fof(t34_ami_1,theorem,(
    ! [A,B] : k4_partfun1(A,B) = k7_ami_1(k2_funcop_1(A,B)) ),
    inference(mizar_proof,[status(thm)],[t33_ami_1,t122_partfun1,t14_funcop_1,t19_funcop_1,t31_zfmisc_1,d3_tarski,d5_partfun1,t19_funcop_1,d5_funct_1,t13_funcop_1,d16_ami_1,t31_ami_1,d10_xboole_0]),
    [file(ami_1,t34_ami_1),interesting(1.00)]).

fof(t33_ami_1,theorem,(
    k7_ami_1(k1_xboole_0) = k1_tarski(k1_xboole_0) ),
    inference(mizar_proof,[status(thm)],[t31_ami_1,t60_relat_1,t2_zfmisc_1,t122_partfun1,d10_xboole_0,d3_tarski,d1_tarski,t26_ami_1]),
    [file(ami_1,t33_ami_1),interesting(0.82)]).

fof(t47_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D,E] : 
          ( ( r2_hidden(B,k1_relat_1(A))
            & r2_hidden(D,k1_funct_1(A,B))
            & r2_hidden(C,k1_relat_1(A))
            & r2_hidden(E,k1_funct_1(A,C)) )
         => r2_hidden(k4_funct_4(B,C,D,E),k7_ami_1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_ami_1,t36_ami_1,t18_ami_1,t46_ami_1]),
    [file(ami_1,t47_ami_1),interesting(0.79)]).

fof(t62_ami_1,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)))
             => ! [D] : 
                  ( m1_ami_1(D,A,B)
                 => m1_ami_1(k7_relat_1(C,k1_relat_1(D)),A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_ami_1,t41_ami_1,t90_relat_1,d24_ami_1,t29_finset_1,t15_finset_1,t29_finset_1,d24_ami_1]),
    [file(ami_1,t62_ami_1),interesting(0.75)]).

fof(t10_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => v7_ami_1(k1_ami_1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d13_ami_1,t9_ami_1]),
    [file(ami_1,t10_ami_1),interesting(0.73)]).

fof(t61_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => v13_ami_1(k1_ami_1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_1,d2_ami_1,t66_funct_4,d1_tarski,d27_ami_1,d2_funcop_1,d25_ami_1,t9_ami_1]),
    [file(ami_1,t61_ami_1),interesting(0.73)]).

fof(t8_ami_1,theorem,(
    ! [A] : v6_ami_1(k1_ami_1(A),A) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d12_ami_1,t2_ami_1,t46_funct_2,d1_tarski,d2_ami_1,d2_ami_1,t66_funct_4,d2_ami_1,d2_tarski,d1_tarski,t6_zfmisc_1,d2_ami_1]),
    [file(ami_1,t8_ami_1),interesting(0.73)]).

fof(t60_ami_1,theorem,(
    ! [A] : v10_ami_1(k1_ami_1(A),A) ),
    inference(mizar_proof,[status(thm)],[d2_ami_1,d21_ami_1,t6_zfmisc_1,t2_ami_1]),
    [file(ami_1,t60_ami_1),interesting(0.72)]).

fof(t27_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k4_card_3(A),k7_ami_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_card_3,d16_ami_1]),
    [file(ami_1,t27_ami_1),interesting(0.72)]).

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)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t88_relat_1,t40_ami_1]),
    [file(ami_1,t41_ami_1),interesting(0.72)]).

fof(t6_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => v4_ami_1(k1_ami_1(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_1,d1_tarski,d9_ami_1,d8_ami_1,d2_ami_1,t5_ami_1,d1_tarski,d1_tarski,d1_tarski]),
    [file(ami_1,t6_ami_1),interesting(0.72)]).

fof(t30_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k4_card_3(A) != k1_xboole_0
           => ( r2_hidden(B,k7_ami_1(A))
            <=> ? [C] : 
                  ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & r2_hidden(C,k4_card_3(A))
                  & r1_tarski(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_ami_1,t26_funct_4,t18_card_3,t25_relat_1,t8_grfunc_1,d16_ami_1]),
    [file(ami_1,t30_ami_1),interesting(0.71)]).

fof(t38_ami_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( ( r1_tarski(A,k7_ami_1(B))
          & ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r2_hidden(C,A)
                      & r2_hidden(D,A) )
                   => r1_partfun1(C,D) ) ) ) )
       => r2_hidden(k3_tarski(A),k7_ami_1(B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_fraenkel,t15_ami_1,d3_tarski,d4_relat_1,d4_tarski,d1_fraenkel,d4_relat_1,t25_ami_1,d4_relat_1,d4_tarski,d1_fraenkel,d4_relat_1,t8_funct_1,t8_funct_1,t25_ami_1,d16_ami_1]),
    [file(ami_1,t38_ami_1),interesting(0.71)]).

