% Mizar ND problem: t26_axioms,axioms,86,56 
fof(dh_c1_5__axioms,definition,
    ( ( m1_subset_1(c1_5__axioms,k1_zfmisc_1(k1_numbers))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
         => ~ ( ! [B] : 
                  ( v1_xreal_0(B)
                 => ! [C] : 
                      ( v1_xreal_0(C)
                     => ( ( r2_hidden(B,c1_5__axioms)
                          & r2_hidden(C,A) )
                       => r1_xreal_0(B,C) ) ) )
              & ! [B] : 
                  ( v1_xreal_0(B)
                 => ? [C] : 
                      ( v1_xreal_0(C)
                      & ? [D] : 
                          ( v1_xreal_0(D)
                          & r2_hidden(C,c1_5__axioms)
                          & r2_hidden(D,A)
                          & ~ ( r1_xreal_0(C,B)
                              & r1_xreal_0(B,D) ) ) ) ) ) ) )
   => ! [E] : 
        ( m1_subset_1(E,k1_zfmisc_1(k1_numbers))
       => ! [F] : 
            ( m1_subset_1(F,k1_zfmisc_1(k1_numbers))
           => ~ ( ! [G] : 
                    ( v1_xreal_0(G)
                   => ! [H] : 
                        ( v1_xreal_0(H)
                       => ( ( r2_hidden(G,E)
                            & r2_hidden(H,F) )
                         => r1_xreal_0(G,H) ) ) )
                & ! [G] : 
                    ( v1_xreal_0(G)
                   => ? [H] : 
                        ( v1_xreal_0(H)
                        & ? [I] : 
                            ( v1_xreal_0(I)
                            & r2_hidden(H,E)
                            & r2_hidden(I,F)
                            & ~ ( r1_xreal_0(H,G)
                                & r1_xreal_0(G,I) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_5__axioms),file(axioms,c1_5__axioms)]),
    [interesting(0.8),axiom,file(axioms,c1_5__axioms)]).

fof(dh_c2_5__axioms,definition,
    ( ( m1_subset_1(c2_5__axioms,k1_zfmisc_1(k1_numbers))
     => ~ ( ! [A] : 
              ( v1_xreal_0(A)
             => ! [B] : 
                  ( v1_xreal_0(B)
                 => ( ( r2_hidden(A,c1_5__axioms)
                      & r2_hidden(B,c2_5__axioms) )
                   => r1_xreal_0(A,B) ) ) )
          & ! [A] : 
              ( v1_xreal_0(A)
             => ? [B] : 
                  ( v1_xreal_0(B)
                  & ? [C] : 
                      ( v1_xreal_0(C)
                      & r2_hidden(B,c1_5__axioms)
                      & r2_hidden(C,c2_5__axioms)
                      & ~ ( r1_xreal_0(B,A)
                          & r1_xreal_0(A,C) ) ) ) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,k1_zfmisc_1(k1_numbers))
       => ~ ( ! [E] : 
                ( v1_xreal_0(E)
               => ! [F] : 
                    ( v1_xreal_0(F)
                   => ( ( r2_hidden(E,c1_5__axioms)
                        & r2_hidden(F,D) )
                     => r1_xreal_0(E,F) ) ) )
            & ! [E] : 
                ( v1_xreal_0(E)
               => ? [F] : 
                    ( v1_xreal_0(F)
                    & ? [G] : 
                        ( v1_xreal_0(G)
                        & r2_hidden(F,c1_5__axioms)
                        & r2_hidden(G,D)
                        & ~ ( r1_xreal_0(F,E)
                            & r1_xreal_0(E,G) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_5__axioms),file(axioms,c2_5__axioms)]),
    [interesting(0.8),axiom,file(axioms,c2_5__axioms)]).

fof(e1_5__axioms,assumption,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r2_hidden(A,c1_5__axioms)
              & r2_hidden(B,c2_5__axioms) )
           => r1_xreal_0(A,B) ) ) ) ),
    introduced(assumption,[file(axioms,e1_5__axioms)]),
    [interesting(0.8),axiom,file(axioms,e1_5__axioms)]).

fof(e1_5_1_1__axioms,assumption,
    ( c1_5__axioms = 0
    | c2_5__axioms = 0 ),
    introduced(assumption,[file(axioms,e1_5_1_1__axioms)]),
    [interesting(0.5),axiom,file(axioms,e1_5_1_1__axioms)]).

fof(cc1_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

fof(cc1_xreal_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xreal_0(A) ) ),
    file(xreal_0,cc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]).

fof(cc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(cc2_xcmplx_0,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,cc2_xcmplx_0)]).

fof(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc3_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

fof(cc4_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]).

fof(cc5_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]).

fof(cc8_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]).

fof(fc1_ordinal2,theorem,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]).

fof(rc2_xreal_0,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]).

fof(rc3_xreal_0,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]).

fof(rc4_xreal_0,theorem,(
    ? [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),
    [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(cc1_xcmplx_0,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => v1_xcmplx_0(A) ) ),
    file(xcmplx_0,cc1_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,cc1_xcmplx_0)]).

fof(cc3_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]).

fof(cc6_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]).

fof(cc7_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]).

fof(fc1_numbers,theorem,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    [interesting(0.9),axiom,file(numbers,fc1_numbers)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc1_xcmplx_0,theorem,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,rc1_xcmplx_0)]).

fof(rc1_xreal_0,theorem,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(rc2_xcmplx_0,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_xcmplx_0(A) ) ),
    file(xcmplx_0,rc2_xcmplx_0),
    [interesting(0.9),axiom,file(xcmplx_0,rc2_xcmplx_0)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_c1_5__axioms,assumption,(
    m1_subset_1(c1_5__axioms,k1_zfmisc_1(k1_numbers)) ),
    introduced(assumption,[file(axioms,c1_5__axioms)]),
    [interesting(0.8),axiom,file(axioms,c1_5__axioms)]).

fof(dt_c2_5__axioms,assumption,(
    m1_subset_1(c2_5__axioms,k1_zfmisc_1(k1_numbers)) ),
    introduced(assumption,[file(axioms,c2_5__axioms)]),
    [interesting(0.8),axiom,file(axioms,c2_5__axioms)]).

fof(cc2_xreal_0,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]).

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

fof(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,(
    r1_xreal_0(0,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,(
    ~ r1_xreal_0(1,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,(
    r1_xreal_0(1,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

fof(e2_5_1_1__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r2_hidden(A,c1_5__axioms)
              & r2_hidden(B,c2_5__axioms) )
           => ( r1_xreal_0(A,1)
              & r1_xreal_0(1,B) ) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms,e1_5_1_1__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c1_5__axioms,dt_c2_5__axioms,cc2_xreal_0,rqLessOrEqual__r1_xreal_0__r0_r0,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r1_r0,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,spc0_boole,spc1_boole,spc0_numerals,spc1_numerals,e1_5_1_1__axioms]),
    [interesting(0.5),file(axioms,e2_5_1_1__axioms),[file(axioms,e2_5_1_1__axioms)]]).

fof(i3_5_1_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_1__axioms)]),
    [interesting(0.5),trivial,file(axioms,i3_5_1_1__axioms)]).

fof(i2_5_1_1__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r2_hidden(A,c1_5__axioms)
              & r2_hidden(B,c2_5__axioms) )
           => ( r1_xreal_0(A,1)
              & r1_xreal_0(1,B) ) ) ) ) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms,e1_5_1_1__axioms])],[e2_5_1_1__axioms,i3_5_1_1__axioms]),
    [interesting(0.5),file(axioms,i2_5_1_1__axioms),[file(axioms,i2_5_1_1__axioms)]]).

