fof(t42_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r2_group_6(k3_autalg_1(A),k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A))) ) ),
    inference(mizar_proof,[status(thm)],[s3_funct_1,t40_autalg_1,d15_group_6,t41_autalg_1]),
    [file(autalg_1,t42_autalg_1),interesting(1.00)]).

fof(t9_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k6_partfun1(u1_struct_0(A)) = k2_group_1(k3_autalg_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t4_autalg_1,t8_autalg_1,t74_funct_2,t15_group_1]),
    [file(autalg_1,t9_autalg_1),interesting(0.68)]).

fof(t22_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
           => ! [D] : 
                ( m3_pboole(D,A,B,C)
               => r2_hidden(D,k4_card_3(k12_pboole(A,B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d3_pboole,d18_pboole,d3_pzfmisc1,t11_funct_2,d22_pboole,t18_card_3]),
    [file(autalg_1,t22_autalg_1),interesting(0.68)]).

fof(t4_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r2_hidden(k6_partfun1(u1_struct_0(A)),k1_autalg_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t1_autalg_1,d1_autalg_1]),
    [file(autalg_1,t4_autalg_1),interesting(0.67)]).

fof(t12_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,k1_tarski(A))
     => B = k3_cqc_lang(A,k1_funct_1(B,A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,t14_funct_1,t15_funcop_1]),
    [file(autalg_1,t12_autalg_1),interesting(0.67)]).

fof(t1_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r4_alg_1(A,A,k6_partfun1(u1_struct_0(A))) ) ),
    inference(mizar_proof,[status(thm)],[t6_alg_1,d2_alg_1,d4_alg_1,t6_alg_1,d3_alg_1,t71_relat_1]),
    [file(autalg_1,t1_autalg_1),interesting(0.66)]).

fof(t24_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => v2_msualg_3(k2_msualg_3(A,B),A,B,B) ) ),
    inference(mizar_proof,[status(thm)],[d3_msualg_3,d1_msualg_3,t71_relat_1]),
    [file(autalg_1,t24_autalg_1),interesting(0.61)]).

fof(t21_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
           => ! [D] : 
                ( r2_hidden(D,k4_card_3(k12_pboole(A,B,C)))
               => m3_pboole(D,A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3,d3_pboole,d22_pboole,d2_funct_2,d3_pzfmisc1,d1_funct_2,t11_relset_1,d3_pboole,d18_pboole]),
    [file(autalg_1,t21_autalg_1),interesting(0.60)]).

fof(t14_autalg_1,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( ( v1_msualg_3(D)
                  & v2_msualg_3(D,A,B,C) )
               => ( v1_msualg_3(k4_msualg_3(A,B,C,D))
                  & v2_msualg_3(k4_msualg_3(A,B,C,D),A,C,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,t1_msualg_3,t62_funct_1,d5_msualg_3,t1_msualg_3,d3_msualg_3,d16_pboole,d18_pboole,t1_msualg_3,d1_funct_2,t55_funct_1,d5_msualg_3]),
    [file(autalg_1,t14_autalg_1),interesting(0.58)]).

fof(t25_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => v1_msualg_3(k2_msualg_3(A,B)) ) ),
    inference(mizar_proof,[status(thm)],[d1_msualg_3,t1_msualg_3]),
    [file(autalg_1,t25_autalg_1),interesting(0.57)]).

fof(t23_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
           => v2_relat_1(k12_pboole(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pzfmisc1,t11_funct_2,d22_pboole,d16_pboole]),
    [file(autalg_1,t23_autalg_1),interesting(0.56)]).

fof(t36_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)) = k2_group_1(k6_autalg_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_autalg_1,t35_autalg_1,t3_msualg_3,t15_group_1]),
    [file(autalg_1,t36_autalg_1),interesting(0.53)]).