fof(t46_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,k7_ami_1(B))
                  & r2_hidden(C,k7_ami_1(B)) )
               => r2_hidden(k1_funct_4(A,C),k7_ami_1(B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_ami_1,t8_xboole_1,d1_funct_4,d1_funct_4,t39_xboole_1,t25_ami_1,t14_funct_4,d4_xboole_0,t25_ami_1,d4_xboole_0,t12_funct_4,d2_xboole_0,d16_ami_1]),
    [file(ami_1,t46_ami_1),interesting(0.71)]).

fof(t63_ami_1,theorem,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => m1_ami_1(k1_xboole_0,A,B) ) ),
    inference(mizar_proof,[status(thm)],[t26_ami_1,d24_ami_1]),
    [file(ami_1,t63_ami_1),interesting(0.71)]).

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)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_card_3,t25_ami_1,t12_xboole_1,d1_funct_4,t39_xboole_1,d4_xboole_0,t12_funct_4,d2_xboole_0,t14_funct_4,d2_xboole_0,t25_ami_1,t18_card_3,t18_card_3]),
    [file(ami_1,t29_ami_1),interesting(0.70)]).

fof(t20_ami_1,theorem,(
    ! [A,B,C] : k4_funct_4(A,A,B,C) = k3_cqc_lang(A,C) ),
    inference(mizar_proof,[status(thm)],[t19_funcop_1,t19_funcop_1,d4_funct_4,t20_funct_4]),
    [file(ami_1,t20_ami_1),interesting(0.70)]).

fof(t31_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r1_tarski(k7_ami_1(A),k4_partfun1(k1_relat_1(A),k3_tarski(k2_relat_1(A)))) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t28_ami_1,t119_partfun1]),
    [file(ami_1,t31_ami_1),interesting(0.69)]).

fof(t2_ami_1,theorem,(
    ! [A,B] : 1 != k4_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t8_zfmisc_1,t1_card_5]),
    [file(ami_1,t2_ami_1),interesting(0.69)]).

fof(t19_ami_1,theorem,(
    ! [A,B] : k3_cqc_lang(A,B) = k1_tarski(k4_tarski(A,B)) ),
    inference(mizar_proof,[status(thm)],[d2_funcop_1,t35_zfmisc_1]),
    [file(ami_1,t19_ami_1),interesting(0.67)]).

fof(t39_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_partfun1(A,B)
                  & r2_hidden(A,k7_ami_1(C))
                  & r2_hidden(B,k7_ami_1(C)) )
               => r2_hidden(k2_xboole_0(A,B),k7_ami_1(C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_zfmisc_1,d2_tarski,t93_zfmisc_1,t38_ami_1]),
    [file(ami_1,t39_ami_1),interesting(0.67)]).

fof(t9_ami_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k4_card_3(u5_ami_1(A,k1_ami_1(A))))
     => ! [C] : 
          ( m1_subset_1(C,k4_card_3(u5_ami_1(A,k1_ami_1(A))))
         => B = C ) ) ),
    inference(mizar_proof,[status(thm)],[d2_ami_1,t5_ami_1,d1_tarski,d1_tarski]),
    [file(ami_1,t9_ami_1),interesting(0.66)]).

fof(t11_ami_1,theorem,(
    ! [A] : v8_ami_1(k1_ami_1(A),A) ),
    inference(mizar_proof,[status(thm)],[d14_ami_1,d2_ami_1,d1_tarski,d2_ami_1,t66_funct_4,d2_ami_1]),
    [file(ami_1,t11_ami_1),interesting(0.66)]).

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)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_grfunc_1,t25_ami_1,t1_xboole_1,t25_ami_1,t8_grfunc_1,d16_ami_1]),
    [file(ami_1,t40_ami_1),interesting(0.66)]).

fof(t7_ami_1,theorem,(
    ! [A] : v5_ami_1(k1_ami_1(A),A) ),
    inference(mizar_proof,[status(thm)],[d2_ami_1,d2_ami_1,t66_funct_4,d2_ami_1,d11_ami_1]),
    [file(ami_1,t7_ami_1),interesting(0.66)]).

fof(t5_ami_1,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => k4_card_3(k4_funct_4(A,B,k1_tarski(C),k1_tarski(D))) = k1_tarski(k4_funct_4(A,B,C,D)) ) ),
    inference(mizar_proof,[status(thm)],[t65_funct_4,d1_tarski,t65_funct_4,d2_tarski,t66_funct_4,d1_tarski,d2_tarski,t66_funct_4,d1_tarski,t69_funct_4,d1_tarski,d5_card_3]),
    [file(ami_1,t5_ami_1),interesting(0.65)]).