fof(i1_5_1_1__axioms,plain,(
    ? [A] : 
      ( v1_xreal_0(A)
      & ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms) )
               => ( r1_xreal_0(B,A)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(take,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms,e1_5_1_1__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c1_5__axioms,dt_c2_5__axioms,cc2_xreal_0,spc1_boole,spc1_numerals,i2_5_1_1__axioms]),
    [interesting(0.5),file(axioms,i1_5_1_1__axioms),[file(axioms,i1_5_1_1__axioms)]]).

fof(i1_5_1__axioms,plain,(
    ~ ( ( c1_5__axioms = 0
        | c2_5__axioms = 0 )
      & ! [A] : 
          ( v1_xreal_0(A)
         => ? [B] : 
              ( v1_xreal_0(B)
              & ? [C] : 
                  ( v1_xreal_0(C)
                  & r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms)
                  & ~ ( r1_xreal_0(B,A)
                      & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e1_5_1_1__axioms])],[e1_5_1_1__axioms,i1_5_1_1__axioms]),
    [interesting(0.65),file(axioms,i1_5_1__axioms),[file(axioms,i1_5_1__axioms)]]).

fof(e1_5_1_2__axioms,assumption,(
    c1_5__axioms != 0 ),
    introduced(assumption,[file(axioms,e1_5_1_2__axioms)]),
    [interesting(0.5),axiom,file(axioms,e1_5_1_2__axioms)]).

fof(e2_5_1_2__axioms,assumption,(
    c2_5__axioms != 0 ),
    introduced(assumption,[file(axioms,e2_5_1_2__axioms)]),
    [interesting(0.5),axiom,file(axioms,e2_5_1_2__axioms)]).

fof(e1_5_1_2_1_1_1__axioms,assumption,(
    r1_xboole_0(c1_5__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,e1_5_1_2_1_1_1__axioms)]).

fof(e2_5_1_2_1_1_1__axioms,assumption,(
    r1_xboole_0(c2_5__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    introduced(assumption,[file(axioms,e2_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,e2_5_1_2_1_1_1__axioms)]).

fof(de_c1_5_1_2_1_1_1__axioms,definition,(
    c1_5_1_2_1_1_1__axioms = 0 ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_1__axioms),file(axioms,c1_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,c1_5_1_2_1_1_1__axioms)]).

fof(dt_c1_5_1_2_1_1_1__axioms,plain,(
    m2_subset_1(c1_5_1_2_1_1_1__axioms,k1_numbers,k5_numbers) ),
    inference(mizar_by,[status(thm),assumptions([])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,fc1_xboole_0,rc1_arytm_3,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc1_xcmplx_0,cc3_arytm_3,fc1_ordinal2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,fc1_numbers,spc0_boole,spc0_numerals,de_c1_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,c1_5_1_2_1_1_1__axioms),[file(axioms,c1_5_1_2_1_1_1__axioms)]]).

fof(dh_c2_5_1_2_1_1_1__axioms,definition,
    ( ( v1_xreal_0(c2_5_1_2_1_1_1__axioms)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ( ( r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms)
              & r2_hidden(A,c2_5__axioms) )
           => ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
              & r1_xreal_0(c1_5_1_2_1_1_1__axioms,A) ) ) ) )
   => ! [B] : 
        ( v1_xreal_0(B)
       => ! [C] : 
            ( v1_xreal_0(C)
           => ( ( r2_hidden(B,c1_5__axioms)
                & r2_hidden(C,c2_5__axioms) )
             => ( r1_xreal_0(B,c1_5_1_2_1_1_1__axioms)
                & r1_xreal_0(c1_5_1_2_1_1_1__axioms,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_1__axioms),file(axioms,c2_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,c2_5_1_2_1_1_1__axioms)]).

fof(dh_c3_5_1_2_1_1_1__axioms,definition,
    ( ( v1_xreal_0(c3_5_1_2_1_1_1__axioms)
     => ( ( r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms)
          & r2_hidden(c3_5_1_2_1_1_1__axioms,c2_5__axioms) )
       => ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
          & r1_xreal_0(c1_5_1_2_1_1_1__axioms,c3_5_1_2_1_1_1__axioms) ) ) )
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ( r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms)
            & r2_hidden(A,c2_5__axioms) )
         => ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
            & r1_xreal_0(c1_5_1_2_1_1_1__axioms,A) ) ) ) ),
    introduced(definition,[new_symbol(c3_5_1_2_1_1_1__axioms),file(axioms,c3_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,c3_5_1_2_1_1_1__axioms)]).

fof(e4_5_1_2_1_1_1__axioms,assumption,(
    r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms) ),
    introduced(assumption,[file(axioms,e4_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,e4_5_1_2_1_1_1__axioms)]).

fof(e5_5_1_2_1_1_1__axioms,assumption,(
    r2_hidden(c3_5_1_2_1_1_1__axioms,c2_5__axioms) ),
    introduced(assumption,[file(axioms,e5_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,e5_5_1_2_1_1_1__axioms)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(connectedness_r1_arytm_2,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(arytm_2,r1_arytm_2)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_k2_arytm_2,axiom,(
    $true ),
    file(arytm_2,k2_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,k2_arytm_2)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    [interesting(0.9),axiom,file(tarski,k4_tarski)]).

fof(dt_c2_5_1_2_1_1_1__axioms,assumption,(
    v1_xreal_0(c2_5_1_2_1_1_1__axioms) ),
    introduced(assumption,[file(axioms,c2_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,c2_5_1_2_1_1_1__axioms)]).

fof(fc1_zfmisc_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,fc1_zfmisc_1)]).

fof(fc2_arytm_2,theorem,(
    ~ v1_xboole_0(k2_arytm_2) ),
    file(arytm_2,fc2_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,fc2_arytm_2)]).

fof(d5_tarski,definition,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    [interesting(0.9),axiom,file(tarski,d5_tarski)]).

fof(rc2_arytm_3,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(arytm_3,rc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc2_arytm_3)]).

fof(rc3_arytm_3,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc3_arytm_3)]).

fof(dt_k4_ordinal2,axiom,
    ( v3_ordinal1(k4_ordinal2)
    & ~ v1_xboole_0(k4_ordinal2) ),
    file(ordinal2,k4_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k4_ordinal2)]).

fof(dt_k6_arytm_3,axiom,(
    $true ),
    file(arytm_3,k6_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k6_arytm_3)]).

fof(cc4_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ( v3_ordinal1(A)
       => ( v1_ordinal1(A)
          & v2_ordinal1(A)
          & v3_ordinal1(A)
          & v4_ordinal2(A) ) ) ) ),
    file(arytm_3,cc4_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc4_arytm_3)]).

fof(fc1_arytm_3,theorem,
    ( ~ v1_xboole_0(k4_ordinal2)
    & v1_ordinal1(k4_ordinal2)
    & v2_ordinal1(k4_ordinal2)
    & v3_ordinal1(k4_ordinal2)
    & v4_ordinal2(k4_ordinal2) ),
    file(arytm_3,fc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,fc1_arytm_3)]).

fof(fc8_arytm_3,theorem,(
    ~ v1_xboole_0(k6_arytm_3) ),
    file(arytm_3,fc8_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,fc8_arytm_3)]).

fof(symmetry_r1_subset_1,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(subset_1,r1_subset_1)]).

fof(irreflexivity_r1_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ r1_subset_1(A,A) ) ),
    file(subset_1,r1_subset_1),
    [interesting(0.9),axiom,file(subset_1,r1_subset_1)]).

fof(symmetry_r1_xboole_0,theorem,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,r1_xboole_0)]).

fof(redefinition_k12_arytm_3,definition,(
    k12_arytm_3 = k1_xboole_0 ),
    file(arytm_3,k12_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k12_arytm_3)]).

fof(redefinition_k13_arytm_3,definition,(
    k13_arytm_3 = k4_ordinal2 ),
    file(arytm_3,k13_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k13_arytm_3)]).

fof(redefinition_r1_subset_1,definition,(
    ! [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),
    [interesting(0.9),axiom,file(subset_1,r1_subset_1)]).

