% Mizar ND problem: t195_orders_1,orders_1,2249,40 
fof(dh_c1_96__orders_1,definition,
    ( ( ( v1_relat_1(c1_96__orders_1)
        & v1_funct_1(c1_96__orders_1) )
     => ! [A] : 
          ~ ( v1_finset_1(A)
            & r1_tarski(A,k2_relat_1(c1_96__orders_1))
            & ! [B] : 
                ~ ( r1_tarski(B,k1_relat_1(c1_96__orders_1))
                  & v1_finset_1(B)
                  & k9_relat_1(c1_96__orders_1,B) = A ) ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ! [D] : 
            ~ ( v1_finset_1(D)
              & r1_tarski(D,k2_relat_1(C))
              & ! [E] : 
                  ~ ( r1_tarski(E,k1_relat_1(C))
                    & v1_finset_1(E)
                    & k9_relat_1(C,E) = D ) ) ) ),
    introduced(definition,[new_symbol(c1_96__orders_1),file(orders_1,c1_96__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_96__orders_1)]).

fof(dh_c2_96__orders_1,definition,
    ( ~ ( v1_finset_1(c2_96__orders_1)
        & r1_tarski(c2_96__orders_1,k2_relat_1(c1_96__orders_1))
        & ! [A] : 
            ~ ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
              & v1_finset_1(A)
              & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) )
   => ! [B] : 
        ~ ( v1_finset_1(B)
          & r1_tarski(B,k2_relat_1(c1_96__orders_1))
          & ! [C] : 
              ~ ( r1_tarski(C,k1_relat_1(c1_96__orders_1))
                & v1_finset_1(C)
                & k9_relat_1(c1_96__orders_1,C) = B ) ) ),
    introduced(definition,[new_symbol(c2_96__orders_1),file(orders_1,c2_96__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c2_96__orders_1)]).

fof(e1_96__orders_1,assumption,(
    v1_finset_1(c2_96__orders_1) ),
    introduced(assumption,[file(orders_1,e1_96__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,e1_96__orders_1)]).

fof(e2_96__orders_1,assumption,(
    r1_tarski(c2_96__orders_1,k2_relat_1(c1_96__orders_1)) ),
    introduced(assumption,[file(orders_1,e2_96__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,e2_96__orders_1)]).

fof(e1_96_1_1__orders_1,assumption,(
    c2_96__orders_1 = k1_xboole_0 ),
    introduced(assumption,[file(orders_1,e1_96_1_1__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,e1_96_1_1__orders_1)]).

fof(fc13_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k9_relat_1(A,B)) ) ),
    file(finset_1,fc13_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc13_finset_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_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_1)]).

fof(dt_c1_96__orders_1,assumption,
    ( v1_relat_1(c1_96__orders_1)
    & v1_funct_1(c1_96__orders_1) ),
    introduced(assumption,[file(orders_1,c1_96__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c1_96__orders_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(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(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(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(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_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc1_ordinal1)]).

fof(cc2_ordinal1,theorem,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc2_ordinal1)]).

fof(cc3_ordinal1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,cc3_ordinal1)]).

fof(rc1_ordinal1,theorem,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc1_ordinal1)]).

fof(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

fof(rc2_ordinal1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc2_ordinal1)]).

fof(rc3_ordinal1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,rc3_ordinal1)]).

fof(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(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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc2_ordinal1,theorem,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc2_ordinal1)]).

fof(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(de_c1_96_1_1__orders_1,definition,(
    c1_96_1_1__orders_1 = k1_xboole_0 ),
    introduced(definition,[new_symbol(c1_96_1_1__orders_1),file(orders_1,c1_96_1_1__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c1_96_1_1__orders_1)]).

fof(dt_c1_96_1_1__orders_1,plain,(
    $true ),
    inference(mizar_by,[status(thm),assumptions([])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,dt_k1_xboole_0,fc2_ordinal1,t6_boole,de_c1_96_1_1__orders_1]),
    [interesting(0.5),file(orders_1,c1_96_1_1__orders_1),[file(orders_1,c1_96_1_1__orders_1)]]).

fof(dt_c2_96__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c2_96__orders_1)]),
    [interesting(0.8),axiom,file(orders_1,c2_96__orders_1)]).

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(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

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(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(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(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(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(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(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(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t2_xboole_1)]).

fof(e2_96_1_1__orders_1,plain,
    ( r1_tarski(c1_96_1_1__orders_1,k1_relat_1(c1_96__orders_1))
    & v1_finset_1(c1_96_1_1__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96__orders_1])],[antisymmetry_r2_hidden,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_finset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_xboole_0,dt_c1_96__orders_1,dt_c1_96_1_1__orders_1,de_c1_96_1_1__orders_1,fc2_ordinal1,t3_subset,t6_boole,t2_xboole_1]),
    [interesting(0.5),file(orders_1,e2_96_1_1__orders_1),[file(orders_1,e2_96_1_1__orders_1)]]).

fof(t149_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ),
    file(relat_1,t149_relat_1),
    [interesting(0.9),axiom,file(relat_1,t149_relat_1)]).

fof(e3_96_1_1__orders_1,plain,(
    k9_relat_1(c1_96__orders_1,c1_96_1_1__orders_1) = c2_96__orders_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_1__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,fc13_finset_1,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,dt_k1_xboole_0,dt_k9_relat_1,dt_c1_96__orders_1,dt_c1_96_1_1__orders_1,dt_c2_96__orders_1,de_c1_96_1_1__orders_1,fc2_ordinal1,t6_boole,e1_96_1_1__orders_1,t149_relat_1]),
    [interesting(0.5),file(orders_1,e3_96_1_1__orders_1),[file(orders_1,e3_96_1_1__orders_1)]]).

fof(i4_96_1_1__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i4_96_1_1__orders_1)]),
    [interesting(0.5),trivial,file(orders_1,i4_96_1_1__orders_1)]).

fof(i3_96_1_1__orders_1,plain,(
    k9_relat_1(c1_96__orders_1,c1_96_1_1__orders_1) = c2_96__orders_1 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_1__orders_1])],[e3_96_1_1__orders_1,i4_96_1_1__orders_1]),
    [interesting(0.5),file(orders_1,i3_96_1_1__orders_1),[file(orders_1,i3_96_1_1__orders_1)]]).

fof(i2_96_1_1__orders_1,plain,
    ( r1_tarski(c1_96_1_1__orders_1,k1_relat_1(c1_96__orders_1))
    & v1_finset_1(c1_96_1_1__orders_1)
    & k9_relat_1(c1_96__orders_1,c1_96_1_1__orders_1) = c2_96__orders_1 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_1__orders_1])],[e2_96_1_1__orders_1,i3_96_1_1__orders_1]),
    [interesting(0.5),file(orders_1,i2_96_1_1__orders_1),[file(orders_1,i2_96_1_1__orders_1)]]).

fof(i1_96_1_1__orders_1,plain,(
    ? [A] : 
      ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
      & v1_finset_1(A)
      & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) ),
    inference(take,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_1__orders_1])],[fc13_finset_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k9_relat_1,dt_c1_96__orders_1,dt_c1_96_1_1__orders_1,dt_c2_96__orders_1,i2_96_1_1__orders_1]),
    [interesting(0.5),file(orders_1,i1_96_1_1__orders_1),[file(orders_1,i1_96_1_1__orders_1)]]).

fof(i1_96_1__orders_1,plain,(
    ~ ( c2_96__orders_1 = k1_xboole_0
      & ! [A] : 
          ~ ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
            & v1_finset_1(A)
            & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[e1_96_1_1__orders_1])],[e1_96_1_1__orders_1,i1_96_1_1__orders_1]),
    [interesting(0.65),file(orders_1,i1_96_1__orders_1),[file(orders_1,i1_96_1__orders_1)]]).

fof(e1_96_1_2__orders_1,assumption,(
    c2_96__orders_1 != k1_xboole_0 ),
    introduced(assumption,[file(orders_1,e1_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,e1_96_1_2__orders_1)]).

fof(fc4_ordinal1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(k3_tarski(A))
        & v2_ordinal1(k3_tarski(A))
        & v3_ordinal1(k3_tarski(A)) ) ) ),
    file(ordinal1,fc4_ordinal1),
    [interesting(0.9),axiom,file(ordinal1,fc4_ordinal1)]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_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(dh_c1_96_1_2__orders_1,definition,
    ( ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = c2_96__orders_1
        & ! [B] : 
            ( r2_hidden(B,c2_96__orders_1)
           => k1_funct_1(A,B) = k10_relat_1(c1_96__orders_1,k1_tarski(B)) ) )
   => ( v1_relat_1(c1_96_1_2__orders_1)
      & v1_funct_1(c1_96_1_2__orders_1)
      & k1_relat_1(c1_96_1_2__orders_1) = c2_96__orders_1
      & ! [C] : 
          ( r2_hidden(C,c2_96__orders_1)
         => k1_funct_1(c1_96_1_2__orders_1,C) = k10_relat_1(c1_96__orders_1,k1_tarski(C)) ) ) ),
    introduced(definition,[new_symbol(c1_96_1_2__orders_1),file(orders_1,c1_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c1_96_1_2__orders_1)]).