fof(t26_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => r2_hidden(k1_xboole_0,k7_ami_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t2_xboole_1,d16_ami_1]),
    [file(ami_1,t26_ami_1),interesting(0.65)]).

fof(t28_ami_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k7_ami_1(B))
       => ( v1_funct_1(A)
          & m2_relset_1(A,k1_relat_1(B),k3_tarski(k2_relat_1(B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_ami_1,d3_tarski,d5_funct_1,d5_funct_1,d4_tarski,t11_relset_1]),
    [file(ami_1,t28_ami_1),interesting(0.64)]).

fof(t35_ami_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => k7_ami_1(C) = k7_ami_1(k2_partfun1(A,B,C,a_3_0_ami_1(A,B,C))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d16_ami_1,d1_funct_2,d3_xboole_0,d3_tarski,t90_relat_1,t71_funct_1,d16_ami_1,d10_xboole_0,t88_relat_1,t32_ami_1]),
    [file(ami_1,t35_ami_1),interesting(0.63)]).

fof(t37_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k7_ami_1(A) = k1_tarski(k1_xboole_0)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => k1_funct_1(A,B) = k1_xboole_0 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_ami_1,d1_tarski,t19_ami_1,d16_ami_1,t64_relat_1,d3_tarski,t26_ami_1,d1_tarski]),
    [file(ami_1,t37_ami_1),interesting(0.63)]).

fof(t18_ami_1,theorem,(
    ! [A,B,C,D] : k4_funct_4(A,B,C,D) = k1_funct_4(k3_cqc_lang(A,C),k3_cqc_lang(B,D)) ),
    inference(mizar_proof,[status(thm)],[d4_funct_4]),
    [file(ami_1,t18_ami_1),interesting(0.63)]).

fof(t36_ami_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & r2_hidden(B,k1_funct_1(C,A)) )
       => r2_hidden(k3_cqc_lang(A,B),k7_ami_1(C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_cqc_lang,t37_zfmisc_1,d1_tarski,t6_cqc_lang,d16_ami_1]),
    [file(ami_1,t36_ami_1),interesting(0.62)]).

fof(t3_ami_1,theorem,(
    ! [A,B] : 2 != k4_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t10_zfmisc_1,t1_card_5]),
    [file(ami_1,t3_ami_1),interesting(0.62)]).

fof(t32_ami_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(k7_ami_1(A),k7_ami_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_grfunc_1,d3_tarski,d16_ami_1,t1_xboole_1,t8_grfunc_1,d16_ami_1]),
    [file(ami_1,t32_ami_1),interesting(0.60)]).

fof(t14_ami_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ! [E] : 
          ( ( v1_relat_1(E)
            & v1_funct_1(E) )
         => ( ( r1_partfun1(D,E)
              & r2_hidden(k4_tarski(A,B),D)
              & r2_hidden(k4_tarski(A,C),E) )
           => B = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[t130_partfun1,d2_xboole_0,d1_funct_1]),
    [file(ami_1,t14_ami_1),interesting(0.60)]).

fof(t15_ami_1,theorem,(
    ! [A] : 
      ( ( ! [B] : 
            ( r2_hidden(B,A)
           => ( v1_relat_1(B)
              & v1_funct_1(B) ) )
        & ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B) )
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ( ( r2_hidden(B,A)
                    & r2_hidden(C,A) )
                 => r1_partfun1(B,C) ) ) ) )
     => ( v1_relat_1(k3_tarski(A))
        & v1_funct_1(k3_tarski(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_tarski,d1_relat_1,d4_tarski,d4_tarski,t14_ami_1,d1_funct_1,d1_relat_1]),
    [file(ami_1,t15_ami_1),interesting(0.59)]).

fof(t42_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(k7_relat_1(C,A))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t90_relat_1,t25_ami_1,t26_xboole_1,t70_funct_1,d3_xboole_0,t25_ami_1,d16_ami_1]),
    [file(ami_1,t42_ami_1),interesting(0.57)]).

fof(t72_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( C = k3_cqc_lang(k1_xboole_0,k1_xboole_0)
               => v14_ami_1(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d30_ami_1,t70_ami_1]),
    [file(ami_1,t72_ami_1),interesting(0.57)]).

fof(t75_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( C = k3_cqc_lang(k1_xboole_0,k1_xboole_0)
               => ! [D] : 
                    ( ( v11_ami_1(D,A,B)
                      & v12_ami_1(D,A,B)
                      & m1_ami_1(D,A,B) )
                   => m2_ami_1(D,A,B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t72_ami_1,d31_ami_1,t70_ami_1]),
    [file(ami_1,t75_ami_1),interesting(0.57)]).

