% Mizar ND problem: t3_algspec1,algspec1,86,22 
fof(dh_c1_3__algspec1,definition,
    ( ( ( v1_relat_1(c1_3__algspec1)
        & v1_funct_1(c1_3__algspec1) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(A))
                  & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(B))
                  & r1_xboole_0(k9_relat_1(A,k1_relat_1(B)),k1_relat_1(c1_3__algspec1)) )
               => k5_relat_1(k1_funct_4(A,B),c1_3__algspec1) = k5_relat_1(A,c1_3__algspec1) ) ) ) )
   => ! [C] : 
        ( ( v1_relat_1(C)
          & v1_funct_1(C) )
       => ! [D] : 
            ( ( v1_relat_1(D)
              & v1_funct_1(D) )
           => ! [E] : 
                ( ( v1_relat_1(E)
                  & v1_funct_1(E) )
               => ( ( r1_tarski(k1_relat_1(C),k2_relat_1(D))
                    & r1_xboole_0(k1_relat_1(C),k2_relat_1(E))
                    & r1_xboole_0(k9_relat_1(D,k1_relat_1(E)),k1_relat_1(C)) )
                 => k5_relat_1(k1_funct_4(D,E),C) = k5_relat_1(D,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__algspec1),file(algspec1,c1_3__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c1_3__algspec1)]).

fof(dh_c2_3__algspec1,definition,
    ( ( ( v1_relat_1(c2_3__algspec1)
        & v1_funct_1(c2_3__algspec1) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(c2_3__algspec1))
              & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(A))
              & r1_xboole_0(k9_relat_1(c2_3__algspec1,k1_relat_1(A)),k1_relat_1(c1_3__algspec1)) )
           => k5_relat_1(k1_funct_4(c2_3__algspec1,A),c1_3__algspec1) = k5_relat_1(c2_3__algspec1,c1_3__algspec1) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(B))
                & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(C))
                & r1_xboole_0(k9_relat_1(B,k1_relat_1(C)),k1_relat_1(c1_3__algspec1)) )
             => k5_relat_1(k1_funct_4(B,C),c1_3__algspec1) = k5_relat_1(B,c1_3__algspec1) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__algspec1),file(algspec1,c2_3__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c2_3__algspec1)]).

fof(dh_c3_3__algspec1,definition,
    ( ( ( v1_relat_1(c3_3__algspec1)
        & v1_funct_1(c3_3__algspec1) )
     => ( ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(c2_3__algspec1))
          & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(c3_3__algspec1))
          & r1_xboole_0(k9_relat_1(c2_3__algspec1,k1_relat_1(c3_3__algspec1)),k1_relat_1(c1_3__algspec1)) )
       => k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1) = k5_relat_1(c2_3__algspec1,c1_3__algspec1) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(c2_3__algspec1))
            & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(A))
            & r1_xboole_0(k9_relat_1(c2_3__algspec1,k1_relat_1(A)),k1_relat_1(c1_3__algspec1)) )
         => k5_relat_1(k1_funct_4(c2_3__algspec1,A),c1_3__algspec1) = k5_relat_1(c2_3__algspec1,c1_3__algspec1) ) ) ),
    introduced(definition,[new_symbol(c3_3__algspec1),file(algspec1,c3_3__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c3_3__algspec1)]).

fof(e1_3__algspec1,assumption,
    ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(c2_3__algspec1))
    & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(c3_3__algspec1))
    & r1_xboole_0(k9_relat_1(c2_3__algspec1,k1_relat_1(c3_3__algspec1)),k1_relat_1(c1_3__algspec1)) ),
    introduced(assumption,[file(algspec1,e1_3__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,e1_3__algspec1)]).

fof(rc1_pboole,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    [interesting(0.9),axiom,file(pboole,rc1_pboole)]).

fof(rc2_catalg_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & ~ v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(catalg_1,rc2_catalg_1),
    [interesting(0.9),axiom,file(catalg_1,rc2_catalg_1)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

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

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

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

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

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc1_circcomb,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(circcomb,rc1_circcomb),
    [interesting(0.9),axiom,file(circcomb,rc1_circcomb)]).

