fof(t60_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k3_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l29_ami_3]),
    [file(ami_3,t60_ami_3),interesting(1.00)]).

fof(t61_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k4_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l30_ami_3]),
    [file(ami_3,t61_ami_3),interesting(1.00)]).

fof(t62_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k5_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l31_ami_3]),
    [file(ami_3,t62_ami_3),interesting(1.00)]).

fof(t63_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k6_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l32_ami_3]),
    [file(ami_3,t63_ami_3),interesting(1.00)]).

fof(t64_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k7_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l33_ami_3]),
    [file(ami_3,t64_ami_3),interesting(1.00)]).

fof(l29_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k3_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_ami_3,l27_ami_3]),
    [file(ami_3,l29_ami_3),interesting(0.99)]).

fof(l30_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k4_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_ami_3,l27_ami_3]),
    [file(ami_3,l30_ami_3),interesting(0.99)]).

fof(l31_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k5_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_ami_3,l27_ami_3]),
    [file(ami_3,l31_ami_3),interesting(0.99)]).

fof(l32_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k6_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_ami_3,l27_ami_3]),
    [file(ami_3,l32_ami_3),interesting(0.99)]).

fof(l33_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ~ v3_ami_1(k7_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_ami_3,l27_ami_3]),
    [file(ami_3,l33_ami_3),interesting(0.99)]).

fof(t66_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ~ v3_ami_1(k9_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l35_ami_3]),
    [file(ami_3,t66_ami_3),interesting(0.94)]).

fof(l36_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ~ v3_ami_1(k10_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,d15_ami_2,t37_zfmisc_1,t18_card_3,d1_funct_4,d1_funct_2,t5_cqc_lang,t12_xboole_1,d1_funct_2,t7_ami_2,d1_tarski,t12_funct_4,t18_card_3,t18_card_3,t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,t10_gr_cy_1,d2_ami_3,t5_ami_3,d6_ami_2,d8_ami_1,t25_ami_2,t15_ami_3,d11_ami_3,d15_ami_2,t3_xcmplx_1,d14_ami_2,d7_ami_2,t25_ami_2,d16_ami_2,t7_ami_3,d8_ami_1,t3_xcmplx_1]),
    [file(ami_3,l36_ami_3),interesting(0.94)]).

fof(t67_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ~ v3_ami_1(k10_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l36_ami_3]),
    [file(ami_3,t67_ami_3),interesting(0.94)]).

fof(l35_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ~ v3_ami_1(k9_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,d15_ami_2,t37_zfmisc_1,t18_card_3,d1_funct_4,d1_funct_2,t5_cqc_lang,t12_xboole_1,d1_funct_2,t7_ami_2,d1_tarski,t12_funct_4,t18_card_3,t18_card_3,t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,t10_gr_cy_1,d2_ami_3,t5_ami_3,d6_ami_2,d8_ami_1,t25_ami_2,t14_ami_3,d11_ami_3,d15_ami_2,t3_xcmplx_1,d1_cqc_lang,d7_ami_2,t25_ami_2,d16_ami_2,t7_ami_3,d8_ami_1,t3_xcmplx_1]),
    [file(ami_3,l35_ami_3),interesting(0.93)]).

fof(l39_ami_3,theorem,(
    k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) = k4_tarski(0,k1_xboole_0) ),
    inference(mizar_proof,[status(thm)],[t2_ami_2,l28_ami_3,l38_ami_3]),
    [file(ami_3,l39_ami_3),interesting(0.91)]).

fof(t71_ami_3,theorem,(
    k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) = k4_tarski(0,k1_xboole_0) ),
    inference(mizar_proof,[status(thm)],[l39_ami_3]),
    [file(ami_3,t71_ami_3),interesting(0.90)]).

fof(t56_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => k15_ami_3(A) != k16_ami_3(B) ) ) ),
    inference(mizar_proof,[status(thm)],[t42_int_1,t35_int_1,t40_int_1,t18_ami_3,t36_int_1,d3_int_1,t22_int_1,t32_int_1]),
    [file(ami_3,t56_ami_3),interesting(0.83)]).

fof(l34_ami_3,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ~ v3_ami_1(k8_ami_3(A),k1_tarski(k4_numbers),k1_ami_3) ) ),
    inference(mizar_proof,[status(thm)],[t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,d15_ami_2,t37_zfmisc_1,t18_card_3,d1_funct_4,d1_funct_2,t5_cqc_lang,t12_xboole_1,d1_funct_2,t7_ami_2,d1_tarski,t12_funct_4,t18_card_3,t18_card_3,t5_cqc_lang,d1_tarski,t14_funct_4,t6_cqc_lang,t10_gr_cy_1,d7_ami_2,t24_ami_2,d16_ami_2,t7_ami_3,d8_ami_1,t3_xcmplx_1]),
    [file(ami_3,l34_ami_3),interesting(0.80)]).

fof(t65_ami_3,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ~ v3_ami_1(k8_ami_3(A),k1_tarski(k4_numbers),k1_ami_3) ) ),
    inference(mizar_proof,[status(thm)],[l34_ami_3]),
    [file(ami_3,t65_ami_3),interesting(0.78)]).

fof(t37_ami_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( l1_ami_1(B,A)
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => r1_tarski(k1_relat_1(C),u1_struct_0(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_ami_1,d1_funct_2]),
    [file(ami_3,t37_ami_3),interesting(0.72)]).

fof(t18_ami_3,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => r1_int_1(k3_xcmplx_0(A,B),0,A) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_int_1]),
    [file(ami_3,t18_ami_3),interesting(0.71)]).

fof(t36_ami_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => k1_relat_1(C) = u1_struct_0(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_card_3,d1_funct_2]),
    [file(ami_3,t36_ami_3),interesting(0.69)]).

fof(t1_ami_3,theorem,(
    v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ),
    inference(mizar_proof,[status(thm)],[d12_ami_1,d3_tarski,t46_funct_2,t46_funct_2,d1_tarski,t9_ami_2,t19_nat_1,d3_ami_2]),
    [file(ami_3,t1_ami_3),interesting(0.66)]).

fof(t27_ami_3,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & k1_funct_1(C,A) = B )
       => r1_tarski(k3_cqc_lang(A,B),C) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_funct_1,t37_zfmisc_1,t19_ami_1]),
    [file(ami_3,t27_ami_3),interesting(0.66)]).

fof(t51_ami_3,theorem,(
    v10_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ),
    inference(mizar_proof,[status(thm)],[d21_ami_1,t6_ami_2]),
    [file(ami_3,t51_ami_3),interesting(0.66)]).