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

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(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(s3_funct_1__e2_96_1_2__orders_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & k1_relat_1(C) = B
          & ! [D] : 
              ( r2_hidden(D,B)
             => k1_funct_1(C,D) = k10_relat_1(A,k1_tarski(D)) ) ) ) ),
    file(orders_1,s3_funct_1__e2_96_1_2__orders_1),
    [interesting(0.9),axiom,file(orders_1,s3_funct_1__e2_96_1_2__orders_1)]).

fof(e2_96_1_2__orders_1,plain,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = c2_96__orders_1
      & ! [B] : 
          ( r2_hidden(B,c2_96__orders_1)
         => k1_funct_1(A,B) = k10_relat_1(c1_96__orders_1,k1_tarski(B)) ) ) ),
    inference(mizar_from,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1])],[cc1_ordinal1,cc2_ordinal1,rc1_ordinal1,rc3_ordinal1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c2_96__orders_1,fc1_finset_1,fc2_subset_1,s3_funct_1__e2_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e2_96_1_2__orders_1),[file(orders_1,e2_96_1_2__orders_1)]]).

fof(dt_c1_96_1_2__orders_1,plain,
    ( v1_relat_1(c1_96_1_2__orders_1)
    & v1_funct_1(c1_96_1_2__orders_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1])],[dh_c1_96_1_2__orders_1,e2_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c1_96_1_2__orders_1),[file(orders_1,c1_96_1_2__orders_1)]]).

fof(de_c2_96_1_2__orders_1,definition,(
    c2_96_1_2__orders_1 = k2_relat_1(c1_96_1_2__orders_1) ),
    introduced(definition,[new_symbol(c2_96_1_2__orders_1),file(orders_1,c2_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c2_96_1_2__orders_1)]).

fof(e3_96_1_2__orders_1,plain,(
    k1_relat_1(c1_96_1_2__orders_1) = c2_96__orders_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1])],[dh_c1_96_1_2__orders_1,e2_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e3_96_1_2__orders_1),[file(orders_1,e3_96_1_2__orders_1)]]).

fof(t65_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( k1_relat_1(A) = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(relat_1,t65_relat_1),
    [interesting(0.9),axiom,file(relat_1,t65_relat_1)]).

fof(e5_96_1_2__orders_1,plain,(
    ~ v1_xboole_0(k2_relat_1(c1_96_1_2__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,cc1_ordinal1,cc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t1_subset,dt_k1_relat_1,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,cc1_finset_1,cc3_ordinal1,fc2_ordinal1,t6_boole,t7_boole,t8_boole,e1_96_1_2__orders_1,e3_96_1_2__orders_1,t65_relat_1]),
    [interesting(0.5),file(orders_1,e5_96_1_2__orders_1),[file(orders_1,e5_96_1_2__orders_1)]]).

fof(dt_c2_96_1_2__orders_1,plain,(
    ~ v1_xboole_0(c2_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,rc1_partfun1,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_subset,dt_k2_relat_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,t6_boole,t7_boole,t8_boole,de_c2_96_1_2__orders_1,e5_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c2_96_1_2__orders_1),[file(orders_1,c2_96_1_2__orders_1)]]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(fc14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(rc2_partfun1,theorem,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc2_partfun1)]).

fof(existence_m1_orders_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m1_orders_1(B,A) ) ),
    file(orders_1,m1_orders_1),
    [interesting(0.9),axiom,file(orders_1,m1_orders_1)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_m1_orders_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_orders_1(B,A)
         => ( v1_funct_1(B)
            & v1_funct_2(B,A,k3_tarski(A))
            & m2_relset_1(B,A,k3_tarski(A)) ) ) ) ),
    file(orders_1,m1_orders_1),
    [interesting(0.9),axiom,file(orders_1,m1_orders_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(redefinition_k2_funct_2,definition,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(funct_2,k2_funct_2),
    [interesting(0.9),axiom,file(funct_2,k2_funct_2)]).

fof(dt_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(funct_2,k2_funct_2),
    [interesting(0.9),axiom,file(funct_2,k2_funct_2)]).

fof(dh_c3_96_1_2__orders_1,definition,
    ( ? [A] : m1_orders_1(A,c2_96_1_2__orders_1)
   => m1_orders_1(c3_96_1_2__orders_1,c2_96_1_2__orders_1) ),
    introduced(definition,[new_symbol(c3_96_1_2__orders_1),file(orders_1,c3_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c3_96_1_2__orders_1)]).

fof(e8_96_1_2__orders_1,plain,(
    ? [A] : m1_orders_1(A,c2_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[reflexivity_r1_tarski,rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m1_subset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_ordinal1,cc1_relset_1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc1_subset_1,fc2_ordinal1,fc4_ordinal1,fc4_subset_1,rc1_finset_1,rc1_ordinal1,rc1_subset_1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_relat_1,dt_k3_tarski,dt_m2_relset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,t6_boole,t7_boole,t8_boole,existence_m1_orders_1,dt_m1_orders_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e8_96_1_2__orders_1),[file(orders_1,e8_96_1_2__orders_1)]]).

fof(dt_c3_96_1_2__orders_1,plain,(
    m1_orders_1(c3_96_1_2__orders_1,c2_96_1_2__orders_1) ),
    inference(consider,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dh_c3_96_1_2__orders_1,e8_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c3_96_1_2__orders_1),[file(orders_1,c3_96_1_2__orders_1)]]).

fof(de_c8_96_1_2__orders_1,definition,(
    c8_96_1_2__orders_1 = k2_funct_2(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1,c2_96_1_2__orders_1) ),
    introduced(definition,[new_symbol(c8_96_1_2__orders_1),file(orders_1,c8_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c8_96_1_2__orders_1)]).

fof(dt_c8_96_1_2__orders_1,plain,(
    m1_subset_1(c8_96_1_2__orders_1,k1_zfmisc_1(k3_tarski(c2_96_1_2__orders_1))) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_partfun1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,existence_m1_orders_1,existence_m1_relset_1,dt_k2_relat_1,dt_k9_relat_1,dt_m1_orders_1,dt_m1_relset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k3_tarski,dt_m1_subset_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,de_c2_96_1_2__orders_1,fc1_subset_1,t3_subset,de_c8_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c8_96_1_2__orders_1),[file(orders_1,c8_96_1_2__orders_1)]]).

fof(dt_c1_96_1_2_2__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_96_1_2_2__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c1_96_1_2_2__orders_1)]).

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_96_1_2_2__orders_1,definition,
    ( ~ ( r2_hidden(c1_96_1_2_2__orders_1,c8_96_1_2__orders_1)
        & ~ r2_hidden(c1_96_1_2_2__orders_1,k1_relat_1(c1_96__orders_1)) )
   => ! [A] : 
        ~ ( r2_hidden(A,c8_96_1_2__orders_1)
          & ~ r2_hidden(A,k1_relat_1(c1_96__orders_1)) ) ),
    introduced(definition,[new_symbol(c1_96_1_2_2__orders_1),file(orders_1,c1_96_1_2_2__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c1_96_1_2_2__orders_1)]).

fof(e1_96_1_2_2__orders_1,assumption,(
    r2_hidden(c1_96_1_2_2__orders_1,c8_96_1_2__orders_1) ),
    introduced(assumption,[file(orders_1,e1_96_1_2_2__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,e1_96_1_2_2__orders_1)]).

fof(dh_c3_96_1_2_2__orders_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_96_1_2__orders_1))
        & r2_hidden(A,c2_96__orders_1)
        & k1_funct_1(c1_96_1_2__orders_1,A) = c2_96_1_2_2__orders_1 )
   => ( r2_hidden(c3_96_1_2_2__orders_1,k1_relat_1(c1_96_1_2__orders_1))
      & r2_hidden(c3_96_1_2_2__orders_1,c2_96__orders_1)
      & k1_funct_1(c1_96_1_2__orders_1,c3_96_1_2_2__orders_1) = c2_96_1_2_2__orders_1 ) ),
    introduced(definition,[new_symbol(c3_96_1_2_2__orders_1),file(orders_1,c3_96_1_2_2__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c3_96_1_2_2__orders_1)]).

fof(dh_c2_96_1_2_2__orders_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k4_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1))
        & r2_hidden(A,c2_96_1_2__orders_1)
        & k1_funct_1(c3_96_1_2__orders_1,A) = c1_96_1_2_2__orders_1 )
   => ( r2_hidden(c2_96_1_2_2__orders_1,k4_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1))
      & r2_hidden(c2_96_1_2_2__orders_1,c2_96_1_2__orders_1)
      & k1_funct_1(c3_96_1_2__orders_1,c2_96_1_2_2__orders_1) = c1_96_1_2_2__orders_1 ) ),
    introduced(definition,[new_symbol(c2_96_1_2_2__orders_1),file(orders_1,c2_96_1_2_2__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c2_96_1_2_2__orders_1)]).

fof(redefinition_k4_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    [interesting(0.9),axiom,file(relset_1,k4_relset_1)]).

fof(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.9),axiom,file(funct_1,d12_funct_1)]).

fof(e2_96_1_2_2__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k4_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1))
      & r2_hidden(A,c2_96_1_2__orders_1)
      & k1_funct_1(c3_96_1_2__orders_1,A) = c1_96_1_2_2__orders_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k2_relat_1,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k3_tarski,dt_k4_relset_1,dt_k9_relat_1,dt_c1_96_1_2_2__orders_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,dt_c8_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c8_96_1_2__orders_1,t1_subset,t7_boole,e1_96_1_2_2__orders_1,d12_funct_1]),
    [interesting(0.35),file(orders_1,e2_96_1_2_2__orders_1),[file(orders_1,e2_96_1_2_2__orders_1)]]).