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

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

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

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

fof(fc10_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc10_relat_1)]).

fof(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(fc9_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc9_relat_1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

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

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

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

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

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

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

fof(idempotence_k1_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

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

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

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    [interesting(0.9),axiom,file(funct_4,k1_funct_4)]).

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_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    [interesting(0.9),axiom,file(relat_1,k5_relat_1)]).

fof(dt_c1_3__algspec1,assumption,
    ( v1_relat_1(c1_3__algspec1)
    & v1_funct_1(c1_3__algspec1) ),
    introduced(assumption,[file(algspec1,c1_3__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c1_3__algspec1)]).

fof(dt_c2_3__algspec1,assumption,
    ( v1_relat_1(c2_3__algspec1)
    & v1_funct_1(c2_3__algspec1) ),
    introduced(assumption,[file(algspec1,c2_3__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c2_3__algspec1)]).

fof(dt_c3_3__algspec1,assumption,
    ( v1_relat_1(c3_3__algspec1)
    & v1_funct_1(c3_3__algspec1) ),
    introduced(assumption,[file(algspec1,c3_3__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c3_3__algspec1)]).

fof(fc1_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]).

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

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(dh_c1_3_2__algspec1,definition,
    ( ( r2_hidden(c1_3_2__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
     => k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),c1_3_2__algspec1) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),c1_3_2__algspec1) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
       => k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),A) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),A) ) ),
    introduced(definition,[new_symbol(c1_3_2__algspec1),file(algspec1,c1_3_2__algspec1)]),
    [interesting(0.65),axiom,file(algspec1,c1_3_2__algspec1)]).

fof(e1_3_2__algspec1,assumption,(
    r2_hidden(c1_3_2__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ),
    introduced(assumption,[file(algspec1,e1_3_2__algspec1)]),
    [interesting(0.65),axiom,file(algspec1,e1_3_2__algspec1)]).

fof(dt_c1_3_2__algspec1,assumption,(
    $true ),
    introduced(assumption,[file(algspec1,c1_3_2__algspec1)]),
    [interesting(0.65),axiom,file(algspec1,c1_3_2__algspec1)]).

fof(e1_3_2_1__algspec1,assumption,(
    r2_hidden(c1_3_2__algspec1,k1_relat_1(c3_3__algspec1)) ),
    introduced(assumption,[file(algspec1,e1_3_2_1__algspec1)]),
    [interesting(0.5),axiom,file(algspec1,e1_3_2_1__algspec1)]).

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

fof(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

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

fof(symmetry_r1_xboole_0,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    [interesting(0.9),axiom,file(relat_1,k9_relat_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(t21_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
          <=> ( r2_hidden(A,k1_relat_1(C))
              & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ),
    file(funct_1,t21_funct_1),
    [interesting(0.9),axiom,file(funct_1,t21_funct_1)]).

fof(e2_3_2__algspec1,plain,
    ( r2_hidden(c1_3_2__algspec1,k1_relat_1(c2_3__algspec1))
    & r2_hidden(k1_funct_1(c2_3__algspec1,c1_3_2__algspec1),k1_relat_1(c1_3__algspec1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e1_3_2__algspec1,t21_funct_1]),
    [interesting(0.65),file(algspec1,e2_3_2__algspec1),[file(algspec1,e2_3_2__algspec1)]]).

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_3_2_1__algspec1,plain,(
    r2_hidden(k1_funct_1(c2_3__algspec1,c1_3_2__algspec1),k9_relat_1(c2_3__algspec1,k1_relat_1(c3_3__algspec1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3_2_1__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k9_relat_1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,rc1_funct_1,t1_subset,t7_boole,e1_3_2_1__algspec1,e2_3_2__algspec1,d12_funct_1]),
    [interesting(0.5),file(algspec1,e2_3_2_1__algspec1),[file(algspec1,e2_3_2_1__algspec1)]]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : 
              ~ ( r2_hidden(C,A)
                & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,t3_xboole_0)]).

fof(e3_3_2_1__algspec1,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3_2_1__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k9_relat_1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,t1_subset,t3_subset,t7_boole,e2_3_2_1__algspec1,e1_3__algspec1,e2_3_2__algspec1,t3_xboole_0]),
    [interesting(0.5),file(algspec1,e3_3_2_1__algspec1),[file(algspec1,e3_3_2_1__algspec1)]]).