fof(t54_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k11_ami_3(k16_ami_3(A)) = k16_ami_3(k2_xcmplx_0(A,1)) ) ),
    inference(mizar_proof,[status(thm)],[t6_ami_3,d15_ami_2]),
    [file(ami_3,t54_ami_3),interesting(0.65)]).

fof(t2_ami_3,theorem,(
    v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ),
    inference(mizar_proof,[status(thm)],[d14_ami_1,t11_ami_2]),
    [file(ami_3,t2_ami_3),interesting(0.64)]).

fof(t35_ami_3,theorem,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( ( v1_ami_3(C,A,B)
            & m1_ami_1(C,A,B) )
         => ! [D] : 
              ( ( v1_ami_3(D,A,B)
                & m1_ami_1(D,A,B) )
             => v1_ami_3(k17_ami_1(A,B,C,D),A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_ami_3,d1_funct_4,t8_xboole_1,d13_ami_3]),
    [file(ami_3,t35_ami_3),interesting(0.64)]).

fof(t52_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( A != B
              & k15_ami_3(A) = k15_ami_3(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xcmplx_1]),
    [file(ami_3,t52_ami_3),interesting(0.64)]).

fof(t53_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( A != B
              & k16_ami_3(A) = k16_ami_3(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_xcmplx_1]),
    [file(ami_3,t53_ami_3),interesting(0.64)]).

fof(t31_ami_3,theorem,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => r2_hidden(C,k14_ami_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_ami_1]),
    [file(ami_3,t31_ami_3),interesting(0.63)]).

fof(t39_ami_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ? [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                  & r1_tarski(C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_ami_1,t26_funct_4]),
    [file(ami_3,t39_ami_3),interesting(0.63)]).

fof(t6_ami_3,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => ( B = A
           => k15_ami_2(B) = k11_ami_3(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_ami_3]),
    [file(ami_3,t6_ami_3),interesting(0.61)]).

fof(t29_ami_3,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_1(E)
        & v1_funct_1(E) )
     => ( ( r2_hidden(A,k1_relat_1(E))
          & r2_hidden(C,k1_relat_1(E))
          & k1_funct_1(E,A) = B
          & k1_funct_1(E,C) = D )
       => r1_tarski(k4_funct_4(A,C,B,D),E) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_funct_1,t38_zfmisc_1,t71_funct_4,t20_ami_1,t27_ami_3]),
    [file(ami_3,t29_ami_3),interesting(0.60)]).

fof(t55_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => k3_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k4_numbers ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_ami_2]),
    [file(ami_3,t55_ami_3),interesting(0.59)]).

fof(l28_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ( A = k4_tarski(0,k1_xboole_0)
       => v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_ami_1,t7_mcart_1,t7_mcart_1,t38_finseq_3,t7_mcart_1,t4_trees_1,t7_mcart_1,t38_finseq_3,t7_ami_3,d16_ami_2]),
    [file(ami_3,l28_ami_3),interesting(0.59)]).

fof(t32_ami_3,theorem,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m2_subset_1(C,k7_ami_1(u5_ami_1(A,B)),k14_ami_1(A,B))
         => m1_ami_1(C,A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_ami_1]),
    [file(ami_3,t32_ami_3),interesting(0.58)]).

fof(t8_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),A) = k2_ami_3(C,B)
                & ! [D] : 
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_gr_cy_1,t5_ami_3,t7_ami_3,d16_ami_2,t23_ami_2,t16_ami_2,t6_ami_3,t17_ami_2,t20_ami_2,d2_ami_3,t17_ami_2,t21_ami_2]),
    [file(ami_3,t8_ami_3),interesting(0.58)]).

fof(t19_ami_3,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,B) )
                 => ( ! [E] : 
                        ( m1_subset_1(E,A)
                       => ! [F] : 
                            ( m1_subset_1(F,B)
                           => ( r2_hidden(k4_tarski(E,F),C)
                            <=> r2_hidden(k4_tarski(E,F),D) ) ) )
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,t8_funct_1,t27_partfun1,t8_funct_1,t8_funct_1,t27_partfun1,t8_funct_1,t8_subset_1,t8_funct_1,t27_partfun1,t8_funct_1,t34_partfun1]),
    [file(ami_3,t19_ami_3),interesting(0.57)]).

fof(l46_ami_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r1_xboole_0(B,k1_relat_1(A))
         => k7_relat_1(A,B) = k1_xboole_0 ) ) ),
    inference(mizar_proof,[status(thm)],[t95_relat_1]),
    [file(ami_3,l46_ami_3),interesting(0.57)]).

fof(t46_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( v1_setfam_1(C)
             => ( r1_xreal_0(A,B)
               => ! [D] : 
                    ( ( ~ v3_struct_0(D)
                      & ~ v2_ami_1(D,C)
                      & v4_ami_1(D,C)
                      & v5_ami_1(D,C)
                      & v7_ami_1(D,C)
                      & v8_ami_1(D,C)
                      & l1_ami_1(D,C) )
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
                       => ( r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)))
                         => k11_ami_1(C,D,k10_ami_1(C,D,E),B) = k11_ami_1(C,D,k10_ami_1(C,D,E),A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_ami_3,t44_ami_3,t44_ami_3]),
    [file(ami_3,t46_ami_3),interesting(0.57)]).

fof(t9_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),A) = k2_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] : 
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_gr_cy_1,t5_ami_3,t7_ami_3,d16_ami_2,t23_ami_2,t16_ami_2,t6_ami_3,t17_ami_2,t20_ami_2,d2_ami_3,t17_ami_2,t21_ami_2]),
    [file(ami_3,t9_ami_3),interesting(0.56)]).

fof(t10_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),A) = k6_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] : 
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_gr_cy_1,t5_ami_3,t7_ami_3,d16_ami_2,t23_ami_2,t16_ami_2,t6_ami_3,t17_ami_2,t20_ami_2,d2_ami_3,t17_ami_2,t21_ami_2]),
    [file(ami_3,t10_ami_3),interesting(0.56)]).

fof(t11_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),A) = k3_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] : 
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_gr_cy_1,t5_ami_3,t7_ami_3,d16_ami_2,t23_ami_2,t16_ami_2,t6_ami_3,t17_ami_2,t20_ami_2,d2_ami_3,t17_ami_2,t21_ami_2]),
    [file(ami_3,t11_ami_3),interesting(0.55)]).

fof(l45_ami_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k7_relat_1(A,k1_tarski(B)) = k1_tarski(k4_tarski(B,k1_funct_1(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[t89_grfunc_1]),
    [file(ami_3,l45_ami_3),interesting(0.53)]).

