fof(t84_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
     => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d1_ami_3,d13_ami_3,t37_ami_3,t28_xboole_1,t23_ami_5,t23_xboole_1,t17_xboole_1,t23_xboole_1,d7_xboole_0,t56_zfmisc_1,l70_ami_5,t60_relat_1,t90_relat_1,t83_ami_5]),
    [file(ami_5,t84_ami_5),interesting(1.00)]).

fof(t33_ami_5,theorem,(
    r1_subset_1(k2_ami_2,k3_ami_2) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,t22_nat_1,t7_scm_1,d2_ami_2,d3_ami_2,d7_xboole_0]),
    [file(ami_5,t33_ami_5),interesting(0.98)]).

fof(t72_ami_5,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] : 
              ( ( v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k6_ami_5(A,B,C) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t90_relat_1,d13_ami_3,d3_xboole_0,t63_ami_5,t8_grfunc_1,d10_xboole_0,t9_grfunc_1]),
    [file(ami_5,t72_ami_5),interesting(0.98)]).

fof(l70_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = k7_relat_1(A,k2_ami_2) ) ),
    inference(mizar_proof,[status(thm)],[t16_ami_5,t20_ami_5,t56_zfmisc_1,t33_ami_5,t70_xboole_1,t23_ami_5,d1_ami_3,t4_xboole_1,t40_xboole_1,d1_ami_3,t83_xboole_1]),
    [file(ami_5,l70_ami_5),interesting(0.95)]).

fof(t83_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
     => ( k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != k1_xboole_0
       => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t64_relat_1,t37_ami_3,l70_ami_5,t87_relat_1,d2_ami_3,d24_ami_1,t29_finset_1,t13_finset_1,t37_xboole_1,d4_xboole_0,d1_ami_3,d2_ami_3,d24_ami_1,t29_finset_1,t13_finset_1,t37_xboole_1,d4_xboole_0,t39_ami_3,t39_ami_3,d25_ami_1,d4_xboole_0,d4_xboole_0,t56_zfmisc_1,d7_xboole_0,t56_zfmisc_1,d7_xboole_0,t56_zfmisc_1,d1_funct_4,t34_ami_3,d1_funct_4,t5_cqc_lang,t5_cqc_lang,t23_xboole_1,t23_xboole_1,d7_xboole_0,d7_xboole_0,t33_funct_4,t1_xboole_1,t56_zfmisc_1,d7_xboole_0,t56_zfmisc_1,d7_xboole_0,t56_zfmisc_1,d1_funct_4,t34_ami_3,d1_funct_4,t5_cqc_lang,t5_cqc_lang,t23_xboole_1,t23_xboole_1,d7_xboole_0,d7_xboole_0,t33_funct_4,t1_xboole_1,t62_ami_5,t25_relat_1,t36_ami_3,t37_ami_3,t91_relat_1,t34_ami_3,d1_tarski,d1_funct_4,d2_xboole_0,d1_funct_4,d2_xboole_0,t8_grfunc_1,t14_funct_4,t14_funct_4,t50_ami_3,t5_cqc_lang,d1_tarski,t5_cqc_lang,t22_ami_5,d1_tarski,d1_funct_4,d2_xboole_0,t48_ami_1,d1_tarski,d2_xboole_0,d2_xboole_0,t8_grfunc_1,t14_funct_4,t12_funct_4,t12_funct_4,t6_cqc_lang,d1_tarski,d2_xboole_0,t20_ami_5,d1_tarski,d2_xboole_0,d2_xboole_0,t8_grfunc_1,t14_funct_4,t12_funct_4,t14_funct_4,t6_cqc_lang,d19_ami_1,d19_ami_1,t8_ami_3,t70_funct_1,t36_ami_3,t37_ami_3,t91_relat_1,t34_ami_3,d1_tarski,d1_funct_4,d2_xboole_0,d1_funct_4,d2_xboole_0,t8_grfunc_1,t14_funct_4,t14_funct_4,t50_ami_3,t5_cqc_lang,d1_tarski,t5_cqc_lang,t22_ami_5,d1_tarski,d1_funct_4,d2_xboole_0,t48_ami_1,d1_tarski,d2_xboole_0,d2_xboole_0,t8_grfunc_1,t14_funct_4,t12_funct_4,t12_funct_4,t6_cqc_lang,d1_tarski,d2_xboole_0,t20_ami_5,d1_tarski,d2_xboole_0,d2_xboole_0,t8_grfunc_1,t14_funct_4,t12_funct_4,t14_funct_4,t6_cqc_lang,d19_ami_1,d19_ami_1,t8_ami_3,t70_funct_1]),
    [file(ami_5,t83_ami_5),interesting(0.95)]).

fof(l71_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => ( v1_ami_5(A,k1_tarski(k4_numbers),k1_ami_3)
      <=> r1_tarski(k1_relat_1(A),k2_ami_2) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_3,t23_ami_5,t4_xboole_1,t16_ami_5,t20_ami_5,t56_zfmisc_1,t33_ami_5,t70_xboole_1,t63_xboole_1,t73_xboole_1,d8_ami_5,d1_ami_3]),
    [file(ami_5,l71_ami_5),interesting(0.94)]).

fof(t31_ami_5,theorem,(
    ~ v1_finset_1(k2_ami_2) ),
    inference(mizar_proof,[status(thm)],[s4_funct_2,d1_funct_2,d4_wellord2,d8_funct_1,d1_funct_2,t52_ami_3,d1_funct_2,d3_tarski,d5_funct_1,d1_funct_2,d2_ami_3,d10_xboole_0,d3_tarski,d1_ami_3,d2_ami_3,t18_ami_5,d5_funct_1,t68_card_1,t15_card_4]),
    [file(ami_5,t31_ami_5),interesting(0.92)]).

fof(t27_ami_5,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => r1_tarski(k2_ami_2,k1_relat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t10_xboole_1,t10_xboole_1,t4_xboole_1,t23_ami_5,t36_ami_3]),
    [file(ami_5,t27_ami_5),interesting(0.91)]).

fof(t65_ami_5,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k7_ami_5(A,B,C))) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_relat_1,d4_xboole_0,d2_xboole_0,d1_tarski]),
    [file(ami_5,t65_ami_5),interesting(0.91)]).