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),
    [interesting(0.9),axiom,file(arytm_3,k12_arytm_3)]).

fof(dt_k13_arytm_3,axiom,
    ( ~ v1_xboole_0(k13_arytm_3)
    & v3_ordinal1(k13_arytm_3)
    & m1_subset_1(k13_arytm_3,k6_arytm_3) ),
    file(arytm_3,k13_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,k13_arytm_3)]).

fof(t5_arytm_0,theorem,(
    r1_subset_1(k2_arytm_2,k2_zfmisc_1(k1_tarski(k12_arytm_3),k2_arytm_2)) ),
    file(arytm_0,t5_arytm_0),
    [interesting(0.9),axiom,file(arytm_0,t5_arytm_0)]).

fof(t21_arytm_2,theorem,
    ( r2_hidden(k12_arytm_3,k2_arytm_2)
    & r2_hidden(k13_arytm_3,k2_arytm_2) ),
    file(arytm_2,t21_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,t21_arytm_2)]).

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(0.9),axiom,file(xboole_0,t3_xboole_0)]).

fof(e6_5_1_2_1_1_1__axioms,plain,
    ( ~ r2_hidden(c1_5_1_2_1_1_1__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
    & ~ r2_hidden(c2_5_1_2_1_1_1__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_1__axioms,e1_5_1_2_1_1_1__axioms,e4_5_1_2_1_1_1__axioms])],[reflexivity_r1_tarski,dt_k5_ordinal2,cc1_xreal_0,cc2_xcmplx_0,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_arytm_3,rc1_xcmplx_0,rc1_xreal_0,rc2_arytm_3,rc2_xcmplx_0,rc2_xreal_0,rc3_arytm_3,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_ordinal2,dt_k5_numbers,dt_k6_arytm_3,dt_m1_subset_1,dt_m2_subset_1,cc1_arytm_3,cc1_xcmplx_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc4_arytm_3,cc6_xreal_0,cc7_xreal_0,fc1_arytm_3,fc1_numbers,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,symmetry_r1_subset_1,irreflexivity_r1_subset_1,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k12_arytm_3,redefinition_k13_arytm_3,redefinition_r1_subset_1,dt_k12_arytm_3,dt_k13_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c1_5__axioms,dt_c1_5_1_2_1_1_1__axioms,dt_c2_5_1_2_1_1_1__axioms,de_c1_5_1_2_1_1_1__axioms,fc2_arytm_2,t1_subset,t7_boole,spc0_boole,spc0_numerals,e1_5_1_2_1_1_1__axioms,e4_5_1_2_1_1_1__axioms,t5_arytm_0,t21_arytm_2,t3_xboole_0]),
    [interesting(0.05),file(axioms,e6_5_1_2_1_1_1__axioms),[file(axioms,e6_5_1_2_1_1_1__axioms)]]).

fof(d2_xreal_0,definition,(
    ! [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),
    [interesting(0.9),axiom,file(xreal_0,d2_xreal_0)]).

fof(e7_5_1_2_1_1_1__axioms,plain,(
    r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_1__axioms,e1_5_1_2_1_1_1__axioms,e4_5_1_2_1_1_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c1_5_1_2_1_1_1__axioms,dt_c2_5_1_2_1_1_1__axioms,de_c1_5_1_2_1_1_1__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e6_5_1_2_1_1_1__axioms,d2_xreal_0]),
    [interesting(0.05),file(axioms,e7_5_1_2_1_1_1__axioms),[file(axioms,e7_5_1_2_1_1_1__axioms)]]).

fof(dt_c1__axioms,plain,(
    m1_subset_1(c1__axioms,k2_arytm_2) ),
    file(axioms,c1__axioms),
    [interesting(0.9),axiom,file(axioms,c1__axioms)]).

fof(dt_c3_5_1_2_1_1_1__axioms,assumption,(
    v1_xreal_0(c3_5_1_2_1_1_1__axioms) ),
    introduced(assumption,[file(axioms,c3_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,c3_5_1_2_1_1_1__axioms)]).

fof(de_c4_5_1_2_1_1_1__axioms,definition,(
    c4_5_1_2_1_1_1__axioms = c3_5_1_2_1_1_1__axioms ),
    introduced(definition,[new_symbol(c4_5_1_2_1_1_1__axioms),file(axioms,c4_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),axiom,file(axioms,c4_5_1_2_1_1_1__axioms)]).

fof(t1_boole,theorem,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    [interesting(0.9),axiom,file(boole,t1_boole)]).

fof(fc2_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc2_xboole_0)]).

fof(fc3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc3_xboole_0)]).

fof(commutativity_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(idempotence_k2_xboole_0,theorem,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]).

fof(t3_boole,theorem,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    [interesting(0.9),axiom,file(boole,t3_boole)]).

fof(t4_boole,theorem,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    [interesting(0.9),axiom,file(boole,t4_boole)]).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k4_xboole_0)]).

fof(d1_numbers,definition,(
    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),
    [interesting(0.9),axiom,file(numbers,d1_numbers)]).

fof(t36_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t36_xboole_1)]).

fof(e7_5_1_2__axioms,plain,(
    r1_tarski(k1_numbers,k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))) ),
    inference(mizar_by,[status(thm),assumptions([])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_boole,t1_subset,t3_boole,t4_boole,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k4_tarski,dt_k4_xboole_0,fc1_numbers,fc1_zfmisc_1,fc2_arytm_2,t3_subset,d5_tarski,spc0_boole,spc0_numerals,d1_numbers,t36_xboole_1]),
    [interesting(0.5),file(axioms,e7_5_1_2__axioms),[file(axioms,e7_5_1_2__axioms)]]).

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(0.9),axiom,file(xboole_1,t1_xboole_1)]).

fof(e9_5_1_2__axioms,plain,(
    r1_tarski(c2_5__axioms,k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c2_5__axioms,fc1_numbers,fc2_arytm_2,t3_subset,spc0_boole,spc0_numerals,e7_5_1_2__axioms,t1_xboole_1]),
    [interesting(0.5),file(axioms,e9_5_1_2__axioms),[file(axioms,e9_5_1_2__axioms)]]).

fof(t73_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,k2_xboole_0(B,C))
        & r1_xboole_0(A,C) )
     => r1_tarski(A,B) ) ),
    file(xboole_1,t73_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t73_xboole_1)]).

fof(e3_5_1_2_1_1_1__axioms,plain,(
    r1_tarski(c2_5__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,symmetry_r1_xboole_0,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c2_5__axioms,fc2_arytm_2,t3_subset,spc0_boole,spc0_numerals,e9_5_1_2__axioms,e2_5_1_2_1_1_1__axioms,t73_xboole_1]),
    [interesting(0.05),file(axioms,e3_5_1_2_1_1_1__axioms),[file(axioms,e3_5_1_2_1_1_1__axioms)]]).

fof(e8_5_1_2_1_1_1__axioms,plain,(
    m1_subset_1(c3_5_1_2_1_1_1__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms])],[dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,dt_k1_numbers,dt_k1_zfmisc_1,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5__axioms,dt_c3_5_1_2_1_1_1__axioms,fc2_arytm_2,t1_subset,t3_subset,t7_boole,e3_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,e8_5_1_2_1_1_1__axioms),[file(axioms,e8_5_1_2_1_1_1__axioms)]]).

fof(dt_c4_5_1_2_1_1_1__axioms,plain,(
    m1_subset_1(c4_5_1_2_1_1_1__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc2_xreal_0,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c3_5_1_2_1_1_1__axioms,fc2_arytm_2,de_c4_5_1_2_1_1_1__axioms,e8_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,c4_5_1_2_1_1_1__axioms),[file(axioms,c4_5_1_2_1_1_1__axioms)]]).

fof(de_c1__axioms,definition,(
    c1__axioms = 0 ),
    introduced(definition,[new_symbol(c1__axioms),file(axioms,c1__axioms)]),
    [interesting(0.9),axiom,file(axioms,c1__axioms)]).