fof(t44_ami_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)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)))
                   => k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t40_ami_3,t42_ami_3]),
    [file(ami_3,t44_ami_3),interesting(0.53)]).

fof(t59_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ( A = k4_tarski(0,k1_xboole_0)
       => v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l28_ami_3]),
    [file(ami_3,t59_ami_3),interesting(0.53)]).

fof(t40_ami_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)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( v9_ami_1(C,A,B)
              <=> ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d20_ami_1,t54_ami_1,d15_ami_3,d20_ami_1,t54_ami_1,d15_ami_3]),
    [file(ami_3,t40_ami_3),interesting(0.49)]).

fof(t50_ami_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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => k1_funct_1(k12_ami_3(A,B,C),k2_ami_1(A,B)) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_cqc_lang]),
    [file(ami_3,t50_ami_3),interesting(0.49)]).

fof(t13_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = B
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(B),C),A) = k2_ami_3(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_gr_cy_1,t7_ami_3,d16_ami_2,t24_ami_2,t16_ami_2,d2_ami_3,t17_ami_2]),
    [file(ami_3,t13_ami_3),interesting(0.48)]).

fof(t12_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & ( A != B
                 => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),A) = k5_int_1(k2_ami_3(C,A),k2_ami_3(C,B)) )
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),B) = k6_int_1(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] : 
                    ( m1_ami_3(D)
                   => ~ ( D != A
                        & D != B
                        & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),D) != k2_ami_3(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_gr_cy_1,t5_ami_3,t7_ami_3,d16_ami_2,t23_ami_2,t16_ami_2,t6_ami_3,t17_ami_2,t21_ami_2,t20_ami_2,t17_ami_2,t20_ami_2,d2_ami_3,t17_ami_2,t21_ami_2,t21_ami_2]),
    [file(ami_3,t12_ami_3),interesting(0.48)]).

fof(t34_ami_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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => k1_relat_1(k12_ami_3(A,B,C)) = k1_struct_0(B,k2_ami_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1]),
    [file(ami_3,t34_ami_3),interesting(0.47)]).

fof(t14_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
                 => ( ( k2_ami_3(D,A) = 0
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = C )
                    & ( k2_ami_3(D,A) != 0
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,D)) )
                    & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),B) = k2_ami_3(D,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_gr_cy_1,t5_ami_3,t7_ami_3,d16_ami_2,t25_ami_2,t16_ami_2,d1_cqc_lang,t25_ami_2,t25_ami_2,t16_ami_2,d1_cqc_lang,t6_ami_3,d2_ami_3,t17_ami_2]),
    [file(ami_3,t14_ami_3),interesting(0.47)]).

fof(t43_ami_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( ( v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_tarski(D,C)
                      <=> r1_tarski(D,k11_ami_1(A,B,k10_ami_1(A,B,C),E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_ami_3,t37_ami_3,d13_ami_3,t54_ami_1,t54_ami_1,t8_grfunc_1]),
    [file(ami_3,t43_ami_3),interesting(0.46)]).

fof(t15_ami_3,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
                 => ( ( ~ r1_xreal_0(k2_ami_3(D,A),0)
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = C )
                    & ( r1_xreal_0(k2_ami_3(D,A),0)
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,D)) )
                    & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),B) = k2_ami_3(D,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,t10_gr_cy_1,t5_ami_3,t7_ami_3,d16_ami_2,t25_ami_2,t16_ami_2,d14_ami_2,t25_ami_2,t25_ami_2,t16_ami_2,d14_ami_2,t6_ami_3,d2_ami_3,t17_ami_2]),
    [file(ami_3,t15_ami_3),interesting(0.46)]).

fof(t38_ami_3,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => ( r1_tarski(C,D)
                   => ! [E] : 
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => r1_tarski(C,k11_ami_1(A,B,k10_ami_1(A,B,D),E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_ami_3,t36_ami_3,t8_grfunc_1,d13_ami_3,t54_ami_1,t8_grfunc_1,t8_grfunc_1]),
    [file(ami_3,t38_ami_3),interesting(0.45)]).

fof(t45_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( v1_setfam_1(C)
             => ( r1_xreal_0(A,B)
               => ! [D] : 
                    ( ( ~ v3_struct_0(D)
                      & ~ v2_ami_1(D,C)
                      & v4_ami_1(D,C)
                      & v5_ami_1(D,C)
                      & v7_ami_1(D,C)
                      & v8_ami_1(D,C)
                      & l1_ami_1(D,C) )
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
                       => ( r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)))
                         => r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),B))) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_ami_3,t54_ami_1,t52_ami_1,d15_ami_3]),
    [file(ami_3,t45_ami_3),interesting(0.45)]).

fof(t42_ami_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)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v9_ami_1(C,A,B)
                   => ( k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D)
                    <=> r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d22_ami_1,t54_ami_1,d15_ami_3,d15_ami_3,t54_ami_1,d22_ami_1]),
    [file(ami_3,t42_ami_3),interesting(0.43)]).

fof(t7_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] : 
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ! [C] : 
              ( m1_subset_1(C,k4_ami_2)
             => ( C = A
               => ! [D] : 
                    ( m1_subset_1(D,k4_card_3(k5_ami_2))
                   => ( D = B
                     => k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B) = k16_ami_2(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_ami_2]),
    [file(ami_3,t7_ami_3),interesting(0.38)]).

fof(l85_ami_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] : 
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ! [C] : 
              ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,B,A),C) = k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_ami_2,d2_xboole_0,d2_xboole_0,d17_ami_2,d1_tarski,t7_mcart_1,t7_mcart_1,t38_finseq_3,t7_mcart_1,t4_trees_1,t7_mcart_1,t38_finseq_3,d16_ami_2,d16_ami_2,t18_ami_2,d16_ami_2,t18_ami_2,d16_ami_2,t18_ami_2,d2_tarski,d16_ami_2,t18_ami_2,t22_ami_2,d16_ami_2,t18_ami_2,t22_ami_2,d16_ami_2,t18_ami_2,t22_ami_2,d16_ami_2,t18_ami_2,t22_ami_2,d16_ami_2,t18_ami_2,t22_ami_2,t22_ami_2,d3_enumset1,d2_xboole_0]),
    [file(ami_3,l85_ami_3),interesting(0.30)]).

fof(t58_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ~ ( ? [B] : 
              ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
              & k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)) )
          & v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l27_ami_3]),
    [file(ami_3,t58_ami_3),interesting(0.18)]).