fof(t28_ami_5,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => r1_tarski(k3_ami_2,k1_relat_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t10_xboole_1,t23_ami_5,t36_ami_3]),
    [file(ami_5,t28_ami_5),interesting(0.90)]).

fof(t62_ami_5,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => r1_tarski(k7_ami_5(A,B,C),C) ) ) ),
    inference(mizar_proof,[status(thm)],[t88_relat_1]),
    [file(ami_5,t62_ami_5),interesting(0.87)]).

fof(t18_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k15_ami_3(B) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,d2_ami_2]),
    [file(ami_5,t18_ami_5),interesting(0.86)]).

fof(t32_ami_5,theorem,(
    ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ),
    inference(mizar_proof,[status(thm)],[s4_funct_2,d1_funct_2,d4_wellord2,d8_funct_1,d1_funct_2,t53_ami_3,d1_funct_2,d3_tarski,d5_funct_1,d1_funct_2,d1_ami_3,d10_xboole_0,d3_tarski,d1_ami_3,t19_ami_5,d5_funct_1,d1_ami_3,t68_card_1,t15_card_4]),
    [file(ami_5,t32_ami_5),interesting(0.86)]).

fof(t22_ami_5,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] : 
          ( m1_ami_3(B)
         => A != B ) ) ),
    inference(mizar_proof,[status(thm)],[t19_ami_5,t18_ami_5,t56_ami_3]),
    [file(ami_5,t22_ami_5),interesting(0.86)]).

fof(t16_ami_5,theorem,(
    ! [A] : 
      ( r2_hidden(A,k2_ami_2)
     => m1_ami_3(A) ) ),
    inference(mizar_proof,[status(thm)],[d1_ami_3,d2_ami_3]),
    [file(ami_5,t16_ami_5),interesting(0.85)]).

fof(t20_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => A != k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ),
    inference(mizar_proof,[status(thm)],[t18_ami_5,t57_ami_3]),
    [file(ami_5,t20_ami_5),interesting(0.85)]).

fof(t71_ami_5,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_ami_1(D,A,B)
                 => r1_xboole_0(k1_relat_1(k7_ami_5(A,B,C)),k1_relat_1(k6_ami_5(A,B,D))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t34_xboole_1,t87_relat_1,t1_xboole_1,t87_relat_1,t79_xboole_1,t64_xboole_1]),
    [file(ami_5,t71_ami_5),interesting(0.85)]).

fof(t61_ami_5,theorem,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C,D] : 
          ( m1_ami_1(D,A,B)
         => ( r1_tarski(C,D)
           => m1_ami_1(C,A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_ami_1,t6_grfunc_1,t40_ami_1,t13_finset_1,d24_ami_1]),
    [file(ami_5,t61_ami_5),interesting(0.84)]).

fof(t63_ami_5,theorem,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => r1_tarski(k6_ami_5(A,B,C),C) ) ) ),
    inference(mizar_proof,[status(thm)],[t88_relat_1]),
    [file(ami_5,t63_ami_5),interesting(0.83)]).

fof(t75_ami_5,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_ami_1(C,A,B)
             => ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
               => C = k17_ami_1(A,B,k17_ami_1(A,B,k12_ami_3(A,B,k13_ami_3(A,B,C)),k6_ami_5(A,B,C)),k7_ami_5(A,B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t63_subset_1,t37_ami_3,t39_xboole_1,t4_xboole_1,t12_xboole_1,t12_xboole_1,d1_funct_4,d1_funct_4,t34_ami_3,t28_xboole_1,t90_relat_1,t90_relat_1,t23_xboole_1,t23_xboole_1,t28_xboole_1,d2_xboole_0,d1_tarski,t34_ami_3,d1_tarski,d2_xboole_0,d1_funct_4,d2_xboole_0,t66_ami_5,t65_ami_5,d1_funct_4,d1_funct_4,t50_ami_3,d16_ami_3,d1_tarski,d3_xboole_0,t90_relat_1,d2_xboole_0,d1_funct_4,t70_funct_1,d3_xboole_0,t90_relat_1,d2_xboole_0,d1_funct_4,d2_xboole_0,t71_ami_5,t3_xboole_0,d1_funct_4,d1_funct_4,t70_funct_1,d2_xboole_0,t9_funct_1]),
    [file(ami_5,t75_ami_5),interesting(0.83)]).

fof(t96_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = k7_relat_1(A,k2_ami_2) ) ),
    inference(mizar_proof,[status(thm)],[l70_ami_5]),
    [file(ami_5,t96_ami_5),interesting(0.83)]).

fof(t69_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => r1_tarski(k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)),k2_ami_2) ) ),
    inference(mizar_proof,[status(thm)],[l70_ami_5,t87_relat_1]),
    [file(ami_5,t69_ami_5),interesting(0.82)]).

fof(t97_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => ( v1_ami_5(A,k1_tarski(k4_numbers),k1_ami_3)
      <=> r1_tarski(k1_relat_1(A),k2_ami_2) ) ) ),
    inference(mizar_proof,[status(thm)],[l71_ami_5]),
    [file(ami_5,t97_ami_5),interesting(0.81)]).

fof(t23_ami_5,theorem,(
    u1_struct_0(k1_ami_3) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)),k2_ami_2),k3_ami_2) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t19_nat_1,t46_nat_1,t71_nat_1,t47_nat_1,d1_tarski,d2_xboole_0,d2_xboole_0,d2_xboole_0,d2_xboole_0,d2_xboole_0,t4_ami_3,t37_zfmisc_1,t8_xboole_1,t8_xboole_1,d2_ami_2,d3_ami_2,d1_ami_3,d10_xboole_0]),
    [file(ami_5,t23_ami_5),interesting(0.80)]).

fof(t19_ami_5,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k16_ami_3(B) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_ami_3,d3_ami_2,t22_nat_1]),
    [file(ami_5,t19_ami_5),interesting(0.79)]).