fof(t19_autalg_1,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ! [E] : 
                  ( m3_pboole(E,A,C,B)
                 => ( ( v1_msualg_3(D)
                      & v2_msualg_3(D,A,B,C)
                      & r6_pboole(A,k3_msualg_3(A,B,C,B,D,E),k2_msualg_3(A,B)) )
                   => r6_pboole(A,E,k4_msualg_3(A,B,C,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d18_pboole,d5_msualg_3,d16_pboole,d16_pboole,d3_msualg_3,d1_msualg_3,t2_msualg_3,t1_msualg_3,t36_funct_2,t3_pboole]),
    [file(autalg_1,t19_autalg_1),interesting(0.52)]).

fof(t6_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
         => r2_hidden(k2_funct_1(B),k1_autalg_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autalg_1,l7_autalg_1,t11_alg_1,d1_autalg_1]),
    [file(autalg_1,t6_autalg_1),interesting(0.52)]).

fof(t11_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r1_pzfmisc1(A,B,C)
                  & r1_pzfmisc1(A,C,D) )
               => r1_pzfmisc1(A,B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pzfmisc1,d3_pzfmisc1]),
    [file(autalg_1,t11_autalg_1),interesting(0.51)]).

fof(t15_autalg_1,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( ( v1_msualg_3(D)
                  & v2_msualg_3(D,A,B,C) )
               => r6_pboole(A,k4_msualg_3(A,C,B,k4_msualg_3(A,B,C,D)),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d18_pboole,t14_autalg_1,d5_msualg_3,t1_msualg_3,t65_funct_1,d5_msualg_3,t3_pboole]),
    [file(autalg_1,t15_autalg_1),interesting(0.50)]).

fof(t31_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => r2_hidden(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)),k4_autalg_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_msualg_3,d7_autalg_1]),
    [file(autalg_1,t31_autalg_1),interesting(0.50)]).

fof(t10_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k3_autalg_1(A)))
             => ( B = C
               => k2_funct_1(B) = k3_group_1(k3_autalg_1(A),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l12_autalg_1,l12_autalg_1,d1_autalg_1,d4_alg_1,d2_alg_1,t8_autalg_1,d6_group_1,t9_autalg_1,t36_funct_2]),
    [file(autalg_1,t10_autalg_1),interesting(0.45)]).

fof(t16_autalg_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ( ( v1_msualg_3(A)
              & v1_msualg_3(B) )
           => v1_msualg_3(k13_pboole(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_msualg_3,d24_pboole,d3_xboole_0,d2_msualg_3,t46_funct_1,d24_pboole]),
    [file(autalg_1,t16_autalg_1),interesting(0.45)]).

fof(l12_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
         => ( k1_relat_1(B) = k2_relat_1(B)
            & k1_relat_1(B) = u1_struct_0(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autalg_1,t9_alg_1]),
    [file(autalg_1,l12_autalg_1),interesting(0.44)]).

fof(t13_autalg_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => k13_pboole(A,k13_pboole(B,C)) = k13_pboole(k13_pboole(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_pboole,d24_pboole,t16_xboole_1,d24_pboole,d24_pboole,d3_xboole_0,d24_pboole,d3_xboole_0,d24_pboole,d24_pboole,d24_pboole,t55_relat_1,d24_pboole,d24_pboole,t9_funct_1]),
    [file(autalg_1,t13_autalg_1),interesting(0.43)]).

fof(t17_autalg_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ! [E] : 
                  ( m3_pboole(E,A,B,C)
                 => ! [F] : 
                      ( m3_pboole(F,A,C,D)
                     => ( ( v2_msualg_3(E,A,B,C)
                          & v2_msualg_3(F,A,C,D) )
                       => v2_msualg_3(k3_msualg_3(A,B,C,D,E,F),A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d18_pboole,d16_pboole,d16_pboole,d3_msualg_3,t20_funct_2,t2_msualg_3,d3_msualg_3]),
    [file(autalg_1,t17_autalg_1),interesting(0.43)]).

fof(l40_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_autalg_1(C,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
             => ( v1_msualg_3(C)
                & v2_msualg_3(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_autalg_1,t13_msualg_3]),
    [file(autalg_1,l40_autalg_1),interesting(0.42)]).

