fof(t4_abian,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( v2_abian(B,k1_zfmisc_1(k1_zfmisc_1(A)))
      <=> k5_setfam_1(A,B) = A ) ) ),
    inference(mizar_proof,[status(thm)],[t99_zfmisc_1,t99_zfmisc_1,d6_abian]),
    [file(abian,t4_abian),interesting(1.00)]).

fof(t8_abian,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ~ ( ~ r3_abian(B)
              & ! [C,D,E] : ~ ( k2_xboole_0(k2_xboole_0(C,D),E) = A
                  & r1_xboole_0(k2_funct_2(A,A,B,C),C)
                  & r1_xboole_0(k2_funct_2(A,A,B,D),D)
                  & r1_xboole_0(k2_funct_2(A,A,B,E),E) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_eqrel_1,t28_eqrel_1,s7_domain_1,t1_xboole_1,s7_domain_1,t1_xboole_1,t2_xboole_1,t47_mcart_1,d2_xboole_0,d3_tarski,d10_xboole_0,d3_tarski,t27_eqrel_1,d7_abian,d1_funct_2,d2_xboole_0,t73_funct_7,t23_funct_1,t23_funct_1,t73_funct_7,d2_xboole_0,d2_xboole_0,t73_funct_7,t23_funct_1,t23_funct_1,t73_funct_7,d2_xboole_0,d3_tarski,d12_funct_1,t6_abian,d1_funct_2,t71_funct_7,t23_funct_1,t73_funct_7,t23_funct_1,t73_funct_7,t23_funct_1,t23_funct_1,t73_funct_7,t23_funct_1,t73_funct_7,t63_xboole_1,d3_tarski,d12_funct_1,t6_abian,d1_funct_2,t71_funct_7,t23_funct_1,t73_funct_7,t23_funct_1,t73_funct_7,t23_funct_1,t23_funct_1,t73_funct_7,t23_funct_1,t73_funct_7,t63_xboole_1,t65_xboole_1,t3_xboole_0,d1_funct_2,t79_funct_7,t23_funct_1,t23_funct_1,t79_funct_7,t79_funct_7,t23_funct_1,t23_funct_1,t79_funct_7,d1_funct_2,t18_int_1,t23_funct_1,t79_funct_7,t7_abian,t18_int_1,t23_funct_1,t79_funct_7,t7_abian,t1_xreal_1,s7_domain_1,s12_funct_2,d1_funct_2,d5_eqrel_1,t30_eqrel_1,d7_abian,t3_abian,d1_funct_2,t79_funct_7,t23_funct_1,s1_nat_1,t19_nat_1,t47_nat_1,t46_nat_1,t18_int_1,d1_funct_2,t79_funct_7,t23_funct_1,t23_funct_1,t79_funct_7,d15_funct_1,s4_funct_2,s7_domain_1,t36_xboole_1,t1_xboole_1,t1_xboole_1,s7_domain_1,t1_xboole_1,t37_zfmisc_1,t47_mcart_1,t3_abian,t2_abian,t39_xboole_1,t46_zfmisc_1,d2_xboole_0,d3_tarski,d10_xboole_0,d3_tarski,d2_xboole_0,t4_xboole_1,t3_xboole_0,t7_xboole_1,t63_xboole_1,d8_cqc_sim1,t3_abian,t6_abian,t39_nat_1,t18_int_1,d1_funct_2,t23_funct_1,t71_funct_7,d8_cqc_sim1,d8_cqc_sim1,t71_funct_7,t23_funct_1,d8_cqc_sim1,d8_cqc_sim1,t22_xreal_1,t1_xreal_1,d3_tarski,d12_funct_1,d4_xboole_0,t6_abian,t64_zfmisc_1,t63_xboole_1,d3_tarski,d12_funct_1,t6_abian,t63_xboole_1,t3_xboole_0,d1_tarski,d12_funct_1,d1_tarski,d4_abian,d5_abian,s3_funct_2,d2_xboole_0,d4_tarski,d4_tarski,d4_tarski,d2_xboole_0,d3_tarski,d10_xboole_0,d3_tarski,t28_eqrel_1,d5_eqrel_1,d2_xboole_0,d4_tarski,d2_xboole_0,d2_xboole_0,d4_tarski,d2_xboole_0,d2_xboole_0,d4_tarski,d2_xboole_0,d2_xboole_0,t3_xboole_0,d4_tarski,d12_funct_1,d4_tarski,d2_xboole_0,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,d2_xboole_0,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,d1_funct_2,d2_xboole_0,t72_funct_7,t34_funct_1,t70_funct_7,d7_abian,t44_eqrel_1,d12_funct_1,t3_xboole_0,t3_xboole_0,d4_tarski,d12_funct_1,d4_tarski,d2_xboole_0,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,d2_xboole_0,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,d1_funct_2,d2_xboole_0,t72_funct_7,t34_funct_1,t70_funct_7,d7_abian,t44_eqrel_1,d12_funct_1,t3_xboole_0,t3_xboole_0,d4_tarski,d12_funct_1,d4_tarski,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,d1_funct_2,d2_xboole_0,t72_funct_7,t34_funct_1,t70_funct_7,d7_abian,t44_eqrel_1,d12_funct_1,t3_xboole_0]),
    [file(abian,t8_abian),interesting(0.96)]).