fof(dt_c2_96_1_2_2__orders_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[dh_c2_96_1_2_2__orders_1,e2_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,c2_96_1_2_2__orders_1),[file(orders_1,c2_96_1_2_2__orders_1)]]).

fof(e4_96_1_2_2__orders_1,plain,(
    r2_hidden(c2_96_1_2_2__orders_1,c2_96_1_2__orders_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[dh_c2_96_1_2_2__orders_1,e2_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,e4_96_1_2_2__orders_1),[file(orders_1,e4_96_1_2_2__orders_1)]]).

fof(t146_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ),
    file(relat_1,t146_relat_1),
    [interesting(0.9),axiom,file(relat_1,t146_relat_1)]).

fof(e6_96_1_2_2__orders_1,plain,(
    r2_hidden(c2_96_1_2_2__orders_1,k9_relat_1(c1_96_1_2__orders_1,c2_96__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_relat_1,dt_k9_relat_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,dt_c2_96_1_2__orders_1,dt_c2_96_1_2_2__orders_1,de_c2_96_1_2__orders_1,t1_subset,t7_boole,e3_96_1_2__orders_1,e4_96_1_2_2__orders_1,t146_relat_1]),
    [interesting(0.35),file(orders_1,e6_96_1_2_2__orders_1),[file(orders_1,e6_96_1_2_2__orders_1)]]).

fof(e7_96_1_2_2__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_96_1_2__orders_1))
      & r2_hidden(A,c2_96__orders_1)
      & k1_funct_1(c1_96_1_2__orders_1,A) = c2_96_1_2_2__orders_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k9_relat_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,dt_c2_96_1_2_2__orders_1,t1_subset,t7_boole,e6_96_1_2_2__orders_1,d12_funct_1]),
    [interesting(0.35),file(orders_1,e7_96_1_2_2__orders_1),[file(orders_1,e7_96_1_2_2__orders_1)]]).

fof(dt_c3_96_1_2_2__orders_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[dh_c3_96_1_2_2__orders_1,e7_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,c3_96_1_2_2__orders_1),[file(orders_1,c3_96_1_2_2__orders_1)]]).

fof(dh_c1_96_1_2_1__orders_1,definition,
    ( ~ ( r2_hidden(c1_96_1_2_1__orders_1,c2_96_1_2__orders_1)
        & c1_96_1_2_1__orders_1 = k1_xboole_0 )
   => ! [A] : 
        ~ ( r2_hidden(A,c2_96_1_2__orders_1)
          & A = k1_xboole_0 ) ),
    introduced(definition,[new_symbol(c1_96_1_2_1__orders_1),file(orders_1,c1_96_1_2_1__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c1_96_1_2_1__orders_1)]).

fof(e1_96_1_2_1__orders_1,assumption,(
    r2_hidden(c1_96_1_2_1__orders_1,c2_96_1_2__orders_1) ),
    introduced(assumption,[file(orders_1,e1_96_1_2_1__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,e1_96_1_2_1__orders_1)]).

fof(dt_c1_96_1_2_1__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_96_1_2_1__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c1_96_1_2_1__orders_1)]).

fof(dh_c2_96_1_2_1__orders_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_96_1_2__orders_1))
        & k1_funct_1(c1_96_1_2__orders_1,A) = c1_96_1_2_1__orders_1 )
   => ( r2_hidden(c2_96_1_2_1__orders_1,k1_relat_1(c1_96_1_2__orders_1))
      & k1_funct_1(c1_96_1_2__orders_1,c2_96_1_2_1__orders_1) = c1_96_1_2_1__orders_1 ) ),
    introduced(definition,[new_symbol(c2_96_1_2_1__orders_1),file(orders_1,c2_96_1_2_1__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c2_96_1_2_1__orders_1)]).

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(e2_96_1_2_1__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_96_1_2__orders_1))
      & k1_funct_1(c1_96_1_2__orders_1,A) = c1_96_1_2_1__orders_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_1__orders_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,t1_subset,t7_boole,e1_96_1_2_1__orders_1,d5_funct_1]),
    [interesting(0.35),file(orders_1,e2_96_1_2_1__orders_1),[file(orders_1,e2_96_1_2_1__orders_1)]]).

fof(dt_c2_96_1_2_1__orders_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_1__orders_1])],[dh_c2_96_1_2_1__orders_1,e2_96_1_2_1__orders_1]),
    [interesting(0.35),file(orders_1,c2_96_1_2_1__orders_1),[file(orders_1,c2_96_1_2_1__orders_1)]]).

fof(e4_96_1_2__orders_1,plain,(
    ! [A] : 
      ( r2_hidden(A,c2_96__orders_1)
     => k1_funct_1(c1_96_1_2__orders_1,A) = k10_relat_1(c1_96__orders_1,k1_tarski(A)) ) ),
    inference(consider,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1])],[dh_c1_96_1_2__orders_1,e2_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e4_96_1_2__orders_1),[file(orders_1,e4_96_1_2__orders_1)]]).

fof(e3_96_1_2_1__orders_1,plain,(
    r2_hidden(c2_96_1_2_1__orders_1,k1_relat_1(c1_96_1_2__orders_1)) ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_1__orders_1])],[dh_c2_96_1_2_1__orders_1,e2_96_1_2_1__orders_1]),
    [interesting(0.35),file(orders_1,e3_96_1_2_1__orders_1),[file(orders_1,e3_96_1_2_1__orders_1)]]).

fof(e5_96_1_2_1__orders_1,plain,(
    k1_funct_1(c1_96_1_2__orders_1,c2_96_1_2_1__orders_1) = k10_relat_1(c1_96__orders_1,k1_tarski(c2_96_1_2_1__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,dt_c2_96_1_2_1__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e3_96_1_2__orders_1,e4_96_1_2__orders_1,e3_96_1_2_1__orders_1]),
    [interesting(0.35),file(orders_1,e5_96_1_2_1__orders_1),[file(orders_1,e5_96_1_2_1__orders_1)]]).

fof(e4_96_1_2_1__orders_1,plain,(
    k1_funct_1(c1_96_1_2__orders_1,c2_96_1_2_1__orders_1) = c1_96_1_2_1__orders_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_1__orders_1])],[dh_c2_96_1_2_1__orders_1,e2_96_1_2_1__orders_1]),
    [interesting(0.35),file(orders_1,e4_96_1_2_1__orders_1),[file(orders_1,e4_96_1_2_1__orders_1)]]).

fof(t142_funct_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r2_hidden(A,k2_relat_1(B))
      <=> k10_relat_1(B,k1_tarski(A)) != k1_xboole_0 ) ) ),
    file(funct_1,t142_funct_1),
    [interesting(0.9),axiom,file(funct_1,t142_funct_1)]).

fof(e6_96_1_2_1__orders_1,plain,(
    c1_96_1_2_1__orders_1 != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_1__orders_1])],[existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_finset_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,rc1_finset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t2_subset,t4_subset,t5_subset,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_1__orders_1,dt_c2_96__orders_1,dt_c2_96_1_2_1__orders_1,fc1_finset_1,fc2_ordinal1,fc2_subset_1,t1_subset,t3_subset,t6_boole,t7_boole,e5_96_1_2_1__orders_1,e2_96__orders_1,e3_96_1_2__orders_1,e3_96_1_2_1__orders_1,e4_96_1_2_1__orders_1,t142_funct_1]),
    [interesting(0.35),file(orders_1,e6_96_1_2_1__orders_1),[file(orders_1,e6_96_1_2_1__orders_1)]]).

fof(i3_96_1_2_1__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i3_96_1_2_1__orders_1)]),
    [interesting(0.35),trivial,file(orders_1,i3_96_1_2_1__orders_1)]).

fof(i2_96_1_2_1__orders_1,plain,(
    c1_96_1_2_1__orders_1 != k1_xboole_0 ),
    inference(conclusion,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_1__orders_1])],[e6_96_1_2_1__orders_1,i3_96_1_2_1__orders_1]),
    [interesting(0.35),file(orders_1,i2_96_1_2_1__orders_1),[file(orders_1,i2_96_1_2_1__orders_1)]]).

fof(i1_96_1_2_1__orders_1,plain,(
    ~ ( r2_hidden(c1_96_1_2_1__orders_1,c2_96_1_2__orders_1)
      & c1_96_1_2_1__orders_1 = k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_1__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[e1_96_1_2_1__orders_1])],[e1_96_1_2_1__orders_1,i2_96_1_2_1__orders_1]),
    [interesting(0.35),file(orders_1,i1_96_1_2_1__orders_1),[file(orders_1,i1_96_1_2_1__orders_1)]]).

fof(i1_96_1_2_1_tmp__orders_1,plain,(
    ~ ( r2_hidden(c1_96_1_2_1__orders_1,c2_96_1_2__orders_1)
      & c1_96_1_2_1__orders_1 = k1_xboole_0 ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[dt_c1_96_1_2_1__orders_1])],[dt_c1_96_1_2_1__orders_1,i1_96_1_2_1__orders_1]),
    [interesting(0.5),e6_96_1_2__orders_1]).

