fof(t8_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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,u1_struct_0(A))
                 => ( ( r2_altcat_3(A,B,C)
                      & r2_altcat_3(A,C,D) )
                   => r2_altcat_3(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_altcat_3,d4_altcat_1,d6_altcat_3,d6_altcat_3,d6_altcat_3,t7_altcat_3]),
    [file(altcat_3,t8_altcat_3),interesting(1.00)]).

fof(l21_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))
         => ( v5_altcat_3(k8_altcat_1(A,B),A,B,B)
            & v4_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_altcat_3,d19_altcat_1,d19_altcat_1,d7_altcat_3,t24_altcat_1,t24_altcat_1]),
    [file(altcat_3,l21_altcat_3),interesting(0.79)]).

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(mizar_proof,[status(thm)],[t23_altcat_1,d19_altcat_1,d1_altcat_3,d2_altcat_3,d3_altcat_3]),
    [file(altcat_3,t1_altcat_3),interesting(0.79)]).

fof(t26_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ( ( v6_altcat_3(B,A)
                  & v6_altcat_3(C,A) )
               => r2_altcat_3(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_altcat_3,d9_altcat_3,d6_altcat_3,d9_altcat_3,d4_realset1,d4_realset1,d1_tarski,d1_tarski,d1_altcat_3,d2_altcat_3,d3_altcat_3,t6_altcat_3]),
    [file(altcat_3,t26_altcat_3),interesting(0.75)]).

fof(t29_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ( ( v8_altcat_3(B,A)
                  & v8_altcat_3(C,A) )
               => r2_altcat_3(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_altcat_3,t26_altcat_3]),
    [file(altcat_3,t29_altcat_3),interesting(0.70)]).

fof(t28_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ( ( v7_altcat_3(B,A)
                  & v7_altcat_3(C,A) )
               => r2_altcat_3(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_altcat_3,d10_altcat_3,d6_altcat_3,d10_altcat_3,d4_realset1,d4_realset1,d1_tarski,d1_tarski,d1_altcat_3,d2_altcat_3,d3_altcat_3,t6_altcat_3]),
    [file(altcat_3,t28_altcat_3),interesting(0.67)]).

fof(t4_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_altcat_3(A,B,B,k8_altcat_1(A,B)) = k8_altcat_1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_altcat_1,t1_altcat_3,d4_altcat_3,d19_altcat_1,d1_altcat_3]),
    [file(altcat_3,t4_altcat_3),interesting(0.63)]).

fof(t17_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] : 
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v3_altcat_3(D,A,B,C)
                      & ~ ( v4_altcat_3(D,A,B,C)
                          & v5_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_altcat_3,t25_altcat_1,t2_altcat_3,t25_altcat_1,t2_altcat_3,t24_altcat_1,t24_altcat_1,t25_altcat_1,t2_altcat_3,t25_altcat_1,t2_altcat_3,d19_altcat_1,d19_altcat_1,d7_altcat_3,d8_altcat_3]),
    [file(altcat_3,t17_altcat_3),interesting(0.57)]).

fof(t5_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
                 => ( v3_altcat_3(D,A,B,C)
                   => ( v1_altcat_3(D,A,B,C)
                      & v2_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_altcat_3,d1_altcat_3,d2_altcat_3,d1_altcat_3,d3_altcat_3]),
    [file(altcat_3,t5_altcat_3),interesting(0.50)]).

fof(t15_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] : 
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v1_altcat_3(D,A,B,C)
                      & ~ v5_altcat_3(D,A,B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_altcat_3,d8_altcat_3,d19_altcat_1,d1_altcat_3,t25_altcat_1,t25_altcat_1,d1_altcat_3,d19_altcat_1]),
    [file(altcat_3,t15_altcat_3),interesting(0.43)]).

fof(t7_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_altcat_1(A,B,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_altcat_1(A,C,D))
                         => ( ( v3_altcat_3(E,A,B,C)
                              & v3_altcat_3(F,A,C,D) )
                           => ( k1_altcat_1(A,B,C) = k1_xboole_0
                              | k1_altcat_1(A,C,D) = k1_xboole_0
                              | k1_altcat_1(A,D,B) = k1_xboole_0
                              | ( v3_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D)
                                & k1_altcat_3(A,B,D,k5_altcat_1(A,B,C,D,E,F)) = k5_altcat_1(A,D,C,B,k1_altcat_3(A,C,D,F),k1_altcat_3(A,B,C,E)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_1,t6_altcat_3,t25_altcat_1,t25_altcat_1,t2_altcat_3,t24_altcat_1,t2_altcat_3,d1_altcat_3,d3_altcat_3,t25_altcat_1,t25_altcat_1,t2_altcat_3,t24_altcat_1,t2_altcat_3,d1_altcat_3,d2_altcat_3,d4_altcat_3,d5_altcat_3]),
    [file(altcat_3,t7_altcat_3),interesting(0.39)]).

