fof(t31_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => r2_group_6(k5_autgroup(A),k6_group_6(A,k10_group_5(A))) ) ),
    inference(mizar_proof,[status(thm)],[d5_autgroup,s4_funct_2,t25_group_1,t23_autgroup,t20_autgroup,d7_group_6,d10_group_6,d3_tarski,t21_autgroup,t35_funct_1,d6_autgroup,t20_group_3,t19_group_1,d4_group_1,d6_group_1,d5_group_1,d3_tarski,d4_group_1,d6_group_1,d5_group_1,t19_group_1,t20_group_3,d6_autgroup,t35_funct_1,t113_funct_2,t21_autgroup,d10_xboole_0,d10_group_5,d5_autgroup,t12_funct_2,d4_autgroup,t19_group_1,d6_autgroup,t16_funct_2,d13_group_6,t67_group_6,t90_group_6]),
    [file(autgroup,t31_autgroup),interesting(1.00)]).

fof(t14_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => r1_tarski(k4_autgroup(A),k1_autgroup(A)) ) ),
    inference(mizar_proof,[status(thm)],[t13_autgroup,d3_tarski]),
    [file(autgroup,t14_autgroup),interesting(0.77)]).

fof(t24_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k6_autgroup(A,k2_group_1(A)) = k6_partfun1(u1_struct_0(A)) ) ),
    inference(mizar_proof,[status(thm)],[t24_group_3,d6_autgroup,t13_autgroup,l9_autgroup,t34_funct_1]),
    [file(autgroup,t24_autgroup),interesting(0.74)]).

fof(t28_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_autgroup(A,k3_group_1(A,B)) = k2_funct_1(k6_autgroup(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_autgroup,t24_autgroup,t13_autgroup,l9_autgroup,l9_autgroup,d1_autgroup,d1_autgroup,t36_funct_2]),
    [file(autgroup,t28_autgroup),interesting(0.71)]).

fof(t21_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k6_partfun1(u1_struct_0(A)) = k2_group_1(k5_autgroup(A)) ) ),
    inference(mizar_proof,[status(thm)],[t10_autgroup,t53_group_2]),
    [file(autgroup,t21_autgroup),interesting(0.65)]).

fof(t13_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
         => m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_funct_2,d4_autgroup,d2_group_3,d4_group_1,d4_group_1,d5_group_1,d6_group_1,d4_group_1,d4_group_1,d4_group_1,d4_group_1,d2_group_3,d2_group_3,d7_group_6,d4_autgroup,d8_funct_1,d2_funct_2,d2_group_3,d2_group_3,d4_group_1,d4_group_1,d4_group_1,d4_group_1,d6_group_1,d6_group_1,d5_group_1,d5_group_1,d4_group_1,d4_group_1,d6_group_1,d6_group_1,d5_group_1,d5_group_1,d4_autgroup,d2_funct_2,d5_group_1,d5_group_1,d6_group_1,d6_group_1,d4_group_1,d4_group_1,d4_group_1,d4_group_1,d2_group_3,t19_funct_1,d10_xboole_0,d13_group_6,d1_autgroup]),
    [file(autgroup,t13_autgroup),interesting(0.64)]).

fof(t10_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k6_partfun1(u1_struct_0(A)) = k2_group_1(k3_autgroup(A)) ) ),
    inference(mizar_proof,[status(thm)],[t4_autgroup,d1_autgroup,t74_funct_2,t9_autgroup,t15_group_1]),
    [file(autgroup,t10_autgroup),interesting(0.63)]).

fof(t17_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
         => m2_fraenkel(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_funct_2,t13_autgroup,d1_autgroup,d1_autgroup,d13_group_6,t31_funct_2,t12_funct_2,d4_autgroup,t13_autgroup,d1_autgroup,t5_autgroup,d14_group_6,t68_group_6,d12_group_6,t32_funct_2,d5_group_1,d5_group_1,d6_group_1,d6_group_1,d4_group_1,d4_group_1,d4_group_1,d4_group_1,d2_group_3,t19_group_1,d2_group_3,d4_autgroup]),
    [file(autgroup,t17_autgroup),interesting(0.62)]).

