% Mizar problem: t2_xreal_1,xreal_1,76,29 
fof(t2_xreal_1,conjecture,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_xboole_0,connectedness_r1_arytm_2,connectedness_r1_xreal_0,d1_numbers,d1_xreal_0,d2_xboole_0,d2_xreal_0,d4_xboole_0,dt_k12_arytm_3,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k4_tarski,dt_k4_xboole_0,dt_k6_arytm_3,dt_m1_subset_1,existence_m1_subset_1,fc1_numbers,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,fc2_xboole_0,fc3_xboole_0,fc8_arytm_3,idempotence_k2_xboole_0,irreflexivity_r1_subset_1,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,redefinition_k12_arytm_3,redefinition_r1_subset_1,reflexivity_r1_xreal_0,spc0_boole,symmetry_r1_subset_1,symmetry_r1_xboole_0,t1_boole,t1_real,t1_subset,t2_real,t2_subset,t33_zfmisc_1,t3_arytm_1,t3_boole,t3_real,t3_xboole_0,t4_boole,t4_real,t5_arytm_0,t5_real,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]),
    [file(xreal_1,t2_xreal_1)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_xcmplx_0,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc1_xcmplx_0),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(cc3_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v2_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc3_xreal_0),
    []).

fof(cc4_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v2_xreal_0(A) ) ) ),
    file(xreal_0,cc4_xreal_0),
    []).

fof(cc5_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & v3_xreal_0(A) )
     => ( ~ v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) ) ) ),
    file(xreal_0,cc5_xreal_0),
    []).

fof(cc6_xreal_0,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_xreal_0(A) ) ) ),
    file(xreal_0,cc6_xreal_0),
    []).

fof(cc7_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_xreal_0(A) )
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(xreal_0,cc7_xreal_0),
    []).

fof(cc8_xreal_0,axiom,(
    ! [A] : 
      ( ( v1_xreal_0(A)
        & ~ v2_xreal_0(A)
        & ~ v3_xreal_0(A) )
     => ( v1_xboole_0(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(xreal_0,cc8_xreal_0),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(connectedness_r1_arytm_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k2_arytm_2)
        & m1_subset_1(B,k2_arytm_2) )
     => ( r1_arytm_2(A,B)
        | r1_arytm_2(B,A) ) ) ),
    file(arytm_2,r1_arytm_2),
    []).

fof(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d1_numbers,axiom,(
    k1_numbers = k4_xboole_0(k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)),k1_tarski(k4_tarski(0,0))) ),
    file(numbers,d1_numbers),
    []).

fof(d1_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
    <=> r2_hidden(A,k1_numbers) ) ),
    file(xreal_0,d1_xreal_0),
    []).

fof(d2_xboole_0,axiom,(
    ! [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),
    []).

fof(d2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( ( r2_hidden(A,k2_arytm_2)
                & r2_hidden(B,k2_arytm_2) )
             => ( r1_xreal_0(A,B)
              <=> ? [C] : 
                    ( m1_subset_1(C,k2_arytm_2)
                    & ? [D] : 
                        ( m1_subset_1(D,k2_arytm_2)
                        & A = C
                        & B = D
                        & r1_arytm_2(C,D) ) ) ) )
            & ( ( r2_hidden(A,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
                & r2_hidden(B,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) )
             => ( r1_xreal_0(A,B)
              <=> ? [C] : 
                    ( m1_subset_1(C,k2_arytm_2)
                    & ? [D] : 
                        ( m1_subset_1(D,k2_arytm_2)
                        & A = k4_tarski(0,C)
                        & B = k4_tarski(0,D)
                        & r1_arytm_2(D,C) ) ) ) )
            & ~ ( ~ ( r2_hidden(A,k2_arytm_2)
                    & r2_hidden(B,k2_arytm_2) )
                & ~ ( r2_hidden(A,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
                    & r2_hidden(B,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) )
                & ~ ( r1_xreal_0(A,B)
                  <=> ( r2_hidden(B,k2_arytm_2)
                      & r2_hidden(A,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ) ) ) ) ) ) ),
    file(xreal_0,d2_xreal_0),
    []).

fof(d4_xboole_0,axiom,(
    ! [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),
    []).

fof(dt_k12_arytm_3,axiom,
    ( v1_xboole_0(k12_arytm_3)
    & m1_subset_1(k12_arytm_3,k6_arytm_3) ),
    file(arytm_3,k12_arytm_3),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k2_arytm_2,axiom,(
    $true ),
    file(arytm_2,k2_arytm_2),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k6_arytm_3,axiom,(
    $true ),
    file(arytm_3,k6_arytm_3),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc1_zfmisc_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    []).

fof(fc2_arytm_2,axiom,(
    ~ v1_xboole_0(k2_arytm_2) ),
    file(arytm_2,fc2_arytm_2),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc8_arytm_3,axiom,(
    ~ v1_xboole_0(k6_arytm_3) ),
    file(arytm_3,fc8_arytm_3),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(irreflexivity_r1_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ r1_subset_1(A,A) ) ),
    file(subset_1,r1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc1_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

fof(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc2_xcmplx_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A) ) ),
    file(xcmplx_0,rc2_xcmplx_0),
    []).

fof(rc2_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc2_xreal_0),
    []).

fof(rc3_xreal_0,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & v3_xreal_0(A) ) ),
    file(xreal_0,rc3_xreal_0),
    []).

fof(rc4_xreal_0,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A)
      & ~ v2_xreal_0(A)
      & ~ v3_xreal_0(A) ) ),
    file(xreal_0,rc4_xreal_0),
    []).

fof(redefinition_k12_arytm_3,axiom,(
    k12_arytm_3 = k1_xboole_0 ),
    file(arytm_3,k12_arytm_3),
    []).

fof(redefinition_r1_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r1_subset_1(A,B)
      <=> r1_xboole_0(A,B) ) ) ),
    file(subset_1,r1_subset_1),
    []).

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(symmetry_r1_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( r1_subset_1(A,B)
       => r1_subset_1(B,A) ) ) ),
    file(subset_1,r1_subset_1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t33_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    []).

fof(t3_arytm_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ( ( r1_arytm_2(A,B)
                  & r1_arytm_2(B,C) )
               => r1_arytm_2(A,C) ) ) ) ) ),
    file(arytm_1,t3_arytm_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t3_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    []).

fof(t3_xboole_0,axiom,(
    ! [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),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    []).

fof(t5_arytm_0,axiom,(
    r1_subset_1(k2_arytm_2,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) ),
    file(arytm_0,t5_arytm_0),
    []).

fof(t5_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t6_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t7_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t8_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    []).