fof(t6_arytm_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( A = k1_xboole_0
           => r1_arytm_2(A,B) ) ) ) ),
    file(arytm_1,t6_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,t6_arytm_1)]).

fof(e9_5_1_2_1_1_1__axioms,plain,(
    r1_arytm_2(c1__axioms,c4_5_1_2_1_1_1__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,t1_numerals,t1_subset,dt_c3_5_1_2_1_1_1__axioms,rc1_xboole_0,rc2_xboole_0,spc0_boole,t2_subset,t7_boole,t8_boole,spc0_boole,spc0_numerals,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k1_xboole_0,dt_k2_arytm_2,dt_m1_subset_1,dt_c1__axioms,dt_c4_5_1_2_1_1_1__axioms,de_c1__axioms,de_c4_5_1_2_1_1_1__axioms,fc1_xboole_0,fc2_arytm_2,t6_boole,t6_arytm_1]),
    [interesting(0.05),file(axioms,e9_5_1_2_1_1_1__axioms),[file(axioms,e9_5_1_2_1_1_1__axioms)]]).

fof(e10_5_1_2_1_1_1__axioms,plain,(
    r1_xreal_0(c1_5_1_2_1_1_1__axioms,c3_5_1_2_1_1_1__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c1__axioms,dt_c1_5_1_2_1_1_1__axioms,dt_c3_5_1_2_1_1_1__axioms,dt_c4_5_1_2_1_1_1__axioms,de_c1__axioms,de_c1_5_1_2_1_1_1__axioms,de_c4_5_1_2_1_1_1__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e9_5_1_2_1_1_1__axioms,d2_xreal_0]),
    [interesting(0.05),file(axioms,e10_5_1_2_1_1_1__axioms),[file(axioms,e10_5_1_2_1_1_1__axioms)]]).

fof(i7_5_1_2_1_1_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i7_5_1_2_1_1_1__axioms)]),
    [interesting(0.05),trivial,file(axioms,i7_5_1_2_1_1_1__axioms)]).

fof(i6_5_1_2_1_1_1__axioms,plain,(
    r1_xreal_0(c1_5_1_2_1_1_1__axioms,c3_5_1_2_1_1_1__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms])],[e10_5_1_2_1_1_1__axioms,i7_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,i6_5_1_2_1_1_1__axioms),[file(axioms,i6_5_1_2_1_1_1__axioms)]]).

fof(i5_5_1_2_1_1_1__axioms,plain,
    ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
    & r1_xreal_0(c1_5_1_2_1_1_1__axioms,c3_5_1_2_1_1_1__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_1__axioms,e1_5_1_2_1_1_1__axioms,e4_5_1_2_1_1_1__axioms,dt_c3_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms])],[e7_5_1_2_1_1_1__axioms,i6_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,i5_5_1_2_1_1_1__axioms),[file(axioms,i5_5_1_2_1_1_1__axioms)]]).

fof(i4_5_1_2_1_1_1__axioms,plain,
    ( ( r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms)
      & r2_hidden(c3_5_1_2_1_1_1__axioms,c2_5__axioms) )
   => ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
      & r1_xreal_0(c1_5_1_2_1_1_1__axioms,c3_5_1_2_1_1_1__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_1__axioms,e1_5_1_2_1_1_1__axioms,dt_c3_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms]),discharge_asm(discharge,[e4_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms])],[e4_5_1_2_1_1_1__axioms,e5_5_1_2_1_1_1__axioms,i5_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,i4_5_1_2_1_1_1__axioms),[file(axioms,i4_5_1_2_1_1_1__axioms)]]).

fof(i4_5_1_2_1_1_1_tmp__axioms,plain,
    ( v1_xreal_0(c3_5_1_2_1_1_1__axioms)
   => ( ( r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms)
        & r2_hidden(c3_5_1_2_1_1_1__axioms,c2_5__axioms) )
     => ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
        & r1_xreal_0(c1_5_1_2_1_1_1__axioms,c3_5_1_2_1_1_1__axioms) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_1__axioms,e1_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms]),discharge_asm(discharge,[dt_c3_5_1_2_1_1_1__axioms])],[dt_c3_5_1_2_1_1_1__axioms,i4_5_1_2_1_1_1__axioms]),
    [interesting(0.05),i3_5_1_2_1_1_1__axioms]).

fof(i3_5_1_2_1_1_1__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ( r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms)
          & r2_hidden(A,c2_5__axioms) )
       => ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
          & r1_xreal_0(c1_5_1_2_1_1_1__axioms,A) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_1__axioms,e1_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms])],[i4_5_1_2_1_1_1_tmp__axioms,dh_c3_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,i3_5_1_2_1_1_1__axioms),[file(axioms,i3_5_1_2_1_1_1__axioms)]]).

fof(i3_5_1_2_1_1_1_tmp__axioms,plain,
    ( v1_xreal_0(c2_5_1_2_1_1_1__axioms)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ( r2_hidden(c2_5_1_2_1_1_1__axioms,c1_5__axioms)
            & r2_hidden(A,c2_5__axioms) )
         => ( r1_xreal_0(c2_5_1_2_1_1_1__axioms,c1_5_1_2_1_1_1__axioms)
            & r1_xreal_0(c1_5_1_2_1_1_1__axioms,A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms]),discharge_asm(discharge,[dt_c2_5_1_2_1_1_1__axioms])],[dt_c2_5_1_2_1_1_1__axioms,i3_5_1_2_1_1_1__axioms]),
    [interesting(0.05),i2_5_1_2_1_1_1__axioms]).

fof(i2_5_1_2_1_1_1__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r2_hidden(A,c1_5__axioms)
              & r2_hidden(B,c2_5__axioms) )
           => ( r1_xreal_0(A,c1_5_1_2_1_1_1__axioms)
              & r1_xreal_0(c1_5_1_2_1_1_1__axioms,B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms])],[i3_5_1_2_1_1_1_tmp__axioms,dh_c2_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,i2_5_1_2_1_1_1__axioms),[file(axioms,i2_5_1_2_1_1_1__axioms)]]).

fof(i1_5_1_2_1_1_1__axioms,plain,(
    ? [A] : 
      ( v1_xreal_0(A)
      & ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms) )
               => ( r1_xreal_0(B,A)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(take,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_1__axioms,dt_c2_5__axioms,e2_5_1_2_1_1_1__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_arytm_3,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k5_ordinal2,cc3_arytm_3,cc7_xreal_0,fc1_ordinal2,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xcmplx_0,rc1_xreal_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c1_5__axioms,dt_c1_5_1_2_1_1_1__axioms,dt_c2_5__axioms,cc2_xreal_0,i2_5_1_2_1_1_1__axioms]),
    [interesting(0.05),file(axioms,i1_5_1_2_1_1_1__axioms),[file(axioms,i1_5_1_2_1_1_1__axioms)]]).

fof(i1_5_1_2_1_1__axioms,plain,(
    ~ ( r1_xboole_0(c1_5__axioms,k2_arytm_2)
      & r1_xboole_0(c2_5__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
      & ! [A] : 
          ( v1_xreal_0(A)
         => ? [B] : 
              ( v1_xreal_0(B)
              & ? [C] : 
                  ( v1_xreal_0(C)
                  & r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms)
                  & ~ ( r1_xreal_0(B,A)
                      & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_1__axioms,e2_5_1_2_1_1_1__axioms])],[e1_5_1_2_1_1_1__axioms,e2_5_1_2_1_1_1__axioms,i1_5_1_2_1_1_1__axioms]),
    [interesting(0.2),file(axioms,i1_5_1_2_1_1__axioms),[file(axioms,i1_5_1_2_1_1__axioms)]]).

fof(e1_5_1_2_1_1_2__axioms,assumption,(
    ~ r1_xboole_0(c2_5__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,e1_5_1_2_1_1_2__axioms)]).