fof(e6_96_1_2__orders_1,plain,(
    ! [A] : 
      ~ ( r2_hidden(A,c2_96_1_2__orders_1)
        & A = k1_xboole_0 ) ),
    inference(let,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[i1_96_1_2_1_tmp__orders_1,dh_c1_96_1_2_1__orders_1]),
    [interesting(0.5),file(orders_1,e6_96_1_2__orders_1),[file(orders_1,e6_96_1_2__orders_1)]]).

fof(e7_96_1_2__orders_1,plain,(
    ~ r2_hidden(k1_xboole_0,c2_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_finset_1,existence_m1_subset_1,dt_k2_relat_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,e6_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e7_96_1_2__orders_1),[file(orders_1,e7_96_1_2__orders_1)]]).

fof(e5_96_1_2_2__orders_1,plain,(
    k1_funct_1(c3_96_1_2__orders_1,c2_96_1_2_2__orders_1) = c1_96_1_2_2__orders_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[dh_c2_96_1_2_2__orders_1,e2_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,e5_96_1_2_2__orders_1),[file(orders_1,e5_96_1_2_2__orders_1)]]).

fof(e9_96_1_2_2__orders_1,plain,(
    k1_funct_1(c1_96_1_2__orders_1,c3_96_1_2_2__orders_1) = c2_96_1_2_2__orders_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[dh_c3_96_1_2_2__orders_1,e7_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,e9_96_1_2_2__orders_1),[file(orders_1,e9_96_1_2_2__orders_1)]]).

fof(d1_orders_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ r2_hidden(k1_xboole_0,A)
       => ! [B] : 
            ( ( v1_funct_1(B)
              & v1_funct_2(B,A,k3_tarski(A))
              & m2_relset_1(B,A,k3_tarski(A)) )
           => ( m1_orders_1(B,A)
            <=> ! [C] : 
                  ( r2_hidden(C,A)
                 => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) ) ),
    file(orders_1,d1_orders_1),
    [interesting(0.9),axiom,file(orders_1,d1_orders_1)]).

fof(e11_96_1_2_2__orders_1,plain,(
    r2_hidden(c1_96_1_2_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c3_96_1_2_2__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_ordinal1,cc1_relset_1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc1_subset_1,fc4_ordinal1,fc4_subset_1,rc1_finset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_orders_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_xboole_0,dt_k3_tarski,dt_m1_orders_1,dt_m2_relset_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_2__orders_1,dt_c2_96_1_2__orders_1,dt_c2_96_1_2_2__orders_1,dt_c3_96_1_2__orders_1,dt_c3_96_1_2_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,t8_boole,e7_96_1_2__orders_1,e4_96_1_2_2__orders_1,e5_96_1_2_2__orders_1,e9_96_1_2_2__orders_1,d1_orders_1]),
    [interesting(0.35),file(orders_1,e11_96_1_2_2__orders_1),[file(orders_1,e11_96_1_2_2__orders_1)]]).

fof(e8_96_1_2_2__orders_1,plain,
    ( r2_hidden(c3_96_1_2_2__orders_1,k1_relat_1(c1_96_1_2__orders_1))
    & r2_hidden(c3_96_1_2_2__orders_1,c2_96__orders_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[dh_c3_96_1_2_2__orders_1,e7_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,e8_96_1_2_2__orders_1),[file(orders_1,e8_96_1_2_2__orders_1)]]).

fof(e10_96_1_2_2__orders_1,plain,(
    k1_funct_1(c1_96_1_2__orders_1,c3_96_1_2_2__orders_1) = k10_relat_1(c1_96__orders_1,k1_tarski(c3_96_1_2_2__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,dt_c3_96_1_2_2__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e4_96_1_2__orders_1,e8_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,e10_96_1_2_2__orders_1),[file(orders_1,e10_96_1_2_2__orders_1)]]).

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(e12_96_1_2_2__orders_1,plain,(
    r2_hidden(c1_96_1_2_2__orders_1,k1_relat_1(c1_96__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_2__orders_1,dt_c3_96_1_2_2__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e11_96_1_2_2__orders_1,e10_96_1_2_2__orders_1,d13_funct_1]),
    [interesting(0.35),file(orders_1,e12_96_1_2_2__orders_1),[file(orders_1,e12_96_1_2_2__orders_1)]]).

fof(i3_96_1_2_2__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i3_96_1_2_2__orders_1)]),
    [interesting(0.35),trivial,file(orders_1,i3_96_1_2_2__orders_1)]).

fof(i2_96_1_2_2__orders_1,plain,(
    r2_hidden(c1_96_1_2_2__orders_1,k1_relat_1(c1_96__orders_1)) ),
    inference(conclusion,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_2__orders_1])],[e12_96_1_2_2__orders_1,i3_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,i2_96_1_2_2__orders_1),[file(orders_1,i2_96_1_2_2__orders_1)]]).

fof(i1_96_1_2_2__orders_1,plain,(
    ~ ( r2_hidden(c1_96_1_2_2__orders_1,c8_96_1_2__orders_1)
      & ~ r2_hidden(c1_96_1_2_2__orders_1,k1_relat_1(c1_96__orders_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_2__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[e1_96_1_2_2__orders_1])],[e1_96_1_2_2__orders_1,i2_96_1_2_2__orders_1]),
    [interesting(0.35),file(orders_1,i1_96_1_2_2__orders_1),[file(orders_1,i1_96_1_2_2__orders_1)]]).

fof(i1_96_1_2_2_tmp__orders_1,plain,(
    ~ ( r2_hidden(c1_96_1_2_2__orders_1,c8_96_1_2__orders_1)
      & ~ r2_hidden(c1_96_1_2_2__orders_1,k1_relat_1(c1_96__orders_1)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[dt_c1_96_1_2_2__orders_1])],[dt_c1_96_1_2_2__orders_1,i1_96_1_2_2__orders_1]),
    [interesting(0.5),e16_96_1_2__orders_1]).

fof(e16_96_1_2__orders_1,plain,(
    r1_tarski(c8_96_1_2__orders_1,k1_relat_1(c1_96__orders_1)) ),
    inference(let,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[i1_96_1_2_2_tmp__orders_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,cc1_finset_1,cc3_ordinal1,rc1_subset_1,rc2_subset_1,dt_k1_zfmisc_1,dt_k3_tarski,dt_m1_subset_1,dt_c2_96_1_2__orders_1,fc1_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_relat_1,dt_c1_96__orders_1,dt_c8_96_1_2__orders_1,d3_tarski,dh_c1_96_1_2_2__orders_1]),
    [interesting(0.5),file(orders_1,e16_96_1_2__orders_1),[file(orders_1,e16_96_1_2__orders_1)]]).

fof(e17_96_1_2__orders_1,plain,(
    c2_96_1_2__orders_1 = k9_relat_1(c1_96_1_2__orders_1,c2_96__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,rc1_partfun1,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_subset,cc1_finset_1,cc3_ordinal1,t6_boole,t7_boole,t8_boole,dt_k1_relat_1,dt_k2_relat_1,dt_k9_relat_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,e3_96_1_2__orders_1,t146_relat_1]),
    [interesting(0.5),file(orders_1,e17_96_1_2__orders_1),[file(orders_1,e17_96_1_2__orders_1)]]).

fof(t17_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_finset_1(A)
       => v1_finset_1(k9_relat_1(B,A)) ) ) ),
    file(finset_1,t17_finset_1),
    [interesting(0.9),axiom,file(finset_1,t17_finset_1)]).

fof(e18_96_1_2__orders_1,plain,(
    v1_finset_1(c2_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,rc1_partfun1,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,t1_subset,dt_k2_relat_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t6_boole,t7_boole,t8_boole,dt_k9_relat_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,fc13_finset_1,e17_96_1_2__orders_1,e1_96__orders_1,t17_finset_1]),
    [interesting(0.5),file(orders_1,e18_96_1_2__orders_1),[file(orders_1,e18_96_1_2__orders_1)]]).

fof(e19_96_1_2__orders_1,plain,(
    v1_finset_1(c8_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_orders_1,existence_m1_relset_1,dt_k1_xboole_0,dt_m1_orders_1,dt_m1_relset_1,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_ordinal1,rc2_partfun1,rc3_ordinal1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k2_relat_1,dt_k3_tarski,dt_m1_subset_1,dt_c1_96_1_2__orders_1,dt_c3_96_1_2__orders_1,cc1_finset_1,cc2_finset_1,cc3_ordinal1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,dt_k9_relat_1,dt_c2_96_1_2__orders_1,dt_c8_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c8_96_1_2__orders_1,fc13_finset_1,e18_96_1_2__orders_1,t17_finset_1]),
    [interesting(0.5),file(orders_1,e19_96_1_2__orders_1),[file(orders_1,e19_96_1_2__orders_1)]]).

fof(dh_c1_96_1_2_3__orders_1,definition,
    ( ( r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1))
    <=> r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1) )
   => ! [A] : 
        ( r2_hidden(A,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1))
      <=> r2_hidden(A,c2_96__orders_1) ) ),
    introduced(definition,[new_symbol(c1_96_1_2_3__orders_1),file(orders_1,c1_96_1_2_3__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c1_96_1_2_3__orders_1)]).

fof(e1_96_1_2_3_1__orders_1,assumption,(
    r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1)) ),
    introduced(assumption,[file(orders_1,e1_96_1_2_3_1__orders_1)]),
    [interesting(0.2),axiom,file(orders_1,e1_96_1_2_3_1__orders_1)]).

fof(dt_c1_96_1_2_3__orders_1,assumption,(
    $true ),
    introduced(assumption,[file(orders_1,c1_96_1_2_3__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,c1_96_1_2_3__orders_1)]).

