_3]).

fof(i2_3__amistd_3,plain,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_tarski(c1_3__amistd_3)
          & k2_relat_1(A) = k1_tarski(c2_3__amistd_3) )
       => A = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__amistd_3,dt_c2_3__amistd_3])],[i3_3_tmp__amistd_3,dh_c3_3__amistd_3]),
    [interesting(0.8),file(amistd_3,i2_3__amistd_3),[file(amistd_3,i2_3__amistd_3)]]).

fof(i2_3_tmp__amistd_3,plain,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_tarski(c1_3__amistd_3)
          & k2_relat_1(A) = k1_tarski(c2_3__amistd_3) )
       => A = k3_cqc_lang(c1_3__amistd_3,c2_3__amistd_3) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__amistd_3]),discharge_asm(discharge,[dt_c2_3__amistd_3])],[dt_c2_3__amistd_3,i2_3__amistd_3]),
    [interesting(0.8),i1_3__amistd_3]).

fof(i1_3__amistd_3,plain,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( ( k1_relat_1(B) = k1_tarski(c1_3__amistd_3)
          & k2_relat_1(B) = k1_tarski(A) )
       => B = k3_cqc_lang(c1_3__amistd_3,A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__amistd_3])],[i2_3_tmp__amistd_3,dh_c2_3__amistd_3]),
    [interesting(0.8),file(amistd_3,i1_3__amistd_3),[file(amistd_3,i1_3__amistd_3)]]).

fof(i1_3_tmp__amistd_3,plain,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( ( k1_relat_1(B) = k1_tarski(c1_3__amistd_3)
          & k2_relat_1(B) = k1_tarski(A) )
       => B = k3_cqc_lang(c1_3__amistd_3,A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__amistd_3])],[dt_c1_3__amistd_3,i1_3__amistd_3]),
    [interesting(1),t1_amistd_3]).

fof(t1_amistd_3,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( k1_relat_1(C) = k1_tarski(A)
          & k2_relat_1(C) = k1_tarski(B) )
       => C = k3_cqc_lang(A,B) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__amistd_3,dh_c1_3__amistd_3]),
    [interesting(1),file(amistd_3,t1_amistd_3),[file(amistd_3,t1_amistd_3)]]).