% Mizar ND problem: t3_amistd_2,amistd_2,109,67 
fof(dh_c1_6__amistd_2,definition,
    ( ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(A),k1_relat_1(B)))
             => k1_funct_1(k4_xboole_0(A,B),c1_6__amistd_2) = k1_funct_1(A,c1_6__amistd_2) ) ) )
   => ! [C,D] : 
        ( ( v1_relat_1(D)
          & v1_funct_1(D) )
       => ! [E] : 
            ( ( v1_relat_1(E)
              & v1_funct_1(E) )
           => ( r2_hidden(C,k4_xboole_0(k1_relat_1(D),k1_relat_1(E)))
             => k1_funct_1(k4_xboole_0(D,E),C) = k1_funct_1(D,C) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__amistd_2),file(amistd_2,c1_6__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c1_6__amistd_2)]).

fof(dh_c2_6__amistd_2,definition,
    ( ( ( v1_relat_1(c2_6__amistd_2)
        & v1_funct_1(c2_6__amistd_2) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(c2_6__amistd_2),k1_relat_1(A)))
           => k1_funct_1(k4_xboole_0(c2_6__amistd_2,A),c1_6__amistd_2) = k1_funct_1(c2_6__amistd_2,c1_6__amistd_2) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(B),k1_relat_1(C)))
             => k1_funct_1(k4_xboole_0(B,C),c1_6__amistd_2) = k1_funct_1(B,c1_6__amistd_2) ) ) ) ),
    introduced(definition,[new_symbol(c2_6__amistd_2),file(amistd_2,c2_6__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c2_6__amistd_2)]).

fof(dh_c3_6__amistd_2,definition,
    ( ( ( v1_relat_1(c3_6__amistd_2)
        & v1_funct_1(c3_6__amistd_2) )
     => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(c2_6__amistd_2),k1_relat_1(c3_6__amistd_2)))
       => k1_funct_1(k4_xboole_0(c2_6__amistd_2,c3_6__amistd_2),c1_6__amistd_2) = k1_funct_1(c2_6__amistd_2,c1_6__amistd_2) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(c2_6__amistd_2),k1_relat_1(A)))
         => k1_funct_1(k4_xboole_0(c2_6__amistd_2,A),c1_6__amistd_2) = k1_funct_1(c2_6__amistd_2,c1_6__amistd_2) ) ) ),
    introduced(definition,[new_symbol(c3_6__amistd_2),file(amistd_2,c3_6__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c3_6__amistd_2)]).

fof(e1_6__amistd_2,assumption,(
    r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(c2_6__amistd_2),k1_relat_1(c3_6__amistd_2))) ),
    introduced(assumption,[file(amistd_2,e1_6__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,e1_6__amistd_2)]).

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(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_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_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_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(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(cc3_int_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    [interesting(0.9),axiom,file(int_1,cc3_int_1)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

fof(cc4_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    [interesting(0.9),axiom,file(int_1,cc4_int_1)]).

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_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_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_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_int_1,theorem,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    [interesting(0.9),axiom,file(int_1,rc2_int_1)]).

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

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

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

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

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

fof(cc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]).

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

fof(cc2_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]).

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

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

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

fof(fc12_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc12_finset_1)]).

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(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(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

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(fc37_membered,theorem,(
    ! [A,B] : 
      ( v1_membered(A)
     => v1_membered(k4_xboole_0(A,B)) ) ),
    file(membered,fc37_membered),
    [interesting(0.9),axiom,file(membered,fc37_membered)]).

fof(fc38_membered,theorem,(
    ! [A,B] : 
      ( v2_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc38_membered),
    [interesting(0.9),axiom,file(membered,fc38_membered)]).

fof(fc39_membered,theorem,(
    ! [A,B] : 
      ( v3_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc39_membered),
    [interesting(0.9),axiom,file(membered,fc39_membered)]).

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(fc40_membered,theorem,(
    ! [A,B] : 
      ( v4_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc40_membered),
    [interesting(0.9),axiom,file(membered,fc40_membered)]).

fof(fc41_membered,theorem,(
    ! [A,B] : 
      ( v5_membered(A)
     => ( v1_membered(k4_xboole_0(A,B))
        & v2_membered(k4_xboole_0(A,B))
        & v3_membered(k4_xboole_0(A,B))
        & v4_membered(k4_xboole_0(A,B))
        & v5_membered(k4_xboole_0(A,B)) ) ) ),
    file(membered,fc41_membered),
    [interesting(0.9),axiom,file(membered,fc41_membered)]).

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_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_pre_circ,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(pre_circ,rc1_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,rc1_pre_circ)]).

fof(rc2_tex_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]).

fof(rc3_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]).

fof(rc3_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]).

fof(rc4_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]).

fof(rc4_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]).

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(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

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(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(cc1_setfam_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,cc1_setfam_1)]).

fof(cc2_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]).