fof(t86_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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)))
         => ( r1_tarski(A,B)
           => ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),C)),k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_ami_5,t53_ami_3,d1_ami_3,t68_funct_1,d1_ami_3,d3_xboole_0,d1_funct_4,t5_cqc_lang,d1_tarski,d2_xboole_0,t39_ami_3,t39_ami_3,t84_ami_5,d25_ami_1,t36_ami_3,t37_ami_3,d2_xboole_0,t56_zfmisc_1,t17_funct_4,t8_grfunc_1,t8_grfunc_1,d2_xboole_0,t56_zfmisc_1,t17_funct_4,t8_grfunc_1,t8_grfunc_1,t6_cqc_lang,t14_funct_4,t8_grfunc_1,d19_ami_1,d19_ami_1,t54_ami_1,d25_ami_1,t72_funct_1,d25_ami_1,t72_funct_1,t13_ami_3,t72_funct_1]),
    [file(ami_5,t86_ami_5),interesting(0.77)]).

fof(t67_ami_5,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => r1_xboole_0(k1_struct_0(B,k2_ami_1(A,B)),k1_relat_1(k7_ami_5(A,B,C))) ) ) ),
    inference(mizar_proof,[status(thm)],[t65_ami_5,t56_zfmisc_1]),
    [file(ami_5,t67_ami_5),interesting(0.76)]).

fof(t76_ami_5,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_ami_1(C,A,B)
             => ~ ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
                  & v1_ami_3(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t72_ami_5,t66_ami_5]),
    [file(ami_5,t76_ami_5),interesting(0.76)]).

fof(t66_ami_5,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_ami_1(C,A,B)
             => ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_relat_1,t48_ami_1]),
    [file(ami_5,t66_ami_5),interesting(0.74)]).

fof(t29_ami_5,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => k1_relat_1(k7_relat_1(A,k2_ami_2)) = k2_ami_2 ) ),
    inference(mizar_proof,[status(thm)],[t27_ami_5,t91_relat_1]),
    [file(ami_5,t29_ami_5),interesting(0.73)]).

fof(t30_ami_5,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => k1_relat_1(k7_relat_1(A,k3_ami_2)) = k3_ami_2 ) ),
    inference(mizar_proof,[status(thm)],[t28_ami_5,t91_relat_1]),
    [file(ami_5,t30_ami_5),interesting(0.72)]).

fof(t37_ami_5,theorem,(
    k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = 0 ),
    inference(mizar_proof,[status(thm)],[t71_ami_3,t7_mcart_1]),
    [file(ami_5,t37_ami_5),interesting(0.72)]).

fof(t55_ami_5,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k11_ami_2(k2_ami_5(k8_ami_3(A))) = A ) ),
    inference(mizar_proof,[status(thm)],[t10_gr_cy_1,d1_ami_3,t24_ami_2]),
    [file(ami_5,t55_ami_5),interesting(0.71)]).

fof(t74_ami_5,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] : 
              ( ( v1_ami_5(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] : 
                  ( m1_ami_1(D,A,B)
                 => ( r1_tarski(C,D)
                  <=> r1_tarski(C,k7_ami_5(A,B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t105_relat_1,t39_xboole_1,t12_xboole_1,d8_ami_5,t37_ami_3,t73_xboole_1,t97_relat_1,t88_relat_1,t1_xboole_1]),
    [file(ami_5,t74_ami_5),interesting(0.71)]).

fof(t38_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = 1 ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t38_ami_5),interesting(0.69)]).

fof(t39_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = 2 ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t39_ami_5),interesting(0.69)]).

fof(t40_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = 3 ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t40_ami_5),interesting(0.69)]).

fof(t41_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = 4 ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t41_ami_5),interesting(0.69)]).

fof(t42_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = 5 ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t42_ami_5),interesting(0.69)]).

fof(t79_ami_5,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => k6_ami_1(A,B,k8_ami_5(A,B,C,k12_ami_3(A,B,D))) = D ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_ami_3,d1_tarski,d2_xboole_0,d1_funct_4,t50_ami_3]),
    [file(ami_5,t79_ami_5),interesting(0.68)]).

fof(t43_ami_5,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = 6 ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t43_ami_5),interesting(0.63)]).

fof(t70_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => r1_tarski(k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)),k3_ami_2) ) ),
    inference(mizar_proof,[status(thm)],[d1_ami_3,t87_relat_1]),
    [file(ami_5,t70_ami_5),interesting(0.63)]).

fof(t73_ami_5,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))
                 => ( r2_hidden(D,k1_relat_1(C))
                   => r2_hidden(D,k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t90_relat_1,d3_xboole_0]),
    [file(ami_5,t73_ami_5),interesting(0.62)]).

fof(t52_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 6
          & ! [B] : 
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => A != k8_ami_3(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,d2_tarski,t7_mcart_1,d3_enumset1,d4_ami_2,d1_ami_3,d2_xboole_0,d2_xboole_0,d2_xboole_0]),
    [file(ami_5,t52_ami_5),interesting(0.62)]).

fof(t44_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = 7 ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t44_ami_5),interesting(0.61)]).

fof(t45_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [B] : 
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = 8 ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1]),
    [file(ami_5,t45_ami_5),interesting(0.61)]).

fof(t78_ami_5,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)
             => ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
               => r1_tarski(k12_ami_3(A,B,k13_ami_3(A,B,C)),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_ami_3,t8_funct_1,t37_zfmisc_1,t35_ami_5]),
    [file(ami_5,t78_ami_5),interesting(0.61)]).

fof(t53_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 7
          & ! [B] : 
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k9_ami_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,t7_mcart_1,d3_enumset1,d2_xboole_0,d4_ami_2,d1_ami_3,d2_xboole_0,d2_xboole_0,t7_mcart_1]),
    [file(ami_5,t53_ami_5),interesting(0.59)]).

fof(t54_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 8
          & ! [B] : 
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k10_ami_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,t7_mcart_1,d3_enumset1,d2_xboole_0,d4_ami_2,d1_ami_3,d2_xboole_0,d2_xboole_0,t7_mcart_1]),
    [file(ami_5,t54_ami_5),interesting(0.59)]).

fof(t25_ami_5,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => r2_hidden(k2_ami_1(A,B),k1_relat_1(C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_ami_3]),
    [file(ami_5,t25_ami_5),interesting(0.57)]).

fof(t77_ami_5,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] : 
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_ami_3)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_ami_3) )
             => k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,B,C)) = k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_ami_3,t3_xboole_0,d1_tarski,t48_ami_1,d1_ami_3,t33_ami_5,t70_xboole_1,d1_ami_3,t63_xboole_1,t76_funct_4,t76_funct_4,t58_ami_5,t59_ami_5,t75_funct_4,t59_ami_5,t75_funct_4,t97_relat_1,t23_ami_5,t36_ami_3,t83_funct_4,t83_funct_4,t23_ami_5,t36_ami_3,t97_relat_1]),
    [file(ami_5,t77_ami_5),interesting(0.56)]).