fof(t3_abian,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => k8_funct_2(A,A,k1_abian(A,B,0),C) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d2_xboole_0,t70_funct_7,t34_funct_1]),
    [file(abian,t3_abian),interesting(0.82)]).

fof(t2_abian,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
     => ( r2_hidden(0,A)
       => k10_cqc_sim1(A) = 0 ) ) ),
    inference(mizar_proof,[status(thm)],[d8_cqc_sim1,t19_nat_1]),
    [file(abian,t2_abian),interesting(0.78)]).

fof(t6_abian,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] : 
              ( m2_subset_1(C,k1_zfmisc_1(A),k8_eqrel_1(A,k2_abian(A,B)))
             => ! [D] : 
                  ( m2_subset_1(D,A,C)
                 => r2_hidden(k8_funct_2(A,A,B,D),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,t72_funct_7,t34_funct_1,t70_funct_7,d7_abian,t27_eqrel_1]),
    [file(abian,t6_abian),interesting(0.71)]).

fof(t1_abian,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( ~ ( ~ v1_abian(A)
            & ! [B] : 
                ( v1_int_1(B)
               => A != k2_xcmplx_0(k3_xcmplx_0(2,B),1) ) )
        & ~ ( ? [B] : 
                ( v1_int_1(B)
                & A = k2_xcmplx_0(k3_xcmplx_0(2,B),1) )
            & v1_abian(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t8_int_1,t1_scheme1,d1_abian,d1_abian,d1_abian,t22_int_1]),
    [file(abian,t1_abian),interesting(0.35)]).

fof(t7_abian,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] : 
              ( m2_subset_1(C,k1_zfmisc_1(A),k8_eqrel_1(A,k2_abian(A,B)))
             => ! [D] : 
                  ( m2_subset_1(D,A,C)
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => r2_hidden(k8_funct_2(A,A,k1_abian(A,B,E),D),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,d2_xboole_0,d5_eqrel_1,t31_eqrel_1,t34_funct_1,t70_funct_7,d7_abian,t27_eqrel_1]),
    [file(abian,t7_abian),interesting(0.20)]).

fof(t8_int_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ~ ( v1_int_1(A)
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( A != B
                & A != k1_real_1(B) ) ) ) ) ),
    file(int_1,t8_int_1),
    [interesting(0.00)]).

fof(t1_scheme1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ~ ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( A != k2_nat_1(2,B)
              & A != k1_nat_1(k2_nat_1(2,B),1) ) ) ) ),
    file(scheme1,t1_scheme1),
    [interesting(0.00)]).

fof(d1_abian,definition,(
    ! [A] : 
      ( v1_abian(A)
    <=> ? [B] : 
          ( v1_int_1(B)
          & A = k3_xcmplx_0(2,B) ) ) ),
    file(abian,d1_abian),
    [interesting(0.00)]).