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_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_setfam_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,rc1_setfam_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(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

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(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

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

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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_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_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(dt_c1_6__amistd_2,assumption,(
    $true ),
    introduced(assumption,[file(amistd_2,c1_6__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c1_6__amistd_2)]).

fof(dt_c2_6__amistd_2,assumption,
    ( v1_relat_1(c2_6__amistd_2)
    & v1_funct_1(c2_6__amistd_2) ),
    introduced(assumption,[file(amistd_2,c2_6__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c2_6__amistd_2)]).

fof(dt_c3_6__amistd_2,assumption,
    ( v1_relat_1(c3_6__amistd_2)
    & v1_funct_1(c3_6__amistd_2) ),
    introduced(assumption,[file(amistd_2,c3_6__amistd_2)]),
    [interesting(0.8),axiom,file(amistd_2,c3_6__amistd_2)]).

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(fc3_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc3_relat_1)]).

fof(fc4_amistd_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k4_xboole_0(A,B))
        & v1_funct_1(k4_xboole_0(A,B))
        & v1_setfam_1(k4_xboole_0(A,B)) ) ) ),
    file(amistd_2,fc4_amistd_2),
    [interesting(0.9),axiom,file(amistd_2,fc4_amistd_2)]).

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(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(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(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t36_xboole_1)]).

fof(e3_6__amistd_2,plain,(
    r1_tarski(k4_xboole_0(c2_6__amistd_2,c3_6__amistd_2),c2_6__amistd_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_6__amistd_2,dt_c3_6__amistd_2])],[cc1_funct_7,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_finseq_1,cc1_xreal_0,cc2_funct_7,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc4_int_1,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc12_finset_1,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc37_membered,fc38_membered,fc39_membered,fc3_funct_7,fc40_membered,fc41_membered,fc4_relat_1,fc6_membered,rc1_finset_1,rc1_membered,rc1_pre_circ,rc2_tex_2,rc3_finset_1,rc3_tex_2,rc4_finset_1,rc4_tex_2,rc7_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,t8_boole,cc15_membered,cc1_finset_1,cc1_relat_1,cc1_setfam_1,cc2_tex_2,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_amistd_1,fc1_subset_1,fc3_relat_1,fc4_amistd_2,reflexivity_r1_tarski,dt_k4_xboole_0,dt_c2_6__amistd_2,dt_c3_6__amistd_2,t3_subset,t36_xboole_1]),
    [interesting(0.8),file(amistd_2,e3_6__amistd_2),[file(amistd_2,e3_6__amistd_2)]]).

fof(t15_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))) ) ) ),
    file(relat_1,t15_relat_1),
    [interesting(0.9),axiom,file(relat_1,t15_relat_1)]).

fof(e2_6__amistd_2,plain,(
    r1_tarski(k4_xboole_0(k1_relat_1(c2_6__amistd_2),k1_relat_1(c3_6__amistd_2)),k1_relat_1(k4_xboole_0(c2_6__amistd_2,c3_6__amistd_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_6__amistd_2,dt_c3_6__amistd_2])],[cc1_funct_7,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_finseq_1,cc1_xreal_0,cc2_funct_7,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc4_int_1,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,rc3_finseq_1,rc3_relat_1,rc6_finseq_1,rc8_finseq_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc12_finset_1,fc12_relat_1,fc17_finseq_1,fc1_xboole_0,fc2_finseq_1,fc37_membered,fc38_membered,fc39_membered,fc3_funct_7,fc40_membered,fc41_membered,fc4_relat_1,fc6_membered,rc1_finset_1,rc1_membered,rc1_pre_circ,rc2_tex_2,rc3_finset_1,rc3_tex_2,rc4_finset_1,rc4_tex_2,rc7_finseq_1,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,t8_boole,cc15_membered,cc1_finset_1,cc1_relat_1,cc1_setfam_1,cc2_tex_2,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,fc1_subset_1,fc4_amistd_2,reflexivity_r1_tarski,dt_k1_relat_1,dt_k4_xboole_0,dt_c2_6__amistd_2,dt_c3_6__amistd_2,cc1_amistd_1,fc3_relat_1,t3_subset,t15_relat_1]),
    [interesting(0.8),file(amistd_2,e2_6__amistd_2),[file(amistd_2,e2_6__amistd_2)]]).

fof(t8_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    [interesting(0.9),axiom,file(grfunc_1,t8_grfunc_1)]).