fof(d4_ami_2,definition,(
    k4_ami_2 = k2_xboole_0(k2_xboole_0(k2_xboole_0(k1_tarski(k4_tarski(k1_ami_2,k1_xboole_0)),a_0_2_ami_2),a_0_3_ami_2),a_0_4_ami_2) ),
    file(ami_2,d4_ami_2),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.00)]).

fof(d17_ami_2,definition,(
    ! [A] : 
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2)))
        & m2_relset_1(A,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) )
     => ( A = k17_ami_2
      <=> ! [B] : 
            ( m2_subset_1(B,k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
           => ! [C] : 
                ( m1_subset_1(C,k4_card_3(k5_ami_2))
               => k8_funct_2(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2),k1_cat_2(k4_ami_2,k4_card_3(k5_ami_2),k4_card_3(k5_ami_2),k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2)),A,B),C) = k16_ami_2(B,C) ) ) ) ) ),
    file(ami_2,d17_ami_2),
    [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(t7_mcart_1,theorem,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    [interesting(0.00)]).

fof(t38_finseq_3,theorem,(
    ! [A,B] : k1_xboole_0 != k10_finseq_1(A,B) ),
    file(finseq_3,t38_finseq_3),
    [interesting(0.00)]).

fof(t4_trees_1,theorem,(
    ! [A] : k1_xboole_0 != k9_finseq_1(A) ),
    file(trees_1,t4_trees_1),
    [interesting(0.00)]).

fof(d16_ami_2,definition,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
     => ! [B] : 
          ( m1_subset_1(B,k4_card_3(k5_ami_2))
         => ( ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k2_ami_2)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_numbers,k2_ami_2)
                      & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),1,k2_finseq_4(k2_ami_2,C,D)) ) )
             => k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k1_funct_1(B,k10_ami_2(A))),k15_ami_2(k6_ami_2(B))) )
            & ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k2_ami_2)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_numbers,k2_ami_2)
                      & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),2,k2_finseq_4(k2_ami_2,C,D)) ) )
             => k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k2_xcmplx_0(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
            & ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k2_ami_2)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_numbers,k2_ami_2)
                      & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),3,k2_finseq_4(k2_ami_2,C,D)) ) )
             => k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k6_xcmplx_0(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
            & ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k2_ami_2)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_numbers,k2_ami_2)
                      & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),4,k2_finseq_4(k2_ami_2,C,D)) ) )
             => k16_ami_2(A,B) = k7_ami_2(k8_ami_2(B,k9_ami_2(A),k3_xcmplx_0(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
            & ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k2_ami_2)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_numbers,k2_ami_2)
                      & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),5,k2_finseq_4(k2_ami_2,C,D)) ) )
             => k16_ami_2(A,B) = k7_ami_2(k8_ami_2(k8_ami_2(B,k9_ami_2(A),k5_int_1(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k10_ami_2(A),k6_int_1(k1_funct_1(B,k9_ami_2(A)),k1_funct_1(B,k10_ami_2(A)))),k15_ami_2(k6_ami_2(B))) )
            & ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k3_ami_2)
                  & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),6,k12_finseq_1(k3_ami_2,C)) )
             => k16_ami_2(A,B) = k7_ami_2(B,k11_ami_2(A)) )
            & ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k3_ami_2)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_numbers,k2_ami_2)
                      & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),7,k2_finseq_4(k5_numbers,C,D)) ) )
             => k16_ami_2(A,B) = k7_ami_2(B,k2_cqc_lang(k3_ami_2,k1_funct_1(B,k13_ami_2(A)),0,k12_ami_2(A),k15_ami_2(k6_ami_2(B)))) )
            & ( ? [C] : 
                  ( m2_subset_1(C,k5_numbers,k3_ami_2)
                  & ? [D] : 
                      ( m2_subset_1(D,k5_numbers,k2_ami_2)
                      & A = k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),8,k2_finseq_4(k5_numbers,C,D)) ) )
             => k16_ami_2(A,B) = k7_ami_2(B,k14_ami_2(k3_ami_2,k1_funct_1(B,k13_ami_2(A)),0,k12_ami_2(A),k15_ami_2(k6_ami_2(B)))) )
            & ( ( ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k2_ami_2)
                   => ! [D] : 
                        ( m2_subset_1(D,k5_numbers,k2_ami_2)
                       => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),1,k2_finseq_4(k2_ami_2,C,D)) ) )
                & ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k2_ami_2)
                   => ! [D] : 
                        ( m2_subset_1(D,k5_numbers,k2_ami_2)
                       => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),2,k2_finseq_4(k2_ami_2,C,D)) ) )
                & ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k2_ami_2)
                   => ! [D] : 
                        ( m2_subset_1(D,k5_numbers,k2_ami_2)
                       => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),3,k2_finseq_4(k2_ami_2,C,D)) ) )
                & ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k2_ami_2)
                   => ! [D] : 
                        ( m2_subset_1(D,k5_numbers,k2_ami_2)
                       => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),4,k2_finseq_4(k2_ami_2,C,D)) ) )
                & ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k2_ami_2)
                   => ! [D] : 
                        ( m2_subset_1(D,k5_numbers,k2_ami_2)
                       => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),5,k2_finseq_4(k2_ami_2,C,D)) ) )
                & ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k3_ami_2)
                   => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),6,k12_finseq_1(k3_ami_2,C)) )
                & ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k3_ami_2)
                   => ! [D] : 
                        ( m2_subset_1(D,k5_numbers,k2_ami_2)
                       => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),7,k2_finseq_4(k5_numbers,C,D)) ) )
                & ! [C] : 
                    ( m2_subset_1(C,k5_numbers,k3_ami_2)
                   => ! [D] : 
                        ( m2_subset_1(D,k5_numbers,k2_ami_2)
                       => A != k1_domain_1(k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),8,k2_finseq_4(k5_numbers,C,D)) ) ) )
             => k16_ami_2(A,B) = B ) ) ) ) ),
    file(ami_2,d16_ami_2),
    [interesting(0.00)]).

fof(t18_ami_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k3_ami_2)
             => k1_funct_1(k7_ami_2(A,B),C) = k1_funct_1(A,C) ) ) ) ),
    file(ami_2,t18_ami_2),
    [interesting(0.00)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.00)]).

fof(t22_ami_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k2_ami_2)
         => ! [C] : 
              ( v1_int_1(C)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k3_ami_2)
                 => k1_funct_1(k8_ami_2(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ),
    file(ami_2,t22_ami_2),
    [interesting(0.00)]).