fof(t24_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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) ) ) )
       => ! [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))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,B) != k1_xboole_0
                        & ~ v3_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_altcat_3,t15_altcat_3,t23_altcat_1,d1_altcat_3,d19_altcat_1,t25_altcat_1,t24_altcat_1,d8_altcat_3,d1_altcat_3,d3_altcat_3,t6_altcat_3]),
    [file(altcat_3,t24_altcat_3),interesting(0.37)]).

fof(t6_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ~ ! [D] : 
                        ( m1_subset_1(D,k1_altcat_1(A,B,C))
                       => ( v3_altcat_3(D,A,B,C)
                        <=> ( v1_altcat_3(D,A,B,C)
                            & v2_altcat_3(D,A,B,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_altcat_3,d4_altcat_3,d1_altcat_3,d5_altcat_3]),
    [file(altcat_3,t6_altcat_3),interesting(0.34)]).

fof(t20_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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)
                      & v4_altcat_3(D,A,B,C) )
                   => ( k1_altcat_1(A,B,C) = k1_xboole_0
                      | k1_altcat_1(A,C,B) = k1_xboole_0
                      | v3_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_altcat_1,d2_altcat_3,d1_altcat_3,t25_altcat_1,t24_altcat_1,d19_altcat_1,d7_altcat_3,d1_altcat_3,d3_altcat_3,d4_altcat_3,d1_altcat_3,d4_altcat_3,d7_altcat_3,d5_altcat_3]),
    [file(altcat_3,t20_altcat_3),interesting(0.29)]).

fof(t21_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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)
                      & v5_altcat_3(D,A,B,C) )
                   => ( k1_altcat_1(A,B,C) = k1_xboole_0
                      | k1_altcat_1(A,C,B) = k1_xboole_0
                      | v3_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_altcat_1,d3_altcat_3,d1_altcat_3,d19_altcat_1,t24_altcat_1,t25_altcat_1,d8_altcat_3,d1_altcat_3,d2_altcat_3,d4_altcat_3,d8_altcat_3,d4_altcat_3,d1_altcat_3,d5_altcat_3]),
    [file(altcat_3,t21_altcat_3),interesting(0.29)]).

fof(t16_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] : 
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v2_altcat_3(D,A,B,C)
                      & ~ v4_altcat_3(D,A,B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_altcat_3,d7_altcat_3,t24_altcat_1,d1_altcat_3,t25_altcat_1,t25_altcat_1,d1_altcat_3,t24_altcat_1]),
    [file(altcat_3,t16_altcat_3),interesting(0.28)]).

fof(t10_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_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,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & v5_altcat_3(E,A,B,C)
                              & v5_altcat_3(F,A,C,D)
                              & ~ v5_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_altcat_3,t25_altcat_1,t25_altcat_1,d4_altcat_1,d8_altcat_3,d8_altcat_3]),
    [file(altcat_3,t10_altcat_3),interesting(0.24)]).

fof(t9_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_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,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & v4_altcat_3(E,A,B,C)
                              & v4_altcat_3(F,A,C,D)
                              & ~ v4_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_altcat_3,t25_altcat_1,t25_altcat_1,d4_altcat_1,d7_altcat_3,d7_altcat_3]),
    [file(altcat_3,t9_altcat_3),interesting(0.24)]).

fof(t11_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_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,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & v4_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D)
                              & ~ v4_altcat_3(E,A,B,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_altcat_3,t25_altcat_1,t25_altcat_1,d7_altcat_3]),
    [file(altcat_3,t11_altcat_3),interesting(0.23)]).

fof(t12_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_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,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & v5_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D)
                              & ~ v5_altcat_3(F,A,C,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_altcat_3,t25_altcat_1,t25_altcat_1,d8_altcat_3]),
    [file(altcat_3,t12_altcat_3),interesting(0.23)]).