fof(t4_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m2_fraenkel(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ),
    inference(mizar_proof,[status(thm)],[t47_group_6,t71_relat_1,d13_group_6,d1_autgroup]),
    [file(autgroup,t4_autgroup),interesting(0.62)]).

fof(t7_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
         => m2_fraenkel(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autgroup,t5_autgroup,t6_autgroup,t73_group_6,d14_group_6,d12_group_6,d1_autgroup]),
    [file(autgroup,t7_autgroup),interesting(0.59)]).

fof(t16_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => m2_fraenkel(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) ) ),
    inference(mizar_proof,[status(thm)],[t11_funct_2,t16_group_1,t35_funct_1,d5_group_1,d5_group_1,d2_group_3,d4_autgroup]),
    [file(autgroup,t16_autgroup),interesting(0.50)]).

fof(t12_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => r1_tarski(k4_autgroup(A),k1_fraenkel(u1_struct_0(A),u1_struct_0(A))) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t12_funct_2]),
    [file(autgroup,t12_autgroup),interesting(0.47)]).

fof(t3_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => r1_tarski(k1_autgroup(A),k1_fraenkel(u1_struct_0(A),u1_struct_0(A))) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t12_funct_2]),
    [file(autgroup,t3_autgroup),interesting(0.47)]).

fof(l2_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( v1_group_3(B,A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( m1_subset_1(D,u1_struct_0(B))
                     => r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_rlvect_1,t88_group_2,t140_group_3,t128_group_2,t127_group_2,d6_group_1,t132_group_2,t71_group_3,d6_group_3,t33_group_2,t34_group_2,t20_group_3,t59_group_3,t88_group_2]),
    [file(autgroup,l2_autgroup),interesting(0.46)]).

fof(l1_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( m1_subset_1(D,u1_struct_0(B))
                     => r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) )
           => v1_group_3(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t126_group_2,d1_rlvect_1,t88_group_2,t20_group_3,t33_group_2,d4_group_1,d4_group_1,d4_group_1,d6_group_1,d5_group_1,d13_group_2,t142_group_3]),
    [file(autgroup,l1_autgroup),interesting(0.43)]).

fof(t1_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( m1_subset_1(D,u1_struct_0(B))
                     => r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) )
          <=> v1_group_3(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l1_autgroup,l2_autgroup]),
    [file(autgroup,t1_autgroup),interesting(0.42)]).

fof(l9_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
         => ( k1_relat_1(B) = k2_relat_1(B)
            & k1_relat_1(B) = u1_struct_0(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autgroup,t5_autgroup,t71_group_6]),
    [file(autgroup,l9_autgroup),interesting(0.42)]).

fof(t25_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_funct_2(u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d6_autgroup,t24_group_3]),
    [file(autgroup,t25_autgroup),interesting(0.40)]).

fof(t11_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k3_autgroup(A)))
             => ( B = C
               => k2_funct_1(B) = k3_group_1(k3_autgroup(A),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l9_autgroup,l9_autgroup,d1_autgroup,d1_autgroup,t9_autgroup,d6_group_1,t10_autgroup,t36_funct_2]),
    [file(autgroup,t11_autgroup),interesting(0.37)]).

fof(t32_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( ( ~ v3_struct_0(A)
          & v3_group_1(A)
          & v4_group_1(A)
          & v7_group_1(A)
          & l1_group_1(A) )
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(k5_autgroup(A)))
           => B = k2_group_1(k5_autgroup(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_autgroup,t11_funct_2,d4_autgroup,t35_group_3,t35_funct_1,t113_funct_2,t21_autgroup]),
    [file(autgroup,t32_autgroup),interesting(0.36)]).

fof(t22_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
             => ( B = C
               => k2_funct_1(B) = k3_group_1(k5_autgroup(A),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_autgroup,t51_group_2,t11_autgroup,t57_group_2]),
    [file(autgroup,t22_autgroup),interesting(0.32)]).