fof(d3_enumset1,definition,(
    ! [A,B,C,D,E,F] : 
      ( F = k3_enumset1(A,B,C,D,E)
    <=> ! [G] : 
          ( r2_hidden(G,F)
        <=> ~ ( G != A
              & G != B
              & G != C
              & G != D
              & G != E ) ) ) ),
    file(enumset1,d3_enumset1),
    [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(t47_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(A,0)
           => B = k2_xcmplx_0(k3_xcmplx_0(A,k3_nat_1(B,A)),k4_nat_1(B,A)) ) ) ) ),
    file(nat_1,t47_nat_1),
    [interesting(0.00)]).

fof(t46_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(A,k4_nat_1(B,A)) ) ) ) ),
    file(nat_1,t46_nat_1),
    [interesting(0.00)]).

fof(s1_ami_3,theorem,
    ( ( p1_s1_ami_3(0)
      & ~ r1_xreal_0(f1_s1_ami_3,0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ( p1_s1_ami_3(k2_nat_1(f1_s1_ami_3,A))
                  & r1_xreal_0(B,f1_s1_ami_3) )
               => ( B = 0
                  | p1_s1_ami_3(k1_nat_1(k2_nat_1(f1_s1_ami_3,A),B)) ) ) ) ) )
   => p1_s1_ami_3(f2_s1_ami_3) ),
    inference(mizar_proof,[status(thm)],[s1_nat_1,t47_nat_1,t47_nat_1,t46_nat_1]),
    [file(ami_3,s1_ami_3),interesting(0.00)]).

fof(d24_ami_1,definition,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_subset_1(C,k7_ami_1(u5_ami_1(A,B)))
         => ( m1_ami_1(C,A,B)
          <=> v1_finset_1(C) ) ) ) ),
    file(ami_1,d24_ami_1),
    [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(t8_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(k4_tarski(A,B),C)
      <=> ( r2_hidden(A,k1_relat_1(C))
          & B = k1_funct_1(C,A) ) ) ) ),
    file(funct_1,t8_funct_1),
    [interesting(0.00)]).

fof(t27_partfun1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,k4_relset_1(A,B,D))
       => r2_hidden(k1_funct_1(D,C),B) ) ) ),
    file(partfun1,t27_partfun1),
    [interesting(0.00)]).

fof(t8_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ( r2_hidden(D,B)
                <=> r2_hidden(D,C) ) )
           => B = C ) ) ) ),
    file(subset_1,t8_subset_1),
    [interesting(0.00)]).

fof(t34_partfun1,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & m2_relset_1(D,A,B) )
         => ( ( k4_relset_1(A,B,C) = k4_relset_1(A,B,D)
              & ! [E] : 
                  ( m1_subset_1(E,A)
                 => ( r2_hidden(E,k4_relset_1(A,B,C))
                   => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) )
           => C = D ) ) ) ),
    file(partfun1,t34_partfun1),
    [interesting(0.00)]).

fof(t33_ami_3,theorem,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & m2_relset_1(D,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( ! [E] : 
                    ( m1_ami_1(E,A,B)
                   => ! [F] : 
                        ( m1_ami_1(F,A,B)
                       => ( r2_hidden(k4_tarski(E,F),C)
                        <=> r2_hidden(k4_tarski(E,F),D) ) ) )
               => C = D ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t32_ami_3,t19_ami_3]),
    [file(ami_3,t33_ami_3),interesting(0.00)]).

fof(s2_ami_3,theorem,
    ( ( ! [A] : 
          ( m1_ami_1(A,f1_s2_ami_3,f2_s2_ami_3)
         => ! [B] : 
              ( m1_ami_1(B,f1_s2_ami_3,f2_s2_ami_3)
             => ( r2_hidden(k4_tarski(A,B),f3_s2_ami_3)
              <=> p1_s2_ami_3(A,B) ) ) )
      & ! [A] : 
          ( m1_ami_1(A,f1_s2_ami_3,f2_s2_ami_3)
         => ! [B] : 
              ( m1_ami_1(B,f1_s2_ami_3,f2_s2_ami_3)
             => ( r2_hidden(k4_tarski(A,B),f4_s2_ami_3)
              <=> p1_s2_ami_3(A,B) ) ) ) )
   => f3_s2_ami_3 = f4_s2_ami_3 ),
    inference(mizar_proof,[status(thm)],[t33_ami_3]),
    [file(ami_3,s2_ami_3),interesting(0.00)]).

fof(t10_gr_cy_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(A,0)
           => ( r2_hidden(B,k1_gr_cy_1(A))
            <=> ~ r1_xreal_0(A,B) ) ) ) ) ),
    file(gr_cy_1,t10_gr_cy_1),
    [interesting(0.00)]).

fof(t24_ami_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k1_gr_cy_1(9))
             => ( A = k1_domain_1(k1_gr_cy_1(9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k3_ami_2)),C,k12_finseq_1(k3_ami_2,B))
               => k11_ami_2(A) = B ) ) ) ) ),
    file(ami_2,t24_ami_2),
    [interesting(0.00)]).

fof(t16_ami_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => k1_funct_1(k7_ami_2(A,B),0) = B ) ) ),
    file(ami_2,t16_ami_2),
    [interesting(0.00)]).

fof(d2_ami_3,definition,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(k1_ami_3))
     => ( m1_ami_3(A)
      <=> r2_hidden(A,k2_ami_2) ) ) ),
    file(ami_3,d2_ami_3),
    [interesting(0.00)]).

fof(t17_ami_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k2_ami_2)
             => k1_funct_1(k7_ami_2(A,B),C) = k1_funct_1(A,C) ) ) ) ),
    file(ami_2,t17_ami_2),
    [interesting(0.00)]).

fof(t16_ami_3,theorem,(
    $true ),
    file(ami_3,t16_ami_3),
    [interesting(0.00)]).

fof(t17_ami_3,theorem,(
    $true ),
    file(ami_3,t17_ami_3),
    [interesting(0.00)]).

fof(d12_ami_1,definition,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v6_ami_1(B,A)
      <=> r1_tarski(k3_funct_2(u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))),u5_ami_1(A,B),k1_tarski(u4_ami_1(A,B))),u2_ami_1(A,B)) ) ) ),
    file(ami_1,d12_ami_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(t46_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( r2_hidden(E,k10_relat_1(D,C))
          <=> ( r2_hidden(E,A)
              & r2_hidden(k1_funct_1(D,E),C) ) ) ) ) ),
    file(funct_2,t46_funct_2),
    [interesting(0.00)]).

fof(t9_ami_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_ami_2
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & A = k1_nat_1(k2_nat_1(2,B),2) ) ) ) ),
    file(ami_2,t9_ami_2),
    [interesting(0.00)]).

fof(t19_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( 0 != A
          & r1_xreal_0(A,0) ) ) ),
    file(nat_1,t19_nat_1),
    [interesting(0.00)]).