fof(t13_altcat_3,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k7_altcat_1(A)))
             => ( k1_altcat_1(k7_altcat_1(A),B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k1_altcat_1(k7_altcat_1(A),B,C))
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,B,C)
                          & m2_relset_1(E,B,C) )
                       => ( E = D
                         => ( v4_altcat_3(D,k7_altcat_1(A),B,C)
                          <=> v2_funct_1(E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d8_funct_1,t23_altcat_1,t19_funcop_1,t13_funcop_1,t19_funcop_1,t13_funcop_1,d3_tarski,d5_funct_1,d2_funct_2,d16_altcat_1,d3_tarski,d5_funct_1,d2_funct_2,d16_altcat_1,t46_relat_1,t46_relat_1,t22_funct_1,t22_funct_1,t9_funct_1,t18_altcat_1,t18_altcat_1,d7_altcat_3,d7_altcat_3,d16_altcat_1,d2_funct_2,d2_funct_2,d4_altcat_1,t18_altcat_1,t18_altcat_1,d5_funct_1,t23_funct_1,t23_funct_1,d8_funct_1,t9_funct_1,t57_partfun1,d1_funct_2,t55_funct_2,t60_relat_1,t59_partfun1,d7_altcat_3,d16_altcat_1,d2_funct_2,d2_funct_2,d16_altcat_1,d2_funct_2,t3_xboole_1,t65_relat_1,t3_xboole_1,t65_relat_1,t64_relat_1,t64_relat_1]),
    [file(altcat_3,t13_altcat_3),interesting(0.21)]).

fof(t3_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] : 
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v1_altcat_3(D,A,B,C)
                      & v2_altcat_3(D,A,B,C)
                      & k1_altcat_3(A,C,B,k1_altcat_3(A,B,C,D)) != D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_3,d2_altcat_3,d3_altcat_3,d4_altcat_3,t24_altcat_1,d1_altcat_3,t25_altcat_1,d1_altcat_3,d19_altcat_1]),
    [file(altcat_3,t3_altcat_3),interesting(0.21)]).

fof(t18_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & k1_altcat_1(A,D,B) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & v1_altcat_3(E,A,B,C)
                              & v1_altcat_3(F,A,C,D)
                              & ~ v1_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_1,d2_altcat_3,d2_altcat_3,d2_altcat_3,t25_altcat_1,t25_altcat_1,d1_altcat_3,t24_altcat_1,d1_altcat_3,d1_altcat_3]),
    [file(altcat_3,t18_altcat_3),interesting(0.12)]).

fof(t19_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & k1_altcat_1(A,D,B) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & v2_altcat_3(E,A,B,C)
                              & v2_altcat_3(F,A,C,D)
                              & ~ v2_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_1,d3_altcat_3,d3_altcat_3,d3_altcat_3,t23_altcat_1,t25_altcat_1,t25_altcat_1,d1_altcat_3,t25_altcat_1,t24_altcat_1,d1_altcat_3,d1_altcat_3]),
    [file(altcat_3,t19_altcat_3),interesting(0.12)]).

fof(t14_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k7_altcat_1(A)))
             => ( k1_altcat_1(k7_altcat_1(A),B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k1_altcat_1(k7_altcat_1(A),B,C))
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,B,C)
                          & m2_relset_1(E,B,C) )
                       => ( E = D
                         => ( v5_altcat_3(D,k7_altcat_1(A),B,C)
                          <=> v2_funct_2(E,B,C) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t57_partfun1,d1_funct_2,d3_funct_2,t10_partfun1,d16_altcat_1,d4_realset1,t12_relset_1,d16_altcat_1,d4_realset1,d1_funct_2,t65_relat_1,t39_zfmisc_1,d3_funct_2,d8_altcat_3,d16_altcat_1,d2_funct_2,d2_funct_2,d4_altcat_1,t18_altcat_1,t18_altcat_1,t9_funct_1,d3_funct_2,d5_funct_1,t23_funct_1,t23_funct_1,d1_funct_2,d16_altcat_1,t12_relset_1,d3_funct_2,d10_xboole_0,d3_tarski,d9_setfam_1,t4_realset1,d4_xboole_0,d4_xboole_0,d1_tarski,s3_funct_1,t19_funcop_1,t13_funcop_1,d1_cqc_lang,d3_tarski,d5_funct_1,d1_cqc_lang,d1_cqc_lang,d2_funct_2,d16_altcat_1,d16_altcat_1,d3_tarski,d5_funct_1,d2_funct_2,d16_altcat_1,t46_relat_1,t25_funct_1,d3_tarski,t1_xboole_1,d2_funct_2,d16_altcat_1,t46_relat_1,d5_funct_1,d1_cqc_lang,t22_funct_1,t22_funct_1,t9_funct_1,t18_altcat_1,t18_altcat_1,d8_altcat_3,d8_altcat_3,d16_altcat_1,d2_funct_2,d2_funct_2,d4_altcat_1,t18_altcat_1,t18_altcat_1,t9_funct_1,d3_funct_2,d5_funct_1,t23_funct_1,t23_funct_1,t57_partfun1,d1_funct_2,d3_funct_2,t10_partfun1,d8_altcat_3,d16_altcat_1,d2_funct_2,d2_funct_2,t64_relat_1]),
    [file(altcat_3,t14_altcat_3),interesting(0.10)]).