fof(t27_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,B),k6_autgroup(A,k3_group_1(A,B))) = k6_autgroup(A,k2_group_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_autgroup,d6_autgroup,t30_group_3,t21_funct_2,t25_autgroup,t113_funct_2]),
    [file(autgroup,t27_autgroup),interesting(0.28)]).

fof(t29_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),k6_autgroup(A,B)) = k6_autgroup(A,B)
            & k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,B),k6_autgroup(A,k2_group_1(A))) = k6_autgroup(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_autgroup,t23_funct_2]),
    [file(autgroup,t29_autgroup),interesting(0.23)]).

fof(t5_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v1_group_6(B,A,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r2_hidden(B,k1_autgroup(A))
          <=> v4_group_6(B,A,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autgroup,d1_autgroup,d12_group_6,d14_group_6,d14_group_6,d12_group_6,d1_autgroup]),
    [file(autgroup,t5_autgroup),interesting(0.18)]).

fof(t6_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
         => ( v1_funct_1(k2_funct_1(B))
            & v1_funct_2(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A))
            & v1_group_6(k2_funct_1(B),A,A)
            & m2_relset_1(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autgroup,t5_autgroup,t72_group_6]),
    [file(autgroup,t6_autgroup),interesting(0.17)]).

fof(t30_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
         => ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k2_group_1(A)),B) = B
            & k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_autgroup(A,k2_group_1(A))) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_autgroup,t23_funct_2]),
    [file(autgroup,t30_autgroup),interesting(0.14)]).

fof(t26_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,k3_group_1(A,B)),k6_autgroup(A,B)) = k6_autgroup(A,k2_group_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_autgroup,d6_autgroup,t30_group_3,t21_funct_2,t25_autgroup,t113_funct_2]),
    [file(autgroup,t26_autgroup),interesting(0.11)]).

fof(t20_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k5_autgroup(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_autgroup(A)))
             => ! [D] : 
                  ( m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
                 => ! [E] : 
                      ( m2_fraenkel(E,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
                     => ( ( B = D
                          & C = E )
                       => k1_group_1(k5_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_autgroup,t51_group_2,t9_autgroup,t52_group_2]),
    [file(autgroup,t20_autgroup),interesting(0.10)]).

fof(t15_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
             => k1_binop_1(k2_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_autgroup,d2_autgroup]),
    [file(autgroup,t15_autgroup),interesting(0.09)]).

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(t12_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => r2_hidden(B,k1_funct_2(A,A)) ) ),
    file(funct_2,t12_funct_2),
    [interesting(0.00)]).

fof(d4_autgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k4_autgroup(A)
          <=> ! [C] : 
                ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_fraenkel(u1_struct_0(A),u1_struct_0(A)))
               => ( r2_hidden(C,B)
                <=> ? [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E) = k2_group_3(A,E,D) ) ) ) ) ) ) ) ),
    file(autgroup,d4_autgroup),
    [interesting(0.00)]).

fof(d2_group_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_group_3(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C) ) ) ) ),
    file(group_3,d2_group_3),
    [interesting(0.00)]).

fof(d4_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v4_group_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_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)) ) ) ) ) ) ),
    file(group_1,d4_group_1),
    [interesting(0.00)]).

fof(d5_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ( v2_group_1(A)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ( B = k2_group_1(A)
            <=> ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( k1_group_1(A,C,B) = C
                    & k1_group_1(A,B,C) = C ) ) ) ) ) ) ),
    file(group_1,d5_group_1),
    [interesting(0.00)]).

fof(d6_group_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( C = k3_group_1(A,B)
              <=> ( k1_group_1(A,B,C) = k2_group_1(A)
                  & k1_group_1(A,C,B) = k2_group_1(A) ) ) ) ) ) ),
    file(group_1,d6_group_1),
    [interesting(0.00)]).