fof(d3_ami_2,definition,(
    k3_ami_2 = a_0_1_ami_2 ),
    file(ami_2,d3_ami_2),
    [interesting(0.00)]).

fof(t20_ami_3,theorem,(
    $true ),
    file(ami_3,t20_ami_3),
    [interesting(0.00)]).

fof(t21_ami_3,theorem,(
    $true ),
    file(ami_3,t21_ami_3),
    [interesting(0.00)]).

fof(t22_ami_3,theorem,(
    $true ),
    file(ami_3,t22_ami_3),
    [interesting(0.00)]).

fof(t23_ami_3,theorem,(
    $true ),
    file(ami_3,t23_ami_3),
    [interesting(0.00)]).

fof(t89_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k1_relat_1(A))
         => k7_relat_1(A,k1_tarski(B)) = k1_tarski(k4_tarski(B,k1_funct_1(A,B))) ) ) ),
    file(grfunc_1,t89_grfunc_1),
    [interesting(0.00)]).

fof(t56_zfmisc_1,theorem,(
    ! [A,B] : 
      ( ~ r2_hidden(A,B)
     => r1_xboole_0(k1_tarski(A),B) ) ),
    file(zfmisc_1,t56_zfmisc_1),
    [interesting(0.00)]).

fof(t95_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( k7_relat_1(B,A) = k1_xboole_0
      <=> r1_xboole_0(k1_relat_1(B),A) ) ) ),
    file(relat_1,t95_relat_1),
    [interesting(0.00)]).

fof(t24_ami_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( k1_relat_1(A) = k1_relat_1(B)
                & k1_funct_1(A,C) = k1_funct_1(B,C) )
             => k7_relat_1(A,k1_tarski(C)) = k7_relat_1(B,k1_tarski(C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l45_ami_3,l45_ami_3,t56_zfmisc_1,l46_ami_3,l46_ami_3]),
    [file(ami_3,t24_ami_3),interesting(0.00)]).

fof(t41_enumset1,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    file(enumset1,t41_enumset1),
    [interesting(0.00)]).

fof(t185_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ! [C,D] : 
              ( ( k7_relat_1(A,C) = k7_relat_1(B,C)
                & k7_relat_1(A,D) = k7_relat_1(B,D) )
             => k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)) ) ) ) ),
    file(relat_1,t185_relat_1),
    [interesting(0.00)]).

fof(l44_ami_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] : 
              ( ( k7_relat_1(A,C) = k7_relat_1(B,C)
                & k7_relat_1(A,D) = k7_relat_1(B,D) )
             => k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t185_relat_1]),
    [file(ami_3,l44_ami_3),interesting(0.00)]).

fof(t25_ami_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] : 
              ( ( k1_relat_1(A) = k1_relat_1(B)
                & k1_funct_1(A,C) = k1_funct_1(B,C)
                & k1_funct_1(A,D) = k1_funct_1(B,D) )
             => k7_relat_1(A,k2_tarski(C,D)) = k7_relat_1(B,k2_tarski(C,D)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_ami_3,t24_ami_3,t41_enumset1,l44_ami_3]),
    [file(ami_3,t25_ami_3),interesting(0.00)]).

fof(t43_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) ),
    file(enumset1,t43_enumset1),
    [interesting(0.00)]).

fof(t26_ami_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D,E] : 
              ( ( k1_relat_1(A) = k1_relat_1(B)
                & k1_funct_1(A,C) = k1_funct_1(B,C)
                & k1_funct_1(A,D) = k1_funct_1(B,D)
                & k1_funct_1(A,E) = k1_funct_1(B,E) )
             => k7_relat_1(A,k1_enumset1(C,D,E)) = k7_relat_1(B,k1_enumset1(C,D,E)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_ami_3,t24_ami_3,t43_enumset1,l44_ami_3]),
    [file(ami_3,t26_ami_3),interesting(0.00)]).

fof(t28_ami_3,theorem,(
    $true ),
    file(ami_3,t28_ami_3),
    [interesting(0.00)]).

fof(t38_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t38_zfmisc_1),
    [interesting(0.00)]).

fof(t71_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( A != C
     => k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) ) ),
    file(funct_4,t71_funct_4),
    [interesting(0.00)]).

fof(t20_ami_1,theorem,(
    ! [A,B,C] : k4_funct_4(A,A,B,C) = k3_cqc_lang(A,C) ),
    file(ami_1,t20_ami_1),
    [interesting(0.00)]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [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(d14_ami_1,definition,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ( v8_ami_1(B,A)
      <=> ! [C] : 
            ( m1_struct_0(C,B,u2_ami_1(A,B))
           => k3_ami_1(A,B,C) = u4_ami_1(A,B) ) ) ) ),
    file(ami_1,d14_ami_1),
    [interesting(0.00)]).

fof(t11_ami_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k3_ami_2)
     => k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_ami_2 ) ),
    file(ami_2,t11_ami_2),
    [interesting(0.00)]).

fof(t30_ami_3,theorem,(
    $true ),
    file(ami_3,t30_ami_3),
    [interesting(0.00)]).

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

fof(d13_ami_3,definition,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ( v1_ami_3(C,A,B)
          <=> r1_tarski(k1_relat_1(C),u2_ami_1(A,B)) ) ) ) ),
    file(ami_3,d13_ami_3),
    [interesting(0.00)]).

fof(d1_funct_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_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(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(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(t54_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => k13_ami_1(A,B,C,D) = k13_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E),D) ) ) ) ) ) ),
    file(ami_1,t54_ami_1),
    [interesting(0.00)]).

fof(t29_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( r2_hidden(A,k4_card_3(B))
                  & r2_hidden(C,k7_ami_1(B)) )
               => r2_hidden(k1_funct_4(A,C),k4_card_3(B)) ) ) ) ) ),
    file(ami_1,t29_ami_1),
    [interesting(0.00)]).

fof(t26_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(A,k1_funct_4(B,A)) ) ) ),
    file(funct_4,t26_funct_4),
    [interesting(0.00)]).

fof(t3_ami_3,theorem,(
    $true ),
    file(ami_3,t3_ami_3),
    [interesting(0.00)]).

fof(d18_ami_3,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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r4_ami_3(A,B,C,D)
                  <=> ( r2_hidden(D,k1_relat_1(C))
                      & k1_funct_1(C,D) = k5_ami_1(A,B) ) ) ) ) ) ) ),
    file(ami_3,d18_ami_3),
    [interesting(0.00)]).

