% Mizar ND problem: t1_rfinseq,rfinseq,52,69 
fof(dh_c1_3__rfinseq,definition,
    ( ( ( v1_relat_1(c1_3__rfinseq)
        & v1_funct_1(c1_3__rfinseq) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( r1_rfinseq(c1_3__rfinseq,A)
           => k2_relat_1(c1_3__rfinseq) = k2_relat_1(A) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( r1_rfinseq(B,C)
             => k2_relat_1(B) = k2_relat_1(C) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__rfinseq),file(rfinseq,c1_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c1_3__rfinseq)]).

fof(dh_c2_3__rfinseq,definition,
    ( ( ( v1_relat_1(c2_3__rfinseq)
        & v1_funct_1(c2_3__rfinseq) )
     => ( r1_rfinseq(c1_3__rfinseq,c2_3__rfinseq)
       => k2_relat_1(c1_3__rfinseq) = k2_relat_1(c2_3__rfinseq) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r1_rfinseq(c1_3__rfinseq,A)
         => k2_relat_1(c1_3__rfinseq) = k2_relat_1(A) ) ) ),
    introduced(definition,[new_symbol(c2_3__rfinseq),file(rfinseq,c2_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c2_3__rfinseq)]).

fof(e1_3__rfinseq,assumption,(
    r1_rfinseq(c1_3__rfinseq,c2_3__rfinseq) ),
    introduced(assumption,[file(rfinseq,e1_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,e1_3__rfinseq)]).

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

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

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_c1_3__rfinseq,assumption,
    ( v1_relat_1(c1_3__rfinseq)
    & v1_funct_1(c1_3__rfinseq) ),
    introduced(assumption,[file(rfinseq,c1_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c1_3__rfinseq)]).

fof(dt_c2_3__rfinseq,assumption,
    ( v1_relat_1(c2_3__rfinseq)
    & v1_funct_1(c2_3__rfinseq) ),
    introduced(assumption,[file(rfinseq,c2_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c2_3__rfinseq)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]).

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_c1_3_1__rfinseq,assumption,(
    $true ),
    introduced(assumption,[file(rfinseq,c1_3_1__rfinseq)]),
    [interesting(0.65),axiom,file(rfinseq,c1_3_1__rfinseq)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_3_1__rfinseq,definition,
    ( ~ ( r2_hidden(c1_3_1__rfinseq,k2_relat_1(c1_3__rfinseq))
        & ~ r2_hidden(c1_3_1__rfinseq,k2_relat_1(c2_3__rfinseq)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_relat_1(c1_3__rfinseq))
          & ~ r2_hidden(A,k2_relat_1(c2_3__rfinseq)) ) ),
    introduced(definition,[new_symbol(c1_3_1__rfinseq),file(rfinseq,c1_3_1__rfinseq)]),
    [interesting(0.65),axiom,file(rfinseq,c1_3_1__rfinseq)]).

fof(e1_3_1__rfinseq,assumption,(
    r2_hidden(c1_3_1__rfinseq,k2_relat_1(c1_3__rfinseq)) ),
    introduced(assumption,[file(rfinseq,e1_3_1__rfinseq)]),
    [interesting(0.65),axiom,file(rfinseq,e1_3_1__rfinseq)]).

fof(e2_3_1__rfinseq,assumption,(
    ~ r2_hidden(c1_3_1__rfinseq,k2_relat_1(c2_3__rfinseq)) ),
    introduced(assumption,[file(rfinseq,e2_3_1__rfinseq)]),
    [interesting(0.65),axiom,file(rfinseq,e2_3_1__rfinseq)]).

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(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(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_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(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(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_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_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_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

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

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

fof(cc2_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(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(fc18_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k10_relat_1(A,B)) ) ),
    file(finseq_1,fc18_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc18_finseq_1)]).

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

fof(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_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

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

fof(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(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(dt_k10_relat_1,axiom,(
    $true ),
    file(relat_1,k10_relat_1),
    [interesting(0.9),axiom,file(relat_1,k10_relat_1)]).