fof(dh_c11_5_1_2_1_1_2__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & ! [B] : 
            ( m1_subset_1(B,k2_arytm_2)
           => ! [C] : 
                ( m1_subset_1(C,k2_arytm_2)
               => ( ( r2_hidden(B,c6_5_1_2_1_1_2__axioms)
                    & r2_hidden(C,c10_5_1_2_1_1_2__axioms) )
                 => ( r1_arytm_2(B,A)
                    & r1_arytm_2(A,C) ) ) ) ) )
   => ( m1_subset_1(c11_5_1_2_1_1_2__axioms,k2_arytm_2)
      & ! [D] : 
          ( m1_subset_1(D,k2_arytm_2)
         => ! [E] : 
              ( m1_subset_1(E,k2_arytm_2)
             => ( ( r2_hidden(D,c6_5_1_2_1_1_2__axioms)
                  & r2_hidden(E,c10_5_1_2_1_1_2__axioms) )
               => ( r1_arytm_2(D,c11_5_1_2_1_1_2__axioms)
                  & r1_arytm_2(c11_5_1_2_1_1_2__axioms,E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c11_5_1_2_1_1_2__axioms),file(axioms,c11_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c11_5_1_2_1_1_2__axioms)]).

fof(dh_c2_5_1_2_1_1_2__axioms,definition,
    ( ? [A,B] : 
        ( r2_hidden(A,k1_tarski(0))
        & r2_hidden(B,k2_arytm_2)
        & c1_5_1_2_1_1_2__axioms = k4_tarski(A,B) )
   => ? [C] : 
        ( r2_hidden(c2_5_1_2_1_1_2__axioms,k1_tarski(0))
        & r2_hidden(C,k2_arytm_2)
        & c1_5_1_2_1_1_2__axioms = k4_tarski(c2_5_1_2_1_1_2__axioms,C) ) ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_2__axioms),file(axioms,c2_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c2_5_1_2_1_1_2__axioms)]).

fof(dh_c3_5_1_2_1_1_2__axioms,definition,
    ( ? [A] : 
        ( r2_hidden(c2_5_1_2_1_1_2__axioms,k1_tarski(0))
        & r2_hidden(A,k2_arytm_2)
        & c1_5_1_2_1_1_2__axioms = k4_tarski(c2_5_1_2_1_1_2__axioms,A) )
   => ( r2_hidden(c2_5_1_2_1_1_2__axioms,k1_tarski(0))
      & r2_hidden(c3_5_1_2_1_1_2__axioms,k2_arytm_2)
      & c1_5_1_2_1_1_2__axioms = k4_tarski(c2_5_1_2_1_1_2__axioms,c3_5_1_2_1_1_2__axioms) ) ),
    introduced(definition,[new_symbol(c3_5_1_2_1_1_2__axioms),file(axioms,c3_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c3_5_1_2_1_1_2__axioms)]).

fof(dh_c1_5_1_2_1_1_2__axioms,definition,
    ( ? [A] : 
        ( r2_hidden(A,c2_5__axioms)
        & r2_hidden(A,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) )
   => ( r2_hidden(c1_5_1_2_1_1_2__axioms,c2_5__axioms)
      & r2_hidden(c1_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_2__axioms),file(axioms,c1_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c1_5_1_2_1_1_2__axioms)]).

fof(e2_5_1_2_1_1_2__axioms,plain,(
    ? [A] : 
      ( r2_hidden(A,c2_5__axioms)
      & r2_hidden(A,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c2_5__axioms,fc2_arytm_2,t1_subset,t7_boole,spc0_boole,spc0_numerals,e1_5_1_2_1_1_2__axioms,t3_xboole_0]),
    [interesting(0.05),file(axioms,e2_5_1_2_1_1_2__axioms),[file(axioms,e2_5_1_2_1_1_2__axioms)]]).

fof(dt_c1_5_1_2_1_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c1_5_1_2_1_1_2__axioms,e2_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c1_5_1_2_1_1_2__axioms),[file(axioms,c1_5_1_2_1_1_2__axioms)]]).

fof(e4_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c1_5_1_2_1_1_2__axioms,e2_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e4_5_1_2_1_1_2__axioms),[file(axioms,e4_5_1_2_1_1_2__axioms)]]).

fof(t103_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ~ ( r1_tarski(A,k2_zfmisc_1(B,C))
        & r2_hidden(D,A)
        & ! [E,F] : 
            ~ ( r2_hidden(E,B)
              & r2_hidden(F,C)
              & D = k4_tarski(E,F) ) ) ),
    file(zfmisc_1,t103_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t103_zfmisc_1)]).

fof(e5_5_1_2_1_1_2__axioms,plain,(
    ? [A,B] : 
      ( r2_hidden(A,k1_tarski(0))
      & r2_hidden(B,k2_arytm_2)
      & c1_5_1_2_1_1_2__axioms = k4_tarski(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_5_1_2_1_1_2__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t3_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e4_5_1_2_1_1_2__axioms,t103_zfmisc_1]),
    [interesting(0.05),file(axioms,e5_5_1_2_1_1_2__axioms),[file(axioms,e5_5_1_2_1_1_2__axioms)]]).

fof(dt_c3_5_1_2_1_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c2_5_1_2_1_1_2__axioms,dh_c3_5_1_2_1_1_2__axioms,e5_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c3_5_1_2_1_1_2__axioms),[file(axioms,c3_5_1_2_1_1_2__axioms)]]).

fof(dh_c7_5_1_2_1_1_2__axioms,definition,
    ( ? [A,B] : 
        ( r2_hidden(A,k1_tarski(0))
        & r2_hidden(B,k2_arytm_2)
        & c1_5_1_2__axioms = k4_tarski(A,B) )
   => ? [C] : 
        ( r2_hidden(c7_5_1_2_1_1_2__axioms,k1_tarski(0))
        & r2_hidden(C,k2_arytm_2)
        & c1_5_1_2__axioms = k4_tarski(c7_5_1_2_1_1_2__axioms,C) ) ),
    introduced(definition,[new_symbol(c7_5_1_2_1_1_2__axioms),file(axioms,c7_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c7_5_1_2_1_1_2__axioms)]).

fof(dh_c8_5_1_2_1_1_2__axioms,definition,
    ( ? [A] : 
        ( r2_hidden(c7_5_1_2_1_1_2__axioms,k1_tarski(0))
        & r2_hidden(A,k2_arytm_2)
        & c1_5_1_2__axioms = k4_tarski(c7_5_1_2_1_1_2__axioms,A) )
   => ( r2_hidden(c7_5_1_2_1_1_2__axioms,k1_tarski(0))
      & r2_hidden(c8_5_1_2_1_1_2__axioms,k2_arytm_2)
      & c1_5_1_2__axioms = k4_tarski(c7_5_1_2_1_1_2__axioms,c8_5_1_2_1_1_2__axioms) ) ),
    introduced(definition,[new_symbol(c8_5_1_2_1_1_2__axioms),file(axioms,c8_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c8_5_1_2_1_1_2__axioms)]).

fof(dh_c1_5_1_2__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & r2_hidden(A,c1_5__axioms) )
   => ( m1_subset_1(c1_5_1_2__axioms,k1_numbers)
      & r2_hidden(c1_5_1_2__axioms,c1_5__axioms) ) ),
    introduced(definition,[new_symbol(c1_5_1_2__axioms),file(axioms,c1_5_1_2__axioms)]),
    [interesting(0.5),axiom,file(axioms,c1_5_1_2__axioms)]).

fof(t10_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ~ ( B != k1_xboole_0
          & ! [C] : 
              ( m1_subset_1(C,A)
             => ~ r2_hidden(C,B) ) ) ) ),
    file(subset_1,t10_subset_1),
    [interesting(0.9),axiom,file(subset_1,t10_subset_1)]).

