fof(l13_amistd_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r1_tarski(B,A)
           => v1_finset_1(k2_wellord2(k1_wellord2(B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_wellord2,d2_wellord2,t9_amistd_3,t7_amistd_3]),
    [file(amistd_3,l13_amistd_3),interesting(1.00)]).

fof(t10_amistd_3,theorem,(
    ! [A,B] : r3_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B)),k3_cqc_lang(A,B)) ),
    inference(mizar_proof,[status(thm)],[t2_amistd_3,t5_cqc_lang,d7_wellord1,t2_amistd_3,t5_cqc_lang,d1_tarski,t33_zfmisc_1,d1_tarski,t6_cqc_lang,d1_tarski,d1_tarski,d1_tarski]),
    [file(amistd_3,t10_amistd_3),interesting(0.99)]).

fof(t19_amistd_3,theorem,(
    r2_wellord2(k5_numbers,k1_amistd_3) ),
    inference(mizar_proof,[status(thm)],[s3_funct_2,d4_wellord2,d8_funct_1,d1_funct_2,t16_amistd_3,d1_funct_2,t12_relset_1,d10_xboole_0,d3_tarski,d5_funct_1]),
    [file(amistd_3,t19_amistd_3),interesting(0.99)]).

fof(t13_amistd_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( r1_tarski(B,A)
           => k2_wellord2(k1_wellord2(B)) = k4_card_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_card_5,l13_amistd_3,t7_card_4,t66_card_1]),
    [file(amistd_3,t13_amistd_3),interesting(0.99)]).

fof(t14_amistd_3,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r1_tarski(k1_tarski(A),B)
       => k2_wellord2(k1_wellord2(k1_tarski(A))) = 1 ) ) ),
    inference(mizar_proof,[status(thm)],[t60_card_2,t13_amistd_3]),
    [file(amistd_3,t14_amistd_3),interesting(0.98)]).

fof(t15_amistd_3,theorem,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r1_tarski(k1_tarski(A),B)
       => k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k1_tarski(A)))),k1_wellord2(k1_tarski(A))) = k3_cqc_lang(0,A) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_wellord2,d2_wellord2,t50_wellord1,t9_wellord2,d9_wellord1,t5_amistd_3,t14_amistd_3,t1_card_5,d7_wellord1,t2_amistd_3,d7_wellord1,d1_wellord2,t1_amistd_3]),
    [file(amistd_3,t15_amistd_3),interesting(0.98)]).

fof(t6_amistd_3,theorem,(
    ! [A] : r1_tarski(k1_wellord2(A),k2_zfmisc_1(A,A)) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_relat_1,t30_relat_1,d1_wellord2,t106_zfmisc_1]),
    [file(amistd_3,t6_amistd_3),interesting(0.98)]).

fof(t5_amistd_3,theorem,(
    ! [A] : k1_wellord2(k1_tarski(A)) = k1_tarski(k4_tarski(A,A)) ),
    inference(mizar_proof,[status(thm)],[t2_amistd_3,d1_tarski,d1_tarski,d1_wellord2]),
    [file(amistd_3,t5_amistd_3),interesting(0.97)]).

fof(t9_amistd_3,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( ( r4_wellord1(A,B)
              & v1_finset_1(A) )
           => v1_finset_1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_wellord1,d7_wellord1,t26_finset_1,d7_wellord1,t3_amistd_3]),
    [file(amistd_3,t9_amistd_3),interesting(0.96)]).

fof(t7_amistd_3,theorem,(
    ! [A] : 
      ( v1_finset_1(k1_wellord2(A))
     => v1_finset_1(A) ) ),
    inference(mizar_proof,[status(thm)],[d1_wellord2]),
    [file(amistd_3,t7_amistd_3),interesting(0.95)]).

fof(t11_amistd_3,theorem,(
    ! [A,B] : r4_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B))) ),
    inference(mizar_proof,[status(thm)],[d8_wellord1,t10_amistd_3]),
    [file(amistd_3,t11_amistd_3),interesting(0.94)]).