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 ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_ami_1,d14_ami_1,d21_ami_1]),
    [file(ami_1,t48_ami_1),interesting(0.56)]).

fof(t76_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v11_ami_1(C,A,B)
                & v12_ami_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k14_ami_1(A,B),k14_ami_1(A,B)) )
                 => ( D = k3_cqc_lang(k1_xboole_0,k18_ami_1(A,B,C))
                   => m2_ami_1(C,A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t73_ami_1,d31_ami_1,t69_ami_1]),
    [file(ami_1,t76_ami_1),interesting(0.56)]).

fof(t22_ami_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k4_card_3(B))
       => ( v1_relat_1(A)
          & v1_funct_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_card_3]),
    [file(ami_1,t22_ami_1),interesting(0.55)]).

fof(t70_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ( ( v11_ami_1(C,A,B)
                  & v12_ami_1(C,A,B)
                  & m1_ami_1(C,A,B) )
              <=> r1_ami_1(A,B,C,k3_cqc_lang(k1_xboole_0,k1_xboole_0)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d29_ami_1,t5_cqc_lang,d1_tarski,t63_ami_1,t22_funct_4,t6_cqc_lang,t2_xboole_1,t5_cqc_lang,d1_tarski,d29_ami_1,t22_funct_4]),
    [file(ami_1,t70_ami_1),interesting(0.55)]).

fof(t69_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ( ( v11_ami_1(C,A,B)
                  & v12_ami_1(C,A,B)
                  & m1_ami_1(C,A,B) )
              <=> r1_ami_1(A,B,C,k3_cqc_lang(k1_xboole_0,k18_ami_1(A,B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d29_ami_1,t5_cqc_lang,d1_tarski,t63_ami_1,t22_funct_4,t6_cqc_lang,t22_funct_4,t5_cqc_lang,d1_tarski,d29_ami_1,t22_funct_4]),
    [file(ami_1,t69_ami_1),interesting(0.55)]).

fof(t68_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => r1_ami_1(A,B,C,k1_xboole_0) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d29_ami_1]),
    [file(ami_1,t68_ami_1),interesting(0.53)]).

fof(t73_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v11_ami_1(C,A,B)
                & v12_ami_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,k14_ami_1(A,B),k14_ami_1(A,B)) )
                 => ( D = k3_cqc_lang(k1_xboole_0,k18_ami_1(A,B,C))
                   => v14_ami_1(D,A,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d30_ami_1,t69_ami_1]),
    [file(ami_1,t73_ami_1),interesting(0.52)]).

fof(t71_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( C = k1_xboole_0
               => v14_ami_1(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d30_ami_1,t68_ami_1]),
    [file(ami_1,t71_ami_1),interesting(0.51)]).

fof(t25_ami_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k7_ami_1(B))
           => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_ami_1]),
    [file(ami_1,t25_ami_1),interesting(0.50)]).

fof(t74_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( C = k1_xboole_0
               => ! [D] : 
                    ( m1_ami_1(D,A,B)
                   => m2_ami_1(D,A,B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_ami_1,d31_ami_1,t68_ami_1]),
    [file(ami_1,t74_ami_1),interesting(0.47)]).

fof(t57_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & k13_ami_1(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) = k5_ami_1(A,B) )
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k12_ami_1(A,B,C) = k12_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_ami_1,t28_nat_1,t51_ami_1,d20_ami_1,t56_ami_1,d22_ami_1,t52_ami_1,d19_ami_1,d20_ami_1,t56_ami_1,d22_ami_1]),
    [file(ami_1,t57_ami_1),interesting(0.45)]).

fof(t59_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C,D] : 
              ( m1_subset_1(D,u1_struct_0(B))
             => ( k3_ami_1(A,B,D) = C
               => ! [E] : 
                    ( m1_subset_1(E,C)
                   => m1_ami_1(k3_cqc_lang(D,E),A,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_cqc_lang,d1_funct_2,d1_tarski,t6_cqc_lang,d16_ami_1,t5_cqc_lang,t29_finset_1,d24_ami_1]),
    [file(ami_1,t59_ami_1),interesting(0.45)]).

fof(t58_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C,D,E] : 
              ( m1_subset_1(E,u1_struct_0(B))
             => ! [F] : 
                  ( m1_subset_1(F,u1_struct_0(B))
                 => ( ( k3_ami_1(A,B,E) = C
                      & k3_ami_1(A,B,F) = D )
                   => ! [G] : 
                        ( m1_subset_1(G,C)
                       => ! [H] : 
                            ( m1_subset_1(H,D)
                           => m1_ami_1(k4_funct_4(E,F,G,H),A,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t65_funct_4,d1_funct_2,t66_funct_4,t66_funct_4,t20_ami_1,t6_cqc_lang,d2_tarski,d16_ami_1,t65_funct_4,t29_finset_1,d24_ami_1]),
    [file(ami_1,t58_ami_1),interesting(0.43)]).