fof(t30_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => r1_tarski(k4_autalg_1(A,B),k4_card_3(k12_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t22_autalg_1]),
    [file(autalg_1,t30_autalg_1),interesting(0.40)]).

fof(t27_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => r2_hidden(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)),k4_card_3(k12_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_autalg_1]),
    [file(autalg_1,t27_autalg_1),interesting(0.35)]).

fof(t2_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r1_tarski(k1_autalg_1(A),k1_fraenkel(u1_struct_0(A),u1_struct_0(A))) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t12_funct_2]),
    [file(autalg_1,t2_autalg_1),interesting(0.33)]).

fof(t29_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_autalg_1(C,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
             => r2_hidden(C,k4_card_3(k12_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_autalg_1]),
    [file(autalg_1,t29_autalg_1),interesting(0.31)]).

fof(t37_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_autalg_1(C,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k6_autalg_1(A,B)))
                 => ( C = D
                   => k4_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C) = k3_group_1(k6_autalg_1(A,B),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l40_autalg_1,t35_autalg_1,d6_group_1,t36_autalg_1,t19_autalg_1]),
    [file(autalg_1,t37_autalg_1),interesting(0.29)]).

fof(l52_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(B) = k1_autalg_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_autalg_1(A))
                 => k1_funct_1(B,C) = k3_cqc_lang(0,C) ) )
           => k2_relat_1(B) = k4_autalg_1(k7_msualg_1(A),k10_msualg_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_funct_1,t39_autalg_1,d1_autalg_1,t20_msuhom_1,d3_msuhom_1,t9_msuhom_1,d7_autalg_1,d10_xboole_0,d3_tarski,d7_autalg_1,d7_autalg_1,t7_msualg_1,d13_msualg_1,t12_autalg_1,t9_msuhom_1,t38_autalg_1,d3_msuhom_1,t9_msuhom_1,t24_msuhom_1,d1_autalg_1,d5_funct_1]),
    [file(autalg_1,l52_autalg_1),interesting(0.28)]).

fof(t32_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_autalg_1(C,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
             => r2_hidden(k4_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C),k4_autalg_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_autalg_1,t14_msualg_3,d7_autalg_1]),
    [file(autalg_1,t32_autalg_1),interesting(0.26)]).

fof(t39_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
         => m3_pboole(k3_cqc_lang(0,B),u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_msuhom_1,d3_msuhom_1]),
    [file(autalg_1,t39_autalg_1),interesting(0.24)]).

fof(t8_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k3_autalg_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k3_autalg_1(A)))
             => ! [D] : 
                  ( m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
                 => ! [E] : 
                      ( m2_fraenkel(E,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
                     => ( ( B = D
                          & C = E )
                       => k1_group_1(k3_autalg_1(A),B,C) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_autalg_1]),
    [file(autalg_1,t8_autalg_1),interesting(0.20)]).

fof(t35_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k6_autalg_1(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k6_autalg_1(A,B)))
                 => ! [E] : 
                      ( m2_autalg_1(E,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
                     => ! [F] : 
                          ( m2_autalg_1(F,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
                         => ( ( C = E
                              & D = F )
                           => k1_group_1(k6_autalg_1(A,B),C,D) = k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),u4_msualg_1(A,B),E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_autalg_1]),
    [file(autalg_1,t35_autalg_1),interesting(0.15)]).

fof(t40_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(B) = k1_autalg_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_autalg_1(A))
                 => k1_funct_1(B,C) = k3_cqc_lang(0,C) ) )
           => ( v1_funct_1(B)
              & v1_funct_2(B,u1_struct_0(k3_autalg_1(A)),u1_struct_0(k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A))))
              & v1_group_6(B,k3_autalg_1(A),k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A)))
              & m2_relset_1(B,u1_struct_0(k3_autalg_1(A)),u1_struct_0(k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A)))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l52_autalg_1,d1_funct_2,t11_relset_1,t39_autalg_1,t34_autalg_1,t7_autalg_1,t8_autalg_1,d3_msuhom_1,t26_msuhom_1,d3_msuhom_1,d3_msuhom_1,t35_autalg_1,d7_group_6]),
    [file(autalg_1,t40_autalg_1),interesting(0.10)]).