fof(t68_ami_5,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_ami_1(C,A,B)
             => r1_xboole_0(k1_struct_0(B,k2_ami_1(A,B)),k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_ami_5,t56_zfmisc_1]),
    [file(ami_5,t68_ami_5),interesting(0.55)]).

fof(t58_ami_5,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(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ( k7_relat_1(A,k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) = k7_relat_1(B,k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3))))
           => ! [C] : 
                ( m2_subset_1(C,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))
               => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,A),k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,B),k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d2_xboole_0,t23_ami_5,t7_xboole_1,t36_ami_3,t91_relat_1,t36_ami_3,t91_relat_1,t70_funct_1,t70_funct_1,t36_ami_3,t36_ami_3,t7_xboole_1,t1_xboole_1,t1_xboole_1,t36_ami_5,t46_ami_5,d8_ami_1,d8_ami_1,t47_ami_5,d2_ami_3,t46_zfmisc_1,t39_xboole_1,t36_xboole_1,t1_xboole_1,t91_relat_1,t36_xboole_1,t1_xboole_1,t91_relat_1,d4_xboole_0,d4_xboole_0,d1_ami_3,d2_ami_3,d1_tarski,d2_xboole_0,t72_funct_1,t8_ami_3,t72_funct_1,t72_funct_1,t8_ami_3,t72_funct_1,t9_funct_1,d2_ami_3,t8_ami_3,t72_funct_1,t72_funct_1,t8_ami_3,t24_ami_3,t185_relat_1,t8_ami_3,t8_ami_3,t24_ami_3,t185_relat_1,t48_ami_5,d2_ami_3,t46_zfmisc_1,t39_xboole_1,t36_xboole_1,t1_xboole_1,t91_relat_1,t36_xboole_1,t1_xboole_1,t91_relat_1,d4_xboole_0,d4_xboole_0,d1_ami_3,d2_ami_3,d1_tarski,d2_xboole_0,t72_funct_1,t9_ami_3,t72_funct_1,t72_funct_1,t9_ami_3,t72_funct_1,t9_funct_1,d2_ami_3,d2_ami_3,t72_funct_1,t72_funct_1,t72_funct_1,t72_funct_1,t9_ami_3,t9_ami_3,t24_ami_3,t185_relat_1,t9_ami_3,t9_ami_3,t24_ami_3,t185_relat_1,t49_ami_5,d2_ami_3,t46_zfmisc_1,t39_xboole_1,t36_xboole_1,t1_xboole_1,t91_relat_1,t36_xboole_1,t1_xboole_1,t91_relat_1,d4_xboole_0,d4_xboole_0,d1_ami_3,d2_ami_3,d1_tarski,d2_xboole_0,t72_funct_1,t10_ami_3,t72_funct_1,t72_funct_1,t10_ami_3,t72_funct_1,t9_funct_1,d2_ami_3,d2_ami_3,t72_funct_1,t72_funct_1,t72_funct_1,t72_funct_1,t10_ami_3,t10_ami_3,t24_ami_3,t185_relat_1,t10_ami_3,t10_ami_3,t24_ami_3,t185_relat_1,t50_ami_5,d2_ami_3,t46_zfmisc_1,t39_xboole_1,t36_xboole_1,t1_xboole_1,t91_relat_1,t36_xboole_1,t1_xboole_1,t91_relat_1,d4_xboole_0,d4_xboole_0,d1_ami_3,d2_ami_3,d1_tarski,d2_xboole_0,t72_funct_1,t11_ami_3,t72_funct_1,t72_funct_1,t11_ami_3,t72_funct_1,t9_funct_1,d2_ami_3,d2_ami_3,t72_funct_1,t72_funct_1,t72_funct_1,t72_funct_1,t11_ami_3,t11_ami_3,t24_ami_3,t185_relat_1,t11_ami_3,t11_ami_3,t24_ami_3,t185_relat_1,t51_ami_5,d2_ami_3,t46_zfmisc_1,t39_xboole_1,t36_xboole_1,t1_xboole_1,t91_relat_1,t36_xboole_1,t1_xboole_1,t91_relat_1,d4_xboole_0,d4_xboole_0,d1_ami_3,d2_ami_3,d1_tarski,d2_xboole_0,t72_funct_1,t15_ami_5,t72_funct_1,t72_funct_1,t15_ami_5,t72_funct_1,t9_funct_1,d2_ami_3,t72_funct_1,t72_funct_1,t15_ami_5,t15_ami_5,t24_ami_3,t185_relat_1,t15_ami_5,t15_ami_5,t24_ami_3,t185_relat_1,d2_ami_3,d2_ami_3,t48_zfmisc_1,t39_xboole_1,t36_xboole_1,t1_xboole_1,t91_relat_1,t36_xboole_1,t1_xboole_1,t91_relat_1,d4_xboole_0,d4_xboole_0,d1_ami_3,d2_ami_3,d2_tarski,d2_xboole_0,t72_funct_1,t12_ami_3,t72_funct_1,t72_funct_1,t12_ami_3,t72_funct_1,t9_funct_1,d2_ami_3,d2_ami_3,t72_funct_1,t72_funct_1,t72_funct_1,t72_funct_1,t12_ami_3,t12_ami_3,t12_ami_3,t12_ami_3,t25_ami_3,t185_relat_1,t12_ami_3,t12_ami_3,t24_ami_3,t185_relat_1,t52_ami_5,t91_relat_1,t91_relat_1,d1_ami_3,d2_ami_3,d2_xboole_0,t72_funct_1,t13_ami_3,t72_funct_1,t72_funct_1,t13_ami_3,t72_funct_1,t9_funct_1,t13_ami_3,t13_ami_3,t24_ami_3,t185_relat_1,t53_ami_5,t91_relat_1,t91_relat_1,d1_ami_3,d2_ami_3,d2_xboole_0,t72_funct_1,t14_ami_3,t72_funct_1,t72_funct_1,t14_ami_3,t72_funct_1,t9_funct_1,d2_ami_3,t72_funct_1,t72_funct_1,t14_ami_3,t14_ami_3,t14_ami_3,t14_ami_3,t24_ami_3,t185_relat_1,t54_ami_5,t91_relat_1,t91_relat_1,d1_ami_3,d2_ami_3,d2_xboole_0,t72_funct_1,t15_ami_3,t72_funct_1,t72_funct_1,t15_ami_3,t72_funct_1,t9_funct_1,d2_ami_3,t72_funct_1,t72_funct_1,t15_ami_3,t15_ami_3,t15_ami_3,t15_ami_3,t24_ami_3,t185_relat_1,t9_cqc_the1]),
    [file(ami_5,t58_ami_5),interesting(0.54)]).