fof(t3_amistd_3,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finset_1(k3_relat_1(A))
       => v1_finset_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t180_orders_1,t13_finset_1]),
    [file(amistd_3,t3_amistd_3),interesting(0.94)]).

fof(t32_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => k5_amistd_3(A,B,k7_amistd_2(A,B)) = k9_trees_2(u2_ami_1(A,B),k1_amistd_3,k5_amistd_1(A,B,0)) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_amistd_2,t5_cqc_lang,t6_cqc_lang,d5_amistd_3,t15_amistd_1,t50_card_1,t20_card_2,t1_card_5,t21_amistd_3,d5_amistd_3,d1_tarski,d13_amistd_1,d5_ami_5,d1_tarski,d1_tarski,d1_tarski,d3_tarski,d10_xboole_0,d3_tarski,d1_tarski,t14_trees_2,d1_tarski,t29_amistd_3,t15_amistd_3,t6_cqc_lang,d13_amistd_1,d5_amistd_3,d4_amistd_3,d1_tarski,s1_hilbert2,t17_qc_lang4,t17_qc_lang4,d6_trees_2,t69_finseq_2,t17_amistd_3,d6_trees_2,d5_amistd_3,d1_tarski,d5_ami_5,d1_tarski,d21_ordinal2,t20_amistd_3,t29_nat_1,t7_finseq_1,d3_finseq_1,t91_relat_1,d3_finseq_1,t61_finseq_3,t14_trees_2,d1_tarski,d1_tarski,d3_tarski,d10_xboole_0,d3_tarski,d1_tarski,d1_tarski,t3_finseq_1,t72_funct_1,d1_tarski,t70_finseq_2,t20_finseq_2,t8_finseq_2,t70_finseq_2,t18_finseq_1,d1_tarski,d3_tarski,d10_xboole_0,d3_tarski,d1_tarski,t72_finseq_2,t47_trees_1,d5_amistd_3,d1_tarski,d5_ami_5,d1_tarski,t74_finseq_2,s1_nat_1,t20_amistd_3,s1_nat_1,t18_amistd_3,t5_cqc_lang,d1_tarski,t17_funcop_1]),
    [file(amistd_3,t32_amistd_3),interesting(0.93)]).

fof(t2_amistd_3,theorem,(
    ! [A] : k3_relat_1(k1_tarski(k4_tarski(A,A))) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[t32_relat_1,t69_enumset1]),
    [file(amistd_3,t2_amistd_3),interesting(0.92)]).

fof(t1_amistd_3,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( k1_relat_1(C) = k1_tarski(A)
          & k2_relat_1(C) = k1_tarski(B) )
       => C = k3_cqc_lang(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_ami_1,t20_relat_1,d1_tarski,d1_tarski,d1_tarski,t33_zfmisc_1,d1_tarski,d4_relat_1,t20_relat_1,d1_tarski,d2_relat_1]),
    [file(amistd_3,t1_amistd_3),interesting(0.91)]).

fof(t16_amistd_3,theorem,(
    ! [A,B] : 
      ( v4_ordinal2(B)
     => ! [C] : 
          ( v4_ordinal2(C)
         => ( k2_finseq_2(B,A) = k2_finseq_2(C,A)
           => B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t69_finseq_2]),
    [file(amistd_3,t16_amistd_3),interesting(0.88)]).

fof(t12_amistd_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k2_wellord2(k1_wellord2(A)) = A ) ),
    inference(mizar_proof,[status(thm)],[t7_wellord2,t48_wellord1,d2_wellord2]),
    [file(amistd_3,t12_amistd_3),interesting(0.85)]).

fof(t8_amistd_3,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( ( r4_wellord1(A,B)
              & v2_wellord1(A) )
           => v2_wellord1(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_wellord1,t54_wellord1]),
    [file(amistd_3,t8_amistd_3),interesting(0.84)]).

fof(t17_amistd_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m1_trees_1(C,B)
             => r2_hidden(k2_partfun1(k5_numbers,k5_numbers,C,k2_finseq_1(A)),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t88_relat_1,t45_trees_1]),
    [file(amistd_3,t17_amistd_3),interesting(0.82)]).