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

fof(d5_abian,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( r3_abian(A)
      <=> ? [B] : r1_abian(B,A) ) ) ),
    file(abian,d5_abian),
    [interesting(0.00)]).

fof(d3_abian,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_abian(A,B)
      <=> ( r2_hidden(A,k1_relat_1(B))
          & A = k1_funct_1(B,A) ) ) ) ),
    file(abian,d3_abian),
    [interesting(0.00)]).

fof(t67_funct_2,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ( k4_relset_1(A,A,B) = A
        & r1_tarski(k2_relat_1(B),A) ) ) ),
    file(funct_2,t67_funct_2),
    [interesting(0.00)]).

fof(t99_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_zfmisc_1(A)) = A ),
    file(zfmisc_1,t99_zfmisc_1),
    [interesting(0.00)]).

fof(d6_abian,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,A)
     => ( v2_abian(B,A)
      <=> k3_tarski(B) = k3_tarski(k3_tarski(A)) ) ) ),
    file(abian,d6_abian),
    [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(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_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(t5_abian,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( ~ v1_xboole_0(C)
            & v2_abian(C,k1_zfmisc_1(k1_zfmisc_1(A)))
            & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
         => ~ ( ! [D] : 
                  ( m2_subset_1(D,k1_zfmisc_1(A),C)
                 => r1_xboole_0(D,k2_funct_2(A,A,B,D)) )
              & r3_abian(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_abian,d3_abian,t67_funct_2,t4_abian,d4_tarski,d12_funct_1,t3_xboole_0]),
    [file(abian,t5_abian),interesting(0.00)]).

fof(d5_eqrel_1,definition,(
    ! [A,B] : 
      ( ( v3_relat_2(B)
        & v8_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
         => ( C = k7_eqrel_1(A,B)
          <=> ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ( r2_hidden(D,C)
                <=> ? [E] : 
                      ( r2_hidden(E,A)
                      & D = k6_eqrel_1(A,B,E) ) ) ) ) ) ) ),
    file(eqrel_1,d5_eqrel_1),
    [interesting(0.00)]).

fof(t28_eqrel_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_2(B)
        & v3_relat_2(B)
        & v1_partfun1(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,k6_eqrel_1(A,B,C)) ) ) ),
    file(eqrel_1,t28_eqrel_1),
    [interesting(0.00)]).

fof(s7_domain_1,theorem,(
    m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(f1_s7_domain_1)) ),
    file(domain_1,s7_domain_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(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.00)]).

fof(t47_mcart_1,theorem,(
    ! [A,B,C] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & C != k1_xboole_0
      & ? [D] : 
          ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
          & ? [E,F,G] : 
              ( D = k3_mcart_1(E,F,G)
              & ~ ( k5_mcart_1(A,B,C,D) = E
                  & k6_mcart_1(A,B,C,D) = F
                  & k7_mcart_1(A,B,C,D) = G ) ) ) ) ),
    file(mcart_1,t47_mcart_1),
    [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(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(t27_eqrel_1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_relat_2(D)
        & v3_relat_2(D)
        & v1_partfun1(D,A,A)
        & m2_relset_1(D,A,A) )
     => ( r2_hidden(B,k6_eqrel_1(A,D,C))
      <=> r2_hidden(k4_tarski(B,C),D) ) ) ),
    file(eqrel_1,t27_eqrel_1),
    [interesting(0.00)]).

fof(d7_abian,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & m2_relset_1(B,A,A) )
     => ! [C] : 
          ( ( v3_relat_2(C)
            & v8_relat_2(C)
            & v1_partfun1(C,A,A)
            & m2_relset_1(C,A,A) )
         => ( C = k2_abian(A,B)
          <=> ! [D,E] : 
                ( ( r2_hidden(D,A)
                  & r2_hidden(E,A) )
               => ( r2_hidden(k4_tarski(D,E),C)
                <=> ? [F] : 
                      ( m2_subset_1(F,k1_numbers,k5_numbers)
                      & ? [G] : 
                          ( m2_subset_1(G,k1_numbers,k5_numbers)
                          & k1_funct_1(k1_abian(A,B,F),D) = k1_funct_1(k1_abian(A,B,G),E) ) ) ) ) ) ) ) ),
    file(abian,d7_abian),
    [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(t73_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k9_funct_7(A,k1_nat_1(B,1)) = k5_relat_1(k9_funct_7(A,B),A) ) ) ),
    file(funct_7,t73_funct_7),
    [interesting(0.00)]).

fof(t23_funct_1,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(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.00)]).