fof(i2_3_2_1__algspec1,theorem,(
    $true ),
    introduced(tautology,[file(algspec1,i2_3_2_1__algspec1)]),
    [interesting(0.5),trivial,file(algspec1,i2_3_2_1__algspec1)]).

fof(i1_3_2_1__algspec1,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c3_3__algspec1,e1_3_2_1__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[e3_3_2_1__algspec1,i2_3_2_1__algspec1]),
    [interesting(0.5),file(algspec1,i1_3_2_1__algspec1),[file(algspec1,i1_3_2_1__algspec1)]]).

fof(e3_3_2__algspec1,plain,(
    ~ r2_hidden(c1_3_2__algspec1,k1_relat_1(c3_3__algspec1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1]),discharge_asm(discharge,[e1_3_2_1__algspec1])],[e1_3_2_1__algspec1,i1_3_2_1__algspec1]),
    [interesting(0.65),file(algspec1,e3_3_2__algspec1),[file(algspec1,e3_3_2__algspec1)]]).

fof(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.9),axiom,file(funct_4,t12_funct_4)]).

fof(t13_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k1_funct_4(B,C)))
          <=> ( r2_hidden(A,k1_relat_1(B))
              | r2_hidden(A,k1_relat_1(C)) ) ) ) ) ),
    file(funct_4,t13_funct_4),
    [interesting(0.9),axiom,file(funct_4,t13_funct_4)]).

fof(e4_3_2__algspec1,plain,
    ( r2_hidden(c1_3_2__algspec1,k1_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1)))
    & k1_funct_1(c2_3__algspec1,c1_3_2__algspec1) = k1_funct_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3_2__algspec1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,rc1_funct_1,t1_subset,t7_boole,e3_3_2__algspec1,e2_3_2__algspec1,t12_funct_4,t13_funct_4]),
    [interesting(0.65),file(algspec1,e4_3_2__algspec1),[file(algspec1,e4_3_2__algspec1)]]).

fof(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.9),axiom,file(funct_1,t23_funct_1)]).

fof(e1_3_2_2__algspec1,plain,(
    k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),c1_3_2__algspec1) = k1_funct_1(c1_3__algspec1,k1_funct_1(c2_3__algspec1,c1_3_2__algspec1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e4_3_2__algspec1,t23_funct_1]),
    [interesting(0.5),file(algspec1,e1_3_2_2__algspec1),[file(algspec1,e1_3_2_2__algspec1)]]).

fof(e2_3_2_2__algspec1,plain,(
    k1_funct_1(c1_3__algspec1,k1_funct_1(c2_3__algspec1,c1_3_2__algspec1)) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),c1_3_2__algspec1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e2_3_2__algspec1,t23_funct_1]),
    [interesting(0.5),file(algspec1,e2_3_2_2__algspec1),[file(algspec1,e2_3_2_2__algspec1)]]).

fof(e5_3_2__algspec1,plain,(
    k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),c1_3_2__algspec1) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),c1_3_2__algspec1) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[e1_3_2_2__algspec1,e2_3_2_2__algspec1]),
    [interesting(0.65),file(algspec1,e5_3_2__algspec1),[file(algspec1,e5_3_2__algspec1)]]).

fof(i3_3_2__algspec1,theorem,(
    $true ),
    introduced(tautology,[file(algspec1,i3_3_2__algspec1)]),
    [interesting(0.65),trivial,file(algspec1,i3_3_2__algspec1)]).

fof(i2_3_2__algspec1,plain,(
    k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),c1_3_2__algspec1) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),c1_3_2__algspec1) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1,e1_3_2__algspec1])],[e5_3_2__algspec1,i3_3_2__algspec1]),
    [interesting(0.65),file(algspec1,i2_3_2__algspec1),[file(algspec1,i2_3_2__algspec1)]]).

fof(i1_3_2__algspec1,plain,
    ( r2_hidden(c1_3_2__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
   => k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),c1_3_2__algspec1) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),c1_3_2__algspec1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_2__algspec1,dt_c2_3__algspec1]),discharge_asm(discharge,[e1_3_2__algspec1])],[e1_3_2__algspec1,i2_3_2__algspec1]),
    [interesting(0.65),file(algspec1,i1_3_2__algspec1),[file(algspec1,i1_3_2__algspec1)]]).