fof(d7_group_6,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v1_group_6(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_group_1(A,D,E)) = k1_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ),
    file(group_6,d7_group_6),
    [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(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(t19_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ! [C] : ~ ( r2_hidden(C,A)
            & ! [D] : ~ ( r2_hidden(D,k1_relat_1(B))
                & C = k1_funct_1(B,D) ) )
       => r1_tarski(A,k2_relat_1(B)) ) ) ),
    file(funct_1,t19_funct_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(d13_group_6,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_group_6(C,A,B)
              <=> k9_group_6(A,B,C) = u1_struct_0(B) ) ) ) ) ),
    file(group_6,d13_group_6),
    [interesting(0.00)]).

fof(d1_autgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k1_autgroup(A)
          <=> ( ! [C] : 
                  ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),B)
                 => ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & v1_group_6(C,A,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) )
              & ! [C] : 
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & v1_group_6(C,A,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => ( r2_hidden(C,B)
                  <=> ( v2_funct_1(C)
                      & v3_group_6(C,A,A) ) ) ) ) ) ) ) ),
    file(autgroup,d1_autgroup),
    [interesting(0.00)]).

fof(d2_autgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
            & m2_relset_1(B,k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A)) )
         => ( B = k2_autgroup(A)
          <=> ! [C] : 
                ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
               => ! [D] : 
                    ( m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
                   => k2_binop_1(k1_autgroup(A),k1_autgroup(A),k1_autgroup(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,C) ) ) ) ) ) ),
    file(autgroup,d2_autgroup),
    [interesting(0.00)]).

fof(t11_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => r2_hidden(C,k1_funct_2(A,B)) ) ) ),
    file(funct_2,t11_funct_2),
    [interesting(0.00)]).

fof(t16_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => k3_group_1(A,k2_group_1(A)) = k2_group_1(A) ) ),
    file(group_1,t16_group_1),
    [interesting(0.00)]).

fof(t35_funct_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t35_funct_1),
    [interesting(0.00)]).

fof(t31_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( v2_funct_1(C)
          & k2_relat_1(C) = B )
       => ( v1_funct_1(k2_funct_1(C))
          & v1_funct_2(k2_funct_1(C),B,A)
          & m2_relset_1(k2_funct_1(C),B,A) ) ) ) ),
    file(funct_2,t31_funct_2),
    [interesting(0.00)]).

fof(d12_group_6,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v2_group_6(C,A,B)
              <=> v2_funct_1(C) ) ) ) ) ),
    file(group_6,d12_group_6),
    [interesting(0.00)]).

fof(d14_group_6,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
              <=> ( v3_group_6(C,A,B)
                  & v2_group_6(C,A,B) ) ) ) ) ) ),
    file(group_6,d14_group_6),
    [interesting(0.00)]).

fof(t68_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_group_6(C,A,B)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) = D ) ) ) ) ) ) ),
    file(group_6,t68_group_6),
    [interesting(0.00)]).

fof(t32_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( ( v2_funct_1(D)
          & r2_hidden(C,A) )
       => ( B = k1_xboole_0
          | k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) = C ) ) ) ),
    file(funct_2,t32_funct_2),
    [interesting(0.00)]).

fof(t19_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_group_1(A,k3_group_1(A,B)) = B ) ) ),
    file(group_1,t19_group_1),
    [interesting(0.00)]).

fof(t21_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( r2_hidden(C,A)
           => ( B = k1_xboole_0
              | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ),
    file(funct_2,t21_funct_2),
    [interesting(0.00)]).

fof(t20_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_group_3(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C)
                & k2_group_3(A,B,C) = k1_group_1(A,k3_group_1(A,C),k1_group_1(A,B,C)) ) ) ) ) ),
    file(group_3,t20_group_3),
    [interesting(0.00)]).

fof(t25_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k3_group_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) ) ) ) ),
    file(group_1,t25_group_1),
    [interesting(0.00)]).

fof(t18_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
             => m2_fraenkel(k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_funct_2,t12_funct_2,d4_autgroup,d4_autgroup,t21_funct_2,t20_group_3,t20_group_3,d4_group_1,d4_group_1,d4_group_1,d4_group_1,d4_group_1,t25_group_1,t20_group_3,d4_autgroup]),
    [file(autgroup,t18_autgroup),interesting(0.00)]).