fof(d15_ami_3,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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r2_ami_3(A,B,C,D)
                  <=> k1_funct_1(C,D) = k5_ami_1(A,B) ) ) ) ) ) ),
    file(ami_3,d15_ami_3),
    [interesting(0.00)]).

fof(t41_ami_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)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_ami_1(D,A,B)
                 => ! [E] : 
                      ( m1_struct_0(E,B,u2_ami_1(A,B))
                     => ( ( r1_tarski(D,C)
                          & r4_ami_3(A,B,D,E) )
                       => r2_ami_3(A,B,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_ami_3,t8_grfunc_1,d15_ami_3]),
    [file(ami_3,t41_ami_3),interesting(0.00)]).

fof(t25_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k7_ami_1(B))
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(ami_1,t25_ami_1),
    [interesting(0.00)]).

fof(t52_ami_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => ! [C] : 
                ( v1_setfam_1(C)
               => ! [D] : 
                    ( ( ~ v3_struct_0(D)
                      & ~ v2_ami_1(D,C)
                      & v4_ami_1(D,C)
                      & v5_ami_1(D,C)
                      & v8_ami_1(D,C)
                      & l1_ami_1(D,C) )
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
                       => ( k8_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)) = k5_ami_1(C,D)
                         => k11_ami_1(C,D,k10_ami_1(C,D,E),B) = k11_ami_1(C,D,k10_ami_1(C,D,E),A) ) ) ) ) ) ) ) ),
    file(ami_1,t52_ami_1),
    [interesting(0.00)]).

fof(d20_ami_1,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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( v9_ami_1(C,A,B)
              <=> ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) = k5_ami_1(A,B) ) ) ) ) ) ),
    file(ami_1,d20_ami_1),
    [interesting(0.00)]).

fof(d22_ami_1,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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( v9_ami_1(C,A,B)
               => ! [D] : 
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ( D = k12_ami_1(A,B,C)
                    <=> ? [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                          & D = k11_ami_1(A,B,k10_ami_1(A,B,C),E)
                          & k8_ami_1(A,B,D) = k5_ami_1(A,B) ) ) ) ) ) ) ) ),
    file(ami_1,d22_ami_1),
    [interesting(0.00)]).

fof(t57_ami_1,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)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & k13_ami_1(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) = k5_ami_1(A,B) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k12_ami_1(A,B,C) = k12_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) ) ) ) ) ) ),
    file(ami_1,t57_ami_1),
    [interesting(0.00)]).

fof(t47_ami_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)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k12_ami_1(A,B,C) = k12_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_ami_3,t57_ami_1]),
    [file(ami_3,t47_ami_3),interesting(0.00)]).

fof(t48_ami_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)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r2_ami_3(A,B,C,D)
                      <=> r2_ami_3(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_ami_3,t54_ami_1,d15_ami_3,d15_ami_3,t54_ami_1,d15_ami_3]),
    [file(ami_3,t48_ami_3),interesting(0.00)]).

fof(d17_ami_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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r3_ami_3(A,B,C,D)
                  <=> ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
                      & k13_ami_3(A,B,C) = D ) ) ) ) ) ) ),
    file(ami_3,d17_ami_3),
    [interesting(0.00)]).

fof(d16_ami_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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
               => k13_ami_3(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ) ),
    file(ami_3,d16_ami_3),
    [interesting(0.00)]).

fof(d14_ami_3,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r1_ami_3(A,B,C,D)
                  <=> k6_ami_1(A,B,C) = D ) ) ) ) ) ),
    file(ami_3,d14_ami_3),
    [interesting(0.00)]).

fof(t49_ami_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)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r3_ami_3(A,B,C,D)
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
                       => ( r1_tarski(C,E)
                         => r1_ami_3(A,B,E,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_ami_3,t8_grfunc_1,d16_ami_3,d14_ami_3]),
    [file(ami_3,t49_ami_3),interesting(0.00)]).

fof(t4_ami_3,theorem,(
    k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) = 0 ),
    file(ami_3,t4_ami_3),
    [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(d21_ami_1,definition,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v10_ami_1(B,A)
      <=> u4_ami_1(A,B) != u2_ami_1(A,B) ) ) ),
    file(ami_1,d21_ami_1),
    [interesting(0.00)]).

fof(t6_ami_2,theorem,
    ( k3_ami_2 != k4_numbers
    & k4_ami_2 != k4_numbers
    & k3_ami_2 != k4_ami_2 ),
    file(ami_2,t6_ami_2),
    [interesting(0.00)]).

fof(t2_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B)
               => A = C ) ) ) ) ),
    file(xcmplx_1,t2_xcmplx_1),
    [interesting(0.00)]).

fof(d11_ami_3,definition,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ( B = k11_ami_3(A)
          <=> ? [C] : 
                ( m2_subset_1(C,k5_numbers,k3_ami_2)
                & C = A
                & B = k15_ami_2(C) ) ) ) ) ),
    file(ami_3,d11_ami_3),
    [interesting(0.00)]).

fof(d15_ami_2,definition,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k3_ami_2)
     => k15_ami_2(A) = k1_nat_1(A,2) ) ),
    file(ami_2,d15_ami_2),
    [interesting(0.00)]).

fof(t10_ami_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k5_numbers,k2_ami_2)
     => k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k4_numbers ) ),
    file(ami_2,t10_ami_2),
    [interesting(0.00)]).

fof(t42_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( v1_int_1(C)
             => ( r1_int_1(A,B,C)
              <=> r1_int_1(k2_xcmplx_0(A,C),B,C) ) ) ) ) ),
    file(int_1,t42_int_1),
    [interesting(0.00)]).

fof(t35_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( v1_int_1(C)
             => ( r1_int_1(A,B,C)
               => r1_int_1(B,A,C) ) ) ) ) ),
    file(int_1,t35_int_1),
    [interesting(0.00)]).

fof(t40_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( v1_int_1(C)
             => ! [D] : 
                  ( v1_int_1(D)
                 => ( r1_int_1(k2_xcmplx_0(A,B),C,D)
                  <=> r1_int_1(A,k6_xcmplx_0(C,B),D) ) ) ) ) ) ),
    file(int_1,t40_int_1),
    [interesting(0.00)]).

fof(d3_int_1,definition,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( v1_int_1(C)
             => ( r1_int_1(A,B,C)
              <=> ? [D] : 
                    ( v1_int_1(D)
                    & k3_xcmplx_0(C,D) = k6_xcmplx_0(A,B) ) ) ) ) ) ),
    file(int_1,d3_int_1),
    [interesting(0.00)]).