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

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

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

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

fof(dh_c2_3_1__rfinseq,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_3__rfinseq))
        & k1_funct_1(c1_3__rfinseq,A) = c1_3_1__rfinseq )
   => ( r2_hidden(c2_3_1__rfinseq,k1_relat_1(c1_3__rfinseq))
      & k1_funct_1(c1_3__rfinseq,c2_3_1__rfinseq) = c1_3_1__rfinseq ) ),
    introduced(definition,[new_symbol(c2_3_1__rfinseq),file(rfinseq,c2_3_1__rfinseq)]),
    [interesting(0.65),axiom,file(rfinseq,c2_3_1__rfinseq)]).

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_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(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(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(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_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.9),axiom,file(funct_1,d5_funct_1)]).

fof(e5_3_1__rfinseq,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_3__rfinseq))
      & k1_funct_1(c1_3__rfinseq,A) = c1_3_1__rfinseq ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,e1_3_1__rfinseq])],[cc1_finseq_1,cc3_nat_1,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,rc1_funct_1,t1_subset,t7_boole,e1_3_1__rfinseq,d5_funct_1]),
    [interesting(0.65),file(rfinseq,e5_3_1__rfinseq),[file(rfinseq,e5_3_1__rfinseq)]]).

fof(dt_c2_3_1__rfinseq,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,e1_3_1__rfinseq])],[dh_c2_3_1__rfinseq,e5_3_1__rfinseq]),
    [interesting(0.65),file(rfinseq,c2_3_1__rfinseq),[file(rfinseq,c2_3_1__rfinseq)]]).

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(symmetry_r2_wellord2,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
     => r2_wellord2(B,A) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(reflexivity_r2_wellord2,theorem,(
    ! [A,B] : r2_wellord2(A,A) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(redefinition_r2_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> r2_tarski(A,B) ) ),
    file(wellord2,r2_wellord2),
    [interesting(0.9),axiom,file(wellord2,r2_wellord2)]).

fof(l2_rfinseq,plain,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ~ r2_hidden(B,k2_relat_1(A))
         => k10_relat_1(A,k1_tarski(B)) = k1_xboole_0 ) ) ),
    file(rfinseq,l2_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,l2_rfinseq)]).

fof(e8_3_1__rfinseq,plain,(
    k10_relat_1(c2_3__rfinseq,k1_tarski(c1_3_1__rfinseq)) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,e2_3_1__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc18_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,fc1_finset_1,fc2_finseq_1,fc6_membered,rc1_funct_1,t1_subset,t6_boole,t7_boole,e2_3_1__rfinseq,l2_rfinseq]),
    [interesting(0.65),file(rfinseq,e8_3_1__rfinseq),[file(rfinseq,e8_3_1__rfinseq)]]).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_1)]).

fof(symmetry_r1_rfinseq,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => ( r1_rfinseq(A,B)
       => r1_rfinseq(B,A) ) ) ),
    file(rfinseq,r1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]).

fof(reflexivity_r1_rfinseq,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => r1_rfinseq(A,A) ) ),
    file(rfinseq,r1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,r1_rfinseq)]).

fof(d1_rfinseq,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_rfinseq(A,B)
          <=> ! [C] : k1_card_1(k10_relat_1(A,k1_tarski(C))) = k1_card_1(k10_relat_1(B,k1_tarski(C))) ) ) ) ),
    file(rfinseq,d1_rfinseq),
    [interesting(0.9),axiom,file(rfinseq,d1_rfinseq)]).

fof(e3_3_1__rfinseq,plain,(
    k1_card_1(k10_relat_1(c1_3__rfinseq,k1_tarski(c1_3_1__rfinseq))) = k1_card_1(k10_relat_1(c2_3__rfinseq,k1_tarski(c1_3_1__rfinseq))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,e1_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_finseq_1,t1_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc18_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,dt_k10_relat_1,dt_k1_card_1,dt_k1_tarski,dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,fc1_finset_1,e1_3__rfinseq,d1_rfinseq]),
    [interesting(0.65),file(rfinseq,e3_3_1__rfinseq),[file(rfinseq,e3_3_1__rfinseq)]]).