fof(t67_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
                 => ( D = C
                   => ! [E] : 
                        ( m1_subset_1(E,k3_ami_1(A,B,C))
                       => ( E = k5_ami_1(A,B)
                         => v11_ami_1(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),A,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d25_ami_1,t64_grfunc_1,t66_ami_1]),
    [file(ami_1,t67_ami_1),interesting(0.43)]).

fof(t64_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
                 => ( D = C
                   => ! [E] : 
                        ( m1_subset_1(E,k3_ami_1(A,B,C))
                       => ( E = k5_ami_1(A,B)
                         => ! [F] : 
                              ( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
                             => ( r1_tarski(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),F)
                               => k8_ami_1(A,B,F) = k5_ami_1(A,B) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_ami_1,t65_funct_4,d2_tarski,t66_funct_4,t8_grfunc_1,t8_grfunc_1,t66_funct_4,t66_funct_4]),
    [file(ami_1,t64_ami_1),interesting(0.38)]).

fof(t65_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
                 => ( D = C
                   => ! [E] : 
                        ( m1_subset_1(E,k3_ami_1(A,B,C))
                       => ( E = k5_ami_1(A,B)
                         => v12_ami_1(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),A,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d26_ami_1,d20_ami_1,d19_ami_1,t64_ami_1]),
    [file(ami_1,t65_ami_1),interesting(0.38)]).

fof(t66_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k3_ami_1(A,B,k2_ami_1(A,B)))
                 => ( D = C
                   => ! [E] : 
                        ( m1_subset_1(E,k3_ami_1(A,B,C))
                       => ( E = k5_ami_1(A,B)
                         => ! [F] : 
                              ( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
                             => ( r1_tarski(k16_ami_1(A,B,k2_ami_1(A,B),C,D,E),F)
                               => ! [G] : 
                                    ( m2_subset_1(G,k1_numbers,k5_numbers)
                                   => k11_ami_1(A,B,k10_ami_1(A,B,F),G) = F ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_ami_1,d19_ami_1,t64_ami_1,d8_ami_1,s1_nat_1]),
    [file(ami_1,t66_ami_1),interesting(0.36)]).

fof(t56_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( k13_ami_1(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) = k5_ami_1(A,B)
                   => k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_ami_1,d20_ami_1,d22_ami_1]),
    [file(ami_1,t56_ami_1),interesting(0.21)]).

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(d2_ami_1,definition,(
    ! [A,B] : 
      ( ( v1_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ( B = k1_ami_1(A)
      <=> ( u1_struct_0(B) = k2_tarski(0,1)
          & u1_ami_1(A,B) = 0
          & u2_ami_1(A,B) = k1_tarski(1)
          & u3_ami_1(A,B) = k1_tarski(0)
          & u4_ami_1(A,B) = k1_tarski(k4_tarski(0,k1_xboole_0))
          & u5_ami_1(A,B) = k4_funct_4(0,1,k1_tarski(1),k1_tarski(k4_tarski(0,k1_xboole_0)))
          & u6_ami_1(A,B) = k3_cqc_lang(k4_tarski(0,k1_xboole_0),k6_partfun1(k4_card_3(k4_funct_4(0,1,k1_tarski(1),k1_tarski(k4_tarski(0,k1_xboole_0)))))) ) ) ) ),
    file(ami_1,d2_ami_1),
    [interesting(0.00)]).

fof(t65_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B)
      & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) ) ),
    file(funct_4,t65_funct_4),
    [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(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(t66_funct_4,theorem,(
    ! [A,B,C,D] : 
      ( A != B
     => ( k1_funct_1(k4_funct_4(A,B,C,D),A) = C
        & k1_funct_1(k4_funct_4(A,B,C,D),B) = D ) ) ),
    file(funct_4,t66_funct_4),
    [interesting(0.00)]).

fof(t69_funct_4,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_1(E)
        & v1_funct_1(E) )
     => ( ( k1_relat_1(E) = k2_tarski(A,B)
          & k1_funct_1(E,A) = C
          & k1_funct_1(E,B) = D )
       => E = k4_funct_4(A,B,C,D) ) ) ),
    file(funct_4,t69_funct_4),
    [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(d14_ami_1,definition,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ( v8_ami_1(B,A)
      <=> ! [C] : 
            ( m1_struct_0(C,B,u2_ami_1(A,B))
           => k3_ami_1(A,B,C) = u4_ami_1(A,B) ) ) ) ),
    file(ami_1,d14_ami_1),
    [interesting(0.00)]).

fof(t12_ami_1,theorem,(
    $true ),
    file(ami_1,t12_ami_1),
    [interesting(0.00)]).

fof(t13_ami_1,theorem,(
    $true ),
    file(ami_1,t13_ami_1),
    [interesting(0.00)]).

fof(t16_ami_1,theorem,(
    $true ),
    file(ami_1,t16_ami_1),
    [interesting(0.00)]).

fof(t17_ami_1,theorem,(
    $true ),
    file(ami_1,t17_ami_1),
    [interesting(0.00)]).

fof(t1_ami_1,theorem,(
    $true ),
    file(ami_1,t1_ami_1),
    [interesting(0.00)]).

fof(t21_ami_1,theorem,(
    $true ),
    file(ami_1,t21_ami_1),
    [interesting(0.00)]).

fof(t23_ami_1,theorem,(
    $true ),
    file(ami_1,t23_ami_1),
    [interesting(0.00)]).

fof(t24_ami_1,theorem,(
    $true ),
    file(ami_1,t24_ami_1),
    [interesting(0.00)]).