fof(t18_amistd_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_trees_2(A,C) = k2_trees_2(B,C) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_trees_2,t16_trees_2,d4_tarski,d4_tarski,t7_trees_2]),
    [file(amistd_3,t18_amistd_3),interesting(0.82)]).

fof(t4_amistd_3,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( v1_finset_1(k1_relat_1(A))
          & v1_finset_1(k2_relat_1(A)) )
       => v1_finset_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_finset_1,d6_relat_1,t3_amistd_3]),
    [file(amistd_3,t4_amistd_3),interesting(0.82)]).

fof(t27_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
             => r2_wellord2(C,k3_amistd_3(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_amistd_1,s1_funct_2,d4_wellord2,d8_funct_1,d1_funct_2,t25_amistd_1,d1_funct_2,t12_relset_1,d10_xboole_0,d3_tarski,d13_amistd_1,d5_funct_1]),
    [file(amistd_3,t27_amistd_3),interesting(0.81)]).

fof(t20_amistd_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_trees_2(k1_amistd_3,A) = k1_tarski(k2_finseq_2(A,0)) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t69_finseq_2,d3_tarski,d10_xboole_0,d3_tarski,t69_finseq_2,d1_tarski,d6_trees_2]),
    [file(amistd_3,t20_amistd_3),interesting(0.81)]).

fof(t21_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => r2_hidden(k2_amistd_3(A,B,C),k1_relat_1(C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_amistd_3,d8_cqc_sim1,d13_amistd_1]),
    [file(amistd_3,t21_amistd_3),interesting(0.72)]).

fof(t31_amistd_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_setfam_1(B)
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & l1_ami_1(C,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C)))
                 => ( D = k1_struct_0(C,k5_amistd_1(B,C,A))
                   => k4_amistd_3(B,C,D) = k3_cqc_lang(0,k5_amistd_1(B,C,A)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_amistd_3,d3_tarski,d1_tarski,d21_ordinal2,t15_amistd_3,t6_cqc_lang,d4_amistd_3,t50_card_1,t20_card_2,t1_card_5,t5_cqc_lang,d1_tarski,d4_amistd_3,t6_cqc_lang,t9_funct_1]),
    [file(amistd_3,t31_amistd_3),interesting(0.71)]).

fof(t23_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ( r2_hidden(C,k1_relat_1(D))
                   => r1_amistd_1(A,B,k2_amistd_3(A,B,D),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_amistd_3,d13_amistd_1,d8_cqc_sim1,t29_amistd_1]),
    [file(amistd_3,t23_amistd_3),interesting(0.64)]).

fof(t24_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => k2_amistd_3(A,B,C) = k5_amistd_1(A,B,0) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_amistd_3,t21_amistd_3,t28_amistd_1,d20_amistd_1,t23_amistd_3,d9_amistd_1]),
    [file(amistd_3,t24_amistd_3),interesting(0.61)]).

fof(t28_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
             => r1_ordinal1(k1_card_1(C),k2_wellord2(k1_wellord2(k3_amistd_3(A,B,C)))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_card_5,t27_amistd_3,t21_card_1,t24_card_1]),
    [file(amistd_3,t28_amistd_3),interesting(0.58)]).

fof(t26_amistd_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_setfam_1(B)
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & l1_ami_1(C,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C)))
                 => ( D = k1_struct_0(C,k5_amistd_1(B,C,A))
                   => k3_amistd_3(B,C,D) = k1_tarski(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d13_amistd_1,d1_tarski,d13_amistd_1,d1_tarski,d3_tarski,d10_xboole_0,d3_tarski,d1_tarski]),
    [file(amistd_3,t26_amistd_3),interesting(0.58)]).

fof(t22_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] : 
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ( r1_tarski(C,D)
                   => r1_amistd_1(A,B,k2_amistd_3(A,B,D),k2_amistd_3(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_amistd_3,d2_amistd_3,d3_tarski,t8_grfunc_1,t19_cqc_sim1,t28_amistd_1]),
    [file(amistd_3,t22_amistd_3),interesting(0.50)]).