fof(t21_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    [interesting(0.9),axiom,file(card_1,t21_card_1)]).

fof(e4_3_1__rfinseq,plain,(
    r2_tarski(k10_relat_1(c1_3__rfinseq,k1_tarski(c1_3_1__rfinseq)),k10_relat_1(c2_3__rfinseq,k1_tarski(c1_3_1__rfinseq))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,e1_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_finseq_1,t1_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc18_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k10_relat_1,dt_k1_card_1,dt_k1_tarski,dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,fc1_finset_1,e3_3_1__rfinseq,t21_card_1]),
    [interesting(0.65),file(rfinseq,e4_3_1__rfinseq),[file(rfinseq,e4_3_1__rfinseq)]]).

fof(t46_card_1,theorem,(
    ! [A] : 
      ( r2_wellord2(A,k1_xboole_0)
    <=> A = k1_xboole_0 ) ),
    file(card_1,t46_card_1),
    [interesting(0.9),axiom,file(card_1,t46_card_1)]).

fof(e9_3_1__rfinseq,plain,(
    k10_relat_1(c1_3__rfinseq,k1_tarski(c1_3_1__rfinseq)) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e2_3_1__rfinseq,dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,e1_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,t2_subset,antisymmetry_r2_hidden,t1_subset,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc18_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k10_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,dt_c2_3__rfinseq,fc1_finset_1,fc2_finseq_1,fc6_membered,t6_boole,e8_3_1__rfinseq,e4_3_1__rfinseq,t46_card_1]),
    [interesting(0.65),file(rfinseq,e9_3_1__rfinseq),[file(rfinseq,e9_3_1__rfinseq)]]).

fof(e6_3_1__rfinseq,plain,
    ( r2_hidden(c2_3_1__rfinseq,k1_relat_1(c1_3__rfinseq))
    & k1_funct_1(c1_3__rfinseq,c2_3_1__rfinseq) = c1_3_1__rfinseq ),
    inference(consider,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,e1_3_1__rfinseq])],[dh_c2_3_1__rfinseq,e5_3_1__rfinseq]),
    [interesting(0.65),file(rfinseq,e6_3_1__rfinseq),[file(rfinseq,e6_3_1__rfinseq)]]).

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(e7_3_1__rfinseq,plain,(
    r2_hidden(c1_3_1__rfinseq,k1_tarski(c1_3_1__rfinseq)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3_1__rfinseq])],[cc1_finseq_1,cc2_funct_1,cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_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_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_c1_3_1__rfinseq,fc1_finset_1,t1_subset,t7_boole,d1_tarski]),
    [interesting(0.65),file(rfinseq,e7_3_1__rfinseq),[file(rfinseq,e7_3_1__rfinseq)]]).

fof(d13_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k10_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( r2_hidden(D,k1_relat_1(A))
                & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) ),
    file(funct_1,d13_funct_1),
    [interesting(0.9),axiom,file(funct_1,d13_funct_1)]).

fof(e10_3_1__rfinseq,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e2_3_1__rfinseq,dt_c2_3__rfinseq,e1_3__rfinseq,dt_c1_3__rfinseq,e1_3_1__rfinseq,dt_c1_3_1__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_c1_3__rfinseq,dt_c1_3_1__rfinseq,dt_c2_3_1__rfinseq,fc1_finset_1,fc2_finseq_1,fc6_membered,rc1_funct_1,t1_subset,t6_boole,t7_boole,e9_3_1__rfinseq,e6_3_1__rfinseq,e7_3_1__rfinseq,d13_funct_1]),
    [interesting(0.65),file(rfinseq,e10_3_1__rfinseq),[file(rfinseq,e10_3_1__rfinseq)]]).