fof(dh_c1_96_1_2_3_1__orders_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_96__orders_1))
        & r2_hidden(A,c8_96_1_2__orders_1)
        & k1_funct_1(c1_96__orders_1,A) = c1_96_1_2_3__orders_1 )
   => ( r2_hidden(c1_96_1_2_3_1__orders_1,k1_relat_1(c1_96__orders_1))
      & r2_hidden(c1_96_1_2_3_1__orders_1,c8_96_1_2__orders_1)
      & k1_funct_1(c1_96__orders_1,c1_96_1_2_3_1__orders_1) = c1_96_1_2_3__orders_1 ) ),
    introduced(definition,[new_symbol(c1_96_1_2_3_1__orders_1),file(orders_1,c1_96_1_2_3_1__orders_1)]),
    [interesting(0.2),axiom,file(orders_1,c1_96_1_2_3_1__orders_1)]).

fof(e2_96_1_2_3_1__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_96__orders_1))
      & r2_hidden(A,c8_96_1_2__orders_1)
      & k1_funct_1(c1_96__orders_1,A) = c1_96_1_2_3__orders_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,existence_m1_orders_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_relat_1,dt_m1_orders_1,dt_m1_relset_1,dt_c1_96_1_2__orders_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_partfun1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k3_tarski,dt_m1_subset_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k9_relat_1,dt_c1_96__orders_1,dt_c1_96_1_2_3__orders_1,dt_c8_96_1_2__orders_1,de_c8_96_1_2__orders_1,t1_subset,t7_boole,e1_96_1_2_3_1__orders_1,d12_funct_1]),
    [interesting(0.2),file(orders_1,e2_96_1_2_3_1__orders_1),[file(orders_1,e2_96_1_2_3_1__orders_1)]]).

fof(dt_c1_96_1_2_3_1__orders_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c1_96_1_2_3_1__orders_1,e2_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,c1_96_1_2_3_1__orders_1),[file(orders_1,c1_96_1_2_3_1__orders_1)]]).

fof(dh_c3_96_1_2_3_1__orders_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k1_relat_1(c1_96_1_2__orders_1))
        & k1_funct_1(c1_96_1_2__orders_1,A) = c2_96_1_2_3_1__orders_1 )
   => ( r2_hidden(c3_96_1_2_3_1__orders_1,k1_relat_1(c1_96_1_2__orders_1))
      & k1_funct_1(c1_96_1_2__orders_1,c3_96_1_2_3_1__orders_1) = c2_96_1_2_3_1__orders_1 ) ),
    introduced(definition,[new_symbol(c3_96_1_2_3_1__orders_1),file(orders_1,c3_96_1_2_3_1__orders_1)]),
    [interesting(0.2),axiom,file(orders_1,c3_96_1_2_3_1__orders_1)]).

fof(dh_c2_96_1_2_3_1__orders_1,definition,
    ( ? [A] : 
        ( r2_hidden(A,k4_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1))
        & r2_hidden(A,c2_96_1_2__orders_1)
        & k1_funct_1(c3_96_1_2__orders_1,A) = c1_96_1_2_3_1__orders_1 )
   => ( r2_hidden(c2_96_1_2_3_1__orders_1,k4_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1))
      & r2_hidden(c2_96_1_2_3_1__orders_1,c2_96_1_2__orders_1)
      & k1_funct_1(c3_96_1_2__orders_1,c2_96_1_2_3_1__orders_1) = c1_96_1_2_3_1__orders_1 ) ),
    introduced(definition,[new_symbol(c2_96_1_2_3_1__orders_1),file(orders_1,c2_96_1_2_3_1__orders_1)]),
    [interesting(0.2),axiom,file(orders_1,c2_96_1_2_3_1__orders_1)]).

fof(e4_96_1_2_3_1__orders_1,plain,(
    r2_hidden(c1_96_1_2_3_1__orders_1,c8_96_1_2__orders_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c1_96_1_2_3_1__orders_1,e2_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,e4_96_1_2_3_1__orders_1),[file(orders_1,e4_96_1_2_3_1__orders_1)]]).

fof(e6_96_1_2_3_1__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k4_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1))
      & r2_hidden(A,c2_96_1_2__orders_1)
      & k1_funct_1(c3_96_1_2__orders_1,A) = c1_96_1_2_3_1__orders_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k2_relat_1,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k3_tarski,dt_k4_relset_1,dt_k9_relat_1,dt_c1_96_1_2_3_1__orders_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,dt_c8_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c8_96_1_2__orders_1,t1_subset,t7_boole,e4_96_1_2_3_1__orders_1,d12_funct_1]),
    [interesting(0.2),file(orders_1,e6_96_1_2_3_1__orders_1),[file(orders_1,e6_96_1_2_3_1__orders_1)]]).

fof(dt_c2_96_1_2_3_1__orders_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c2_96_1_2_3_1__orders_1,e6_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,c2_96_1_2_3_1__orders_1),[file(orders_1,c2_96_1_2_3_1__orders_1)]]).

fof(e7_96_1_2_3_1__orders_1,plain,
    ( r2_hidden(c2_96_1_2_3_1__orders_1,k4_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1))
    & r2_hidden(c2_96_1_2_3_1__orders_1,c2_96_1_2__orders_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c2_96_1_2_3_1__orders_1,e6_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,e7_96_1_2_3_1__orders_1),[file(orders_1,e7_96_1_2_3_1__orders_1)]]).

fof(e9_96_1_2_3_1__orders_1,plain,(
    ? [A] : 
      ( r2_hidden(A,k1_relat_1(c1_96_1_2__orders_1))
      & k1_funct_1(c1_96_1_2__orders_1,A) = c2_96_1_2_3_1__orders_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m2_relset_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_tarski,dt_k4_relset_1,dt_c1_96_1_2__orders_1,dt_c2_96_1_2__orders_1,dt_c2_96_1_2_3_1__orders_1,dt_c3_96_1_2__orders_1,de_c2_96_1_2__orders_1,t1_subset,t7_boole,e7_96_1_2_3_1__orders_1,d5_funct_1]),
    [interesting(0.2),file(orders_1,e9_96_1_2_3_1__orders_1),[file(orders_1,e9_96_1_2_3_1__orders_1)]]).

fof(dt_c3_96_1_2_3_1__orders_1,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c3_96_1_2_3_1__orders_1,e9_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,c3_96_1_2_3_1__orders_1),[file(orders_1,c3_96_1_2_3_1__orders_1)]]).

fof(e10_96_1_2_3_1__orders_1,plain,(
    r2_hidden(c3_96_1_2_3_1__orders_1,k1_relat_1(c1_96_1_2__orders_1)) ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c3_96_1_2_3_1__orders_1,e9_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,e10_96_1_2_3_1__orders_1),[file(orders_1,e10_96_1_2_3_1__orders_1)]]).

fof(e12_96_1_2_3_1__orders_1,plain,(
    k1_funct_1(c1_96_1_2__orders_1,c3_96_1_2_3_1__orders_1) = k10_relat_1(c1_96__orders_1,k1_tarski(c3_96_1_2_3_1__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c2_96__orders_1,dt_c3_96_1_2_3_1__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e3_96_1_2__orders_1,e4_96_1_2__orders_1,e10_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,e12_96_1_2_3_1__orders_1),[file(orders_1,e12_96_1_2_3_1__orders_1)]]).

fof(e8_96_1_2_3_1__orders_1,plain,(
    k1_funct_1(c3_96_1_2__orders_1,c2_96_1_2_3_1__orders_1) = c1_96_1_2_3_1__orders_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c2_96_1_2_3_1__orders_1,e6_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,e8_96_1_2_3_1__orders_1),[file(orders_1,e8_96_1_2_3_1__orders_1)]]).

fof(e11_96_1_2_3_1__orders_1,plain,(
    k1_funct_1(c1_96_1_2__orders_1,c3_96_1_2_3_1__orders_1) = c2_96_1_2_3_1__orders_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c3_96_1_2_3_1__orders_1,e9_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,e11_96_1_2_3_1__orders_1),[file(orders_1,e11_96_1_2_3_1__orders_1)]]).

fof(e13_96_1_2_3_1__orders_1,plain,(
    r2_hidden(c1_96_1_2_3_1__orders_1,k10_relat_1(c1_96__orders_1,k1_tarski(c3_96_1_2_3_1__orders_1))) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_ordinal1,cc1_relset_1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc1_subset_1,fc4_ordinal1,fc4_subset_1,rc1_finset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_orders_1,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_k4_relset_1,dt_m1_orders_1,dt_m2_relset_1,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3_1__orders_1,dt_c2_96_1_2__orders_1,dt_c2_96_1_2_3_1__orders_1,dt_c3_96_1_2__orders_1,dt_c3_96_1_2_3_1__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_ordinal1,fc2_subset_1,t1_subset,t6_boole,t7_boole,t8_boole,e12_96_1_2_3_1__orders_1,e7_96_1_2__orders_1,e7_96_1_2_3_1__orders_1,e8_96_1_2_3_1__orders_1,e11_96_1_2_3_1__orders_1,d1_orders_1]),
    [interesting(0.2),file(orders_1,e13_96_1_2_3_1__orders_1),[file(orders_1,e13_96_1_2_3_1__orders_1)]]).

fof(e14_96_1_2_3_1__orders_1,plain,(
    r2_hidden(k1_funct_1(c1_96__orders_1,c1_96_1_2_3_1__orders_1),k1_tarski(c3_96_1_2_3_1__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2_3_1__orders_1,dt_c3_96_1_2_3_1__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e13_96_1_2_3_1__orders_1,d13_funct_1]),
    [interesting(0.2),file(orders_1,e14_96_1_2_3_1__orders_1),[file(orders_1,e14_96_1_2_3_1__orders_1)]]).

fof(e5_96_1_2_3_1__orders_1,plain,(
    k1_funct_1(c1_96__orders_1,c1_96_1_2_3_1__orders_1) = c1_96_1_2_3__orders_1 ),
    inference(consider,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[dh_c1_96_1_2_3_1__orders_1,e2_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,e5_96_1_2_3_1__orders_1),[file(orders_1,e5_96_1_2_3_1__orders_1)]]).