fof(t22_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_altcat_1(A,B,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_altcat_1(A,C,D))
                         => ( v1_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D)
                           => ( k1_altcat_1(A,B,C) = k1_xboole_0
                              | k1_altcat_1(A,C,D) = k1_xboole_0
                              | k1_altcat_1(A,D,B) = k1_xboole_0
                              | v1_altcat_3(F,A,C,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_altcat_3,d1_altcat_3,t25_altcat_1,d1_altcat_3,d2_altcat_3]),
    [file(altcat_3,t22_altcat_3),interesting(0.09)]).

fof(t23_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_altcat_1(A,B,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_altcat_1(A,C,D))
                         => ( v2_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D)
                           => ( k1_altcat_1(A,B,C) = k1_xboole_0
                              | k1_altcat_1(A,C,D) = k1_xboole_0
                              | k1_altcat_1(A,D,B) = k1_xboole_0
                              | v2_altcat_3(E,A,B,C) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_altcat_3,t25_altcat_1,d1_altcat_3,d1_altcat_3,d3_altcat_3]),
    [file(altcat_3,t23_altcat_3),interesting(0.09)]).

fof(d8_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(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))
                 => ( v5_altcat_3(D,A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k1_altcat_1(A,C,E) != k1_xboole_0
                         => ! [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,E))
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_altcat_1(A,C,E))
                                 => ( k5_altcat_1(A,B,C,E,D,F) = k5_altcat_1(A,B,C,E,D,G)
                                   => F = G ) ) ) ) ) ) ) ) ) ) ),
    file(altcat_3,d8_altcat_3),
    [interesting(0.00)]).

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(0.00)]).

fof(d7_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(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))
                 => ( v4_altcat_3(D,A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( k1_altcat_1(A,E,B) != k1_xboole_0
                         => ! [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,E,B))
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_altcat_1(A,E,B))
                                 => ( k5_altcat_1(A,E,B,C,F,D) = k5_altcat_1(A,E,B,C,G,D)
                                   => F = G ) ) ) ) ) ) ) ) ) ) ),
    file(altcat_3,d7_altcat_3),
    [interesting(0.00)]).

fof(t24_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))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_altcat_1(A,B,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => k5_altcat_1(A,B,C,C,D,k8_altcat_1(A,C)) = D ) ) ) ) ) ),
    file(altcat_1,t24_altcat_1),
    [interesting(0.00)]).

fof(t25_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_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,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                          & k1_altcat_1(A,C,D) != k1_xboole_0
                          & k1_altcat_1(A,D,E) != k1_xboole_0
                          & ~ ! [F] : 
                                ( m1_subset_1(F,k1_altcat_1(A,B,C))
                               => ! [G] : 
                                    ( m1_subset_1(G,k1_altcat_1(A,C,D))
                                   => ! [H] : 
                                        ( m1_subset_1(H,k1_altcat_1(A,D,E))
                                       => k5_altcat_1(A,B,D,E,k5_altcat_1(A,B,C,D,F,G),H) = k5_altcat_1(A,B,C,E,F,k5_altcat_1(A,C,D,E,G,H)) ) ) ) ) ) ) ) ) ) ),
    file(altcat_1,t25_altcat_1),
    [interesting(0.00)]).

fof(d4_altcat_1,definition,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ( v2_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,u1_struct_0(A))
                   => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                        & k1_altcat_1(A,C,D) != k1_xboole_0
                        & k1_altcat_1(A,B,D) = k1_xboole_0 ) ) ) ) ) ) ),
    file(altcat_1,d4_altcat_1),
    [interesting(0.00)]).

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(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.00)]).

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(0.00)]).