fof(t25_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(A,B)))
                 => ( r2_hidden(k7_amistd_1(A,B,C),k3_amistd_3(A,B,D))
                  <=> r2_hidden(C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_amistd_1]),
    [file(amistd_3,t25_amistd_3),interesting(0.47)]).

fof(t29_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ( ( v10_ami_1(B,A)
                      & v3_ami_1(D,A,B) )
                   => k3_amistd_3(A,B,k1_amistd_1(A,B,C,D)) = k15_cqc_sim1(k5_numbers,k7_amistd_1(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_amistd_1,d13_amistd_1,t26_amistd_3]),
    [file(amistd_3,t29_amistd_3),interesting(0.28)]).

fof(d8_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & r3_wellord1(A,B,C) ) ) ) ) ),
    file(wellord1,d8_wellord1),
    [interesting(0.00)]).

fof(t32_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( C = k1_tarski(k4_tarski(A,B))
       => k3_relat_1(C) = k2_tarski(A,B) ) ) ),
    file(relat_1,t32_relat_1),
    [interesting(0.00)]).

fof(t69_enumset1,theorem,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    file(enumset1,t69_enumset1),
    [interesting(0.00)]).

fof(t5_cqc_lang,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
      & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ),
    file(cqc_lang,t5_cqc_lang),
    [interesting(0.00)]).

fof(d7_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( r3_wellord1(A,B,C)
              <=> ( k1_relat_1(C) = k3_relat_1(A)
                  & k2_relat_1(C) = k3_relat_1(B)
                  & v2_funct_1(C)
                  & ! [D,E] : 
                      ( r2_hidden(k4_tarski(D,E),A)
                    <=> ( r2_hidden(D,k3_relat_1(A))
                        & r2_hidden(E,k3_relat_1(A))
                        & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) ) ) ) ) ) ) ) ),
    file(wellord1,d7_wellord1),
    [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(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.00)]).

fof(t6_cqc_lang,theorem,(
    ! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ),
    file(cqc_lang,t6_cqc_lang),
    [interesting(0.00)]).

fof(t7_wellord2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => v2_wellord1(k1_wellord2(A)) ) ),
    file(wellord2,t7_wellord2),
    [interesting(0.00)]).

fof(t48_wellord1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => r4_wellord1(A,A) ) ),
    file(wellord1,t48_wellord1),
    [interesting(0.00)]).

fof(d2_wellord2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
       => ! [B] : 
            ( v3_ordinal1(B)
           => ( B = k2_wellord2(A)
            <=> r4_wellord1(A,k1_wellord2(B)) ) ) ) ) ),
    file(wellord2,d2_wellord2),
    [interesting(0.00)]).

fof(s3_funct_2,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s3_funct_2)
       => ? [B] : 
            ( m1_subset_1(B,f2_s3_funct_2)
            & p1_s3_funct_2(A,B) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2)
        & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2)
        & ! [B] : 
            ( m1_subset_1(B,f1_s3_funct_2)
           => p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)) ) ) ),
    file(funct_2,s3_funct_2),
    [interesting(0.00)]).

fof(d4_wellord2,definition,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & k1_relat_1(C) = A
          & k2_relat_1(C) = B ) ) ),
    file(wellord2,d4_wellord2),
    [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(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(t69_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k3_finseq_1(k2_finseq_2(A,B)) = A ) ),
    file(finseq_2,t69_finseq_2),
    [interesting(0.00)]).

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

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

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(d2_amistd_3,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ( v1_ami_3(C,A,B)
               => ( v1_xboole_0(C)
                  | ! [D] : 
                      ( m1_struct_0(D,B,u2_ami_1(A,B))
                     => ( D = k2_amistd_3(A,B,C)
                      <=> ? [E] : 
                            ( ~ v1_xboole_0(E)
                            & m1_subset_1(E,k1_zfmisc_1(k5_numbers))
                            & E = a_3_0_amistd_3(A,B,C)
                            & D = k5_amistd_1(A,B,k10_cqc_sim1(E)) ) ) ) ) ) ) ) ) ),
    file(amistd_3,d2_amistd_3),
    [interesting(0.00)]).