fof(t5_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,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))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
                  & C = k2_funct_1(B) )
               => r4_alg_1(A,A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autalg_1,t11_alg_1]),
    [file(autalg_1,t5_autalg_1),interesting(0.03)]).

fof(d1_autalg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_fraenkel(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k1_autalg_1(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))
                    & 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))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => ( r2_hidden(C,B)
                  <=> r4_alg_1(A,A,C) ) ) ) ) ) ) ),
    file(autalg_1,d1_autalg_1),
    [interesting(0.00)]).

fof(t9_alg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( r4_alg_1(A,B,C)
               => ( k4_relset_1(u1_struct_0(A),u1_struct_0(B),C) = u1_struct_0(A)
                  & k2_relat_1(C) = u1_struct_0(B) ) ) ) ) ) ),
    file(alg_1,t9_alg_1),
    [interesting(0.00)]).

fof(d4_alg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( r4_alg_1(A,B,C)
              <=> ( r2_alg_1(A,B,C)
                  & r3_alg_1(A,B,C) ) ) ) ) ) ),
    file(alg_1,d4_alg_1),
    [interesting(0.00)]).

fof(d2_alg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( r2_alg_1(A,B,C)
              <=> ( r1_alg_1(A,B,C)
                  & v2_funct_1(C) ) ) ) ) ) ),
    file(alg_1,d2_alg_1),
    [interesting(0.00)]).

fof(d2_autalg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(k1_autalg_1(A),k1_autalg_1(A)),k1_autalg_1(A))
            & m2_relset_1(B,k2_zfmisc_1(k1_autalg_1(A),k1_autalg_1(A)),k1_autalg_1(A)) )
         => ( B = k2_autalg_1(A)
          <=> ! [C] : 
                ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
               => ! [D] : 
                    ( m2_fraenkel(D,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
                   => k2_binop_1(k1_autalg_1(A),k1_autalg_1(A),k1_autalg_1(A),B,C,D) = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,D) ) ) ) ) ) ),
    file(autalg_1,d2_autalg_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(t6_alg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => r1_alg_1(A,A,k6_partfun1(u1_struct_0(A))) ) ),
    file(alg_1,t6_alg_1),
    [interesting(0.00)]).

fof(d3_alg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( r3_alg_1(A,B,C)
              <=> ( r1_alg_1(A,B,C)
                  & k2_relat_1(C) = u1_struct_0(B) ) ) ) ) ) ),
    file(alg_1,d3_alg_1),
    [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(d3_pzfmisc1,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r1_pzfmisc1(A,B,C)
          <=> ! [D] : 
                ( ( r2_hidden(D,A)
                  & k1_funct_1(C,D) = k1_xboole_0 )
               => k1_funct_1(B,D) = k1_xboole_0 ) ) ) ) ),
    file(pzfmisc1,d3_pzfmisc1),
    [interesting(0.00)]).

fof(d24_pboole,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( C = k13_pboole(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pboole,d24_pboole),
    [interesting(0.00)]).

fof(t16_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) ),
    file(xboole_1,t16_xboole_1),
    [interesting(0.00)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t55_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( v1_relat_1(C)
             => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ),
    file(relat_1,t55_relat_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(d18_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    [interesting(0.00)]).

fof(t1_msualg_3,theorem,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => ( v1_msualg_3(B)
      <=> ! [C] : 
            ( r2_hidden(C,A)
           => v2_funct_1(k1_funct_1(B,C)) ) ) ) ),
    file(msualg_3,t1_msualg_3),
    [interesting(0.00)]).

fof(t62_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => v2_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,t62_funct_1),
    [interesting(0.00)]).