fof(i3_3_1__rfinseq,theorem,(
    $true ),
    introduced(tautology,[file(rfinseq,i3_3_1__rfinseq)]),
    [interesting(0.65),trivial,file(rfinseq,i3_3_1__rfinseq)]).

fof(i2_3_1__rfinseq,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e2_3_1__rfinseq,dt_c2_3__rfinseq,e1_3__rfinseq,dt_c1_3__rfinseq,e1_3_1__rfinseq,dt_c1_3_1__rfinseq])],[e10_3_1__rfinseq,i3_3_1__rfinseq]),
    [interesting(0.65),file(rfinseq,i2_3_1__rfinseq),[file(rfinseq,i2_3_1__rfinseq)]]).

fof(i1_3_1__rfinseq,plain,(
    ~ ( r2_hidden(c1_3_1__rfinseq,k2_relat_1(c1_3__rfinseq))
      & ~ r2_hidden(c1_3_1__rfinseq,k2_relat_1(c2_3__rfinseq)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__rfinseq,e1_3__rfinseq,dt_c1_3__rfinseq,dt_c1_3_1__rfinseq]),discharge_asm(discharge,[e1_3_1__rfinseq,e2_3_1__rfinseq])],[e1_3_1__rfinseq,e2_3_1__rfinseq,i2_3_1__rfinseq]),
    [interesting(0.65),file(rfinseq,i1_3_1__rfinseq),[file(rfinseq,i1_3_1__rfinseq)]]).

fof(i1_3_1_tmp__rfinseq,plain,(
    ~ ( r2_hidden(c1_3_1__rfinseq,k2_relat_1(c1_3__rfinseq))
      & ~ r2_hidden(c1_3_1__rfinseq,k2_relat_1(c2_3__rfinseq)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_3__rfinseq,e1_3__rfinseq,dt_c1_3__rfinseq]),discharge_asm(discharge,[dt_c1_3_1__rfinseq])],[dt_c1_3_1__rfinseq,i1_3_1__rfinseq]),
    [interesting(0.8),e2_3__rfinseq]).

fof(e2_3__rfinseq,plain,(
    r1_tarski(k2_relat_1(c1_3__rfinseq),k2_relat_1(c2_3__rfinseq)) ),
    inference(let,[status(thm),assumptions([dt_c2_3__rfinseq,e1_3__rfinseq,dt_c1_3__rfinseq])],[i1_3_1_tmp__rfinseq,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_c1_3__rfinseq,dt_c2_3__rfinseq,d3_tarski,dh_c1_3_1__rfinseq]),
    [interesting(0.8),file(rfinseq,e2_3__rfinseq),[file(rfinseq,e2_3__rfinseq)]]).

fof(dt_c3_3__rfinseq,assumption,(
    $true ),
    introduced(assumption,[file(rfinseq,c3_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c3_3__rfinseq)]).

fof(dh_c3_3__rfinseq,definition,
    ( ~ ( r2_hidden(c3_3__rfinseq,k2_relat_1(c2_3__rfinseq))
        & ~ r2_hidden(c3_3__rfinseq,k2_relat_1(c1_3__rfinseq)) )
   => ! [A] : 
        ~ ( r2_hidden(A,k2_relat_1(c2_3__rfinseq))
          & ~ r2_hidden(A,k2_relat_1(c1_3__rfinseq)) ) ),
    introduced(definition,[new_symbol(c3_3__rfinseq),file(rfinseq,c3_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c3_3__rfinseq)]).

fof(e3_3__rfinseq,assumption,(
    r2_hidden(c3_3__rfinseq,k2_relat_1(c2_3__rfinseq)) ),
    introduced(assumption,[file(rfinseq,e3_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,e3_3__rfinseq)]).

fof(e4_3__rfinseq,assumption,(
    ~ r2_hidden(c3_3__rfinseq,k2_relat_1(c1_3__rfinseq)) ),
    introduced(assumption,[file(rfinseq,e4_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,e4_3__rfinseq)]).