fof(e3_5_1_2__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & r2_hidden(A,c1_5__axioms) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,reflexivity_r1_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_m2_subset_1,rc1_xboole_0,rc1_xcmplx_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_5__axioms,cc1_xcmplx_0,fc1_numbers,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,spc0_boole,spc0_numerals,e1_5_1_2__axioms,t10_subset_1]),
    [interesting(0.5),file(axioms,e3_5_1_2__axioms),[file(axioms,e3_5_1_2__axioms)]]).

fof(dt_c1_5_1_2__axioms,plain,(
    m1_subset_1(c1_5_1_2__axioms,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c1_5_1_2__axioms,e3_5_1_2__axioms]),
    [interesting(0.5),file(axioms,c1_5_1_2__axioms),[file(axioms,c1_5_1_2__axioms)]]).

fof(dt_c1_5_1_2_1_1_2_2__axioms,assumption,(
    $true ),
    introduced(assumption,[file(axioms,c1_5_1_2_1_1_2_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_2__axioms)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.9),axiom,file(tarski,d3_tarski)]).

fof(dh_c1_5_1_2_1_1_2_2__axioms,definition,
    ( ~ ( r2_hidden(c1_5_1_2_1_1_2_2__axioms,c1_5__axioms)
        & ~ r2_hidden(c1_5_1_2_1_1_2_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) )
   => ! [A] : 
        ~ ( r2_hidden(A,c1_5__axioms)
          & ~ r2_hidden(A,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_2_2__axioms),file(axioms,c1_5_1_2_1_1_2_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_2__axioms)]).

fof(e1_5_1_2_1_1_2_2__axioms,assumption,(
    r2_hidden(c1_5_1_2_1_1_2_2__axioms,c1_5__axioms) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_2_2__axioms)]).

fof(de_c2_5_1_2_1_1_2_2__axioms,definition,(
    c2_5_1_2_1_1_2_2__axioms = c1_5_1_2_1_1_2_2__axioms ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_2_2__axioms),file(axioms,c2_5_1_2_1_1_2_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c2_5_1_2_1_1_2_2__axioms)]).

fof(d1_xreal_0,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
    <=> r2_hidden(A,k1_numbers) ) ),
    file(xreal_0,d1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,d1_xreal_0)]).

fof(e2_5_1_2_1_1_2_2__axioms,plain,(
    v1_xreal_0(c1_5_1_2_1_1_2_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,e1_5_1_2_1_1_2_2__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,cc7_xreal_0,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,cc2_xreal_0,fc1_numbers,t1_subset,t7_boole,e1_5_1_2_1_1_2_2__axioms,d1_xreal_0]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_2_2__axioms),[file(axioms,e2_5_1_2_1_1_2_2__axioms)]]).

fof(dt_c2_5_1_2_1_1_2_2__axioms,plain,(
    v1_xreal_0(c2_5_1_2_1_1_2_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,e1_5_1_2_1_1_2_2__axioms])],[rc1_xcmplx_0,rc1_xreal_0,dt_c1_5_1_2_1_1_2_2__axioms,cc2_xreal_0,de_c2_5_1_2_1_1_2_2__axioms,e2_5_1_2_1_1_2_2__axioms]),
    [interesting(0.02),file(axioms,c2_5_1_2_1_1_2_2__axioms),[file(axioms,c2_5_1_2_1_1_2_2__axioms)]]).

fof(e1_5_1_2_1_1_2_2_1__axioms,assumption,(
    r2_hidden(c2_5_1_2_1_1_2_2__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2_2_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_2_2_1__axioms)]).

fof(de_c4_5_1_2_1_1_2__axioms,definition,(
    c4_5_1_2_1_1_2__axioms = c3_5_1_2_1_1_2__axioms ),
    introduced(definition,[new_symbol(c4_5_1_2_1_1_2__axioms),file(axioms,c4_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c4_5_1_2_1_1_2__axioms)]).

fof(e7_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c3_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c2_5_1_2_1_1_2__axioms,dh_c3_5_1_2_1_1_2__axioms,e5_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e7_5_1_2_1_1_2__axioms),[file(axioms,e7_5_1_2_1_1_2__axioms)]]).

fof(e9_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c3_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c3_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,e7_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e9_5_1_2_1_1_2__axioms),[file(axioms,e9_5_1_2_1_1_2__axioms)]]).

fof(dt_c4_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c4_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c3_5_1_2_1_1_2__axioms,fc2_arytm_2,de_c4_5_1_2_1_1_2__axioms,e9_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c4_5_1_2_1_1_2__axioms),[file(axioms,c4_5_1_2_1_1_2__axioms)]]).

fof(de_c5_5_1_2_1_1_2__axioms,definition,(
    c5_5_1_2_1_1_2__axioms = k4_tarski(0,c4_5_1_2_1_1_2__axioms) ),
    introduced(definition,[new_symbol(c5_5_1_2_1_1_2__axioms),file(axioms,c5_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c5_5_1_2_1_1_2__axioms)]).

fof(dt_c2_5_1_2_1_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c2_5_1_2_1_1_2__axioms,e5_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c2_5_1_2_1_1_2__axioms),[file(axioms,c2_5_1_2_1_1_2__axioms)]]).

fof(e3_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2__axioms,c2_5__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c1_5_1_2_1_1_2__axioms,e2_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e3_5_1_2_1_1_2__axioms),[file(axioms,e3_5_1_2_1_1_2__axioms)]]).

fof(e10_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2__axioms,k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_c1_5_1_2_1_1_2__axioms,dt_c2_5__axioms,fc1_numbers,t1_subset,t7_boole,e3_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e10_5_1_2_1_1_2__axioms),[file(axioms,e10_5_1_2_1_1_2__axioms)]]).

fof(e6_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c2_5_1_2_1_1_2__axioms,k1_tarski(0)) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c2_5_1_2_1_1_2__axioms,dh_c3_5_1_2_1_1_2__axioms,e5_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e6_5_1_2_1_1_2__axioms),[file(axioms,e6_5_1_2_1_1_2__axioms)]]).

fof(e8_5_1_2_1_1_2__axioms,plain,(
    c1_5_1_2_1_1_2__axioms = k4_tarski(c2_5_1_2_1_1_2__axioms,c3_5_1_2_1_1_2__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[dh_c2_5_1_2_1_1_2__axioms,dh_c3_5_1_2_1_1_2__axioms,e5_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e8_5_1_2_1_1_2__axioms),[file(axioms,e8_5_1_2_1_1_2__axioms)]]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e11_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(k4_tarski(0,c4_5_1_2_1_1_2__axioms),k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_k1_tarski,dt_k4_tarski,dt_c1_5_1_2_1_1_2__axioms,dt_c2_5_1_2_1_1_2__axioms,dt_c3_5_1_2_1_1_2__axioms,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,fc1_numbers,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e10_5_1_2_1_1_2__axioms,e6_5_1_2_1_1_2__axioms,e8_5_1_2_1_1_2__axioms,d1_tarski]),
    [interesting(0.05),file(axioms,e11_5_1_2_1_1_2__axioms),[file(axioms,e11_5_1_2_1_1_2__axioms)]]).

fof(e12_5_1_2_1_1_2__axioms,plain,(
    v1_xreal_0(k4_tarski(0,c4_5_1_2_1_1_2__axioms)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c3_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_k4_tarski,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_numbers,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e11_5_1_2_1_1_2__axioms,d1_xreal_0]),
    [interesting(0.05),file(axioms,e12_5_1_2_1_1_2__axioms),[file(axioms,e12_5_1_2_1_1_2__axioms)]]).

fof(dt_c5_5_1_2_1_1_2__axioms,plain,(
    v1_xreal_0(c5_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c3_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,dt_k4_tarski,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_zfmisc_1,d5_tarski,spc0_boole,spc0_numerals,de_c5_5_1_2_1_1_2__axioms,e12_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c5_5_1_2_1_1_2__axioms),[file(axioms,c5_5_1_2_1_1_2__axioms)]]).