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

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(0.00)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.00)]).

fof(d16_altcat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_altcat_1(B)
            & v10_altcat_1(B)
            & l2_altcat_1(B) )
         => ( B = k7_altcat_1(A)
          <=> ( u1_struct_0(B) = A
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(B))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(B))
                     => k1_altcat_1(B,C,D) = k1_funct_2(C,D) ) ) ) ) ) ) ),
    file(altcat_1,d16_altcat_1),
    [interesting(0.00)]).

fof(t46_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    [interesting(0.00)]).

fof(t22_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)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    [interesting(0.00)]).

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(0.00)]).

fof(t18_altcat_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_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,u1_struct_0(A))
                 => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                      & k1_altcat_1(A,C,D) != k1_xboole_0
                      & k1_altcat_1(A,B,D) != k1_xboole_0
                      & ? [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,C,D))
                              & ? [G] : 
                                  ( v1_relat_1(G)
                                  & v1_funct_1(G)
                                  & ? [H] : 
                                      ( v1_relat_1(H)
                                      & v1_funct_1(H)
                                      & E = G
                                      & F = H
                                      & k5_altcat_1(A,B,C,D,E,F) != k5_relat_1(G,H) ) ) ) ) ) ) ) ) ) ),
    file(altcat_1,t18_altcat_1),
    [interesting(0.00)]).

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(0.00)]).

fof(t57_partfun1,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => B = k1_xboole_0 ) ),
    file(partfun1,t57_partfun1),
    [interesting(0.00)]).

fof(t55_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_xboole_0
       => ( v1_funct_1(B)
          & v1_funct_2(B,k1_xboole_0,A)
          & m2_relset_1(B,k1_xboole_0,A) ) ) ) ),
    file(funct_2,t55_funct_2),
    [interesting(0.00)]).

fof(t60_relat_1,theorem,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    [interesting(0.00)]).

fof(t59_partfun1,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k1_xboole_0,A) )
     => v2_funct_1(B) ) ),
    file(partfun1,t59_partfun1),
    [interesting(0.00)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.00)]).

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(0.00)]).

fof(t64_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    [interesting(0.00)]).

fof(d3_funct_2,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_2(C,A,B)
      <=> k2_relat_1(C) = B ) ) ),
    file(funct_2,d3_funct_2),
    [interesting(0.00)]).

fof(t10_partfun1,theorem,(
    k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(partfun1,t10_partfun1),
    [interesting(0.00)]).

fof(d4_realset1,definition,(
    ! [A] : 
      ( v1_realset1(A)
    <=> ~ ( ~ v1_xboole_0(A)
          & ! [B] : A != k1_tarski(B) ) ) ),
    file(realset1,d4_realset1),
    [interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(t39_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,k1_tarski(B))
    <=> ( A = k1_xboole_0
        | A = k1_tarski(B) ) ) ),
    file(zfmisc_1,t39_zfmisc_1),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(d9_setfam_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
    <=> ~ r2_hidden(k1_xboole_0,A) ) ),
    file(setfam_1,d9_setfam_1),
    [interesting(0.00)]).

fof(t4_realset1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_realset1(A)
      <=> ! [B] : ~ v1_xboole_0(k4_xboole_0(A,k1_tarski(B))) ) ) ),
    file(realset1,t4_realset1),
    [interesting(0.00)]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

fof(d1_cqc_lang,definition,(
    ! [A,B,C,D] : 
      ( ( A = B
       => k1_cqc_lang(A,B,C,D) = C )
      & ( A != B
       => k1_cqc_lang(A,B,C,D) = D ) ) ),
    file(cqc_lang,d1_cqc_lang),
    [interesting(0.00)]).

fof(t25_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,k2_relat_1(k5_relat_1(C,B)))
           => r2_hidden(A,k2_relat_1(B)) ) ) ) ),
    file(funct_1,t25_funct_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

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(0.00)]).

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(0.00)]).

fof(d5_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
                 => ( v3_altcat_3(D,A,B,C)
                  <=> ( k5_altcat_1(A,C,B,C,k1_altcat_3(A,B,C,D),D) = k8_altcat_1(A,C)
                      & k5_altcat_1(A,B,C,B,D,k1_altcat_3(A,B,C,D)) = k8_altcat_1(A,B) ) ) ) ) ) ) ),
    file(altcat_3,d5_altcat_3),
    [interesting(0.00)]).