fof(t87_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m2_subset_1(E,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))
                       => ( E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                         => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D))
                            & E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_ami_5,t72_funct_1,d25_ami_1,t86_ami_5,t63_ami_5,t8_grfunc_1,t72_funct_1,d25_ami_1]),
    [file(ami_5,t87_ami_5),interesting(0.41)]).

fof(t94_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_struct_0(F,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k9_ami_3(F,E) )
                                 => ( F = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)))
                                    | ( k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E) = 0
                                    <=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E) = 0 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_ami_5,t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,d25_ami_1,t14_ami_3,t87_ami_5,t14_ami_3,d25_ami_1]),
    [file(ami_5,t94_ami_5),interesting(0.20)]).

fof(t88_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_ami_3(F)
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k3_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,t8_ami_3,d25_ami_1]),
    [file(ami_5,t88_ami_5),interesting(0.14)]).

fof(t95_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_struct_0(F,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k10_ami_3(F,E) )
                                 => ( F = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)))
                                    | ( ~ ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),0)
                                          & r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),0) )
                                      & ~ ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),0)
                                          & r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),0) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t84_ami_5,t87_ami_5,t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,d25_ami_1,t15_ami_3,t15_ami_3,t15_ami_3,t15_ami_3]),
    [file(ami_5,t95_ami_5),interesting(0.06)]).

fof(t89_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_ami_3(F)
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k4_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,t9_ami_3,d25_ami_1]),
    [file(ami_5,t89_ami_5),interesting(0.01)]).

fof(t91_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_ami_3(F)
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k6_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,t11_ami_3,d25_ami_1]),
    [file(ami_5,t91_ami_5),interesting(0.01)]).

fof(t10_ami_5,theorem,(
    $true ),
    file(ami_5,t10_ami_5),
    [interesting(0.00)]).

fof(t11_ami_5,theorem,(
    $true ),
    file(ami_5,t11_ami_5),
    [interesting(0.00)]).

fof(t12_ami_5,theorem,(
    $true ),
    file(ami_5,t12_ami_5),
    [interesting(0.00)]).

fof(t13_ami_5,theorem,(
    $true ),
    file(ami_5,t13_ami_5),
    [interesting(0.00)]).

fof(t14_ami_5,theorem,(
    $true ),
    file(ami_5,t14_ami_5),
    [interesting(0.00)]).

fof(t17_ami_5,theorem,(
    $true ),
    file(ami_5,t17_ami_5),
    [interesting(0.00)]).

fof(t1_ami_5,theorem,(
    $true ),
    file(ami_5,t1_ami_5),
    [interesting(0.00)]).

fof(t21_ami_5,theorem,(
    $true ),
    file(ami_5,t21_ami_5),
    [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(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(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(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(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(t71_nat_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ( ~ r1_xreal_0(2,A)
          & A != 0
          & A != 1 ) ) ),
    file(nat_1,t71_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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [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(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(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(d2_ami_2,definition,(
    k2_ami_2 = a_0_0_ami_2 ),
    file(ami_2,d2_ami_2),
    [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(d1_ami_3,definition,(
    k1_ami_3 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,0,k3_ami_2,k1_gr_cy_1(9),k4_ami_2,k5_ami_2,k17_ami_2) ),
    file(ami_3,d1_ami_3),
    [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(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) ) ) ) ),
    file(ami_3,t36_ami_3),
    [interesting(0.00)]).

fof(t24_ami_5,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] : 
          ( m1_ami_3(B)
         => ! [C] : 
              ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ( r2_hidden(B,k1_relat_1(A))
                & r2_hidden(C,k1_relat_1(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_3,d2_xboole_0,d2_xboole_0,t23_ami_5,t36_ami_3,d1_ami_3,d2_xboole_0,t23_ami_5,t36_ami_3]),
    [file(ami_5,t24_ami_5),interesting(0.00)]).

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

fof(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(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(t26_ami_5,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(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)
              & ! [C] : 
                  ( m1_ami_3(C)
                 => k2_ami_3(A,C) = k2_ami_3(B,C) )
              & ! [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,A,C) = k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,B,C) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_ami_3,d5_card_3,d1_ami_3,d5_card_3,d1_funct_2,t23_ami_5,d1_ami_3,d2_xboole_0,d1_tarski,t16_ami_5,d1_ami_3,d2_xboole_0,t9_funct_1]),
    [file(ami_5,t26_ami_5),interesting(0.00)]).

fof(t10_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(A,k2_xboole_0(C,B)) ) ),
    file(xboole_1,t10_xboole_1),
    [interesting(0.00)]).

fof(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_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(t2_ami_5,theorem,(
    $true ),
    file(ami_5,t2_ami_5),
    [interesting(0.00)]).

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

fof(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(t52_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( A != B
              & k15_ami_3(A) = k15_ami_3(B) ) ) ) ),
    file(ami_3,t52_ami_3),
    [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(t68_card_1,theorem,(
    ! [A,B] : 
      ( ( r2_wellord2(A,B)
        & v1_finset_1(A) )
     => v1_finset_1(B) ) ),
    file(card_1,t68_card_1),
    [interesting(0.00)]).

fof(t15_card_4,theorem,(
    ~ v1_finset_1(k5_numbers) ),
    file(card_4,t15_card_4),
    [interesting(0.00)]).

fof(t53_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( A != B
              & k16_ami_3(A) = k16_ami_3(B) ) ) ) ),
    file(ami_3,t53_ami_3),
    [interesting(0.00)]).