fof(t36_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ! [C] : 
              ( v1_int_1(C)
             => ! [D] : 
                  ( v1_int_1(D)
                 => ( ( r1_int_1(A,B,C)
                      & r1_int_1(B,D,C) )
                   => r1_int_1(A,D,C) ) ) ) ) ) ),
    file(int_1,t36_int_1),
    [interesting(0.00)]).

fof(t22_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( k3_xcmplx_0(A,B) = 1
          <=> ( ( A = 1
                & B = 1 )
              | ( A = k1_real_1(1)
                & B = k1_real_1(1) ) ) ) ) ) ),
    file(int_1,t22_int_1),
    [interesting(0.00)]).

fof(t32_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => r1_int_1(A,A,B) ) ) ),
    file(int_1,t32_int_1),
    [interesting(0.00)]).

fof(t57_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k15_ami_3(A)
        & k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k16_ami_3(A) ) ) ),
    file(ami_3,t57_ami_3),
    [interesting(0.00)]).

fof(d6_ami_2,definition,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => k6_ami_2(A) = k1_funct_1(A,0) ) ),
    file(ami_2,d6_ami_2),
    [interesting(0.00)]).

fof(d8_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m2_subset_1(C,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(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => k4_ami_1(A,B,C,D) = D ) ) ) ) ) ),
    file(ami_1,d8_ami_1),
    [interesting(0.00)]).

fof(t3_xcmplx_1,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( A = k2_xcmplx_0(A,B)
           => B = 0 ) ) ) ),
    file(xcmplx_1,t3_xcmplx_1),
    [interesting(0.00)]).

fof(l27_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ~ ( ? [B] : 
              ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
              & k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)) )
          & v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ami_2,d8_ami_1,d11_ami_3,d15_ami_2,t3_xcmplx_1]),
    [file(ami_3,l27_ami_3),interesting(0.00)]).

fof(t5_ami_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] : 
          ( m1_subset_1(B,k4_card_3(k5_ami_2))
         => ( B = A
           => k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k6_ami_2(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_ami_2]),
    [file(ami_3,t5_ami_3),interesting(0.00)]).

fof(t23_ami_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k2_ami_2)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k2_ami_2)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_gr_cy_1(9))
                 => ( A = k1_domain_1(k1_gr_cy_1(9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k2_ami_2)),D,k2_finseq_4(k2_ami_2,B,C))
                   => ( k9_ami_2(A) = B
                      & k10_ami_2(A) = C ) ) ) ) ) ) ),
    file(ami_2,t23_ami_2),
    [interesting(0.00)]).

fof(t20_ami_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k2_ami_2)
         => ! [C] : 
              ( v1_int_1(C)
             => k1_funct_1(k8_ami_2(A,B,C),B) = C ) ) ) ),
    file(ami_2,t20_ami_2),
    [interesting(0.00)]).

fof(t21_ami_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k2_ami_2)
         => ! [C] : 
              ( v1_int_1(C)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k2_ami_2)
                 => ( D != B
                   => k1_funct_1(k8_ami_2(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ) ),
    file(ami_2,t21_ami_2),
    [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(t14_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).

fof(t7_ami_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( k8_funct_2(k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2)),k5_ami_2,A) = k3_ami_2
      <=> A = 0 ) ) ),
    file(ami_2,t7_ami_2),
    [interesting(0.00)]).

fof(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.00)]).

fof(d7_ami_2,definition,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(k5_ami_2))
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => k7_ami_2(A,B) = k1_funct_4(A,k3_cqc_lang(0,B)) ) ) ),
    file(ami_2,d7_ami_2),
    [interesting(0.00)]).

fof(t25_ami_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
     => ! [B] : 
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => ! [C] : 
              ( m2_subset_1(C,k5_numbers,k2_ami_2)
             => ! [D] : 
                  ( m2_subset_1(D,k5_numbers,k1_gr_cy_1(9))
                 => ( A = k1_domain_1(k1_gr_cy_1(9),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),D,k2_finseq_4(k5_numbers,B,C))
                   => ( k12_ami_2(A) = B
                      & k13_ami_2(A) = C ) ) ) ) ) ) ),
    file(ami_2,t25_ami_2),
    [interesting(0.00)]).

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

fof(d14_ami_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m1_subset_1(E,A)
                     => ( ( ~ r1_xreal_0(B,C)
                         => k14_ami_2(A,B,C,D,E) = D )
                        & ( r1_xreal_0(B,C)
                         => k14_ami_2(A,B,C,D,E) = E ) ) ) ) ) ) ) ),
    file(ami_2,d14_ami_2),
    [interesting(0.00)]).

fof(t2_ami_2,theorem,(
    r2_hidden(k4_tarski(0,k1_xboole_0),k4_ami_2) ),
    file(ami_2,t2_ami_2),
    [interesting(0.00)]).

fof(t68_ami_3,theorem,(
    m2_subset_1(k4_tarski(0,k1_xboole_0),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ),
    inference(mizar_proof,[status(thm)],[t2_ami_2]),
    [file(ami_3,t68_ami_3),interesting(0.00)]).

fof(d1_ami_2,definition,(
    k1_ami_2 = 0 ),
    file(ami_2,d1_ami_2),
    [interesting(0.00)]).

fof(l37_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
    <=> ~ ( A != k4_tarski(0,k1_xboole_0)
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k3_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k4_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k5_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k6_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k7_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => A != k8_ami_3(B) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => A != k9_ami_3(C,B) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => A != k10_ami_3(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_ami_2,d2_xboole_0,d2_xboole_0,d1_ami_2,d1_tarski,d2_ami_3,d2_tarski,d2_ami_3,d3_enumset1,d2_xboole_0,t2_ami_2]),
    [file(ami_3,l37_ami_3),interesting(0.00)]).

fof(t69_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
    <=> ~ ( A != k4_tarski(0,k1_xboole_0)
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k3_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k4_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k5_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k6_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k7_ami_3(B,C) ) )
          & ! [B] : 
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => A != k8_ami_3(B) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => A != k9_ami_3(C,B) ) )
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => A != k10_ami_3(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l37_ami_3]),
    [file(ami_3,t69_ami_3),interesting(0.00)]).

fof(d9_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( v4_ami_1(B,A)
          <=> ? [C] : 
                ( m2_subset_1(C,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(C,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)
                     => C = D ) ) ) ) ) ) ),
    file(ami_1,d9_ami_1),
    [interesting(0.00)]).

fof(l38_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ( v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
       => A = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_ami_1]),
    [file(ami_3,l38_ami_3),interesting(0.00)]).

fof(t70_ami_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ( v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
       => A = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[l38_ami_3]),
    [file(ami_3,t70_ami_3),interesting(0.00)]).