fof(dh_c4_3__rfinseq,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c2_3__rfinseq))
        & k1_funct_1(c2_3__rfinseq,A) = c3_3__rfinseq )
   => ( r2_hidden(c4_3__rfinseq,k1_relat_1(c2_3__rfinseq))
      & k1_funct_1(c2_3__rfinseq,c4_3__rfinseq) = c3_3__rfinseq ) ),
    introduced(definition,[new_symbol(c4_3__rfinseq),file(rfinseq,c4_3__rfinseq)]),
    [interesting(0.8),axiom,file(rfinseq,c4_3__rfinseq)]).

fof(e7_3__rfinseq,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c2_3__rfinseq))
      & k1_funct_1(c2_3__rfinseq,A) = c3_3__rfinseq ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_3__rfinseq,dt_c3_3__rfinseq,e3_3__rfinseq])],[cc1_finseq_1,cc3_nat_1,rc1_finseq_1,rc1_nat_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc6_membered,rc1_finset_1,rc1_membered,rc3_funct_1,rc6_finseq_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,rc2_funct_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c2_3__rfinseq,dt_c3_3__rfinseq,rc1_funct_1,t1_subset,t7_boole,e3_3__rfinseq,d5_funct_1]),
    [interesting(0.8),file(rfinseq,e7_3__rfinseq),[file(rfinseq,e7_3__rfinseq)]]).

fof(dt_c4_3__rfinseq,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_3__rfinseq,dt_c3_3__rfinseq,e3_3__rfinseq])],[dh_c4_3__rfinseq,e7_3__rfinseq]),
    [interesting(0.8),file(rfinseq,c4_3__rfinseq),[file(rfinseq,c4_3__rfinseq)]]).

fof(e10_3__rfinseq,plain,(
    k10_relat_1(c1_3__rfinseq,k1_tarski(c3_3__rfinseq)) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c3_3__rfinseq,e4_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc11_finseq_1,fc18_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_3__rfinseq,dt_c3_3__rfinseq,fc1_finset_1,fc2_finseq_1,fc6_membered,rc1_funct_1,t1_subset,t6_boole,t7_boole,e4_3__rfinseq,l2_rfinseq]),
    [interesting(0.8),file(rfinseq,e10_3__rfinseq),[file(rfinseq,e10_3__rfinseq)]]).

fof(e5_3__rfinseq,plain,(
    k1_card_1(k10_relat_1(c2_3__rfinseq,k1_tarski(c3_3__rfinseq))) = k1_card_1(k10_relat_1(c1_3__rfinseq,k1_tarski(c3_3__rfinseq))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c2_3__rfinseq,dt_c3_3__rfinseq,e1_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_finseq_1,t1_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc18_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,symmetry_r1_rfinseq,reflexivity_r1_rfinseq,dt_k10_relat_1,dt_k1_card_1,dt_k1_tarski,dt_c1_3__rfinseq,dt_c2_3__rfinseq,dt_c3_3__rfinseq,fc1_finset_1,e1_3__rfinseq,d1_rfinseq]),
    [interesting(0.8),file(rfinseq,e5_3__rfinseq),[file(rfinseq,e5_3__rfinseq)]]).

fof(e6_3__rfinseq,plain,(
    r2_tarski(k10_relat_1(c2_3__rfinseq,k1_tarski(c3_3__rfinseq)),k10_relat_1(c1_3__rfinseq,k1_tarski(c3_3__rfinseq))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c2_3__rfinseq,dt_c3_3__rfinseq,e1_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc4_funct_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,rc3_funct_1,rc6_finseq_1,t1_subset,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc18_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,t6_boole,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k10_relat_1,dt_k1_card_1,dt_k1_tarski,dt_c1_3__rfinseq,dt_c2_3__rfinseq,dt_c3_3__rfinseq,fc1_finset_1,e5_3__rfinseq,t21_card_1]),
    [interesting(0.8),file(rfinseq,e6_3__rfinseq),[file(rfinseq,e6_3__rfinseq)]]).