fof(d5_msualg_3,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( ( v1_msualg_3(D)
                  & v2_msualg_3(D,A,B,C) )
               => ! [E] : 
                    ( m3_pboole(E,A,C,B)
                   => ( E = k4_msualg_3(A,B,C,D)
                    <=> ! [F] : 
                          ( r2_hidden(F,A)
                         => k1_funct_1(E,F) = k2_funct_1(k1_funct_1(D,F)) ) ) ) ) ) ) ) ),
    file(msualg_3,d5_msualg_3),
    [interesting(0.00)]).

fof(d3_msualg_3,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( v2_msualg_3(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k2_relat_1(k1_funct_1(D,E)) = k1_funct_1(C,E) ) ) ) ) ) ),
    file(msualg_3,d3_msualg_3),
    [interesting(0.00)]).

fof(d16_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v2_relat_1(B)
      <=> ! [C] : ~ ( r2_hidden(C,A)
            & v1_xboole_0(k1_funct_1(B,C)) ) ) ) ),
    file(pboole,d16_pboole),
    [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(t55_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A))
          & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ),
    file(funct_1,t55_funct_1),
    [interesting(0.00)]).

fof(t65_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => k2_funct_1(k2_funct_1(A)) = A ) ) ),
    file(funct_1,t65_funct_1),
    [interesting(0.00)]).

fof(t3_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    [interesting(0.00)]).

fof(d2_msualg_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_msualg_3(A)
      <=> ! [B,C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C) )
           => ( ( r2_hidden(B,k1_relat_1(A))
                & k1_funct_1(A,B) = C )
             => v2_funct_1(C) ) ) ) ) ),
    file(msualg_3,d2_msualg_3),
    [interesting(0.00)]).

fof(t46_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => v2_funct_1(k5_relat_1(A,B)) ) ) ) ),
    file(funct_1,t46_funct_1),
    [interesting(0.00)]).

fof(t20_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_funct_1(E)
            & v1_funct_2(E,B,C)
            & m2_relset_1(E,B,C) )
         => ( ( k2_relat_1(D) = B
              & k2_relat_1(E) = C )
           => ( B = k1_xboole_0
              | C = k1_xboole_0
              | k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C ) ) ) ) ),
    file(funct_2,t20_funct_2),
    [interesting(0.00)]).

fof(t2_msualg_3,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ! [E] : 
                  ( m3_pboole(E,A,B,C)
                 => ! [F] : 
                      ( m3_pboole(F,A,C,D)
                     => ( k1_relat_1(k13_pboole(E,F)) = A
                        & ! [G] : 
                            ( r2_hidden(G,A)
                           => k1_funct_1(k13_pboole(E,F),G) = k5_relat_1(k1_funct_1(E,G),k1_funct_1(F,G)) ) ) ) ) ) ) ) ),
    file(msualg_3,t2_msualg_3),
    [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(t66_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => k2_funct_1(k5_relat_1(A,B)) = k5_relat_1(k2_funct_1(B),k2_funct_1(A)) ) ) ) ),
    file(funct_1,t66_funct_1),
    [interesting(0.00)]).

fof(t18_autalg_1,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( ( v2_relat_1(D)
                & m1_pboole(D,A) )
             => ! [E] : 
                  ( m3_pboole(E,A,B,C)
                 => ! [F] : 
                      ( m3_pboole(F,A,C,D)
                     => ( ( v1_msualg_3(E)
                          & v2_msualg_3(E,A,B,C)
                          & v1_msualg_3(F)
                          & v2_msualg_3(F,A,C,D) )
                       => r6_pboole(A,k4_msualg_3(A,B,D,k3_msualg_3(A,B,C,D,E,F)),k3_msualg_3(A,D,C,B,k4_msualg_3(A,C,D,F),k4_msualg_3(A,B,C,E))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_pboole,d18_pboole,d5_msualg_3,d5_msualg_3,t16_autalg_1,t17_autalg_1,t1_msualg_3,t1_msualg_3,t2_msualg_3,d5_msualg_3,d3_msualg_3,t31_funct_2,d3_msualg_3,t31_funct_2,t2_msualg_3,d5_msualg_3,d5_msualg_3,t66_funct_1,t3_pboole]),
    [file(autalg_1,t18_autalg_1),interesting(0.00)]).