fof(t19_autgroup,theorem,(
    $true ),
    file(autgroup,t19_autgroup),
    [interesting(0.00)]).

fof(t126_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] : 
              ( m1_group_2(D,B)
             => ( r2_hidden(A,k13_group_2(B,D,C))
              <=> ? [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,E,C)
                    & r1_rlvect_1(D,E) ) ) ) ) ) ),
    file(group_2,t126_group_2),
    [interesting(0.00)]).

fof(d1_rlvect_1,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( r1_rlvect_1(A,B)
        <=> r2_hidden(B,u1_struct_0(A)) ) ) ),
    file(rlvect_1,d1_rlvect_1),
    [interesting(0.00)]).

fof(t88_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_group_1(B)
        & v4_group_1(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_group_2(C,B)
         => ( r2_hidden(A,k7_group_2(B,C))
          <=> r1_rlvect_1(C,A) ) ) ) ),
    file(group_2,t88_group_2),
    [interesting(0.00)]).

fof(t33_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k3_group_2(B,D,C))
              <=> ? [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,D,E)
                    & r2_hidden(E,C) ) ) ) ) ) ),
    file(group_2,t33_group_2),
    [interesting(0.00)]).

fof(d13_group_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_group_2(A,B,C) = k3_group_2(A,C,k7_group_2(A,B)) ) ) ) ),
    file(group_2,d13_group_2),
    [interesting(0.00)]).

fof(t142_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( ( v1_group_3(B,A)
              & m1_group_2(B,A) )
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_tarski(k13_group_2(A,B,C),k12_group_2(A,B,C)) ) ) ) ) ),
    file(group_3,t142_group_3),
    [interesting(0.00)]).

fof(t140_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( ( v1_group_3(B,A)
              & m1_group_2(B,A) )
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k12_group_2(A,B,C) = k13_group_2(A,B,C) ) ) ) ) ),
    file(group_3,t140_group_3),
    [interesting(0.00)]).

fof(t128_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_group_2(D,A)
                 => k4_group_2(A,C,k12_group_2(A,D,B)) = k3_group_2(A,B,k13_group_2(A,D,C)) ) ) ) ) ),
    file(group_2,t128_group_2),
    [interesting(0.00)]).

fof(t127_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_group_2(D,A)
                 => k12_group_2(A,D,k1_group_1(A,B,C)) = k3_group_2(A,B,k12_group_2(A,D,C)) ) ) ) ) ),
    file(group_2,t127_group_2),
    [interesting(0.00)]).

fof(t132_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( k12_group_2(A,B,k2_group_1(A)) = k7_group_2(A,B)
            & k13_group_2(A,B,k2_group_1(A)) = k7_group_2(A,B) ) ) ) ),
    file(group_2,t132_group_2),
    [interesting(0.00)]).

fof(t71_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_group_2(C,A)
             => u1_struct_0(k6_group_3(A,C,B)) = k4_group_2(A,B,k12_group_2(A,C,k3_group_1(A,B))) ) ) ) ),
    file(group_3,t71_group_3),
    [interesting(0.00)]).

fof(d6_group_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( ( v1_group_1(D)
                    & m1_group_2(D,A) )
                 => ( D = k6_group_3(A,B,C)
                  <=> u1_struct_0(D) = k4_group_3(A,k7_group_2(A,B),C) ) ) ) ) ) ),
    file(group_3,d6_group_3),
    [interesting(0.00)]).

fof(t34_group_2,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_group_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k4_group_2(B,D,C))
              <=> ? [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                    & A = k1_group_1(B,E,D)
                    & r2_hidden(E,C) ) ) ) ) ) ),
    file(group_2,t34_group_2),
    [interesting(0.00)]).

fof(t59_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k4_group_3(A,C,B) = k4_group_2(A,B,k3_group_2(A,k3_group_1(A,B),C)) ) ) ) ),
    file(group_3,t59_group_3),
    [interesting(0.00)]).

fof(t51_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) ),
    file(group_2,t51_group_2),
    [interesting(0.00)]).