fof(e11_3__rfinseq,plain,(
    k10_relat_1(c2_3__rfinseq,k1_tarski(c3_3__rfinseq)) = k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e4_3__rfinseq,dt_c1_3__rfinseq,dt_c2_3__rfinseq,dt_c3_3__rfinseq,e1_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,t2_subset,antisymmetry_r2_hidden,t1_subset,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc18_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t7_boole,t8_boole,symmetry_r2_wellord2,reflexivity_r2_wellord2,redefinition_r2_wellord2,dt_k10_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_c1_3__rfinseq,dt_c2_3__rfinseq,dt_c3_3__rfinseq,fc1_finset_1,fc2_finseq_1,fc6_membered,t6_boole,e10_3__rfinseq,e6_3__rfinseq,t46_card_1]),
    [interesting(0.8),file(rfinseq,e11_3__rfinseq),[file(rfinseq,e11_3__rfinseq)]]).

fof(e8_3__rfinseq,plain,
    ( r2_hidden(c4_3__rfinseq,k1_relat_1(c2_3__rfinseq))
    & k1_funct_1(c2_3__rfinseq,c4_3__rfinseq) = c3_3__rfinseq ),
    inference(consider,[status(thm),assumptions([dt_c2_3__rfinseq,dt_c3_3__rfinseq,e3_3__rfinseq])],[dh_c4_3__rfinseq,e7_3__rfinseq]),
    [interesting(0.8),file(rfinseq,e8_3__rfinseq),[file(rfinseq,e8_3__rfinseq)]]).

fof(e9_3__rfinseq,plain,(
    r2_hidden(c3_3__rfinseq,k1_tarski(c3_3__rfinseq)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__rfinseq])],[cc1_finseq_1,cc2_funct_1,cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_finseq_1,rc1_funct_1,rc1_nat_1,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_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_membered,cc2_membered,cc3_membered,cc4_membered,fc2_finseq_1,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_c3_3__rfinseq,fc1_finset_1,t1_subset,t7_boole,d1_tarski]),
    [interesting(0.8),file(rfinseq,e9_3__rfinseq),[file(rfinseq,e9_3__rfinseq)]]).

fof(e12_3__rfinseq,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e4_3__rfinseq,dt_c1_3__rfinseq,e1_3__rfinseq,dt_c2_3__rfinseq,e3_3__rfinseq,dt_c3_3__rfinseq])],[cc3_nat_1,fc10_membered,fc11_membered,fc7_membered,fc8_membered,fc9_membered,rc1_nat_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc3_membered,cc4_membered,fc17_finseq_1,fc18_finseq_1,rc1_finseq_1,rc1_finset_1,rc1_membered,rc2_funct_1,rc3_finseq_1,rc3_funct_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_c2_3__rfinseq,dt_c3_3__rfinseq,dt_c4_3__rfinseq,fc1_finset_1,fc2_finseq_1,fc6_membered,rc1_funct_1,t1_subset,t6_boole,t7_boole,e11_3__rfinseq,e8_3__rfinseq,e9_3__rfinseq,d13_funct_1]),
    [interesting(0.8),file(rfinseq,e12_3__rfinseq),[file(rfinseq,e12_3__rfinseq)]]).

fof(i6_3__rfinseq,theorem,(
    $true ),
    introduced(tautology,[file(rfinseq,i6_3__rfinseq)]),
    [interesting(0.8),trivial,file(rfinseq,i6_3__rfinseq)]).

fof(i5_3__rfinseq,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e4_3__rfinseq,dt_c1_3__rfinseq,e1_3__rfinseq,dt_c2_3__rfinseq,e3_3__rfinseq,dt_c3_3__rfinseq])],[e12_3__rfinseq,i6_3__rfinseq]),
    [interesting(0.8),file(rfinseq,i5_3__rfinseq),[file(rfinseq,i5_3__rfinseq)]]).