fof(t8_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(A,B)
          <=> ( r1_tarski(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) ) ) ) ) ) ),
    file(grfunc_1,t8_grfunc_1),
    [interesting(0.00)]).

fof(t19_cqc_sim1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
         => ( r1_tarski(A,B)
           => r1_xreal_0(k10_cqc_sim1(B),k10_cqc_sim1(A)) ) ) ) ),
    file(cqc_sim1,t19_cqc_sim1),
    [interesting(0.00)]).

fof(t28_amistd_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ! [D] : 
                  ( v4_ordinal2(D)
                 => ( r1_amistd_1(A,B,k5_amistd_1(A,B,C),k5_amistd_1(A,B,D))
                  <=> r1_xreal_0(C,D) ) ) ) ) ) ),
    file(amistd_1,t28_amistd_1),
    [interesting(0.00)]).

fof(d8_cqc_sim1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k10_cqc_sim1(A)
          <=> ( r2_hidden(B,A)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,A)
                   => r1_xreal_0(B,C) ) ) ) ) ) ) ),
    file(cqc_sim1,d8_cqc_sim1),
    [interesting(0.00)]).

fof(d13_amistd_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( v4_ordinal2(D)
                 => ( D = k6_amistd_1(A,B,C)
                  <=> k5_amistd_1(A,B,D) = C ) ) ) ) ) ),
    file(amistd_1,d13_amistd_1),
    [interesting(0.00)]).

fof(d20_amistd_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ( v9_amistd_1(C,A,B)
              <=> ! [D] : 
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => ( r2_hidden(D,k1_relat_1(C))
                     => ! [E] : 
                          ( m1_struct_0(E,B,u2_ami_1(A,B))
                         => ( r1_amistd_1(A,B,E,D)
                           => r2_hidden(E,k1_relat_1(C)) ) ) ) ) ) ) ) ) ),
    file(amistd_1,d20_amistd_1),
    [interesting(0.00)]).

fof(t29_amistd_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r1_xreal_0(k7_amistd_1(A,B,C),k7_amistd_1(A,B,D))
                  <=> r1_amistd_1(A,B,C,D) ) ) ) ) ) ),
    file(amistd_1,t29_amistd_1),
    [interesting(0.00)]).

fof(d9_amistd_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( v3_amistd_1(B,A)
          <=> ! [C] : 
                ( m1_struct_0(C,B,u2_ami_1(A,B))
               => ! [D] : 
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => ( ( r1_amistd_1(A,B,C,D)
                        & r1_amistd_1(A,B,D,C) )
                     => C = D ) ) ) ) ) ) ),
    file(amistd_1,d9_amistd_1),
    [interesting(0.00)]).

fof(t27_amistd_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( k7_amistd_1(A,B,C) = k7_amistd_1(A,B,D)
                   => C = D ) ) ) ) ) ),
    file(amistd_1,t27_amistd_1),
    [interesting(0.00)]).

fof(t16_card_5,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => k1_card_1(B) = k1_card_1(k2_wellord2(k1_wellord2(B))) ) ) ),
    file(card_5,t16_card_5),
    [interesting(0.00)]).

fof(s1_funct_2,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s1_funct_2)
        & ! [B] : ~ ( r2_hidden(B,f2_s1_funct_2)
            & p1_s1_funct_2(A,B) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2)
        & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2)
        & ! [B] : 
            ( r2_hidden(B,f1_s1_funct_2)
           => p1_s1_funct_2(B,k1_funct_1(A,B)) ) ) ),
    file(funct_2,s1_funct_2),
    [interesting(0.00)]).

fof(t25_amistd_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ! [D] : 
                  ( v4_ordinal2(D)
                 => ( k5_amistd_1(A,B,C) = k5_amistd_1(A,B,D)
                   => C = D ) ) ) ) ) ),
    file(amistd_1,t25_amistd_1),
    [interesting(0.00)]).

fof(t21_card_1,theorem,(
    ! [A,B] : 
      ( r2_wellord2(A,B)
    <=> k1_card_1(A) = k1_card_1(B) ) ),
    file(card_1,t21_card_1),
    [interesting(0.00)]).