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(0.00)]).

fof(d4_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] : 
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v1_altcat_3(D,A,B,C)
                      & v2_altcat_3(D,A,B,C)
                      & ~ ! [E] : 
                            ( m1_subset_1(E,k1_altcat_1(A,C,B))
                           => ( E = k1_altcat_3(A,B,C,D)
                            <=> ( r1_altcat_3(A,C,B,E,D)
                                & r1_altcat_3(A,B,C,D,E) ) ) ) ) ) ) ) ) ),
    file(altcat_3,d4_altcat_3),
    [interesting(0.00)]).

fof(t2_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] : 
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v1_altcat_3(D,A,B,C)
                      & v2_altcat_3(D,A,B,C)
                      & ~ ( k5_altcat_1(A,B,C,B,D,k1_altcat_3(A,B,C,D)) = k8_altcat_1(A,B)
                          & k5_altcat_1(A,C,B,C,k1_altcat_3(A,B,C,D),D) = k8_altcat_1(A,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_altcat_3,d1_altcat_3]),
    [file(altcat_3,t2_altcat_3),interesting(0.00)]).

fof(d9_altcat_3,definition,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v6_altcat_3(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                    & r2_hidden(D,k1_altcat_1(A,B,C))
                    & v1_realset1(k1_altcat_1(A,B,C)) ) ) ) ) ) ),
    file(altcat_3,d9_altcat_3),
    [interesting(0.00)]).

fof(t25_altcat_3,theorem,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v6_altcat_3(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                    & r2_hidden(D,k1_altcat_1(A,B,C))
                    & ! [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,B,C))
                       => ( r2_hidden(E,k1_altcat_1(A,B,C))
                         => D = E ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_altcat_3,d4_realset1,d1_tarski,d1_tarski,d9_altcat_3,d3_tarski,d1_tarski,d3_tarski,d1_tarski,d10_xboole_0]),
    [file(altcat_3,t25_altcat_3),interesting(0.00)]).

fof(d10_altcat_3,definition,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v7_altcat_3(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_subset_1(D,k1_altcat_1(A,C,B))
                    & r2_hidden(D,k1_altcat_1(A,C,B))
                    & v1_realset1(k1_altcat_1(A,C,B)) ) ) ) ) ) ),
    file(altcat_3,d10_altcat_3),
    [interesting(0.00)]).

fof(t27_altcat_3,theorem,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v7_altcat_3(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_subset_1(D,k1_altcat_1(A,C,B))
                    & r2_hidden(D,k1_altcat_1(A,C,B))
                    & ! [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,C,B))
                       => ( r2_hidden(E,k1_altcat_1(A,C,B))
                         => D = E ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_altcat_3,d4_realset1,d1_tarski,d1_tarski,d10_altcat_3,d3_tarski,d1_tarski,d3_tarski,d1_tarski,d10_xboole_0]),
    [file(altcat_3,t27_altcat_3),interesting(0.00)]).

fof(d6_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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))
             => ( r2_altcat_3(A,B,C)
              <=> ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ? [D] : 
                      ( m1_subset_1(D,k1_altcat_1(A,B,C))
                      & v3_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    file(altcat_3,d6_altcat_3),
    [interesting(0.00)]).

fof(d11_altcat_3,definition,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v8_altcat_3(B,A)
          <=> ( v6_altcat_3(B,A)
              & v7_altcat_3(B,A) ) ) ) ) ),
    file(altcat_3,d11_altcat_3),
    [interesting(0.00)]).

fof(d12_altcat_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(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))
                 => ( v9_altcat_3(D,A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( v8_altcat_3(E,A)
                         => ! [F] : 
                              ( m1_subset_1(F,k1_altcat_1(A,B,E))
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_altcat_1(A,E,C))
                                 => D = k5_altcat_1(A,B,E,C,F,G) ) ) ) ) ) ) ) ) ) ),
    file(altcat_3,d12_altcat_3),
    [interesting(0.00)]).

fof(t30_altcat_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(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,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_altcat_1(A,B,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_altcat_1(A,C,D))
                         => ( ( v9_altcat_3(E,A,B,C)
                              & v9_altcat_3(F,A,C,D) )
                           => v9_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_altcat_3,d11_altcat_3,d9_altcat_3,d9_altcat_3,d10_altcat_3,d10_altcat_3,d12_altcat_3,d4_realset1,d1_tarski,d4_realset1,d1_tarski,d10_altcat_3,d4_realset1,d1_tarski,d4_altcat_1,d12_altcat_3,t25_altcat_1,t25_altcat_1,d19_altcat_1]),
    [file(altcat_3,t30_altcat_3),interesting(0.00)]).