% Mizar ND problem: t1_altcat_3,altcat_3,60,43 
fof(dh_c1_5__altcat_3,definition,
    ( ( ( ~ v3_struct_0(c1_5__altcat_3)
        & v12_altcat_1(c1_5__altcat_3)
        & l2_altcat_1(c1_5__altcat_3) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_5__altcat_3))
         => ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A)
            & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A) ) ) )
   => ! [B] : 
        ( ( ~ v3_struct_0(B)
          & v12_altcat_1(B)
          & l2_altcat_1(B) )
       => ! [C] : 
            ( m1_subset_1(C,u1_struct_0(B))
           => ( v1_altcat_3(k8_altcat_1(B,C),B,C,C)
              & v2_altcat_3(k8_altcat_1(B,C),B,C,C) ) ) ) ),
    introduced(definition,[new_symbol(c1_5__altcat_3),file(altcat_3,c1_5__altcat_3)]),
    [interesting(0.8),axiom,file(altcat_3,c1_5__altcat_3)]).

fof(dh_c2_5__altcat_3,definition,
    ( ( m1_subset_1(c2_5__altcat_3,u1_struct_0(c1_5__altcat_3))
     => ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3)
        & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3) ) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_5__altcat_3))
       => ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A)
          & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A) ) ) ),
    introduced(definition,[new_symbol(c2_5__altcat_3),file(altcat_3,c2_5__altcat_3)]),
    [interesting(0.8),axiom,file(altcat_3,c2_5__altcat_3)]).

fof(existence_l1_altcat_1,axiom,(
    ? [A] : l1_altcat_1(A) ),
    file(altcat_1,l1_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,l1_altcat_1)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_l1_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => l1_struct_0(A) ) ),
    file(altcat_1,l1_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,l1_altcat_1)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(existence_l2_altcat_1,axiom,(
    ? [A] : l2_altcat_1(A) ),
    file(altcat_1,l2_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,l2_altcat_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_k1_altcat_1,axiom,(
    $true ),
    file(altcat_1,k1_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,k1_altcat_1)]).

fof(dt_k8_altcat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k8_altcat_1(A,B),k1_altcat_1(A,B,B)) ) ),
    file(altcat_1,k8_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,k8_altcat_1)]).

fof(dt_l2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => l1_altcat_1(A) ) ),
    file(altcat_1,l2_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,l2_altcat_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(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_5__altcat_3,assumption,
    ( ~ v3_struct_0(c1_5__altcat_3)
    & v12_altcat_1(c1_5__altcat_3)
    & l2_altcat_1(c1_5__altcat_3) ),
    introduced(assumption,[file(altcat_3,c1_5__altcat_3)]),
    [interesting(0.8),axiom,file(altcat_3,c1_5__altcat_3)]).

fof(dt_c2_5__altcat_3,assumption,(
    m1_subset_1(c2_5__altcat_3,u1_struct_0(c1_5__altcat_3)) ),
    introduced(assumption,[file(altcat_3,c2_5__altcat_3)]),
    [interesting(0.8),axiom,file(altcat_3,c2_5__altcat_3)]).

fof(dt_k5_altcat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,k1_altcat_1(A,B,C))
        & m1_subset_1(F,k1_altcat_1(A,C,D)) )
     => m1_subset_1(k5_altcat_1(A,B,C,D,E,F),k1_altcat_1(A,B,D)) ) ),
    file(altcat_1,k5_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,k5_altcat_1)]).

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

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

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

fof(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(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(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(t23_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_hidden(k8_altcat_1(A,B),k1_altcat_1(A,B,B)) ) ) ),
    file(altcat_1,t23_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,t23_altcat_1)]).

fof(e1_5__altcat_3,plain,(
    k1_altcat_1(c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3) != k1_xboole_0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__altcat_3,dt_c2_5__altcat_3])],[existence_l1_altcat_1,existence_l1_struct_0,dt_l1_altcat_1,dt_l1_struct_0,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t8_boole,antisymmetry_r2_hidden,existence_l2_altcat_1,existence_m1_subset_1,dt_k1_altcat_1,dt_k1_xboole_0,dt_k8_altcat_1,dt_l2_altcat_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__altcat_3,dt_c2_5__altcat_3,fc1_xboole_0,t1_subset,t6_boole,t7_boole,t23_altcat_1]),
    [interesting(0.8),file(altcat_3,e1_5__altcat_3),[file(altcat_3,e1_5__altcat_3)]]).

fof(d19_altcat_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_altcat_1(A,B,B))
             => ( C = k8_altcat_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( k1_altcat_1(A,B,D) != k1_xboole_0
                     => ! [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,D))
                         => k5_altcat_1(A,B,B,D,C,E) = E ) ) ) ) ) ) ) ),
    file(altcat_1,d19_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,d19_altcat_1)]).