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

fof(d16_ami_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k7_ami_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & r1_tarski(k1_relat_1(D),k1_relat_1(A))
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(D))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(ami_1,d16_ami_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(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(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(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(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(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(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(t26_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(A,k1_funct_4(B,A)) ) ) ),
    file(funct_4,t26_funct_4),
    [interesting(0.00)]).

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

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

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

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

fof(t119_partfun1,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => r2_hidden(C,k4_partfun1(A,B)) ) ),
    file(partfun1,t119_partfun1),
    [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(t2_zfmisc_1,theorem,(
    k3_tarski(k1_xboole_0) = k1_xboole_0 ),
    file(zfmisc_1,t2_zfmisc_1),
    [interesting(0.00)]).

fof(t122_partfun1,theorem,(
    ! [A] : k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0) ),
    file(partfun1,t122_partfun1),
    [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(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.00)]).

fof(t14_funcop_1,theorem,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B) ) ),
    file(funcop_1,t14_funcop_1),
    [interesting(0.00)]).

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

fof(t31_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_tarski(A)) = A ),
    file(zfmisc_1,t31_zfmisc_1),
    [interesting(0.00)]).

fof(d5_partfun1,definition,(
    ! [A,B,C] : 
      ( C = k4_partfun1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & r1_tarski(k1_relat_1(E),A)
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(partfun1,d5_partfun1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(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(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(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(t71_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k3_xboole_0(k1_relat_1(C),A))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t71_funct_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(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(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(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(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(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(t38_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t38_zfmisc_1),
    [interesting(0.00)]).

fof(t93_zfmisc_1,theorem,(
    ! [A,B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) ),
    file(zfmisc_1,t93_zfmisc_1),
    [interesting(0.00)]).

fof(d1_fraenkel,definition,(
    ! [A] : 
      ( v1_fraenkel(A)
    <=> ! [B] : 
          ( r2_hidden(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,d1_fraenkel),
    [interesting(0.00)]).

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

fof(t130_partfun1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & k2_xboole_0(A,B) = C ) ) ) ) ),
    file(partfun1,t130_partfun1),
    [interesting(0.00)]).

fof(d1_funct_1,definition,(
    ! [A] : 
      ( v1_funct_1(A)
    <=> ! [B,C,D] : 
          ( ( r2_hidden(k4_tarski(B,C),A)
            & r2_hidden(k4_tarski(B,D),A) )
         => C = D ) ) ),
    file(funct_1,d1_funct_1),
    [interesting(0.00)]).

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

fof(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(t10_zfmisc_1,theorem,(
    ! [A,B,C,D] : ~ ( k2_tarski(A,B) = k2_tarski(C,D)
      & A != C
      & A != D ) ),
    file(zfmisc_1,t10_zfmisc_1),
    [interesting(0.00)]).

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

fof(t26_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ),
    file(xboole_1,t26_xboole_1),
    [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(t25_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A) ) ) ),
    file(funct_4,t25_funct_4),
    [interesting(0.00)]).

fof(t24_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)) = B ) ) ),
    file(funct_4,t24_funct_4),
    [interesting(0.00)]).

fof(t74_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( r1_tarski(k1_relat_1(A),k2_xboole_0(B,C))
         => k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = A ) ) ),
    file(funct_4,t74_funct_4),
    [interesting(0.00)]).

fof(t43_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,k7_ami_1(k1_funct_4(B,C)))
                  & ! [D] : 
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D) )
                     => ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E) )
                         => ~ ( r2_hidden(D,k7_ami_1(B))
                              & r2_hidden(E,k7_ami_1(C))
                              & A = k1_funct_4(D,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t42_ami_1,t25_funct_4,t32_ami_1,t24_funct_4,t42_ami_1,t25_ami_1,d1_funct_4,t39_xboole_1,t74_funct_4]),
    [file(ami_1,t43_ami_1),interesting(0.00)]).