fof(t22_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( A != 0
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => A != k1_nat_1(B,1) ) ) ) ),
    file(nat_1,t22_nat_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(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(t34_ami_5,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => k12_ami_3(A,B,k6_ami_1(A,B,C)) = k7_relat_1(C,k1_struct_0(B,k2_ami_1(A,B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_ami_5,t19_ami_1,t89_grfunc_1]),
    [file(ami_5,t34_ami_5),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(t3_ami_5,theorem,(
    $true ),
    file(ami_5,t3_ami_5),
    [interesting(0.00)]).

fof(t4_ami_5,theorem,(
    $true ),
    file(ami_5,t4_ami_5),
    [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(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(t56_ami_5,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] : 
          ( m1_ami_3(B)
         => ( k12_ami_2(k2_ami_5(k9_ami_3(A,B))) = A
            & k13_ami_2(k2_ami_5(k9_ami_3(A,B))) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_gr_cy_1,d1_ami_3,d2_ami_3,t25_ami_2]),
    [file(ami_5,t56_ami_5),interesting(0.00)]).

fof(t57_ami_5,theorem,(
    ! [A] : 
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] : 
          ( m1_ami_3(B)
         => ( k12_ami_2(k2_ami_5(k10_ami_3(A,B))) = A
            & k13_ami_2(k2_ami_5(k10_ami_3(A,B))) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_gr_cy_1,d1_ami_3,d2_ami_3,t25_ami_2]),
    [file(ami_5,t57_ami_5),interesting(0.00)]).

fof(t5_ami_5,theorem,(
    $true ),
    file(ami_5,t5_ami_5),
    [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(t6_grfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( r1_tarski(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(grfunc_1,t6_grfunc_1),
    [interesting(0.00)]).

fof(t40_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) )
             => ( ( r1_tarski(A,B)
                  & r2_hidden(B,k7_ami_1(C)) )
               => r2_hidden(A,k7_ami_1(C)) ) ) ) ) ),
    file(ami_1,t40_ami_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(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(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(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)) ) ) ) ) ) ) ),
    file(ami_3,t38_ami_3),
    [interesting(0.00)]).

fof(t64_ami_5,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_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(k6_ami_5(A,B,C),k11_ami_1(A,B,k10_ami_1(A,B,D),E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t63_ami_5,t1_xboole_1,t38_ami_3]),
    [file(ami_5,t64_ami_5),interesting(0.00)]).

fof(t87_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k1_relat_1(k7_relat_1(B,A)),A) ) ),
    file(relat_1,t87_relat_1),
    [interesting(0.00)]).

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

fof(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(t48_ami_1,theorem,(
    ! [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) )
     => ( v10_ami_1(B,A)
       => ! [C] : 
            ( m1_struct_0(C,B,u2_ami_1(A,B))
           => k2_ami_1(A,B) != C ) ) ) ),
    file(ami_1,t48_ami_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(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t7_scm_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k16_ami_3(A)
            & k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k15_ami_3(A)
            & k16_ami_3(A) != k15_ami_3(B) ) ) ) ),
    file(scm_1,t7_scm_1),
    [interesting(0.00)]).

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(t70_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ~ ( ~ r1_xboole_0(A,k2_xboole_0(B,C))
          & r1_xboole_0(A,B)
          & r1_xboole_0(A,C) )
      & ~ ( ~ ( r1_xboole_0(A,B)
              & r1_xboole_0(A,C) )
          & r1_xboole_0(A,k2_xboole_0(B,C)) ) ) ),
    file(xboole_1,t70_xboole_1),
    [interesting(0.00)]).

fof(t40_xboole_1,theorem,(
    ! [A,B] : k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B) ),
    file(xboole_1,t40_xboole_1),
    [interesting(0.00)]).

fof(t83_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k4_xboole_0(A,B) = A ) ),
    file(xboole_1,t83_xboole_1),
    [interesting(0.00)]).

fof(t6_ami_5,theorem,(
    $true ),
    file(ami_5,t6_ami_5),
    [interesting(0.00)]).

fof(t90_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    [interesting(0.00)]).

fof(t105_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ! [C] : 
          ( v1_relat_1(C)
         => ( r1_tarski(B,C)
           => r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A)) ) ) ) ),
    file(relat_1,t105_relat_1),
    [interesting(0.00)]).

fof(t39_xboole_1,theorem,(
    ! [A,B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) ),
    file(xboole_1,t39_xboole_1),
    [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(d8_ami_5,definition,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] : 
          ( m1_ami_1(C,A,B)
         => ( v1_ami_5(C,A,B)
          <=> r1_xboole_0(k1_relat_1(C),k4_subset_1(u1_struct_0(B),k1_struct_0(B,k2_ami_1(A,B)),u2_ami_1(A,B))) ) ) ) ),
    file(ami_5,d8_ami_5),
    [interesting(0.00)]).

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)) ) ) ) ),
    file(ami_3,t37_ami_3),
    [interesting(0.00)]).

fof(t73_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,k2_xboole_0(B,C))
        & r1_xboole_0(A,C) )
     => r1_tarski(A,B) ) ),
    file(xboole_1,t73_xboole_1),
    [interesting(0.00)]).

fof(t97_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k7_relat_1(B,A) = B ) ) ),
    file(relat_1,t97_relat_1),
    [interesting(0.00)]).

fof(t63_subset_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)) ) ),
    file(subset_1,t63_subset_1),
    [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(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)) ) ) ) ),
    file(ami_3,t34_ami_3),
    [interesting(0.00)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.00)]).

fof(t23_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ),
    file(xboole_1,t23_xboole_1),
    [interesting(0.00)]).