fof(t71_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
               => ( k1_relat_1(C) = u1_struct_0(A)
                  & k9_group_6(A,B,C) = u1_struct_0(B) ) ) ) ) ) ),
    file(group_6,t71_group_6),
    [interesting(0.00)]).

fof(t9_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k3_autgroup(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k3_autgroup(A)))
             => ! [D] : 
                  ( m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
                 => ! [E] : 
                      ( m2_fraenkel(E,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
                     => ( ( B = D
                          & C = E )
                       => k1_group_1(k3_autgroup(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_autgroup]),
    [file(autgroup,t9_autgroup),interesting(0.00)]).

fof(t47_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_funct_1(k6_partfun1(u1_struct_0(A)))
        & v1_funct_2(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A))
        & v1_group_6(k6_partfun1(u1_struct_0(A)),A,A)
        & m2_relset_1(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)) ) ) ),
    file(group_6,t47_group_6),
    [interesting(0.00)]).

fof(t71_relat_1,theorem,(
    ! [A] : 
      ( k1_relat_1(k6_relat_1(A)) = A
      & k2_relat_1(k6_relat_1(A)) = A ) ),
    file(relat_1,t71_relat_1),
    [interesting(0.00)]).

fof(t74_funct_2,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => ( k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B
        & k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B ) ) ),
    file(funct_2,t74_funct_2),
    [interesting(0.00)]).

fof(t15_group_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( k1_group_1(A,B,C) = B
                  | k1_group_1(A,C,B) = B )
               => C = k2_group_1(A) ) ) ) ) ),
    file(group_1,t15_group_1),
    [interesting(0.00)]).

fof(t36_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,A)
            & m2_relset_1(D,B,A) )
         => ( ( k2_relat_1(C) = B
              & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A)
              & v2_funct_1(C) )
           => ( A = k1_xboole_0
              | B = k1_xboole_0
              | D = k2_funct_1(C) ) ) ) ) ),
    file(funct_2,t36_funct_2),
    [interesting(0.00)]).

fof(t57_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_group_2(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ( D = B
                   => k3_group_1(C,D) = k3_group_1(A,B) ) ) ) ) ) ),
    file(group_2,t57_group_2),
    [interesting(0.00)]).

fof(d6_autgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A))
             => ( C = k6_autgroup(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k2_group_3(A,D,B) ) ) ) ) ) ),
    file(autgroup,d6_autgroup),
    [interesting(0.00)]).

fof(t30_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k2_group_3(A,k2_group_3(A,B,C),k3_group_1(A,C)) = B
                & k2_group_3(A,k2_group_3(A,B,k3_group_1(A,C)),C) = B ) ) ) ) ),
    file(group_3,t30_group_3),
    [interesting(0.00)]).

fof(t24_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_group_3(A,B,k2_group_1(A)) = B ) ) ),
    file(group_3,t24_group_3),
    [interesting(0.00)]).

fof(t113_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) )
         => ( ! [E] : 
                ( m1_subset_1(E,A)
               => k1_funct_1(C,E) = k1_funct_1(D,E) )
           => C = D ) ) ) ),
    file(funct_2,t113_funct_2),
    [interesting(0.00)]).

fof(t34_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k6_relat_1(A)
      <=> ( k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => k1_funct_1(B,C) = C ) ) ) ) ),
    file(funct_1,t34_funct_1),
    [interesting(0.00)]).

fof(t23_funct_2,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C
        & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ),
    file(funct_2,t23_funct_2),
    [interesting(0.00)]).

fof(t2_autgroup,theorem,(
    $true ),
    file(autgroup,t2_autgroup),
    [interesting(0.00)]).

fof(d5_autgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & v1_group_3(B,k3_autgroup(A))
            & m1_group_2(B,k3_autgroup(A)) )
         => ( B = k5_autgroup(A)
          <=> u1_struct_0(B) = k4_autgroup(A) ) ) ) ),
    file(autgroup,d5_autgroup),
    [interesting(0.00)]).

fof(s4_funct_2,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2)
      & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2)
      & ! [B] : 
          ( m1_subset_1(B,f1_s4_funct_2)
         => k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B) ) ) ),
    file(funct_2,s4_funct_2),
    [interesting(0.00)]).