fof(l24_axioms,plain,(
    r2_hidden(k1_xboole_0,k1_tarski(k1_xboole_0)) ),
    file(axioms,l24_axioms),
    [interesting(0.9),axiom,file(axioms,l24_axioms)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t106_zfmisc_1)]).

fof(e15_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c5_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_c3_5_1_2_1_1_2__axioms,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c5_5_1_2_1_1_2__axioms,de_c5_5_1_2_1_1_2__axioms,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t6_boole,t7_boole,d5_tarski,spc0_boole,spc0_numerals,l24_axioms,t106_zfmisc_1]),
    [interesting(0.05),file(axioms,e15_5_1_2_1_1_2__axioms),[file(axioms,e15_5_1_2_1_1_2__axioms)]]).

fof(e3_5_1_2_1_1_2_2_1__axioms,plain,
    ( ~ r2_hidden(c5_5_1_2_1_1_2__axioms,k2_arytm_2)
    & ~ r2_hidden(c2_5_1_2_1_1_2_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,e1_5_1_2_1_1_2_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_2_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc4_arytm_3,rc1_arytm_3,rc2_arytm_3,rc3_arytm_3,commutativity_k2_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_ordinal2,dt_c3_5_1_2_1_1_2__axioms,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k4_tarski,dt_k5_numbers,dt_k6_arytm_3,dt_m1_subset_1,dt_m2_subset_1,dt_c1_5_1_2_1_1_2_2__axioms,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc1_xboole_0,fc1_zfmisc_1,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,d5_tarski,symmetry_r1_subset_1,irreflexivity_r1_subset_1,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k12_arytm_3,redefinition_r1_subset_1,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c2_5_1_2_1_1_2_2__axioms,dt_c5_5_1_2_1_1_2__axioms,de_c2_5_1_2_1_1_2_2__axioms,de_c5_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,spc0_boole,spc0_numerals,e15_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_2_1__axioms,t5_arytm_0,t3_xboole_0]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_2_2_1__axioms),[file(axioms,e3_5_1_2_1_1_2_2_1__axioms)]]).

fof(e16_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c5_5_1_2_1_1_2__axioms,c2_5__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,fc2_arytm_2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k4_tarski,dt_c1_5_1_2_1_1_2__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_2__axioms,dt_c3_5_1_2_1_1_2__axioms,dt_c5_5_1_2_1_1_2__axioms,de_c5_5_1_2_1_1_2__axioms,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e3_5_1_2_1_1_2__axioms,e6_5_1_2_1_1_2__axioms,e8_5_1_2_1_1_2__axioms,d1_tarski]),
    [interesting(0.05),file(axioms,e16_5_1_2_1_1_2__axioms),[file(axioms,e16_5_1_2_1_1_2__axioms)]]).

fof(e2_5_1_2_1_1_2_2_1__axioms,plain,(
    r1_xreal_0(c2_5_1_2_1_1_2_2__axioms,c5_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c3_5_1_2_1_1_2__axioms,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc2_arytm_2,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_numerals,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc7_xreal_0,fc1_numbers,fc1_zfmisc_1,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,rqLessOrEqual__r1_xreal_0__r0_r0,spc0_boole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d5_tarski,spc0_boole,spc0_numerals,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_2_2__axioms,dt_c5_5_1_2_1_1_2__axioms,de_c2_5_1_2_1_1_2_2__axioms,de_c5_5_1_2_1_1_2__axioms,cc2_xreal_0,t1_subset,t7_boole,e1_5__axioms,e16_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_2__axioms]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_2_2_1__axioms),[file(axioms,e2_5_1_2_1_1_2_2_1__axioms)]]).

fof(e4_5_1_2_1_1_2_2_1__axioms,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2_1_1_2_2_1__axioms,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_c3_5_1_2_1_1_2__axioms,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1_2_1_1_2_2__axioms,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c2_5_1_2_1_1_2_2__axioms,dt_c5_5_1_2_1_1_2__axioms,de_c2_5_1_2_1_1_2_2__axioms,de_c5_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e3_5_1_2_1_1_2_2_1__axioms,e2_5_1_2_1_1_2_2_1__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_2_2_1__axioms),[file(axioms,e4_5_1_2_1_1_2_2_1__axioms)]]).

fof(i2_5_1_2_1_1_2_2_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i2_5_1_2_1_1_2_2_1__axioms)]),
    [interesting(0.02),trivial,file(axioms,i2_5_1_2_1_1_2_2_1__axioms)]).

fof(i1_5_1_2_1_1_2_2_1__axioms,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_5_1_2_1_1_2_2_1__axioms,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_2__axioms])],[e4_5_1_2_1_1_2_2_1__axioms,i2_5_1_2_1_1_2_2_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_2_1__axioms),[file(axioms,i1_5_1_2_1_1_2_2_1__axioms)]]).

fof(e3_5_1_2_1_1_2_2__axioms,plain,(
    ~ r2_hidden(c2_5_1_2_1_1_2_2__axioms,k2_arytm_2) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_2__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2_2_1__axioms])],[e1_5_1_2_1_1_2_2_1__axioms,i1_5_1_2_1_1_2_2_1__axioms]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_2_2__axioms),[file(axioms,e3_5_1_2_1_1_2_2__axioms)]]).

fof(e8_5_1_2__axioms,plain,(
    r1_tarski(c1_5__axioms,k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c1_5__axioms,fc1_numbers,fc2_arytm_2,t3_subset,spc0_boole,spc0_numerals,e7_5_1_2__axioms,t1_xboole_1]),
    [interesting(0.5),file(axioms,e8_5_1_2__axioms),[file(axioms,e8_5_1_2__axioms)]]).

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(0.9),axiom,file(xboole_0,d2_xboole_0)]).

fof(e4_5_1_2_1_1_2_2__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_2_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_2__axioms,dt_c2_5_1_2_1_1_2_2__axioms,de_c2_5_1_2_1_1_2_2__axioms,fc2_arytm_2,t1_subset,t3_subset,t7_boole,spc0_boole,spc0_numerals,e3_5_1_2_1_1_2_2__axioms,e8_5_1_2__axioms,e1_5_1_2_1_1_2_2__axioms,d2_xboole_0]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_2_2__axioms),[file(axioms,e4_5_1_2_1_1_2_2__axioms)]]).

fof(i3_5_1_2_1_1_2_2__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_2_1_1_2_2__axioms)]),
    [interesting(0.02),trivial,file(axioms,i3_5_1_2_1_1_2_2__axioms)]).

fof(i2_5_1_2_1_1_2_2__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_2_2__axioms])],[e4_5_1_2_1_1_2_2__axioms,i3_5_1_2_1_1_2_2__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_2_2__axioms),[file(axioms,i2_5_1_2_1_1_2_2__axioms)]]).

fof(i1_5_1_2_1_1_2_2__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_2_2__axioms,c1_5__axioms)
      & ~ r2_hidden(c1_5_1_2_1_1_2_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2_2__axioms])],[e1_5_1_2_1_1_2_2__axioms,i2_5_1_2_1_1_2_2__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_2__axioms),[file(axioms,i1_5_1_2_1_1_2_2__axioms)]]).

fof(i1_5_1_2_1_1_2_2_tmp__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_2_2__axioms,c1_5__axioms)
      & ~ r2_hidden(c1_5_1_2_1_1_2_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms]),discharge_asm(discharge,[dt_c1_5_1_2_1_1_2_2__axioms])],[dt_c1_5_1_2_1_1_2_2__axioms,i1_5_1_2_1_1_2_2__axioms]),
    [interesting(0.05),e18_5_1_2_1_1_2__axioms]).