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(e15_96_1_2_3_1__orders_1,plain,(
    r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c1_96_1_2_3_1__orders_1,dt_c2_96__orders_1,dt_c3_96_1_2_3_1__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e14_96_1_2_3_1__orders_1,e3_96_1_2__orders_1,e5_96_1_2_3_1__orders_1,e10_96_1_2_3_1__orders_1,d1_tarski]),
    [interesting(0.2),file(orders_1,e15_96_1_2_3_1__orders_1),[file(orders_1,e15_96_1_2_3_1__orders_1)]]).

fof(i2_96_1_2_3_1__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i2_96_1_2_3_1__orders_1)]),
    [interesting(0.2),trivial,file(orders_1,i2_96_1_2_3_1__orders_1)]).

fof(i1_96_1_2_3_1__orders_1,plain,(
    r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1) ),
    inference(conclusion,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e1_96_1_2_3_1__orders_1])],[e15_96_1_2_3_1__orders_1,i2_96_1_2_3_1__orders_1]),
    [interesting(0.2),file(orders_1,i1_96_1_2_3_1__orders_1),[file(orders_1,i1_96_1_2_3_1__orders_1)]]).

fof(e1_96_1_2_3__orders_1,plain,
    ( r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1))
   => r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1) ),
    inference(discharge_asm,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[e1_96_1_2_3_1__orders_1])],[e1_96_1_2_3_1__orders_1,i1_96_1_2_3_1__orders_1]),
    [interesting(0.35),file(orders_1,e1_96_1_2_3__orders_1),[file(orders_1,e1_96_1_2_3__orders_1)]]).

fof(e2_96_1_2_3__orders_1,assumption,(
    r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1) ),
    introduced(assumption,[file(orders_1,e2_96_1_2_3__orders_1)]),
    [interesting(0.35),axiom,file(orders_1,e2_96_1_2_3__orders_1)]).

fof(e6_96_1_2_3__orders_1,plain,(
    k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1) = k10_relat_1(c1_96__orders_1,k1_tarski(c1_96_1_2_3__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e2_96_1_2_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c2_96__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e4_96_1_2__orders_1,e2_96_1_2_3__orders_1]),
    [interesting(0.35),file(orders_1,e6_96_1_2_3__orders_1),[file(orders_1,e6_96_1_2_3__orders_1)]]).

fof(e3_96_1_2_3__orders_1,plain,(
    r2_hidden(k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1),c2_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e2_96_1_2_3__orders_1])],[rc1_partfun1,rc2_ordinal1,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,existence_m1_subset_1,dt_m1_subset_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c2_96__orders_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,t1_subset,t7_boole,e3_96_1_2__orders_1,e2_96_1_2_3__orders_1,d5_funct_1]),
    [interesting(0.35),file(orders_1,e3_96_1_2_3__orders_1),[file(orders_1,e3_96_1_2_3__orders_1)]]).

fof(e7_96_1_2_3__orders_1,plain,(
    r2_hidden(k1_funct_1(c3_96_1_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1)),k10_relat_1(c1_96__orders_1,k1_tarski(c1_96_1_2_3__orders_1))) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e2_96_1_2_3__orders_1])],[reflexivity_r1_tarski,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_ordinal1,cc1_relset_1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc1_subset_1,fc4_ordinal1,fc4_subset_1,rc1_finset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t2_subset,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_orders_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k10_relat_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k3_tarski,dt_m1_orders_1,dt_m2_relset_1,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc1_finset_1,fc2_ordinal1,fc2_subset_1,t1_subset,t6_boole,t7_boole,t8_boole,e6_96_1_2_3__orders_1,e7_96_1_2__orders_1,e3_96_1_2_3__orders_1,d1_orders_1]),
    [interesting(0.35),file(orders_1,e7_96_1_2_3__orders_1),[file(orders_1,e7_96_1_2_3__orders_1)]]).

fof(e8_96_1_2_3__orders_1,plain,(
    r2_hidden(k1_funct_1(c1_96__orders_1,k1_funct_1(c3_96_1_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1))),k1_tarski(c1_96_1_2_3__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,dt_c1_96_1_2_3__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1,e2_96_1_2_3__orders_1])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc2_finset_1,fc14_finset_1,fc1_subset_1,fc4_subset_1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t3_subset,t4_subset,t5_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k3_tarski,dt_m2_relset_1,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_ordinal1,rc3_ordinal1,existence_m1_orders_1,existence_m1_subset_1,dt_m1_orders_1,dt_m1_subset_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k10_relat_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c3_96_1_2__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t7_boole,e7_96_1_2_3__orders_1,d13_funct_1]),
    [interesting(0.35),file(orders_1,e8_96_1_2_3__orders_1),[file(orders_1,e8_96_1_2_3__orders_1)]]).

fof(redefinition_k5_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_1)]).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    [interesting(0.9),axiom,file(relset_1,k5_relset_1)]).

fof(de_c6_96_1_2__orders_1,definition,(
    c6_96_1_2__orders_1 = k3_tarski(c2_96_1_2__orders_1) ),
    introduced(definition,[new_symbol(c6_96_1_2__orders_1),file(orders_1,c6_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c6_96_1_2__orders_1)]).

fof(dh_c4_96_1_2__orders_1,definition,
    ( ? [A] : m1_subset_1(A,c2_96_1_2__orders_1)
   => m1_subset_1(c4_96_1_2__orders_1,c2_96_1_2__orders_1) ),
    introduced(definition,[new_symbol(c4_96_1_2__orders_1),file(orders_1,c4_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c4_96_1_2__orders_1)]).

fof(e9_96_1_2__orders_1,plain,(
    ? [A] : m1_subset_1(A,c2_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_subset,dt_k2_relat_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_m1_subset_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e9_96_1_2__orders_1),[file(orders_1,e9_96_1_2__orders_1)]]).

fof(dt_c4_96_1_2__orders_1,plain,(
    m1_subset_1(c4_96_1_2__orders_1,c2_96_1_2__orders_1) ),
    inference(consider,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dh_c4_96_1_2__orders_1,e9_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c4_96_1_2__orders_1),[file(orders_1,c4_96_1_2__orders_1)]]).

fof(dh_c5_96_1_2__orders_1,definition,
    ( ? [A] : m1_subset_1(A,c4_96_1_2__orders_1)
   => m1_subset_1(c5_96_1_2__orders_1,c4_96_1_2__orders_1) ),
    introduced(definition,[new_symbol(c5_96_1_2__orders_1),file(orders_1,c5_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c5_96_1_2__orders_1)]).

fof(e11_96_1_2__orders_1,plain,(
    ? [A] : m1_subset_1(A,c4_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_partfun1,rc2_ordinal1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_subset,dt_k2_relat_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,t2_subset,t6_boole,t7_boole,t8_boole,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,existence_m1_subset_1,dt_m1_subset_1,dt_c4_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e11_96_1_2__orders_1),[file(orders_1,e11_96_1_2__orders_1)]]).

fof(dt_c5_96_1_2__orders_1,plain,(
    m1_subset_1(c5_96_1_2__orders_1,c4_96_1_2__orders_1) ),
    inference(consider,[status(thm),assumptions([e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dh_c5_96_1_2__orders_1,e11_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c5_96_1_2__orders_1),[file(orders_1,c5_96_1_2__orders_1)]]).

fof(e10_96_1_2__orders_1,plain,(
    c4_96_1_2__orders_1 != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_finset_1,existence_m1_subset_1,dt_k2_relat_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c2_96_1_2__orders_1,dt_c4_96_1_2__orders_1,de_c2_96_1_2__orders_1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,e6_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e10_96_1_2__orders_1),[file(orders_1,e10_96_1_2__orders_1)]]).

fof(e12_96_1_2__orders_1,plain,(
    r2_hidden(c5_96_1_2__orders_1,c4_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dt_k2_relat_1,dt_c1_96_1_2__orders_1,rc1_finset_1,existence_m1_subset_1,dt_m1_subset_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_c4_96_1_2__orders_1,dt_c5_96_1_2__orders_1,fc2_ordinal1,t1_subset,t6_boole,t7_boole,e10_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e12_96_1_2__orders_1),[file(orders_1,e12_96_1_2__orders_1)]]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.9),axiom,file(tarski,d4_tarski)]).