fof(t24_card_1,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => r1_ordinal1(k1_card_1(A),A) ) ),
    file(card_1,t24_card_1),
    [interesting(0.00)]).

fof(t41_amistd_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ( v5_amistd_1(D,A,B)
                   => k1_amistd_1(A,B,C,D) = k1_struct_0(B,k9_amistd_1(A,B,C)) ) ) ) ) ) ),
    file(amistd_1,t41_amistd_1),
    [interesting(0.00)]).

fof(t30_amistd_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ( ( v10_ami_1(B,A)
                      & v5_amistd_1(D,A,B) )
                   => k3_amistd_3(A,B,k1_amistd_1(A,B,C,D)) = k15_cqc_sim1(k5_numbers,k7_amistd_1(A,B,k9_amistd_1(A,B,C))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_amistd_1,d13_amistd_1,t26_amistd_3]),
    [file(amistd_3,t30_amistd_3),interesting(0.00)]).

fof(d21_ordinal2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    [interesting(0.00)]).

fof(t9_wellord2,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( r1_tarski(B,A)
         => v2_wellord1(k1_wellord2(B)) ) ) ),
    file(wellord2,t9_wellord2),
    [interesting(0.00)]).

fof(t50_wellord1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r4_wellord1(A,B)
           => r4_wellord1(B,A) ) ) ) ),
    file(wellord1,t50_wellord1),
    [interesting(0.00)]).

fof(d9_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( ( v2_wellord1(A)
              & r4_wellord1(A,B) )
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ( C = k3_wellord1(A,B)
                <=> r3_wellord1(A,B,C) ) ) ) ) ) ),
    file(wellord1,d9_wellord1),
    [interesting(0.00)]).

fof(d1_wellord2,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k1_wellord2(A)
      <=> ( k3_relat_1(B) = A
          & ! [C,D] : 
              ( ( r2_hidden(C,A)
                & r2_hidden(D,A) )
             => ( r2_hidden(k4_tarski(C,D),B)
              <=> r1_tarski(C,D) ) ) ) ) ) ),
    file(wellord2,d1_wellord2),
    [interesting(0.00)]).

fof(t60_card_2,theorem,(
    ! [A] : 
      ( k1_card_1(A) = 1
    <=> ? [B] : A = k1_tarski(B) ) ),
    file(card_2,t60_card_2),
    [interesting(0.00)]).

fof(t26_finset_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_finset_1(k1_relat_1(A))
       => v1_finset_1(k2_relat_1(A)) ) ) ),
    file(finset_1,t26_finset_1),
    [interesting(0.00)]).

fof(t180_orders_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => r1_tarski(A,k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))) ) ),
    file(orders_1,t180_orders_1),
    [interesting(0.00)]).

fof(t13_finset_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    [interesting(0.00)]).

fof(t7_card_4,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_finset_1(A)
      <=> r2_hidden(A,k5_ordinal2) ) ) ),
    file(card_4,t7_card_4),
    [interesting(0.00)]).

fof(t66_card_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => A = k1_card_1(A) ) ),
    file(card_1,t66_card_1),
    [interesting(0.00)]).

fof(t1_card_5,theorem,
    ( 1 = k1_tarski(0)
    & 2 = k2_tarski(0,1) ),
    file(card_5,t1_card_5),
    [interesting(0.00)]).

fof(t19_ami_1,theorem,(
    ! [A,B] : k3_cqc_lang(A,B) = k1_tarski(k4_tarski(A,B)) ),
    file(ami_1,t19_ami_1),
    [interesting(0.00)]).

fof(t20_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k2_relat_1(C)) ) ) ) ),
    file(relat_1,t20_relat_1),
    [interesting(0.00)]).

fof(d4_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( B = k1_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) ) ),
    file(relat_1,d4_relat_1),
    [interesting(0.00)]).

fof(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_1),
    [interesting(0.00)]).