fof(i1_3_2_tmp__algspec1,plain,
    ( r2_hidden(c1_3_2__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
   => k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),c1_3_2__algspec1) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),c1_3_2__algspec1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1]),discharge_asm(discharge,[dt_c1_3_2__algspec1])],[dt_c1_3_2__algspec1,i1_3_2__algspec1]),
    [interesting(0.8),e3_3__algspec1]).

fof(e3_3__algspec1,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
     => k1_funct_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1),A) = k1_funct_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1),A) ) ),
    inference(let,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1])],[i1_3_2_tmp__algspec1,dh_c1_3_2__algspec1]),
    [interesting(0.8),file(algspec1,e3_3__algspec1),[file(algspec1,e3_3__algspec1)]]).

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

fof(dh_c1_3_1_1__algspec1,definition,
    ( ( r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
     => r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) )
   => ! [A] : 
        ( r2_hidden(A,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
       => r2_hidden(A,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) ) ),
    introduced(definition,[new_symbol(c1_3_1_1__algspec1),file(algspec1,c1_3_1_1__algspec1)]),
    [interesting(0.5),axiom,file(algspec1,c1_3_1_1__algspec1)]).

fof(e1_3_1_1__algspec1,assumption,(
    r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ),
    introduced(assumption,[file(algspec1,e1_3_1_1__algspec1)]),
    [interesting(0.5),axiom,file(algspec1,e1_3_1_1__algspec1)]).

fof(dt_c1_3_1_1__algspec1,assumption,(
    $true ),
    introduced(assumption,[file(algspec1,c1_3_1_1__algspec1)]),
    [interesting(0.5),axiom,file(algspec1,c1_3_1_1__algspec1)]).

fof(e1_3_1_1_1__algspec1,assumption,(
    r2_hidden(c1_3_1_1__algspec1,k1_relat_1(c3_3__algspec1)) ),
    introduced(assumption,[file(algspec1,e1_3_1_1_1__algspec1)]),
    [interesting(0.35),axiom,file(algspec1,e1_3_1_1_1__algspec1)]).

fof(e2_3_1_1__algspec1,plain,
    ( r2_hidden(c1_3_1_1__algspec1,k1_relat_1(c2_3__algspec1))
    & r2_hidden(k1_funct_1(c2_3__algspec1,c1_3_1_1__algspec1),k1_relat_1(c1_3__algspec1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,t8_boole,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e1_3_1_1__algspec1,t21_funct_1]),
    [interesting(0.5),file(algspec1,e2_3_1_1__algspec1),[file(algspec1,e2_3_1_1__algspec1)]]).

fof(e2_3_1_1_1__algspec1,plain,(
    r2_hidden(k1_funct_1(c2_3__algspec1,c1_3_1_1__algspec1),k9_relat_1(c2_3__algspec1,k1_relat_1(c3_3__algspec1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3_1_1_1__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k9_relat_1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,rc1_funct_1,t1_subset,t7_boole,e1_3_1_1_1__algspec1,e2_3_1_1__algspec1,d12_funct_1]),
    [interesting(0.35),file(algspec1,e2_3_1_1_1__algspec1),[file(algspec1,e2_3_1_1_1__algspec1)]]).

fof(e3_3_1_1_1__algspec1,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3_1_1_1__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k9_relat_1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,t1_subset,t3_subset,t7_boole,e2_3_1_1_1__algspec1,e1_3__algspec1,e2_3_1_1__algspec1,t3_xboole_0]),
    [interesting(0.35),file(algspec1,e3_3_1_1_1__algspec1),[file(algspec1,e3_3_1_1_1__algspec1)]]).

fof(i2_3_1_1_1__algspec1,theorem,(
    $true ),
    introduced(tautology,[file(algspec1,i2_3_1_1_1__algspec1)]),
    [interesting(0.35),trivial,file(algspec1,i2_3_1_1_1__algspec1)]).

fof(i1_3_1_1_1__algspec1,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c3_3__algspec1,e1_3_1_1_1__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1])],[e3_3_1_1_1__algspec1,i2_3_1_1_1__algspec1]),
    [interesting(0.35),file(algspec1,i1_3_1_1_1__algspec1),[file(algspec1,i1_3_1_1_1__algspec1)]]).