fof(t29_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_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))
                 => k2_group_3(A,k2_group_3(A,B,C),D) = k2_group_3(A,B,k1_group_1(A,C,D)) ) ) ) ) ),
    file(group_3,t29_group_3),
    [interesting(0.00)]).

fof(t23_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k6_autgroup(A,k1_group_1(A,B,C)) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_autgroup(A,B),k6_autgroup(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_group_3,d6_autgroup,d6_autgroup,d6_autgroup,t21_funct_2,t113_funct_2]),
    [file(autgroup,t23_autgroup),interesting(0.00)]).

fof(t52_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_group_2(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(D))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(D))
                         => ( ( E = B
                              & F = C )
                           => k1_group_1(D,E,F) = k1_group_1(A,B,C) ) ) ) ) ) ) ) ),
    file(group_2,t52_group_2),
    [interesting(0.00)]).

fof(d10_group_6,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] : 
                  ( ( v1_group_1(D)
                    & m1_group_2(D,A) )
                 => ( D = k12_group_6(A,B,C)
                  <=> u1_struct_0(D) = a_3_0_group_6(A,B,C) ) ) ) ) ) ),
    file(group_6,d10_group_6),
    [interesting(0.00)]).

fof(t53_group_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => k2_group_1(B) = k2_group_1(A) ) ) ),
    file(group_2,t53_group_2),
    [interesting(0.00)]).

fof(d10_group_5,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( B = k10_group_5(A)
          <=> u1_struct_0(B) = a_1_0_group_5(A) ) ) ) ),
    file(group_5,d10_group_5),
    [interesting(0.00)]).

fof(t16_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ! [D] : ~ ( r2_hidden(D,B)
            & ! [E] : ~ ( r2_hidden(E,A)
                & D = k1_funct_1(C,E) ) )
       => ( B = k1_xboole_0
          | k2_relat_1(C) = B ) ) ) ),
    file(funct_2,t16_funct_2),
    [interesting(0.00)]).

fof(t67_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v3_group_6(C,A,B)
              <=> k13_group_6(A,B,C) = B ) ) ) ) ),
    file(group_6,t67_group_6),
    [interesting(0.00)]).

fof(t90_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => r2_group_6(k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C)) ) ) ) ),
    file(group_6,t90_group_6),
    [interesting(0.00)]).

fof(t35_group_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( ~ v3_struct_0(A)
                  & v3_group_1(A)
                  & v4_group_1(A)
                  & v7_group_1(A)
                  & l1_group_1(A) )
               => k2_group_3(A,B,C) = B ) ) ) ) ),
    file(group_3,t35_group_3),
    [interesting(0.00)]).

fof(t72_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_group_1(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & v1_group_6(C,A,B)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v4_group_6(C,A,B)
               => ( v1_funct_1(k2_funct_1(C))
                  & v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))
                  & v1_group_6(k2_funct_1(C),B,A)
                  & m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ),
    file(group_6,t72_group_6),
    [interesting(0.00)]).

fof(t73_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
                & v1_group_6(C,B,A)
                & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ( ( v4_group_6(C,B,A)
                      & D = k2_funct_1(C) )
                   => v4_group_6(D,A,B) ) ) ) ) ) ),
    file(group_6,t73_group_6),
    [interesting(0.00)]).

fof(t74_group_6,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & v4_group_1(B)
            & l1_group_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_group_1(C)
                & v4_group_1(C)
                & l1_group_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
                    & v1_group_6(D,A,B)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
                        & v1_group_6(E,B,C)
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( v4_group_6(D,A,B)
                          & v4_group_6(E,B,C) )
                       => v4_group_6(k8_group_6(A,B,C,D,E),A,C) ) ) ) ) ) ) ),
    file(group_6,t74_group_6),
    [interesting(0.00)]).

fof(t8_autgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_group_1(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A))
             => m2_fraenkel(k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autgroup,t5_autgroup,t74_group_6,t5_autgroup]),
    [file(autgroup,t8_autgroup),interesting(0.00)]).