fof(d4_amistd_3,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
             => ! [D] : 
                  ( m1_ordinal1(D,u2_ami_1(A,B))
                 => ( D = k4_amistd_3(A,B,C)
                  <=> ( k1_relat_1(D) = k1_card_1(C)
                      & ! [E] : 
                          ( r2_hidden(E,k1_card_1(C))
                         => k1_funct_1(D,E) = k5_amistd_1(A,B,k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k3_amistd_3(A,B,C)))),k1_wellord2(k3_amistd_3(A,B,C))),E)) ) ) ) ) ) ) ) ),
    file(amistd_3,d4_amistd_3),
    [interesting(0.00)]).

fof(t50_card_1,theorem,(
    ! [A] : k1_card_1(k1_tarski(A)) = k4_ordinal2 ),
    file(card_1,t50_card_1),
    [interesting(0.00)]).

fof(t20_card_2,theorem,(
    1 = k4_ordinal2 ),
    file(card_2,t20_card_2),
    [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(d13_amistd_2,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => k6_amistd_2(A,B) = k14_ami_3(A,B,k5_amistd_1(A,B,0),k5_ami_1(A,B)) ) ) ),
    file(amistd_2,d13_amistd_2),
    [interesting(0.00)]).

fof(d5_amistd_3,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v3_trees_2(D)
                    & m3_trees_2(D,u2_ami_1(A,B)) )
                 => ( D = k5_amistd_3(A,B,C)
                  <=> ( k1_funct_1(D,k1_xboole_0) = k2_amistd_3(A,B,C)
                      & ! [E] : 
                          ( m1_trees_1(E,k1_relat_1(D))
                         => ( k1_trees_2(k1_relat_1(D),E) = a_5_0_amistd_3(A,B,C,D,E)
                            & ! [F] : 
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ( r2_hidden(F,k1_card_1(k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E)))))
                                 => k1_funct_1(D,k8_finseq_1(k5_numbers,E,k12_finseq_1(k5_numbers,F))) = k1_funct_1(k4_amistd_3(A,B,k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E)))),F) ) ) ) ) ) ) ) ) ) ) ),
    file(amistd_3,d5_amistd_3),
    [interesting(0.00)]).

fof(t15_amistd_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ( v3_ami_1(D,A,B)
                   => k1_amistd_1(A,B,C,D) = k1_struct_0(B,C) ) ) ) ) ) ),
    file(amistd_1,t15_amistd_1),
    [interesting(0.00)]).

fof(d5_ami_5,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r2_hidden(D,k1_relat_1(C))
                   => k5_ami_5(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) ) ),
    file(ami_5,d5_ami_5),
    [interesting(0.00)]).

fof(t14_trees_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),k1_trees_2(A,B))
              <=> r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A) ) ) ) ) ),
    file(trees_2,t14_trees_2),
    [interesting(0.00)]).

fof(s1_hilbert2,theorem,
    ( ( p1_s1_hilbert2(k6_finseq_1(k5_numbers))
      & ! [A] : 
          ( m1_trees_1(A,f1_s1_hilbert2)
         => ( p1_s1_hilbert2(A)
           => ! [B] : 
                ( m2_subset_1(B,k1_numbers,k5_numbers)
               => ( r2_hidden(k8_finseq_1(k5_numbers,A,k12_finseq_1(k5_numbers,B)),f1_s1_hilbert2)
                 => p1_s1_hilbert2(k8_finseq_1(k5_numbers,A,k12_finseq_1(k5_numbers,B))) ) ) ) ) )
   => ! [A] : 
        ( m1_trees_1(A,f1_s1_hilbert2)
       => p1_s1_hilbert2(A) ) ),
    file(hilbert2,s1_hilbert2),
    [interesting(0.00)]).

fof(t17_qc_lang4,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => k2_trees_2(A,0) = k1_tarski(k1_xboole_0) ) ),
    file(qc_lang4,t17_qc_lang4),
    [interesting(0.00)]).

fof(d6_trees_2,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_trees_2(A,B) = a_2_0_trees_2(A,B) ) ) ),
    file(trees_2,d6_trees_2),
    [interesting(0.00)]).

fof(t88_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k7_relat_1(B,A),B) ) ),
    file(relat_1,t88_relat_1),
    [interesting(0.00)]).

fof(t45_trees_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r2_hidden(B,A)
                  & r1_tarski(C,B) )
               => r2_hidden(C,A) ) ) ) ) ),
    file(trees_1,t45_trees_1),
    [interesting(0.00)]).

fof(t29_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    [interesting(0.00)]).

fof(t7_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r1_xreal_0(A,B)
          <=> r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) ),
    file(finseq_1,t7_finseq_1),
    [interesting(0.00)]).