fof(i4_3__rfinseq,plain,(
    ~ ( r2_hidden(c3_3__rfinseq,k2_relat_1(c2_3__rfinseq))
      & ~ r2_hidden(c3_3__rfinseq,k2_relat_1(c1_3__rfinseq)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__rfinseq,e1_3__rfinseq,dt_c2_3__rfinseq,dt_c3_3__rfinseq]),discharge_asm(discharge,[e3_3__rfinseq,e4_3__rfinseq])],[e3_3__rfinseq,e4_3__rfinseq,i5_3__rfinseq]),
    [interesting(0.8),file(rfinseq,i4_3__rfinseq),[file(rfinseq,i4_3__rfinseq)]]).

fof(i4_3_tmp__rfinseq,plain,(
    ~ ( r2_hidden(c3_3__rfinseq,k2_relat_1(c2_3__rfinseq))
      & ~ r2_hidden(c3_3__rfinseq,k2_relat_1(c1_3__rfinseq)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__rfinseq,e1_3__rfinseq,dt_c2_3__rfinseq]),discharge_asm(discharge,[dt_c3_3__rfinseq])],[dt_c3_3__rfinseq,i4_3__rfinseq]),
    [interesting(0.8),i3_3__rfinseq]).

fof(i3_3__rfinseq,plain,(
    r1_tarski(k2_relat_1(c2_3__rfinseq),k2_relat_1(c1_3__rfinseq)) ),
    inference(let,[status(thm),assumptions([dt_c1_3__rfinseq,e1_3__rfinseq,dt_c2_3__rfinseq])],[i4_3_tmp__rfinseq,rc1_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_relat_1,dt_c1_3__rfinseq,dt_c2_3__rfinseq,d3_tarski,dh_c3_3__rfinseq]),
    [interesting(0.8),file(rfinseq,i3_3__rfinseq),[file(rfinseq,i3_3__rfinseq)]]).

fof(i2_3__rfinseq,plain,(
    k2_relat_1(c1_3__rfinseq) = k2_relat_1(c2_3__rfinseq) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__rfinseq,e1_3__rfinseq,dt_c2_3__rfinseq])],[rc1_funct_1,reflexivity_r1_tarski,dt_k2_relat_1,dt_c1_3__rfinseq,dt_c2_3__rfinseq,d10_xboole_0,e2_3__rfinseq,i3_3__rfinseq]),
    [interesting(0.8),file(rfinseq,i2_3__rfinseq),[file(rfinseq,i2_3__rfinseq)]]).

fof(i1_3__rfinseq,plain,
    ( r1_rfinseq(c1_3__rfinseq,c2_3__rfinseq)
   => k2_relat_1(c1_3__rfinseq) = k2_relat_1(c2_3__rfinseq) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__rfinseq,dt_c2_3__rfinseq]),discharge_asm(discharge,[e1_3__rfinseq])],[e1_3__rfinseq,i2_3__rfinseq]),
    [interesting(0.8),file(rfinseq,i1_3__rfinseq),[file(rfinseq,i1_3__rfinseq)]]).

fof(i1_3_tmp__rfinseq,plain,
    ( ( v1_relat_1(c1_3__rfinseq)
      & v1_funct_1(c1_3__rfinseq)
      & v1_relat_1(c2_3__rfinseq)
      & v1_funct_1(c2_3__rfinseq) )
   => ( r1_rfinseq(c1_3__rfinseq,c2_3__rfinseq)
     => k2_relat_1(c1_3__rfinseq) = k2_relat_1(c2_3__rfinseq) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__rfinseq,dt_c2_3__rfinseq])],[dt_c1_3__rfinseq,dt_c2_3__rfinseq,i1_3__rfinseq]),
    [interesting(1),t1_rfinseq]).

fof(t1_rfinseq,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_rfinseq(A,B)
           => k2_relat_1(A) = k2_relat_1(B) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__rfinseq,dh_c1_3__rfinseq,dh_c2_3__rfinseq]),
    [interesting(1),file(rfinseq,t1_rfinseq),[file(rfinseq,t1_rfinseq)]]).