fof(e3_3_1_1__algspec1,plain,(
    ~ r2_hidden(c1_3_1_1__algspec1,k1_relat_1(c3_3__algspec1)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1]),discharge_asm(discharge,[e1_3_1_1_1__algspec1])],[e1_3_1_1_1__algspec1,i1_3_1_1_1__algspec1]),
    [interesting(0.5),file(algspec1,e3_3_1_1__algspec1),[file(algspec1,e3_3_1_1__algspec1)]]).

fof(e4_3_1_1__algspec1,plain,
    ( r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1)))
    & k1_funct_1(c2_3__algspec1,c1_3_1_1__algspec1) = k1_funct_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3_1_1__algspec1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,rc1_funct_1,t1_subset,t7_boole,e3_3_1_1__algspec1,e2_3_1_1__algspec1,t12_funct_4,t13_funct_4]),
    [interesting(0.5),file(algspec1,e4_3_1_1__algspec1),[file(algspec1,e4_3_1_1__algspec1)]]).

fof(e5_3_1_1__algspec1,plain,(
    r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e4_3_1_1__algspec1,e2_3_1_1__algspec1,t21_funct_1]),
    [interesting(0.5),file(algspec1,e5_3_1_1__algspec1),[file(algspec1,e5_3_1_1__algspec1)]]).

fof(i3_3_1_1__algspec1,theorem,(
    $true ),
    introduced(tautology,[file(algspec1,i3_3_1_1__algspec1)]),
    [interesting(0.5),trivial,file(algspec1,i3_3_1_1__algspec1)]).

fof(i2_3_1_1__algspec1,plain,(
    r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1,e1_3_1_1__algspec1])],[e5_3_1_1__algspec1,i3_3_1_1__algspec1]),
    [interesting(0.5),file(algspec1,i2_3_1_1__algspec1),[file(algspec1,i2_3_1_1__algspec1)]]).

fof(i1_3_1_1__algspec1,plain,
    ( r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
   => r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1_1__algspec1,dt_c2_3__algspec1]),discharge_asm(discharge,[e1_3_1_1__algspec1])],[e1_3_1_1__algspec1,i2_3_1_1__algspec1]),
    [interesting(0.5),file(algspec1,i1_3_1_1__algspec1),[file(algspec1,i1_3_1_1__algspec1)]]).

fof(i1_3_1_1_tmp__algspec1,plain,
    ( r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
   => r2_hidden(c1_3_1_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1]),discharge_asm(discharge,[dt_c1_3_1_1__algspec1])],[dt_c1_3_1_1__algspec1,i1_3_1_1__algspec1]),
    [interesting(0.65),e1_3_1__algspec1]).

fof(e1_3_1__algspec1,plain,(
    ! [A] : 
      ( r2_hidden(A,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)))
     => r2_hidden(A,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) ) ),
    inference(let,[status(thm),assumptions([dt_c3_3__algspec1,e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1])],[i1_3_1_1_tmp__algspec1,dh_c1_3_1_1__algspec1]),
    [interesting(0.65),file(algspec1,e1_3_1__algspec1),[file(algspec1,e1_3_1__algspec1)]]).

fof(dt_c1_3_1__algspec1,assumption,(
    $true ),
    introduced(assumption,[file(algspec1,c1_3_1__algspec1)]),
    [interesting(0.65),axiom,file(algspec1,c1_3_1__algspec1)]).

fof(dh_c1_3_1__algspec1,definition,
    ( ~ ( r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1)))
        & ~ r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) )
   => ! [A] : 
        ~ ( r2_hidden(A,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1)))
          & ~ r2_hidden(A,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ) ),
    introduced(definition,[new_symbol(c1_3_1__algspec1),file(algspec1,c1_3_1__algspec1)]),
    [interesting(0.65),axiom,file(algspec1,c1_3_1__algspec1)]).

fof(e2_3_1__algspec1,assumption,(
    r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1))) ),
    introduced(assumption,[file(algspec1,e2_3_1__algspec1)]),
    [interesting(0.65),axiom,file(algspec1,e2_3_1__algspec1)]).