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    [interesting(0.00)]).

fof(t91_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    [interesting(0.00)]).

fof(t61_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ( k3_finseq_1(A) = k2_xcmplx_0(C,1)
                  & B = k7_relat_1(A,k2_finseq_1(C)) )
               => A = k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,1)))) ) ) ) ) ),
    file(finseq_3,t61_finseq_3),
    [interesting(0.00)]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    file(finseq_1,t3_finseq_1),
    [interesting(0.00)]).

fof(t72_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    [interesting(0.00)]).

fof(t70_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( r2_hidden(B,k2_finseq_1(A))
         => k1_funct_1(k2_finseq_2(A,C),B) = C ) ) ),
    file(finseq_2,t70_finseq_2),
    [interesting(0.00)]).

fof(t20_finseq_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D) )
         => ( k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B))
           => ( C = D
              & A = B ) ) ) ) ),
    file(finseq_2,t20_finseq_2),
    [interesting(0.00)]).

fof(t8_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,1)))
              & ~ r2_hidden(A,k2_finseq_1(B))
              & A != k1_nat_1(B,1) ) ) ) ),
    file(finseq_2,t8_finseq_2),
    [interesting(0.00)]).

fof(t18_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,C)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t18_finseq_1),
    [interesting(0.00)]).

fof(t72_finseq_2,theorem,(
    ! [A] : k2_finseq_2(0,A) = k1_xboole_0 ),
    file(finseq_2,t72_finseq_2),
    [interesting(0.00)]).

fof(t47_trees_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( r2_hidden(k1_xboole_0,A)
        & r2_hidden(k6_finseq_1(k5_numbers),A) ) ) ),
    file(trees_1,t47_trees_1),
    [interesting(0.00)]).

fof(t74_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : k2_finseq_2(k1_nat_1(A,1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) ) ),
    file(finseq_2,t74_finseq_2),
    [interesting(0.00)]).

fof(s1_nat_1,theorem,
    ( ( p1_s1_nat_1(0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( p1_s1_nat_1(A)
           => p1_s1_nat_1(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => p1_s1_nat_1(A) ) ),
    file(nat_1,s1_nat_1),
    [interesting(0.00)]).

fof(t16_trees_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => A = k3_tarski(a_1_0_trees_2(A)) ) ),
    file(trees_2,t16_trees_2),
    [interesting(0.00)]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.00)]).

fof(t7_trees_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( ! [C] : 
                ( m2_finseq_1(C,k5_numbers)
               => ( r2_hidden(C,A)
                <=> r2_hidden(C,B) ) )
           => A = B ) ) ) ),
    file(trees_2,t7_trees_2),
    [interesting(0.00)]).

fof(t17_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ! [C] : 
              ( r2_hidden(C,k1_relat_1(A))
             => k1_funct_1(A,C) = B )
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) ),
    file(funcop_1,t17_funcop_1),
    [interesting(0.00)]).

fof(t14_finset_1,theorem,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,t14_finset_1),
    [interesting(0.00)]).

fof(d6_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_relat_1),
    [interesting(0.00)]).

fof(d1_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
    <=> ! [B] : ~ ( r2_hidden(B,A)
          & ! [C,D] : B != k4_tarski(C,D) ) ) ),
    file(relat_1,d1_relat_1),
    [interesting(0.00)]).

fof(t30_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) ) ) ) ),
    file(relat_1,t30_relat_1),
    [interesting(0.00)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(t54_wellord1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( v2_wellord1(A)
                  & r3_wellord1(A,B,C) )
               => v2_wellord1(B) ) ) ) ) ),
    file(wellord1,t54_wellord1),
    [interesting(0.00)]).