fof(e2_5__altcat_3,plain,(
    k5_altcat_1(c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3,k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3)) = k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__altcat_3,dt_c2_5__altcat_3])],[antisymmetry_r2_hidden,t1_subset,existence_l1_altcat_1,existence_l1_struct_0,dt_l1_altcat_1,dt_l1_struct_0,cc1_funct_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t7_boole,t8_boole,existence_l2_altcat_1,existence_m1_subset_1,dt_k1_altcat_1,dt_k1_xboole_0,dt_k5_altcat_1,dt_k8_altcat_1,dt_l2_altcat_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__altcat_3,dt_c2_5__altcat_3,fc1_xboole_0,t6_boole,e1_5__altcat_3,d19_altcat_1]),
    [interesting(0.8),file(altcat_3,e2_5__altcat_3),[file(altcat_3,e2_5__altcat_3)]]).

fof(d1_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_altcat_1(A,C,B))
                     => ( r1_altcat_3(A,B,C,D,E)
                      <=> k5_altcat_1(A,C,B,C,E,D) = k8_altcat_1(A,C) ) ) ) ) ) ) ),
    file(altcat_3,d1_altcat_3),
    [interesting(0.9),axiom,file(altcat_3,d1_altcat_3)]).

fof(e3_5__altcat_3,plain,
    ( r1_altcat_3(c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3,k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3))
    & r1_altcat_3(c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3,k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__altcat_3,dt_c2_5__altcat_3])],[existence_l1_altcat_1,existence_l1_struct_0,dt_l1_altcat_1,dt_l1_struct_0,existence_l2_altcat_1,existence_m1_subset_1,dt_k1_altcat_1,dt_k5_altcat_1,dt_k8_altcat_1,dt_l2_altcat_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__altcat_3,dt_c2_5__altcat_3,e2_5__altcat_3,d1_altcat_3]),
    [interesting(0.8),file(altcat_3,e3_5__altcat_3),[file(altcat_3,e3_5__altcat_3)]]).

fof(d2_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v1_altcat_3(D,A,B,C)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,C,B))
                        & r1_altcat_3(A,B,C,D,E) ) ) ) ) ) ) ),
    file(altcat_3,d2_altcat_3),
    [interesting(0.9),axiom,file(altcat_3,d2_altcat_3)]).

fof(d3_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(A,B,C))
                 => ( v2_altcat_3(D,A,B,C)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,C,B))
                        & r1_altcat_3(A,C,B,E,D) ) ) ) ) ) ) ),
    file(altcat_3,d3_altcat_3),
    [interesting(0.9),axiom,file(altcat_3,d3_altcat_3)]).

fof(e4_5__altcat_3,plain,
    ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3)
    & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__altcat_3,dt_c2_5__altcat_3])],[existence_l1_altcat_1,existence_l1_struct_0,dt_l1_altcat_1,dt_l1_struct_0,existence_l2_altcat_1,existence_m1_subset_1,dt_k1_altcat_1,dt_k8_altcat_1,dt_l2_altcat_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_5__altcat_3,dt_c2_5__altcat_3,e3_5__altcat_3,d2_altcat_3,d3_altcat_3]),
    [interesting(0.8),file(altcat_3,e4_5__altcat_3),[file(altcat_3,e4_5__altcat_3)]]).

fof(i3_5__altcat_3,theorem,(
    $true ),
    introduced(tautology,[file(altcat_3,i3_5__altcat_3)]),
    [interesting(0.8),trivial,file(altcat_3,i3_5__altcat_3)]).

fof(i2_5__altcat_3,plain,
    ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3)
    & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__altcat_3,dt_c2_5__altcat_3])],[e4_5__altcat_3,i3_5__altcat_3]),
    [interesting(0.8),file(altcat_3,i2_5__altcat_3),[file(altcat_3,i2_5__altcat_3)]]).

fof(i2_5_tmp__altcat_3,plain,
    ( m1_subset_1(c2_5__altcat_3,u1_struct_0(c1_5__altcat_3))
   => ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3)
      & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,c2_5__altcat_3),c1_5__altcat_3,c2_5__altcat_3,c2_5__altcat_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__altcat_3]),discharge_asm(discharge,[dt_c2_5__altcat_3])],[dt_c2_5__altcat_3,i2_5__altcat_3]),
    [interesting(0.8),i1_5__altcat_3]).

fof(i1_5__altcat_3,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_5__altcat_3))
     => ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A)
        & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__altcat_3])],[i2_5_tmp__altcat_3,dh_c2_5__altcat_3]),
    [interesting(0.8),file(altcat_3,i1_5__altcat_3),[file(altcat_3,i1_5__altcat_3)]]).

fof(i1_5_tmp__altcat_3,plain,
    ( ( ~ v3_struct_0(c1_5__altcat_3)
      & v12_altcat_1(c1_5__altcat_3)
      & l2_altcat_1(c1_5__altcat_3) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_5__altcat_3))
       => ( v1_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A)
          & v2_altcat_3(k8_altcat_1(c1_5__altcat_3,A),c1_5__altcat_3,A,A) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__altcat_3])],[dt_c1_5__altcat_3,i1_5__altcat_3]),
    [interesting(1),t1_altcat_3]).

fof(t1_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_altcat_3(k8_altcat_1(A,B),A,B,B)
            & v2_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__altcat_3,dh_c1_5__altcat_3]),
    [interesting(1),file(altcat_3,t1_altcat_3),[file(altcat_3,t1_altcat_3)]]).