fof(e3_3_1__algspec1,plain,
    ( r2_hidden(c1_3_1__algspec1,k1_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1)))
    & r2_hidden(k1_funct_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3_1__algspec1),k1_relat_1(c1_3__algspec1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,e2_3_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e2_3_1__algspec1,t21_funct_1]),
    [interesting(0.65),file(algspec1,e3_3_1__algspec1),[file(algspec1,e3_3_1__algspec1)]]).

fof(e4_3_1__algspec1,plain,
    ( ( r2_hidden(c1_3_1__algspec1,k1_relat_1(c2_3__algspec1))
      & ~ r2_hidden(c1_3_1__algspec1,k1_relat_1(c3_3__algspec1)) )
    | r2_hidden(c1_3_1__algspec1,k1_relat_1(c3_3__algspec1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,e2_3_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,rc1_funct_1,t1_subset,t7_boole,e3_3_1__algspec1,t13_funct_4]),
    [interesting(0.65),file(algspec1,e4_3_1__algspec1),[file(algspec1,e4_3_1__algspec1)]]).

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(t14_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.9),axiom,file(funct_4,t14_funct_4)]).

fof(e5_3_1__algspec1,plain,
    ( ( r2_hidden(c1_3_1__algspec1,k1_relat_1(c2_3__algspec1))
      & k1_funct_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3_1__algspec1) = k1_funct_1(c2_3__algspec1,c1_3_1__algspec1) )
    | ( k1_funct_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3_1__algspec1) = k1_funct_1(c3_3__algspec1,c1_3_1__algspec1)
      & r2_hidden(k1_funct_1(c3_3__algspec1,c1_3_1__algspec1),k2_relat_1(c3_3__algspec1)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,e2_3_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_relat_1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,rc1_funct_1,t1_subset,t7_boole,e4_3_1__algspec1,d5_funct_1,t12_funct_4,t14_funct_4]),
    [interesting(0.65),file(algspec1,e5_3_1__algspec1),[file(algspec1,e5_3_1__algspec1)]]).

fof(e6_3_1__algspec1,plain,(
    r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,e2_3_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,idempotence_k1_funct_4,reflexivity_r1_tarski,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k2_relat_1,dt_k5_relat_1,dt_k9_relat_1,dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t3_subset,t7_boole,e5_3_1__algspec1,e1_3__algspec1,e3_3_1__algspec1,t21_funct_1,t3_xboole_0]),
    [interesting(0.65),file(algspec1,e6_3_1__algspec1),[file(algspec1,e6_3_1__algspec1)]]).

fof(i4_3_1__algspec1,theorem,(
    $true ),
    introduced(tautology,[file(algspec1,i4_3_1__algspec1)]),
    [interesting(0.65),trivial,file(algspec1,i4_3_1__algspec1)]).

fof(i3_3_1__algspec1,plain,(
    r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ),
    inference(conclusion,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,e2_3_1__algspec1])],[e6_3_1__algspec1,i4_3_1__algspec1]),
    [interesting(0.65),file(algspec1,i3_3_1__algspec1),[file(algspec1,i3_3_1__algspec1)]]).

fof(i2_3_1__algspec1,plain,(
    ~ ( r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1)))
      & ~ r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c1_3_1__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1]),discharge_asm(discharge,[e2_3_1__algspec1])],[e2_3_1__algspec1,i3_3_1__algspec1]),
    [interesting(0.65),file(algspec1,i2_3_1__algspec1),[file(algspec1,i2_3_1__algspec1)]]).

fof(i2_3_1_tmp__algspec1,plain,(
    ~ ( r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1)))
      & ~ r2_hidden(c1_3_1__algspec1,k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1]),discharge_asm(discharge,[dt_c1_3_1__algspec1])],[dt_c1_3_1__algspec1,i2_3_1__algspec1]),
    [interesting(0.65),i1_3_1__algspec1]).

fof(i1_3_1__algspec1,plain,(
    r1_tarski(k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1)),k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1))) ),
    inference(let,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1])],[i2_3_1_tmp__algspec1,fc1_funct_1,rc1_funct_1,idempotence_k1_funct_4,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,d3_tarski,dh_c1_3_1__algspec1]),
    [interesting(0.65),file(algspec1,i1_3_1__algspec1),[file(algspec1,i1_3_1__algspec1)]]).