fof(t20_autalg_1,theorem,(
    $true ),
    file(autalg_1,t20_autalg_1),
    [interesting(0.00)]).

fof(d5_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    [interesting(0.00)]).

fof(d3_pboole,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    [interesting(0.00)]).

fof(d22_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( D = k12_pboole(A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k1_funct_1(D,E) = k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ),
    file(pboole,d22_pboole),
    [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(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [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(d1_msualg_3,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m3_pboole(C,A,B,B)
         => ( C = k2_msualg_3(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k6_partfun1(k1_funct_1(B,D)) ) ) ) ) ),
    file(msualg_3,d1_msualg_3),
    [interesting(0.00)]).

fof(t26_autalg_1,theorem,(
    $true ),
    file(autalg_1,t26_autalg_1),
    [interesting(0.00)]).

fof(t18_card_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    [interesting(0.00)]).

fof(t28_autalg_1,theorem,(
    $true ),
    file(autalg_1,t28_autalg_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(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(d7_autalg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m1_autalg_1(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
             => ( C = k4_autalg_1(A,B)
              <=> ( ! [D] : 
                      ( m2_autalg_1(D,u1_struct_0(A),u4_msualg_1(A,B),C)
                     => m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
                  & ! [D] : 
                      ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
                     => ( r2_hidden(D,C)
                      <=> r4_msualg_3(A,B,B,D) ) ) ) ) ) ) ) ),
    file(autalg_1,d7_autalg_1),
    [interesting(0.00)]).

fof(t14_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                     => ( ( r4_msualg_3(A,B,C,D)
                          & r6_pboole(u1_struct_0(A),E,k4_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D)) )
                       => r4_msualg_3(A,C,B,E) ) ) ) ) ) ) ),
    file(msualg_3,t14_msualg_3),
    [interesting(0.00)]).

fof(t15_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                         => ( ( r4_msualg_3(A,B,C,E)
                              & r4_msualg_3(A,C,D,F) )
                           => r4_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ),
    file(msualg_3,t15_msualg_3),
    [interesting(0.00)]).

fof(t33_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m2_autalg_1(C,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
             => ! [D] : 
                  ( m2_autalg_1(D,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
                 => r2_hidden(k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C),k4_autalg_1(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_autalg_1,t15_msualg_3,d7_autalg_1]),
    [file(autalg_1,t33_autalg_1),interesting(0.00)]).

fof(t13_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r4_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                      & v1_msualg_3(D) ) ) ) ) ) ) ),
    file(msualg_3,t13_msualg_3),
    [interesting(0.00)]).

fof(d8_autalg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(k4_autalg_1(A,B),k4_autalg_1(A,B)),k4_autalg_1(A,B))
                & m2_relset_1(C,k2_zfmisc_1(k4_autalg_1(A,B),k4_autalg_1(A,B)),k4_autalg_1(A,B)) )
             => ( C = k5_autalg_1(A,B)
              <=> ! [D] : 
                    ( m2_autalg_1(D,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
                   => ! [E] : 
                        ( m2_autalg_1(E,u1_struct_0(A),u4_msualg_1(A,B),k4_autalg_1(A,B))
                       => k2_binop_1(k4_autalg_1(A,B),k4_autalg_1(A,B),k4_autalg_1(A,B),C,D,E) = k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),u4_msualg_1(A,B),D,E) ) ) ) ) ) ) ),
    file(autalg_1,d8_autalg_1),
    [interesting(0.00)]).

fof(t16_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ( r4_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)))
            & r5_msualg_3(A,B,B) ) ) ) ),
    file(msualg_3,t16_msualg_3),
    [interesting(0.00)]).

fof(t3_msualg_3,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => k13_pboole(k2_msualg_3(A,B),D) = D ) ) ) ),
    file(msualg_3,t3_msualg_3),
    [interesting(0.00)]).