fof(t81_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_xboole_0(A,k4_xboole_0(B,C))
     => r1_xboole_0(B,k4_xboole_0(A,C)) ) ),
    file(xboole_1,t81_xboole_1),
    [interesting(0.00)]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_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(t44_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) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_xboole_0(k1_relat_1(A),k4_xboole_0(k1_relat_1(C),k1_relat_1(D)))
                      & r2_hidden(C,k7_ami_1(B))
                      & r2_hidden(D,k7_ami_1(A)) )
                   => r2_hidden(k1_funct_4(C,D),k7_ami_1(k1_funct_4(B,A))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_ami_1,t13_xboole_1,d1_funct_4,d1_funct_4,d1_funct_4,t39_xboole_1,d2_xboole_0,d1_funct_4,t3_xboole_0,t25_ami_1,t3_xboole_0,d1_funct_4,d2_xboole_0,t25_ami_1,d1_funct_4,d16_ami_1]),
    [file(ami_1,t44_ami_1),interesting(0.00)]).

fof(t45_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) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_xboole_0(k1_relat_1(C),k4_xboole_0(k1_relat_1(A),k1_relat_1(D)))
                      & r2_hidden(C,k7_ami_1(B))
                      & r2_hidden(D,k7_ami_1(A)) )
                   => r2_hidden(k1_funct_4(C,D),k7_ami_1(k1_funct_4(B,A))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t81_xboole_1,t44_ami_1]),
    [file(ami_1,t45_ami_1),interesting(0.00)]).

fof(d4_funct_4,definition,(
    ! [A,B,C,D] : k4_funct_4(A,B,C,D) = k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D)) ),
    file(funct_4,d4_funct_4),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.00)]).

fof(t49_ami_1,theorem,(
    $true ),
    file(ami_1,t49_ami_1),
    [interesting(0.00)]).

fof(t4_ami_1,theorem,(
    $true ),
    file(ami_1,t4_ami_1),
    [interesting(0.00)]).

fof(t50_ami_1,theorem,(
    $true ),
    file(ami_1,t50_ami_1),
    [interesting(0.00)]).

fof(t53_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))
                 => k1_funct_1(C,D) = k1_funct_1(k9_ami_1(A,B,C),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_ami_1]),
    [file(ami_1,t53_ami_1),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(s1_nat_1,theorem,
    ( ( p1_s1_nat_1(0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( p1_s1_nat_1(A)
           => p1_s1_nat_1(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => p1_s1_nat_1(A) ) ),
    file(nat_1,s1_nat_1),
    [interesting(0.00)]).

fof(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) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_ami_1,d13_ami_1,d19_ami_1,s1_nat_1]),
    [file(ami_1,t54_ami_1),interesting(0.00)]).

fof(t55_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,A)
                & v5_ami_1(C,A)
                & v7_ami_1(C,A)
                & v8_ami_1(C,A)
                & l1_ami_1(C,A) )
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,C)))
                 => k11_ami_1(A,C,k10_ami_1(A,C,D),k1_nat_1(B,1)) = k4_ami_1(A,C,k13_ami_1(A,C,D,k6_ami_1(A,C,k11_ami_1(A,C,k10_ami_1(A,C,D),B))),k11_ami_1(A,C,k10_ami_1(A,C,D),B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_ami_1,t54_ami_1]),
    [file(ami_1,t55_ami_1),interesting(0.00)]).

fof(t28_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => B != k2_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,t28_nat_1),
    [interesting(0.00)]).

fof(t51_ami_1,theorem,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,A)
                & v5_ami_1(C,A)
                & v8_ami_1(C,A)
                & l1_ami_1(C,A) )
             => ! [D] : 
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,C)))
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => k11_ami_1(A,C,k10_ami_1(A,C,D),k1_nat_1(B,E)) = k11_ami_1(A,C,k10_ami_1(A,C,k11_ami_1(A,C,k10_ami_1(A,C,D),B)),E) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_ami_1,d19_ami_1,d19_ami_1,s1_nat_1]),
    [file(ami_1,t51_ami_1),interesting(0.00)]).

fof(d20_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( v9_ami_1(C,A,B)
              <=> ? [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) = k5_ami_1(A,B) ) ) ) ) ) ),
    file(ami_1,d20_ami_1),
    [interesting(0.00)]).

fof(d22_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( v9_ami_1(C,A,B)
               => ! [D] : 
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ( D = k12_ami_1(A,B,C)
                    <=> ? [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                          & D = k11_ami_1(A,B,k10_ami_1(A,B,C),E)
                          & k8_ami_1(A,B,D) = k5_ami_1(A,B) ) ) ) ) ) ) ) ),
    file(ami_1,d22_ami_1),
    [interesting(0.00)]).