fof(e13_96_1_2__orders_1,plain,(
    ~ v1_xboole_0(k3_tarski(c2_96_1_2__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_partfun1,rc2_ordinal1,existence_m1_subset_1,dt_k1_xboole_0,dt_k2_relat_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k3_tarski,dt_c2_96_1_2__orders_1,dt_c4_96_1_2__orders_1,dt_c5_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,t1_subset,t6_boole,t7_boole,t8_boole,e12_96_1_2__orders_1,d4_tarski]),
    [interesting(0.5),file(orders_1,e13_96_1_2__orders_1),[file(orders_1,e13_96_1_2__orders_1)]]).

fof(dt_c6_96_1_2__orders_1,plain,(
    ~ v1_xboole_0(c6_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,rc1_partfun1,rc2_ordinal1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k2_relat_1,dt_c1_96_1_2__orders_1,cc1_ordinal1,cc2_ordinal1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc3_ordinal1,t1_subset,dt_k3_tarski,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,t6_boole,t7_boole,t8_boole,de_c6_96_1_2__orders_1,e13_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c6_96_1_2__orders_1),[file(orders_1,c6_96_1_2__orders_1)]]).

fof(de_c7_96_1_2__orders_1,definition,(
    c7_96_1_2__orders_1 = c3_96_1_2__orders_1 ),
    introduced(definition,[new_symbol(c7_96_1_2__orders_1),file(orders_1,c7_96_1_2__orders_1)]),
    [interesting(0.5),axiom,file(orders_1,c7_96_1_2__orders_1)]).

fof(e14_96_1_2__orders_1,plain,
    ( v1_funct_1(c3_96_1_2__orders_1)
    & v1_funct_2(c3_96_1_2__orders_1,c2_96_1_2__orders_1,c6_96_1_2__orders_1)
    & m2_relset_1(c3_96_1_2__orders_1,c2_96_1_2__orders_1,c6_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_partfun1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,dt_c6_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c6_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,e14_96_1_2__orders_1),[file(orders_1,e14_96_1_2__orders_1)]]).

fof(dt_c7_96_1_2__orders_1,plain,
    ( v1_funct_1(c7_96_1_2__orders_1)
    & v1_funct_2(c7_96_1_2__orders_1,c2_96_1_2__orders_1,c6_96_1_2__orders_1)
    & m2_relset_1(c7_96_1_2__orders_1,c2_96_1_2__orders_1,c6_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_partfun1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,cc1_finset_1,cc1_relset_1,cc3_ordinal1,fc1_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,dt_c6_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c6_96_1_2__orders_1,de_c7_96_1_2__orders_1,e14_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,c7_96_1_2__orders_1),[file(orders_1,c7_96_1_2__orders_1)]]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.9),axiom,file(funct_2,d1_funct_2)]).

fof(e15_96_1_2__orders_1,plain,(
    k4_relset_1(c2_96_1_2__orders_1,c6_96_1_2__orders_1,c7_96_1_2__orders_1) = c2_96_1_2__orders_1 ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_orders_1,dt_m1_orders_1,cc2_finset_1,fc14_finset_1,rc1_finset_1,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_tarski,dt_m1_relset_1,dt_m1_subset_1,dt_c1_96_1_2__orders_1,dt_c3_96_1_2__orders_1,cc1_finset_1,cc1_ordinal1,cc1_relset_1,cc2_ordinal1,cc3_ordinal1,fc1_subset_1,fc4_ordinal1,fc4_subset_1,rc1_ordinal1,rc1_partfun1,rc1_subset_1,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc3_ordinal1,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k4_relset_1,dt_m2_relset_1,dt_c2_96_1_2__orders_1,dt_c6_96_1_2__orders_1,dt_c7_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c6_96_1_2__orders_1,de_c7_96_1_2__orders_1,fc2_ordinal1,t6_boole,d1_funct_2]),
    [interesting(0.5),file(orders_1,e15_96_1_2__orders_1),[file(orders_1,e15_96_1_2__orders_1)]]).

fof(e4_96_1_2_3__orders_1,plain,(
    r2_hidden(k1_funct_1(c3_96_1_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1)),k5_relset_1(c2_96_1_2__orders_1,k3_tarski(c2_96_1_2__orders_1),c3_96_1_2__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e2_96_1_2_3__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_ordinal1,cc1_relset_1,cc2_finset_1,cc2_ordinal1,fc14_finset_1,fc2_ordinal1,fc4_ordinal1,fc4_subset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_relset_1,redefinition_k5_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_tarski,dt_k4_relset_1,dt_k5_relset_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,dt_c6_96_1_2__orders_1,dt_c7_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c6_96_1_2__orders_1,de_c7_96_1_2__orders_1,t1_subset,t7_boole,e3_96_1_2_3__orders_1,e15_96_1_2__orders_1,d5_funct_1]),
    [interesting(0.35),file(orders_1,e4_96_1_2_3__orders_1),[file(orders_1,e4_96_1_2_3__orders_1)]]).

fof(e5_96_1_2_3__orders_1,plain,(
    r2_hidden(k1_funct_1(c3_96_1_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1)),c8_96_1_2__orders_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e2_96_1_2_3__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_ordinal1,cc1_relset_1,cc2_finset_1,cc2_ordinal1,fc13_finset_1,fc14_finset_1,fc2_ordinal1,fc4_ordinal1,fc4_subset_1,rc1_finset_1,rc1_ordinal1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_orders_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_k2_funct_2,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k2_funct_2,dt_m1_orders_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_partfun1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_relset_1,redefinition_k5_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_tarski,dt_k4_relset_1,dt_k5_relset_1,dt_k9_relat_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,dt_c6_96_1_2__orders_1,dt_c7_96_1_2__orders_1,dt_c8_96_1_2__orders_1,de_c2_96_1_2__orders_1,de_c6_96_1_2__orders_1,de_c7_96_1_2__orders_1,de_c8_96_1_2__orders_1,t1_subset,t7_boole,e4_96_1_2_3__orders_1,e15_96_1_2__orders_1,t146_relat_1]),
    [interesting(0.35),file(orders_1,e5_96_1_2_3__orders_1),[file(orders_1,e5_96_1_2_3__orders_1)]]).

fof(e9_96_1_2_3__orders_1,plain,
    ( r2_hidden(k1_funct_1(c3_96_1_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1)),k1_relat_1(c1_96__orders_1))
    & r2_hidden(k1_funct_1(c3_96_1_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1)),c8_96_1_2__orders_1)
    & k1_funct_1(c1_96__orders_1,k1_funct_1(c3_96_1_2__orders_1,k1_funct_1(c1_96_1_2__orders_1,c1_96_1_2_3__orders_1))) = c1_96_1_2_3__orders_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e2_96_1_2_3__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_partfun1,rc2_ordinal1,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k9_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc1_ordinal1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_ordinal1,rc2_partfun1,rc3_ordinal1,existence_m1_orders_1,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k3_tarski,dt_m1_orders_1,dt_m1_subset_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc2_finset_1,cc3_ordinal1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,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_k1_tarski,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c3_96_1_2__orders_1,dt_c8_96_1_2__orders_1,de_c8_96_1_2__orders_1,fc1_finset_1,fc2_subset_1,t1_subset,t3_subset,t7_boole,e8_96_1_2_3__orders_1,e16_96_1_2__orders_1,e5_96_1_2_3__orders_1,d1_tarski]),
    [interesting(0.35),file(orders_1,e9_96_1_2_3__orders_1),[file(orders_1,e9_96_1_2_3__orders_1)]]).

fof(e10_96_1_2_3__orders_1,plain,(
    r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e2_96_1_2_3__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k2_relat_1,dt_m1_relset_1,dt_m2_relset_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_partfun1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_orders_1,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k3_tarski,dt_m1_orders_1,dt_m1_subset_1,dt_c2_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k9_relat_1,dt_c1_96__orders_1,dt_c1_96_1_2__orders_1,dt_c1_96_1_2_3__orders_1,dt_c3_96_1_2__orders_1,dt_c8_96_1_2__orders_1,de_c8_96_1_2__orders_1,t1_subset,t7_boole,e9_96_1_2_3__orders_1,d12_funct_1]),
    [interesting(0.35),file(orders_1,e10_96_1_2_3__orders_1),[file(orders_1,e10_96_1_2_3__orders_1)]]).

fof(i4_96_1_2_3__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i4_96_1_2_3__orders_1)]),
    [interesting(0.35),trivial,file(orders_1,i4_96_1_2_3__orders_1)]).

fof(i3_96_1_2_3__orders_1,plain,(
    r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e2_96_1_2_3__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[e10_96_1_2_3__orders_1,i4_96_1_2_3__orders_1]),
    [interesting(0.35),file(orders_1,i3_96_1_2_3__orders_1),[file(orders_1,i3_96_1_2_3__orders_1)]]).

fof(i2_96_1_2_3__orders_1,plain,
    ( r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1)
   => r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[e2_96_1_2_3__orders_1])],[e2_96_1_2_3__orders_1,i3_96_1_2_3__orders_1]),
    [interesting(0.35),file(orders_1,i2_96_1_2_3__orders_1),[file(orders_1,i2_96_1_2_3__orders_1)]]).

fof(i1_96_1_2_3__orders_1,plain,
    ( r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1))
  <=> r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_96_1_2_3__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[e1_96_1_2_3__orders_1,i2_96_1_2_3__orders_1]),
    [interesting(0.35),file(orders_1,i1_96_1_2_3__orders_1),[file(orders_1,i1_96_1_2_3__orders_1)]]).

fof(i1_96_1_2_3_tmp__orders_1,plain,
    ( r2_hidden(c1_96_1_2_3__orders_1,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1))
  <=> r2_hidden(c1_96_1_2_3__orders_1,c2_96__orders_1) ),
    inference(discharge_asm,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[dt_c1_96_1_2_3__orders_1])],[dt_c1_96_1_2_3__orders_1,i1_96_1_2_3__orders_1]),
    [interesting(0.5),e20_96_1_2__orders_1]).

fof(e20_96_1_2__orders_1,plain,(
    ! [A] : 
      ( r2_hidden(A,k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1))
    <=> r2_hidden(A,c2_96__orders_1) ) ),
    inference(let,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[i1_96_1_2_3_tmp__orders_1,dh_c1_96_1_2_3__orders_1]),
    [interesting(0.5),file(orders_1,e20_96_1_2__orders_1),[file(orders_1,e20_96_1_2__orders_1)]]).