fof(t3_autalg_1,theorem,(
    $true ),
    file(autalg_1,t3_autalg_1),
    [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(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(t9_msuhom_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_msualg_1(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => B = k2_msuhom_1(A,A,B) ) ) ),
    file(msuhom_1,t9_msuhom_1),
    [interesting(0.00)]).

fof(d3_msuhom_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( k7_msualg_1(A) = k7_msualg_1(B)
               => k3_msuhom_1(A,B,C) = k2_pre_circ(k1_tarski(0),C) ) ) ) ) ),
    file(msuhom_1,d3_msuhom_1),
    [interesting(0.00)]).

fof(t20_msuhom_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( r4_alg_1(A,B,C)
               => r4_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) ) ) ) ) ),
    file(msuhom_1,t20_msuhom_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(t7_msualg_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ! [D] : 
              ( ( v1_funct_1(D)
                & m2_relset_1(D,A,B) )
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
                    & v1_funct_2(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C)
                    & m2_relset_1(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) ) ) ) ) ) ),
    file(msualg_1,t7_msualg_1),
    [interesting(0.00)]).

fof(d13_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_realset2(B)
            & v1_msualg_1(B)
            & ~ v2_msualg_1(B)
            & v6_msualg_1(B)
            & l1_msualg_1(B) )
         => ( B = k7_msualg_1(A)
          <=> ( u1_struct_0(B) = k1_tarski(0)
              & u1_msualg_1(B) = k4_finseq_1(k6_msualg_1(A))
              & u2_msualg_1(B) = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(0)),k6_msualg_1(A),k9_pboole(0))
              & u3_msualg_1(B) = k10_pboole(k4_finseq_1(k6_msualg_1(A)),0) ) ) ) ) ),
    file(msualg_1,d13_msualg_1),
    [interesting(0.00)]).

fof(t14_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( k1_relat_1(B) = k1_tarski(A)
       => k2_relat_1(B) = k1_tarski(k1_funct_1(B,A)) ) ) ),
    file(funct_1,t14_funct_1),
    [interesting(0.00)]).

fof(t15_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( k2_relat_1(A) = k1_tarski(B)
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) ),
    file(funcop_1,t15_funcop_1),
    [interesting(0.00)]).

fof(t10_msuhom_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => k7_msualg_1(A) = k7_msualg_1(B) ) ) ) ),
    file(msuhom_1,t10_msuhom_1),
    [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(d14_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k8_msualg_1(A) = k10_pboole(k1_tarski(0),u1_struct_0(A)) ) ),
    file(msualg_1,d14_msualg_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(d16_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => k10_msualg_1(A) = g3_msualg_1(k7_msualg_1(A),k8_msualg_1(A),k9_msualg_1(A)) ) ),
    file(msualg_1,d16_msualg_1),
    [interesting(0.00)]).

fof(t38_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => ! [C] : 
                ( m3_pboole(C,u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B))))
               => ( v1_funct_1(k1_funct_1(C,0))
                  & v1_funct_2(k1_funct_1(C,0),u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(k1_funct_1(C,0),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_msuhom_1,t7_msualg_1,d13_msualg_1,d1_tarski,d14_msualg_1,t13_funcop_1,d16_msualg_1,d14_msualg_1,t13_funcop_1,d16_msualg_1,t9_msuhom_1,d18_pboole]),
    [file(autalg_1,t38_autalg_1),interesting(0.00)]).

fof(t24_msuhom_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( ( r1_unialg_2(A,B)
                  & r4_msualg_3(k7_msualg_1(A),k10_msualg_1(A),k2_msuhom_1(k7_msualg_1(A),k7_msualg_1(B),k10_msualg_1(B)),k3_msuhom_1(A,B,C)) )
               => r4_alg_1(A,B,C) ) ) ) ) ),
    file(msuhom_1,t24_msuhom_1),
    [interesting(0.00)]).