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

fof(t31_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(B,k6_eqrel_1(A,C,D))
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    file(eqrel_1,t31_eqrel_1),
    [interesting(0.00)]).

fof(t72_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k9_funct_7(A,1) = A ) ),
    file(funct_7,t72_funct_7),
    [interesting(0.00)]).

fof(t34_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k6_relat_1(A)
      <=> ( k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => k1_funct_1(B,C) = C ) ) ) ) ),
    file(funct_1,t34_funct_1),
    [interesting(0.00)]).

fof(t70_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k9_funct_7(A,0) = k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) ) ),
    file(funct_7,t70_funct_7),
    [interesting(0.00)]).

fof(t71_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k9_funct_7(A,k1_nat_1(B,1)) = k5_relat_1(A,k9_funct_7(A,B)) ) ) ),
    file(funct_7,t71_funct_7),
    [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(t65_xboole_1,theorem,(
    ! [A] : r1_xboole_0(A,k1_xboole_0) ),
    file(xboole_1,t65_xboole_1),
    [interesting(0.00)]).

fof(t79_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k5_relat_1(k9_funct_7(A,C),k9_funct_7(A,B)) = k9_funct_7(A,k1_nat_1(B,C)) ) ) ) ),
    file(funct_7,t79_funct_7),
    [interesting(0.00)]).

fof(t18_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ! [B] : 
          ( v1_int_1(B)
         => ( r1_xreal_0(A,B)
           => r2_hidden(k6_xcmplx_0(B,A),k5_numbers) ) ) ) ),
    file(int_1,t18_int_1),
    [interesting(0.00)]).

fof(t1_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,A) )
           => A = B ) ) ) ),
    file(xreal_1,t1_xreal_1),
    [interesting(0.00)]).

fof(s12_funct_2,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s12_funct_2)
       => r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2)
        & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2)
        & ! [B] : 
            ( m1_subset_1(B,f1_s12_funct_2)
           => k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B) ) ) ),
    file(funct_2,s12_funct_2),
    [interesting(0.00)]).

fof(t30_eqrel_1,theorem,(
    ! [A,B,C,D,E] : 
      ( ( v1_relat_2(E)
        & v3_relat_2(E)
        & v8_relat_2(E)
        & v1_partfun1(E,A,A)
        & m2_relset_1(E,A,A) )
     => ( ( r2_hidden(B,k6_eqrel_1(A,E,C))
          & r2_hidden(D,k6_eqrel_1(A,E,C)) )
       => r2_hidden(k4_tarski(B,D),E) ) ) ),
    file(eqrel_1,t30_eqrel_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(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(t47_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(A,0)
           => B = k2_xcmplx_0(k3_xcmplx_0(A,k3_nat_1(B,A)),k4_nat_1(B,A)) ) ) ) ),
    file(nat_1,t47_nat_1),
    [interesting(0.00)]).

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

fof(d15_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_relat_1(A)
      <=> ! [B] : ~ ( r2_hidden(B,k1_relat_1(A))
            & v1_xboole_0(k1_funct_1(A,B)) ) ) ) ),
    file(funct_1,d15_funct_1),
    [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(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.00)]).

fof(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [interesting(0.00)]).

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

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

fof(t39_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( ~ r1_xreal_0(1,A)
       => A = 0 ) ) ),
    file(nat_1,t39_nat_1),
    [interesting(0.00)]).

fof(t22_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,k2_xcmplx_0(B,C))
              <=> r1_xreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) ),
    file(xreal_1,t22_xreal_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(t64_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k4_xboole_0(B,k1_tarski(C)))
    <=> ( r2_hidden(A,B)
        & A != C ) ) ),
    file(zfmisc_1,t64_zfmisc_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(d4_abian,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ( r2_abian(A,B,C)
              <=> B = k8_funct_2(A,A,C,B) ) ) ) ) ),
    file(abian,d4_abian),
    [interesting(0.00)]).

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

fof(t44_eqrel_1,theorem,(
    ! [A,B,C] : 
      ( ( v3_relat_2(C)
        & v8_relat_2(C)
        & v1_partfun1(C,A,A)
        & m2_relset_1(C,A,A) )
     => ! [D] : 
          ( r2_hidden(D,A)
         => ( r2_hidden(k4_tarski(D,B),C)
          <=> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) ) ) ) ),
    file(eqrel_1,t44_eqrel_1),
    [interesting(0.00)]).