% Mizar ND problem: t10_algseq_1,algseq_1,54,21 
fof(dh_c1_3__algseq_1,definition,
    ( ( m2_subset_1(c1_3__algseq_1,k1_numbers,k5_numbers)
     => ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( r2_hidden(c1_3__algseq_1,k2_algseq_1(A))
          <=> ~ r1_xreal_0(A,c1_3__algseq_1) ) ) )
   => ! [B] : 
        ( m2_subset_1(B,k1_numbers,k5_numbers)
       => ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_algseq_1(C))
            <=> ~ r1_xreal_0(C,B) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__algseq_1),file(algseq_1,c1_3__algseq_1)]),
    [interesting(0.8),axiom,file(algseq_1,c1_3__algseq_1)]).

fof(dh_c2_3__algseq_1,definition,
    ( ( m2_subset_1(c2_3__algseq_1,k1_numbers,k5_numbers)
     => ( r2_hidden(c1_3__algseq_1,k2_algseq_1(c2_3__algseq_1))
      <=> ~ r1_xreal_0(c2_3__algseq_1,c1_3__algseq_1) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r2_hidden(c1_3__algseq_1,k2_algseq_1(A))
        <=> ~ r1_xreal_0(A,c1_3__algseq_1) ) ) ),
    introduced(definition,[new_symbol(c2_3__algseq_1),file(algseq_1,c2_3__algseq_1)]),
    [interesting(0.8),axiom,file(algseq_1,c2_3__algseq_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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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_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_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(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(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(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_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_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(t1_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

fof(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

fof(t4_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    [interesting(0.9),axiom,file(real,t4_real)]).

fof(t5_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

fof(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

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_algseq_1,axiom,(
    $true ),
    file(algseq_1,k1_algseq_1),
    [interesting(0.9),axiom,file(algseq_1,k1_algseq_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_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

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

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_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

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

fof(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_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(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(d1_algseq_1,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_algseq_1(A) = a_1_0_algseq_1(A) ) ),
    file(algseq_1,d1_algseq_1),
    [interesting(0.9),axiom,file(algseq_1,d1_algseq_1)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_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(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k2_algseq_1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => k2_algseq_1(A) = k1_algseq_1(A) ) ),
    file(algseq_1,k2_algseq_1),
    [interesting(0.9),axiom,file(algseq_1,k2_algseq_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k2_algseq_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m1_subset_1(k2_algseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(algseq_1,k2_algseq_1),
    [interesting(0.9),axiom,file(algseq_1,k2_algseq_1)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_c1_3__algseq_1,assumption,(
    m2_subset_1(c1_3__algseq_1,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(algseq_1,c1_3__algseq_1)]),
    [interesting(0.8),axiom,file(algseq_1,c1_3__algseq_1)]).

fof(dt_c2_3__algseq_1,assumption,(
    m2_subset_1(c2_3__algseq_1,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(algseq_1,c2_3__algseq_1)]),
    [interesting(0.8),axiom,file(algseq_1,c2_3__algseq_1)]).

fof(fc1_numbers,theorem,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    [interesting(0.9),axiom,file(numbers,fc1_numbers)]).

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(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_1_0_algseq_1,definition,(
    ! [A,B] : 
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( r2_hidden(A,a_1_0_algseq_1(B))
      <=> ? [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = C
            & ~ r1_xreal_0(B,C) ) ) ) ),
    file(algseq_1,a_1_0_algseq_1),
    [interesting(0.9),axiom,file(algseq_1,a_1_0_algseq_1)]).

fof(e1_3__algseq_1,plain,
    ( r2_hidden(c1_3__algseq_1,a_1_0_algseq_1(c2_3__algseq_1))
  <=> ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & c1_3__algseq_1 = A
        & ~ r1_xreal_0(c2_3__algseq_1,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algseq_1,dt_c2_3__algseq_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_arytm_3,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc2_xreal_0,cc3_arytm_3,cc7_xreal_0,fc1_ordinal2,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c1_3__algseq_1,dt_c2_3__algseq_1,fc1_numbers,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_algseq_1]),
    [interesting(0.8),file(algseq_1,e1_3__algseq_1),[file(algseq_1,e1_3__algseq_1)]]).

fof(e2_3__algseq_1,plain,
    ( r2_hidden(c1_3__algseq_1,k2_algseq_1(c2_3__algseq_1))
  <=> ~ r1_xreal_0(c2_3__algseq_1,c1_3__algseq_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algseq_1,dt_c2_3__algseq_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_arytm_3,rc1_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_real,t2_real,t3_real,t4_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,dt_k1_algseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc2_xreal_0,cc3_arytm_3,cc7_xreal_0,fc1_ordinal2,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d1_algseq_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_algseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_algseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_3__algseq_1,dt_c2_3__algseq_1,fc1_numbers,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_0_algseq_1,e1_3__algseq_1]),
    [interesting(0.8),file(algseq_1,e2_3__algseq_1),[file(algseq_1,e2_3__algseq_1)]]).

fof(i3_3__algseq_1,theorem,(
    $true ),
    introduced(tautology,[file(algseq_1,i3_3__algseq_1)]),
    [interesting(0.8),trivial,file(algseq_1,i3_3__algseq_1)]).

fof(i2_3__algseq_1,plain,
    ( r2_hidden(c1_3__algseq_1,k2_algseq_1(c2_3__algseq_1))
  <=> ~ r1_xreal_0(c2_3__algseq_1,c1_3__algseq_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_3__algseq_1,dt_c2_3__algseq_1])],[e2_3__algseq_1,i3_3__algseq_1]),
    [interesting(0.8),file(algseq_1,i2_3__algseq_1),[file(algseq_1,i2_3__algseq_1)]]).

fof(i2_3_tmp__algseq_1,plain,
    ( m2_subset_1(c2_3__algseq_1,k1_numbers,k5_numbers)
   => ( r2_hidden(c1_3__algseq_1,k2_algseq_1(c2_3__algseq_1))
    <=> ~ r1_xreal_0(c2_3__algseq_1,c1_3__algseq_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__algseq_1]),discharge_asm(discharge,[dt_c2_3__algseq_1])],[dt_c2_3__algseq_1,i2_3__algseq_1]),
    [interesting(0.8),i1_3__algseq_1]).

fof(i1_3__algseq_1,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( r2_hidden(c1_3__algseq_1,k2_algseq_1(A))
      <=> ~ r1_xreal_0(A,c1_3__algseq_1) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__algseq_1])],[i2_3_tmp__algseq_1,dh_c2_3__algseq_1]),
    [interesting(0.8),file(algseq_1,i1_3__algseq_1),[file(algseq_1,i1_3__algseq_1)]]).

fof(i1_3_tmp__algseq_1,plain,
    ( m2_subset_1(c1_3__algseq_1,k1_numbers,k5_numbers)
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( r2_hidden(c1_3__algseq_1,k2_algseq_1(A))
        <=> ~ r1_xreal_0(A,c1_3__algseq_1) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__algseq_1])],[dt_c1_3__algseq_1,i1_3__algseq_1]),
    [interesting(1),t10_algseq_1]).

fof(t10_algseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r2_hidden(A,k2_algseq_1(B))
          <=> ~ r1_xreal_0(B,A) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__algseq_1,dh_c1_3__algseq_1]),
    [interesting(1),file(algseq_1,t10_algseq_1),[file(algseq_1,t10_algseq_1)]]).