fof(t34_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_pboole(B,u1_struct_0(k7_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)),u4_msualg_1(k7_msualg_1(A),k10_msualg_1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
             => ( B = k3_cqc_lang(0,C)
               => r2_hidden(B,k4_autalg_1(k7_msualg_1(A),k10_msualg_1(A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_msuhom_1,d1_autalg_1,t20_msuhom_1,t9_msuhom_1,d7_autalg_1]),
    [file(autalg_1,t34_autalg_1),interesting(0.00)]).

fof(t12_alg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(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))
                        & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                     => ( ( r4_alg_1(A,B,D)
                          & r4_alg_1(B,C,E) )
                       => r4_alg_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) ),
    file(alg_1,t12_alg_1),
    [interesting(0.00)]).

fof(t7_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_fraenkel(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A))
             => r2_hidden(k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),k1_autalg_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_autalg_1,t12_alg_1,d1_autalg_1]),
    [file(autalg_1,t7_autalg_1),interesting(0.00)]).

fof(t26_msuhom_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ( ( r1_unialg_2(A,B)
                  & r1_unialg_2(B,C) )
               => ! [D] : 
                    ( ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(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))
                          & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
                       => k13_pboole(k3_msuhom_1(A,B,D),k3_msuhom_1(B,C,E)) = k3_msuhom_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) ),
    file(msuhom_1,t26_msuhom_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(d15_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) )
         => ( r1_group_6(A,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) ) ) ) ) ),
    file(group_6,d15_group_6),
    [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(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(d2_funcop_1,definition,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ),
    file(funcop_1,d2_funcop_1),
    [interesting(0.00)]).

fof(t134_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D)
     => ( A = k1_xboole_0
        | B = k1_xboole_0
        | ( A = C
          & B = D ) ) ) ),
    file(zfmisc_1,t134_zfmisc_1),
    [interesting(0.00)]).

fof(t6_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),k1_tarski(B))
     => A = B ) ),
    file(zfmisc_1,t6_zfmisc_1),
    [interesting(0.00)]).

fof(t1_group_6,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ( v2_funct_1(C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => ( k8_funct_2(A,B,C,D) = k8_funct_2(A,B,C,E)
                         => D = E ) ) ) ) ) ) ) ),
    file(group_6,t1_group_6),
    [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(t41_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k3_autalg_1(A)),u1_struct_0(k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A))))
            & v1_group_6(B,k3_autalg_1(A),k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A)))
            & m2_relset_1(B,u1_struct_0(k3_autalg_1(A)),u1_struct_0(k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A)))) )
         => ( ! [C] : 
                ( r2_hidden(C,k1_autalg_1(A))
               => k1_funct_1(B,C) = k3_cqc_lang(0,C) )
           => v4_group_6(B,k3_autalg_1(A),k6_autalg_1(k7_msualg_1(A),k10_msualg_1(A))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,l52_autalg_1,d13_group_6,d14_group_6,d2_funcop_1,d2_funcop_1,t134_zfmisc_1,t6_zfmisc_1,t1_group_6,d12_group_6]),
    [file(autalg_1,t41_autalg_1),interesting(0.00)]).

fof(t11_alg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ( ( r4_alg_1(A,B,C)
                      & D = k2_funct_1(C) )
                   => r4_alg_1(B,A,D) ) ) ) ) ) ),
    file(alg_1,t11_alg_1),
    [interesting(0.00)]).

fof(t8_alg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_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)) )
             => ( r4_alg_1(A,B,C)
              <=> ( r1_alg_1(A,B,C)
                  & k2_relat_1(C) = u1_struct_0(B)
                  & v2_funct_1(C) ) ) ) ) ) ),
    file(alg_1,t8_alg_1),
    [interesting(0.00)]).

fof(l7_autalg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r4_alg_1(A,A,B)
           => ( v1_funct_1(k2_funct_1(B))
              & v1_funct_2(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A))
              & m2_relset_1(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_alg_1,d4_alg_1,d3_alg_1,t31_funct_2]),
    [file(autalg_1,l7_autalg_1),interesting(0.00)]).