% Mizar ND problem: t1_algspec1,algspec1,31,72 
fof(dh_c1_1__algspec1,definition,
    ( ( ( v1_relat_1(c1_1__algspec1)
        & v1_funct_1(c1_1__algspec1) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B) )
             => ( r1_tarski(k3_xboole_0(k1_relat_1(c1_1__algspec1),k1_relat_1(A)),k1_relat_1(B))
               => k1_funct_4(k1_funct_4(c1_1__algspec1,A),B) = k1_funct_4(k1_funct_4(A,c1_1__algspec1),B) ) ) ) )
   => ! [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(k3_xboole_0(k1_relat_1(C),k1_relat_1(D)),k1_relat_1(E))
                 => k1_funct_4(k1_funct_4(C,D),E) = k1_funct_4(k1_funct_4(D,C),E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_1__algspec1),file(algspec1,c1_1__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c1_1__algspec1)]).

fof(dh_c2_1__algspec1,definition,
    ( ( ( v1_relat_1(c2_1__algspec1)
        & v1_funct_1(c2_1__algspec1) )
     => ! [A] : 
          ( ( v1_relat_1(A)
            & v1_funct_1(A) )
         => ( r1_tarski(k3_xboole_0(k1_relat_1(c1_1__algspec1),k1_relat_1(c2_1__algspec1)),k1_relat_1(A))
           => k1_funct_4(k1_funct_4(c1_1__algspec1,c2_1__algspec1),A) = k1_funct_4(k1_funct_4(c2_1__algspec1,c1_1__algspec1),A) ) ) )
   => ! [B] : 
        ( ( v1_relat_1(B)
          & v1_funct_1(B) )
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( r1_tarski(k3_xboole_0(k1_relat_1(c1_1__algspec1),k1_relat_1(B)),k1_relat_1(C))
             => k1_funct_4(k1_funct_4(c1_1__algspec1,B),C) = k1_funct_4(k1_funct_4(B,c1_1__algspec1),C) ) ) ) ),
    introduced(definition,[new_symbol(c2_1__algspec1),file(algspec1,c2_1__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c2_1__algspec1)]).

fof(dh_c3_1__algspec1,definition,
    ( ( ( v1_relat_1(c3_1__algspec1)
        & v1_funct_1(c3_1__algspec1) )
     => ( r1_tarski(k3_xboole_0(k1_relat_1(c1_1__algspec1),k1_relat_1(c2_1__algspec1)),k1_relat_1(c3_1__algspec1))
       => k1_funct_4(k1_funct_4(c1_1__algspec1,c2_1__algspec1),c3_1__algspec1) = k1_funct_4(k1_funct_4(c2_1__algspec1,c1_1__algspec1),c3_1__algspec1) ) )
   => ! [A] : 
        ( ( v1_relat_1(A)
          & v1_funct_1(A) )
       => ( r1_tarski(k3_xboole_0(k1_relat_1(c1_1__algspec1),k1_relat_1(c2_1__algspec1)),k1_relat_1(A))
         => k1_funct_4(k1_funct_4(c1_1__algspec1,c2_1__algspec1),A) = k1_funct_4(k1_funct_4(c2_1__algspec1,c1_1__algspec1),A) ) ) ),
    introduced(definition,[new_symbol(c3_1__algspec1),file(algspec1,c3_1__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c3_1__algspec1)]).

fof(e4_1__algspec1,assumption,(
    r1_tarski(k3_xboole_0(k1_relat_1(c1_1__algspec1),k1_relat_1(c2_1__algspec1)),k1_relat_1(c3_1__algspec1)) ),
    introduced(assumption,[file(algspec1,e4_1__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,e4_1__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(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_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(fc2_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]).

fof(fc3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc3_xboole_0)]).

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

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

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

fof(rc1_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(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

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

fof(dt_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_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_c1_1__algspec1,assumption,
    ( v1_relat_1(c1_1__algspec1)
    & v1_funct_1(c1_1__algspec1) ),
    introduced(assumption,[file(algspec1,c1_1__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c1_1__algspec1)]).

fof(dt_c2_1__algspec1,assumption,
    ( v1_relat_1(c2_1__algspec1)
    & v1_funct_1(c2_1__algspec1) ),
    introduced(assumption,[file(algspec1,c2_1__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c2_1__algspec1)]).

fof(dt_c3_1__algspec1,assumption,
    ( v1_relat_1(c3_1__algspec1)
    & v1_funct_1(c3_1__algspec1) ),
    introduced(assumption,[file(algspec1,c3_1__algspec1)]),
    [interesting(0.8),axiom,file(algspec1,c3_1__algspec1)]).

fof(fc2_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc2_relat_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)]).
ERROR: Line 95 Char 6 Token "ERROR" continuing with " Line 359 Char 6 To"