fof(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(t52_ami_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
           => ! [C] : 
                ( v1_setfam_1(C)
               => ! [D] : 
                    ( ( ~ v3_struct_0(D)
                      & ~ v2_ami_1(D,C)
                      & v4_ami_1(D,C)
                      & v5_ami_1(D,C)
                      & v8_ami_1(D,C)
                      & l1_ami_1(D,C) )
                   => ! [E] : 
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
                       => ( k8_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)) = k5_ami_1(C,D)
                         => k11_ami_1(C,D,k10_ami_1(C,D,E),B) = k11_ami_1(C,D,k10_ami_1(C,D,E),A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_nat_1,d19_ami_1,d8_ami_1,s1_nat_1]),
    [file(ami_1,t52_ami_1),interesting(0.00)]).

fof(t20_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
           => k1_funct_4(A,B) = B ) ) ) ),
    file(funct_4,t20_funct_4),
    [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(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(d21_ami_1,definition,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v10_ami_1(B,A)
      <=> u4_ami_1(A,B) != u2_ami_1(A,B) ) ) ),
    file(ami_1,d21_ami_1),
    [interesting(0.00)]).

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

fof(t8_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => A = B ) ),
    file(zfmisc_1,t8_zfmisc_1),
    [interesting(0.00)]).

fof(d27_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) )
         => ( v13_ami_1(B,A)
          <=> ? [C] : 
                ( m1_ami_1(C,A,B)
                & ~ v1_xboole_0(C)
                & v11_ami_1(C,A,B) ) ) ) ) ),
    file(ami_1,d27_ami_1),
    [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(t15_finset_1,theorem,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,t15_finset_1),
    [interesting(0.00)]).

fof(d26_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ( v12_ami_1(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ( r1_tarski(C,D)
                     => v9_ami_1(D,A,B) ) ) ) ) ) ) ),
    file(ami_1,d26_ami_1),
    [interesting(0.00)]).

fof(d11_ami_1,definition,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ( v5_ami_1(B,A)
      <=> k3_ami_1(A,B,k2_ami_1(A,B)) = u2_ami_1(A,B) ) ) ),
    file(ami_1,d11_ami_1),
    [interesting(0.00)]).

fof(t64_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)
           => k7_relat_1(B,k1_relat_1(A)) = A ) ) ) ),
    file(grfunc_1,t64_grfunc_1),
    [interesting(0.00)]).

fof(d9_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( v4_ami_1(B,A)
          <=> ? [C] : 
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                & v3_ami_1(C,A,B)
                & ! [D] : 
                    ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                   => ( v3_ami_1(D,A,B)
                     => C = D ) ) ) ) ) ) ),
    file(ami_1,d9_ami_1),
    [interesting(0.00)]).

fof(d30_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( v14_ami_1(C,A,B)
              <=> ? [D] : 
                    ( m1_ami_1(D,A,B)
                    & r1_ami_1(A,B,D,C) ) ) ) ) ) ),
    file(ami_1,d30_ami_1),
    [interesting(0.00)]).

fof(d29_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( m1_ami_1(C,A,B)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r1_ami_1(A,B,C,D)
                  <=> ! [E] : ~ ( r2_hidden(E,k1_relat_1(D))
                        & ! [F] : 
                            ( m1_ami_1(F,A,B)
                           => ~ ( E = F
                                & v11_ami_1(k17_ami_1(A,B,C,F),A,B)
                                & v12_ami_1(k17_ami_1(A,B,C,F),A,B)
                                & m1_ami_1(k17_ami_1(A,B,C,F),A,B)
                                & r1_tarski(k1_funct_1(D,F),k18_ami_1(A,B,k17_ami_1(A,B,C,F))) ) ) ) ) ) ) ) ) ),
    file(ami_1,d29_ami_1),
    [interesting(0.00)]).

fof(d31_ami_1,definition,(
    ! [A] : 
      ( v1_setfam_1(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( v14_ami_1(C,A,B)
               => ! [D] : 
                    ( m1_ami_1(D,A,B)
                   => ( m2_ami_1(D,A,B,C)
                    <=> r1_ami_1(A,B,D,C) ) ) ) ) ) ) ),
    file(ami_1,d31_ami_1),
    [interesting(0.00)]).

fof(t22_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k1_funct_4(A,k1_xboole_0) = A ) ),
    file(funct_4,t22_funct_4),
    [interesting(0.00)]).

fof(d12_ami_1,definition,(
    ! [A,B] : 
      ( l1_ami_1(B,A)
     => ( v6_ami_1(B,A)
      <=> r1_tarski(k3_funct_2(u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B))),u5_ami_1(A,B),k1_tarski(u4_ami_1(A,B))),u2_ami_1(A,B)) ) ) ),
    file(ami_1,d12_ami_1),
    [interesting(0.00)]).

fof(t46_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( r2_hidden(E,k10_relat_1(D,C))
          <=> ( r2_hidden(E,A)
              & r2_hidden(k1_funct_1(D,E),C) ) ) ) ) ),
    file(funct_2,t46_funct_2),
    [interesting(0.00)]).