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 ) ) ) ),
    file(ami_3,t50_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(t70_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    [interesting(0.00)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).

fof(t34_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)) ) ),
    file(xboole_1,t34_xboole_1),
    [interesting(0.00)]).

fof(t79_xboole_1,theorem,(
    ! [A,B] : r1_xboole_0(k4_xboole_0(A,B),B) ),
    file(xboole_1,t79_xboole_1),
    [interesting(0.00)]).

fof(t64_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D)
        & r1_xboole_0(B,D) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t64_xboole_1),
    [interesting(0.00)]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [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(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(t9_grfunc_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)
              & r1_tarski(A,B) )
           => A = B ) ) ) ),
    file(grfunc_1,t9_grfunc_1),
    [interesting(0.00)]).

fof(t63_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_xboole_0(B,C) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t63_xboole_1),
    [interesting(0.00)]).

fof(t76_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( r1_xboole_0(C,k1_relat_1(B))
             => k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C) ) ) ) ),
    file(funct_4,t76_funct_4),
    [interesting(0.00)]).

fof(t38_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    [interesting(0.00)]).

fof(t36_ami_5,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))
     => r1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A),8) ) ),
    inference(mizar_proof,[status(thm)],[d1_ami_3,t10_gr_cy_1,t38_nat_1]),
    [file(ami_5,t36_ami_5),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(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(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(d1_ami_2,definition,(
    k1_ami_2 = 0 ),
    file(ami_2,d1_ami_2),
    [interesting(0.00)]).

fof(t71_ami_3,theorem,(
    k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) = k4_tarski(0,k1_xboole_0) ),
    file(ami_3,t71_ami_3),
    [interesting(0.00)]).

fof(t46_ami_5,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))
     => ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 0
       => A = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_mcart_1,d3_enumset1,t7_mcart_1,d2_tarski,t7_mcart_1,d4_ami_2,d1_ami_3,d2_xboole_0,d2_xboole_0,d2_xboole_0,d1_ami_2,t71_ami_3,d1_tarski]),
    [file(ami_5,t46_ami_5),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(t47_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 1
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k3_ami_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,d2_tarski,t7_mcart_1,d2_xboole_0,d2_xboole_0,d4_ami_2,d1_ami_3,d2_xboole_0,t7_mcart_1]),
    [file(ami_5,t47_ami_5),interesting(0.00)]).

fof(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    [interesting(0.00)]).

fof(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_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(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) ) ) ) ) ) ) ),
    file(ami_3,t8_ami_3),
    [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)) ) ) ) ),
    file(ami_3,t24_ami_3),
    [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(t48_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 2
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k4_ami_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,d2_tarski,t7_mcart_1,d2_xboole_0,d2_xboole_0,d4_ami_2,d1_ami_3,d2_xboole_0,t7_mcart_1]),
    [file(ami_5,t48_ami_5),interesting(0.00)]).

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) ) ) ) ) ) ) ),
    file(ami_3,t9_ami_3),
    [interesting(0.00)]).

fof(t49_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 3
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k5_ami_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,d2_tarski,t7_mcart_1,d2_xboole_0,d2_xboole_0,d4_ami_2,d1_ami_3,d2_xboole_0,t7_mcart_1]),
    [file(ami_5,t49_ami_5),interesting(0.00)]).

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) ) ) ) ) ) ) ),
    file(ami_3,t10_ami_3),
    [interesting(0.00)]).

fof(t50_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 4
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k6_ami_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,d2_tarski,t7_mcart_1,d2_xboole_0,d2_xboole_0,d4_ami_2,d1_ami_3,d2_xboole_0,t7_mcart_1]),
    [file(ami_5,t50_ami_5),interesting(0.00)]).

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) ) ) ) ) ) ) ),
    file(ami_3,t11_ami_3),
    [interesting(0.00)]).

fof(t51_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 5
          & ! [B] : 
              ( m1_ami_3(B)
             => ! [C] : 
                  ( m1_ami_3(C)
                 => A != k7_ami_3(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_ami_5,d1_ami_2,t71_ami_3,d1_tarski,t7_mcart_1,d2_tarski,t7_mcart_1,d2_xboole_0,d2_xboole_0,d4_ami_2,d1_ami_3,d2_xboole_0,t7_mcart_1]),
    [file(ami_5,t51_ami_5),interesting(0.00)]).

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) ) ) ) ) ) ) ),
    file(ami_3,t12_ami_3),
    [interesting(0.00)]).

fof(t15_ami_5,theorem,(
    ! [A] : 
      ( m1_ami_3(A)
     => ! [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,k7_ami_3(A,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))
            & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A),B),A) = k6_int_1(k2_ami_3(B,A),k2_ami_3(B,A))
            & ! [C] : 
                ( m1_ami_3(C)
               => ( C != A
                 => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A),B),C) = k2_ami_3(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_ami_3]),
    [file(ami_5,t15_ami_5),interesting(0.00)]).

fof(t48_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r2_hidden(C,B) )
     => k2_xboole_0(k2_tarski(A,C),B) = B ) ),
    file(zfmisc_1,t48_zfmisc_1),
    [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)) ) ) ) ),
    file(ami_3,t25_ami_3),
    [interesting(0.00)]).

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) ) ) ) ) ),
    file(ami_3,t13_ami_3),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(ami_3,t14_ami_3),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(ami_3,t15_ami_3),
    [interesting(0.00)]).

fof(t9_cqc_the1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,8)
          & A != 0
          & A != 1
          & A != 2
          & A != 3
          & A != 4
          & A != 5
          & A != 6
          & A != 7
          & A != 8 ) ) ),
    file(cqc_the1,t9_cqc_the1),
    [interesting(0.00)]).

fof(d13_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( v7_ami_1(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,k4_card_3(u5_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))
                   => ! [E] : 
                        ( m1_struct_0(E,B,u2_ami_1(A,B))
                       => k1_funct_1(k4_ami_1(A,B,D,C),E) = k1_funct_1(C,E) ) ) ) ) ) ) ),
    file(ami_1,d13_ami_1),
    [interesting(0.00)]).

fof(t59_ami_5,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)))
         => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),k3_ami_2) = k7_relat_1(B,k3_ami_2) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_ami_3,d1_ami_3,t91_relat_1,t36_ami_3,d1_ami_3,t91_relat_1,d1_ami_3,t72_funct_1,d13_ami_1,t72_funct_1,t9_funct_1]),
    [file(ami_5,t59_ami_5),interesting(0.00)]).

fof(t75_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) ) ) ),
    file(funct_4,t75_funct_4),
    [interesting(0.00)]).

fof(t83_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k7_relat_1(A,k2_xboole_0(B,C)) = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) ) ),
    file(funct_4,t83_funct_4),
    [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(d2_funcop_1,definition,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ),
    file(funcop_1,d2_funcop_1),
    [interesting(0.00)]).

fof(t35_zfmisc_1,theorem,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) ),
    file(zfmisc_1,t35_zfmisc_1),
    [interesting(0.00)]).

fof(t35_ami_5,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))
             => k12_ami_3(A,B,C) = k1_tarski(k1_domain_1(u1_struct_0(B),u2_ami_1(A,B),k2_ami_1(A,B),C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_funcop_1,t35_zfmisc_1]),
    [file(ami_5,t35_ami_5),interesting(0.00)]).