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(e21_96_1_2__orders_1,plain,(
    k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1) = c2_96__orders_1 ),
    inference(mizar_by,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m2_relset_1,rc1_partfun1,rc2_ordinal1,reflexivity_r1_tarski,existence_m1_orders_1,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_relat_1,dt_m1_orders_1,dt_m1_relset_1,dt_c1_96_1_2__orders_1,cc1_ordinal1,cc2_finset_1,cc2_ordinal1,fc13_finset_1,fc2_ordinal1,fc4_ordinal1,rc1_finset_1,rc1_ordinal1,rc2_partfun1,rc3_finset_1,rc3_ordinal1,rc4_finset_1,existence_m1_subset_1,redefinition_k2_funct_2,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k3_tarski,dt_m1_subset_1,dt_c2_96_1_2__orders_1,dt_c3_96_1_2__orders_1,de_c2_96_1_2__orders_1,cc1_finset_1,cc3_ordinal1,fc1_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k9_relat_1,dt_c1_96__orders_1,dt_c2_96__orders_1,dt_c8_96_1_2__orders_1,de_c8_96_1_2__orders_1,t1_subset,t7_boole,e20_96_1_2__orders_1,t2_tarski]),
    [interesting(0.5),file(orders_1,e21_96_1_2__orders_1),[file(orders_1,e21_96_1_2__orders_1)]]).

fof(i5_96_1_2__orders_1,theorem,(
    $true ),
    introduced(tautology,[file(orders_1,i5_96_1_2__orders_1)]),
    [interesting(0.5),trivial,file(orders_1,i5_96_1_2__orders_1)]).

fof(i4_96_1_2__orders_1,plain,(
    k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1) = c2_96__orders_1 ),
    inference(conclusion,[status(thm),assumptions([e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[e21_96_1_2__orders_1,i5_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,i4_96_1_2__orders_1),[file(orders_1,i4_96_1_2__orders_1)]]).

fof(i3_96_1_2__orders_1,plain,
    ( v1_finset_1(c8_96_1_2__orders_1)
    & k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1) = c2_96__orders_1 ),
    inference(conclusion,[status(thm),assumptions([e1_96__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[e19_96_1_2__orders_1,i4_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,i3_96_1_2__orders_1),[file(orders_1,i3_96_1_2__orders_1)]]).

fof(i2_96_1_2__orders_1,plain,
    ( r1_tarski(c8_96_1_2__orders_1,k1_relat_1(c1_96__orders_1))
    & v1_finset_1(c8_96_1_2__orders_1)
    & k9_relat_1(c1_96__orders_1,c8_96_1_2__orders_1) = c2_96__orders_1 ),
    inference(conclusion,[status(thm),assumptions([e1_96__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[e16_96_1_2__orders_1,i3_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,i2_96_1_2__orders_1),[file(orders_1,i2_96_1_2__orders_1)]]).

fof(i1_96_1_2__orders_1,plain,(
    ? [A] : 
      ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
      & v1_finset_1(A)
      & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) ),
    inference(take,[status(thm),assumptions([e1_96__orders_1,e2_96__orders_1,e1_96_1_2__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[cc1_ordinal1,cc2_ordinal1,fc4_ordinal1,rc1_ordinal1,rc3_ordinal1,cc1_finset_1,cc3_ordinal1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,dt_k1_zfmisc_1,dt_k3_tarski,dt_m1_subset_1,dt_c2_96_1_2__orders_1,cc2_finset_1,fc13_finset_1,fc1_subset_1,reflexivity_r1_tarski,dt_k1_relat_1,dt_k9_relat_1,dt_c1_96__orders_1,dt_c2_96__orders_1,dt_c8_96_1_2__orders_1,i2_96_1_2__orders_1]),
    [interesting(0.5),file(orders_1,i1_96_1_2__orders_1),[file(orders_1,i1_96_1_2__orders_1)]]).

fof(i2_96_1__orders_1,plain,(
    ~ ( c2_96__orders_1 != k1_xboole_0
      & ! [A] : 
          ~ ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
            & v1_finset_1(A)
            & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_96__orders_1,e2_96__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[e1_96_1_2__orders_1])],[e1_96_1_2__orders_1,i1_96_1_2__orders_1]),
    [interesting(0.65),file(orders_1,i2_96_1__orders_1),[file(orders_1,i2_96_1__orders_1)]]).

fof(e1_96_1__orders_1,plain,(
    ~ ( c2_96__orders_1 != k1_xboole_0
      & c2_96__orders_1 = k1_xboole_0 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_96__orders_1])],[existence_m1_subset_1,dt_m1_subset_1,t2_subset,antisymmetry_r2_hidden,rc1_finset_1,t1_subset,cc1_finset_1,cc1_ordinal1,cc2_ordinal1,cc3_ordinal1,rc1_ordinal1,rc1_partfun1,rc2_ordinal1,rc3_ordinal1,t7_boole,t8_boole,dt_k1_xboole_0,dt_c2_96__orders_1,fc2_ordinal1,t6_boole]),
    [interesting(0.65),file(orders_1,e1_96_1__orders_1),[file(orders_1,e1_96_1__orders_1)]]).

fof(i3_96__orders_1,plain,(
    ? [A] : 
      ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
      & v1_finset_1(A)
      & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) ),
    inference(percases,[status(thm),assumptions([e1_96__orders_1,e2_96__orders_1,dt_c1_96__orders_1,dt_c2_96__orders_1])],[i1_96_1__orders_1,i2_96_1__orders_1,e1_96_1__orders_1]),
    [interesting(0.8),file(orders_1,i3_96__orders_1),[file(orders_1,i3_96__orders_1)]]).

fof(i2_96__orders_1,plain,(
    ~ ( v1_finset_1(c2_96__orders_1)
      & r1_tarski(c2_96__orders_1,k2_relat_1(c1_96__orders_1))
      & ! [A] : 
          ~ ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
            & v1_finset_1(A)
            & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_96__orders_1,dt_c2_96__orders_1]),discharge_asm(discharge,[e1_96__orders_1,e2_96__orders_1])],[e1_96__orders_1,e2_96__orders_1,i3_96__orders_1]),
    [interesting(0.8),file(orders_1,i2_96__orders_1),[file(orders_1,i2_96__orders_1)]]).

fof(i2_96_tmp__orders_1,plain,(
    ~ ( v1_finset_1(c2_96__orders_1)
      & r1_tarski(c2_96__orders_1,k2_relat_1(c1_96__orders_1))
      & ! [A] : 
          ~ ( r1_tarski(A,k1_relat_1(c1_96__orders_1))
            & v1_finset_1(A)
            & k9_relat_1(c1_96__orders_1,A) = c2_96__orders_1 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_96__orders_1]),discharge_asm(discharge,[dt_c2_96__orders_1])],[dt_c2_96__orders_1,i2_96__orders_1]),
    [interesting(0.8),i1_96__orders_1]).

fof(i1_96__orders_1,plain,(
    ! [A] : 
      ~ ( v1_finset_1(A)
        & r1_tarski(A,k2_relat_1(c1_96__orders_1))
        & ! [B] : 
            ~ ( r1_tarski(B,k1_relat_1(c1_96__orders_1))
              & v1_finset_1(B)
              & k9_relat_1(c1_96__orders_1,B) = A ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_96__orders_1])],[i2_96_tmp__orders_1,dh_c2_96__orders_1]),
    [interesting(0.8),file(orders_1,i1_96__orders_1),[file(orders_1,i1_96__orders_1)]]).

fof(i1_96_tmp__orders_1,plain,
    ( ( v1_relat_1(c1_96__orders_1)
      & v1_funct_1(c1_96__orders_1) )
   => ! [A] : 
        ~ ( v1_finset_1(A)
          & r1_tarski(A,k2_relat_1(c1_96__orders_1))
          & ! [B] : 
              ~ ( r1_tarski(B,k1_relat_1(c1_96__orders_1))
                & v1_finset_1(B)
                & k9_relat_1(c1_96__orders_1,B) = A ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_96__orders_1])],[dt_c1_96__orders_1,i1_96__orders_1]),
    [interesting(1),t195_orders_1]).

fof(t195_orders_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ~ ( v1_finset_1(B)
            & r1_tarski(B,k2_relat_1(A))
            & ! [C] : 
                ~ ( r1_tarski(C,k1_relat_1(A))
                  & v1_finset_1(C)
                  & k9_relat_1(A,C) = B ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_96_tmp__orders_1,dh_c1_96__orders_1]),
    [interesting(1),file(orders_1,t195_orders_1),[file(orders_1,t195_orders_1)]]).