fof(e2_3__algspec1,plain,(
    k1_relat_1(k5_relat_1(c2_3__algspec1,c1_3__algspec1)) = k1_relat_1(k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1)) ),
    inference(conclusion,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1])],[fc1_funct_1,rc1_funct_1,idempotence_k1_funct_4,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_funct_4,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,d3_tarski,d10_xboole_0,e1_3_1__algspec1,i1_3_1__algspec1]),
    [interesting(0.8),file(algspec1,e2_3__algspec1),[file(algspec1,e2_3__algspec1)]]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.9),axiom,file(funct_1,t9_funct_1)]).

fof(e4_3__algspec1,plain,(
    k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1) = k5_relat_1(c2_3__algspec1,c1_3__algspec1) ),
    inference(mizar_by,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_subset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,idempotence_k1_funct_4,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_funct_4,dt_k1_relat_1,dt_k5_relat_1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e3_3__algspec1,e2_3__algspec1,t9_funct_1]),
    [interesting(0.8),file(algspec1,e4_3__algspec1),[file(algspec1,e4_3__algspec1)]]).

fof(i3_3__algspec1,theorem,(
    $true ),
    introduced(tautology,[file(algspec1,i3_3__algspec1)]),
    [interesting(0.8),trivial,file(algspec1,i3_3__algspec1)]).

fof(i2_3__algspec1,plain,(
    k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1) = k5_relat_1(c2_3__algspec1,c1_3__algspec1) ),
    inference(conclusion,[status(thm),assumptions([e1_3__algspec1,dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1])],[e4_3__algspec1,i3_3__algspec1]),
    [interesting(0.8),file(algspec1,i2_3__algspec1),[file(algspec1,i2_3__algspec1)]]).

fof(i1_3__algspec1,plain,
    ( ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(c2_3__algspec1))
      & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(c3_3__algspec1))
      & r1_xboole_0(k9_relat_1(c2_3__algspec1,k1_relat_1(c3_3__algspec1)),k1_relat_1(c1_3__algspec1)) )
   => k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1) = k5_relat_1(c2_3__algspec1,c1_3__algspec1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1]),discharge_asm(discharge,[e1_3__algspec1])],[e1_3__algspec1,i2_3__algspec1]),
    [interesting(0.8),file(algspec1,i1_3__algspec1),[file(algspec1,i1_3__algspec1)]]).

fof(i1_3_tmp__algspec1,plain,
    ( ( v1_relat_1(c1_3__algspec1)
      & v1_funct_1(c1_3__algspec1)
      & v1_relat_1(c2_3__algspec1)
      & v1_funct_1(c2_3__algspec1)
      & v1_relat_1(c3_3__algspec1)
      & v1_funct_1(c3_3__algspec1) )
   => ( ( r1_tarski(k1_relat_1(c1_3__algspec1),k2_relat_1(c2_3__algspec1))
        & r1_xboole_0(k1_relat_1(c1_3__algspec1),k2_relat_1(c3_3__algspec1))
        & r1_xboole_0(k9_relat_1(c2_3__algspec1,k1_relat_1(c3_3__algspec1)),k1_relat_1(c1_3__algspec1)) )
     => k5_relat_1(k1_funct_4(c2_3__algspec1,c3_3__algspec1),c1_3__algspec1) = k5_relat_1(c2_3__algspec1,c1_3__algspec1) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1])],[dt_c1_3__algspec1,dt_c2_3__algspec1,dt_c3_3__algspec1,i1_3__algspec1]),
    [interesting(1),t3_algspec1]).

fof(t3_algspec1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r1_tarski(k1_relat_1(A),k2_relat_1(B))
                  & r1_xboole_0(k1_relat_1(A),k2_relat_1(C))
                  & r1_xboole_0(k9_relat_1(B,k1_relat_1(C)),k1_relat_1(A)) )
               => k5_relat_1(k1_funct_4(B,C),A) = k5_relat_1(B,A) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__algspec1,dh_c1_3__algspec1,dh_c2_3__algspec1,dh_c3_3__algspec1]),
    [interesting(1),file(algspec1,t3_algspec1),[file(algspec1,t3_algspec1)]]).