fof(t7_ami_5,theorem,(
    $true ),
    file(ami_5,t7_ami_5),
    [interesting(0.00)]).

fof(t80_ami_5,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k4_card_3(u5_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))
         => ! [C] : 
              ( m1_ami_3(C)
             => k2_ami_3(A,C) = k2_ami_3(k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,A,k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,B)),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_ami_3,t36_ami_3,d2_xboole_0,t20_ami_5,d1_tarski,d1_funct_4]),
    [file(ami_5,t80_ami_5),interesting(0.00)]).

fof(t81_ami_5,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ! [E] : 
                      ( m1_struct_0(E,B,u2_ami_1(A,B))
                     => k13_ami_1(A,B,C,E) = k13_ami_1(A,B,k8_ami_5(A,B,C,k12_ami_3(A,B,D)),E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_ami_3,t36_ami_3,d2_xboole_0,t48_ami_1,d1_tarski,d1_funct_4]),
    [file(ami_5,t81_ami_5),interesting(0.00)]).

fof(t27_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k4_card_3(A),k7_ami_1(A)) ) ),
    file(ami_1,t27_ami_1),
    [interesting(0.00)]).

fof(t41_ami_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(B,k7_ami_1(C))
           => r2_hidden(k7_relat_1(B,A),k7_ami_1(C)) ) ) ) ),
    file(ami_1,t41_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(t82_ami_5,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => ! [E] : m1_subset_1(k1_funct_4(C,k7_relat_1(D,E)),k4_card_3(u5_ami_1(A,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_ami_1,t41_ami_1,t29_ami_1]),
    [file(ami_5,t82_ami_5),interesting(0.00)]).

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) ) ) ) ) ),
    file(ami_3,t39_ami_3),
    [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(d25_ami_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)
             => ( v11_ami_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
                       => ( ( r1_tarski(C,D)
                            & r1_tarski(C,E) )
                         => ! [F] : 
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => k7_relat_1(k11_ami_1(A,B,k10_ami_1(A,B,D),F),k1_relat_1(C)) = k7_relat_1(k11_ami_1(A,B,k10_ami_1(A,B,E),F),k1_relat_1(C)) ) ) ) ) ) ) ) ) ),
    file(ami_1,d25_ami_1),
    [interesting(0.00)]).

fof(t33_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => r1_tarski(A,k1_funct_4(A,B)) ) ) ) ),
    file(funct_4,t33_funct_4),
    [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(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(t60_ami_5,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_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => ( ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
                      & r1_tarski(C,D) )
                   => k13_ami_3(A,B,C) = k6_ami_1(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_ami_3,t8_grfunc_1]),
    [file(ami_5,t60_ami_5),interesting(0.00)]).

fof(d19_ami_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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,k4_card_3(u5_ami_1(A,B)))
                    & m2_relset_1(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) )
                 => ( D = k10_ami_1(A,B,C)
                  <=> ( k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,0) = C
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,k1_nat_1(E,1)) = k9_ami_1(A,B,k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,E)) ) ) ) ) ) ) ) ),
    file(ami_1,d19_ami_1),
    [interesting(0.00)]).

fof(t85_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
     => ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A))
       => r2_hidden(k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,A),k1_relat_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t39_ami_3,t39_ami_3,t5_cqc_lang,t5_cqc_lang,d25_ami_1,t56_zfmisc_1,t33_funct_4,t1_xboole_1,d1_tarski,d1_tarski,d1_funct_4,d2_xboole_0,t8_grfunc_1,t14_funct_4,t6_cqc_lang,d1_funct_4,d2_xboole_0,t8_grfunc_1,t14_funct_4,t6_cqc_lang,t60_ami_5,t13_ami_3,t60_ami_5,t13_ami_3,d19_ami_1,d19_ami_1,d19_ami_1,d19_ami_1,t72_funct_1,t72_funct_1]),
    [file(ami_5,t85_ami_5),interesting(0.00)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

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

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

fof(t29_finset_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_finset_1(k1_relat_1(A))
      <=> v1_finset_1(A) ) ) ),
    file(finset_1,t29_finset_1),
    [interesting(0.00)]).

fof(t37_xboole_1,theorem,(
    ! [A,B] : 
      ( k4_xboole_0(A,B) = k1_xboole_0
    <=> r1_tarski(A,B) ) ),
    file(xboole_1,t37_xboole_1),
    [interesting(0.00)]).

fof(t25_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ),
    file(relat_1,t25_relat_1),
    [interesting(0.00)]).

fof(t56_ami_3,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => k15_ami_3(A) != k16_ami_3(B) ) ) ),
    file(ami_3,t56_ami_3),
    [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(t68_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( B = k7_relat_1(C,A)
          <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)
              & ! [D] : 
                  ( r2_hidden(D,k1_relat_1(B))
                 => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ),
    file(funct_1,t68_funct_1),
    [interesting(0.00)]).

fof(t17_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r1_xboole_0(k1_relat_1(B),k1_relat_1(C))
              & r2_hidden(A,k1_relat_1(B)) )
           => k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t17_funct_4),
    [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(t8_ami_5,theorem,(
    $true ),
    file(ami_5,t8_ami_5),
    [interesting(0.00)]).

fof(t90_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_ami_3(F)
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k5_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,t10_ami_3,d25_ami_1]),
    [file(ami_5,t90_ami_5),interesting(0.00)]).

fof(t92_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_ami_3(F)
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k7_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => ( E = F
                                    | k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,t12_ami_3,d25_ami_1]),
    [file(ami_5,t92_ami_5),interesting(0.00)]).

fof(t93_ami_5,theorem,(
    ! [A] : 
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] : 
                        ( m1_ami_3(E)
                       => ! [F] : 
                            ( m1_ami_3(F)
                           => ! [G] : 
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k7_ami_3(E,F)
                                    & r2_hidden(F,k1_relat_1(A)) )
                                 => ( E = F
                                    | k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t87_ami_5,d19_ami_1,d19_ami_1,t72_funct_1,t12_ami_3,d25_ami_1]),
    [file(ami_5,t93_ami_5),interesting(0.00)]).

fof(t9_ami_5,theorem,(
    $true ),
    file(ami_5,t9_ami_5),
    [interesting(0.00)]).