fof(e4_6__amistd_2,plain,(
    k1_funct_1(k4_xboole_0(c2_6__amistd_2,c3_6__amistd_2),c1_6__amistd_2) = k1_funct_1(c2_6__amistd_2,c1_6__amistd_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__amistd_2,e1_6__amistd_2,dt_c2_6__amistd_2,dt_c3_6__amistd_2])],[cc1_funct_7,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_finseq_1,cc1_xreal_0,cc2_funct_7,cc2_xreal_0,cc3_int_1,cc3_nat_1,cc4_int_1,cc7_xreal_0,rc1_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_int_1,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,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_tex_2,cc20_membered,cc2_finset_1,cc2_membered,cc3_membered,cc4_membered,fc12_finset_1,fc12_relat_1,fc17_finseq_1,fc1_xboole_0,fc2_finseq_1,fc37_membered,fc38_membered,fc39_membered,fc3_funct_7,fc40_membered,fc41_membered,fc4_relat_1,fc6_membered,rc1_finset_1,rc1_membered,rc1_pre_circ,rc2_tex_2,rc3_finset_1,rc3_tex_2,rc4_finset_1,rc4_tex_2,rc7_finseq_1,t3_boole,t4_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_relat_1,cc1_setfam_1,cc2_tex_2,fc1_subset_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc1_xboole_0,rc2_relat_1,rc2_subset_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k4_xboole_0,dt_c1_6__amistd_2,dt_c2_6__amistd_2,dt_c3_6__amistd_2,cc1_amistd_1,fc3_relat_1,fc4_amistd_2,t1_subset,t3_subset,t7_boole,e3_6__amistd_2,e1_6__amistd_2,e2_6__amistd_2,t8_grfunc_1]),
    [interesting(0.8),file(amistd_2,e4_6__amistd_2),[file(amistd_2,e4_6__amistd_2)]]).

fof(i4_6__amistd_2,theorem,(
    $true ),
    introduced(tautology,[file(amistd_2,i4_6__amistd_2)]),
    [interesting(0.8),trivial,file(amistd_2,i4_6__amistd_2)]).

fof(i3_6__amistd_2,plain,(
    k1_funct_1(k4_xboole_0(c2_6__amistd_2,c3_6__amistd_2),c1_6__amistd_2) = k1_funct_1(c2_6__amistd_2,c1_6__amistd_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_6__amistd_2,e1_6__amistd_2,dt_c2_6__amistd_2,dt_c3_6__amistd_2])],[e4_6__amistd_2,i4_6__amistd_2]),
    [interesting(0.8),file(amistd_2,i3_6__amistd_2),[file(amistd_2,i3_6__amistd_2)]]).

fof(i2_6__amistd_2,plain,
    ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(c2_6__amistd_2),k1_relat_1(c3_6__amistd_2)))
   => k1_funct_1(k4_xboole_0(c2_6__amistd_2,c3_6__amistd_2),c1_6__amistd_2) = k1_funct_1(c2_6__amistd_2,c1_6__amistd_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__amistd_2,dt_c2_6__amistd_2,dt_c3_6__amistd_2]),discharge_asm(discharge,[e1_6__amistd_2])],[e1_6__amistd_2,i3_6__amistd_2]),
    [interesting(0.8),file(amistd_2,i2_6__amistd_2),[file(amistd_2,i2_6__amistd_2)]]).

fof(i2_6_tmp__amistd_2,plain,
    ( ( v1_relat_1(c2_6__amistd_2)
      & v1_funct_1(c2_6__amistd_2)
      & v1_relat_1(c3_6__amistd_2)
      & v1_funct_1(c3_6__amistd_2) )
   => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(c2_6__amistd_2),k1_relat_1(c3_6__amistd_2)))
     => k1_funct_1(k4_xboole_0(c2_6__amistd_2,c3_6__amistd_2),c1_6__amistd_2) = k1_funct_1(c2_6__amistd_2,c1_6__amistd_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__amistd_2]),discharge_asm(discharge,[dt_c2_6__amistd_2,dt_c3_6__amistd_2])],[dt_c2_6__amistd_2,dt_c3_6__amistd_2,i2_6__amistd_2]),
    [interesting(0.8),i1_6__amistd_2]).

fof(i1_6__amistd_2,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(A),k1_relat_1(B)))
           => k1_funct_1(k4_xboole_0(A,B),c1_6__amistd_2) = k1_funct_1(A,c1_6__amistd_2) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__amistd_2])],[i2_6_tmp__amistd_2,dh_c2_6__amistd_2,dh_c3_6__amistd_2]),
    [interesting(0.8),file(amistd_2,i1_6__amistd_2),[file(amistd_2,i1_6__amistd_2)]]).

fof(i1_6_tmp__amistd_2,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(c1_6__amistd_2,k4_xboole_0(k1_relat_1(A),k1_relat_1(B)))
           => k1_funct_1(k4_xboole_0(A,B),c1_6__amistd_2) = k1_funct_1(A,c1_6__amistd_2) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__amistd_2])],[dt_c1_6__amistd_2,i1_6__amistd_2]),
    [interesting(1),t3_amistd_2]).

fof(t3_amistd_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k4_xboole_0(k1_relat_1(B),k1_relat_1(C)))
           => k1_funct_1(k4_xboole_0(B,C),A) = k1_funct_1(B,A) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__amistd_2,dh_c1_6__amistd_2]),
    [interesting(1),file(amistd_2,t3_amistd_2),[file(amistd_2,t3_amistd_2)]]).