fof(e18_5_1_2_1_1_2__axioms,plain,(
    r1_tarski(c1_5__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(let,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms])],[i1_5_1_2_1_1_2_2_tmp__axioms,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,rc1_xcmplx_0,rc2_xcmplx_0,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c1_5__axioms,fc2_arytm_2,spc0_boole,spc0_numerals,d3_tarski,dh_c1_5_1_2_1_1_2_2__axioms]),
    [interesting(0.05),file(axioms,e18_5_1_2_1_1_2__axioms),[file(axioms,e18_5_1_2_1_1_2__axioms)]]).

fof(e4_5_1_2__axioms,plain,(
    r2_hidden(c1_5_1_2__axioms,c1_5__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c1_5_1_2__axioms,e3_5_1_2__axioms]),
    [interesting(0.5),file(axioms,e4_5_1_2__axioms),[file(axioms,e4_5_1_2__axioms)]]).

fof(e19_5_1_2_1_1_2__axioms,plain,(
    ? [A,B] : 
      ( r2_hidden(A,k1_tarski(0))
      & r2_hidden(B,k2_arytm_2)
      & c1_5_1_2__axioms = k4_tarski(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_5__axioms,dt_c1_5_1_2__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t3_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e18_5_1_2_1_1_2__axioms,e4_5_1_2__axioms,t103_zfmisc_1]),
    [interesting(0.05),file(axioms,e19_5_1_2_1_1_2__axioms),[file(axioms,e19_5_1_2_1_1_2__axioms)]]).

fof(dt_c8_5_1_2_1_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c7_5_1_2_1_1_2__axioms,dh_c8_5_1_2_1_1_2__axioms,e19_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c8_5_1_2_1_1_2__axioms),[file(axioms,c8_5_1_2_1_1_2__axioms)]]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.9),axiom,file(tarski,t2_tarski)]).

fof(fraenkel_a_1_1_axioms,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
     => ( r2_hidden(A,a_1_1_axioms(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k2_arytm_2)
            & A = C
            & r2_hidden(k4_tarski(0,C),B) ) ) ) ),
    file(axioms,a_1_1_axioms),
    [interesting(0.9),axiom,file(axioms,a_1_1_axioms)]).

fof(de_c10_5_1_2_1_1_2__axioms,definition,(
    c10_5_1_2_1_1_2__axioms = a_1_1_axioms(c1_5__axioms) ),
    introduced(definition,[new_symbol(c10_5_1_2_1_1_2__axioms),file(axioms,c10_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c10_5_1_2_1_1_2__axioms)]).

fof(dt_c1_5_1_2_1_1_2_3__axioms,assumption,(
    $true ),
    introduced(assumption,[file(axioms,c1_5_1_2_1_1_2_3__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_3__axioms)]).

fof(dh_c1_5_1_2_1_1_2_3__axioms,definition,
    ( ~ ( r2_hidden(c1_5_1_2_1_1_2_3__axioms,a_1_1_axioms(c1_5__axioms))
        & ~ r2_hidden(c1_5_1_2_1_1_2_3__axioms,k2_arytm_2) )
   => ! [A] : 
        ~ ( r2_hidden(A,a_1_1_axioms(c1_5__axioms))
          & ~ r2_hidden(A,k2_arytm_2) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_2_3__axioms),file(axioms,c1_5_1_2_1_1_2_3__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_3__axioms)]).

fof(e1_5_1_2_1_1_2_3__axioms,assumption,(
    r2_hidden(c1_5_1_2_1_1_2_3__axioms,a_1_1_axioms(c1_5__axioms)) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2_3__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_2_3__axioms)]).

fof(e2_5_1_2_1_1_2_3__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & c1_5_1_2_1_1_2_3__axioms = A
      & r2_hidden(k4_tarski(0,A),c1_5__axioms) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_3__axioms,e1_5_1_2_1_1_2_3__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_3__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_1_axioms,d5_tarski,spc0_boole,spc0_numerals,e1_5_1_2_1_1_2_3__axioms]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_2_3__axioms),[file(axioms,e2_5_1_2_1_1_2_3__axioms)]]).

fof(e3_5_1_2_1_1_2_3__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_3__axioms,e1_5_1_2_1_1_2_3__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_3__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e2_5_1_2_1_1_2_3__axioms]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_2_3__axioms),[file(axioms,e3_5_1_2_1_1_2_3__axioms)]]).

fof(i3_5_1_2_1_1_2_3__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_2_1_1_2_3__axioms)]),
    [interesting(0.02),trivial,file(axioms,i3_5_1_2_1_1_2_3__axioms)]).

fof(i2_5_1_2_1_1_2_3__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2_3__axioms,k2_arytm_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_3__axioms,e1_5_1_2_1_1_2_3__axioms])],[e3_5_1_2_1_1_2_3__axioms,i3_5_1_2_1_1_2_3__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_2_3__axioms),[file(axioms,i2_5_1_2_1_1_2_3__axioms)]]).

fof(i1_5_1_2_1_1_2_3__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_2_3__axioms,a_1_1_axioms(c1_5__axioms))
      & ~ r2_hidden(c1_5_1_2_1_1_2_3__axioms,k2_arytm_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_3__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2_3__axioms])],[e1_5_1_2_1_1_2_3__axioms,i2_5_1_2_1_1_2_3__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_3__axioms),[file(axioms,i1_5_1_2_1_1_2_3__axioms)]]).

fof(i1_5_1_2_1_1_2_3_tmp__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_2_3__axioms,a_1_1_axioms(c1_5__axioms))
      & ~ r2_hidden(c1_5_1_2_1_1_2_3__axioms,k2_arytm_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms]),discharge_asm(discharge,[dt_c1_5_1_2_1_1_2_3__axioms])],[dt_c1_5_1_2_1_1_2_3__axioms,i1_5_1_2_1_1_2_3__axioms]),
    [interesting(0.05),e25_5_1_2_1_1_2__axioms]).

fof(e25_5_1_2_1_1_2__axioms,plain,(
    r1_tarski(a_1_1_axioms(c1_5__axioms),k2_arytm_2) ),
    inference(let,[status(thm),assumptions([dt_c1_5__axioms])],[i1_5_1_2_1_1_2_3_tmp__axioms,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_m2_subset_1,rc1_xcmplx_0,rc2_xcmplx_0,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,cc1_xcmplx_0,fc1_numbers,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,spc0_boole,spc0_numerals,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_arytm_2,dt_c1_5__axioms,fc2_arytm_2,t2_tarski,fraenkel_a_1_1_axioms,d3_tarski,dh_c1_5_1_2_1_1_2_3__axioms]),
    [interesting(0.05),file(axioms,e25_5_1_2_1_1_2__axioms),[file(axioms,e25_5_1_2_1_1_2__axioms)]]).

fof(e26_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(a_1_1_axioms(c1_5__axioms),k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,antisymmetry_r2_hidden,dt_k1_numbers,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,spc0_boole,t1_subset,t2_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d5_tarski,spc0_boole,spc0_numerals,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c1_5__axioms,fc2_arytm_2,t3_subset,t2_tarski,fraenkel_a_1_1_axioms,e25_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e26_5_1_2_1_1_2__axioms),[file(axioms,e26_5_1_2_1_1_2__axioms)]]).

fof(dt_c10_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c10_5_1_2_1_1_2__axioms,k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_numbers,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,spc0_boole,t1_subset,t2_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d5_tarski,spc0_boole,spc0_numerals,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c1_5__axioms,fc2_arytm_2,t3_subset,t2_tarski,fraenkel_a_1_1_axioms,de_c10_5_1_2_1_1_2__axioms,e26_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c10_5_1_2_1_1_2__axioms),[file(axioms,c10_5_1_2_1_1_2__axioms)]]).

fof(de_c6_5_1_2_1_1_2__axioms,definition,(
    c6_5_1_2_1_1_2__axioms = a_1_1_axioms(c2_5__axioms) ),
    introduced(definition,[new_symbol(c6_5_1_2_1_1_2__axioms),file(axioms,c6_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c6_5_1_2_1_1_2__axioms)]).

fof(dt_c1_5_1_2_1_1_2_1__axioms,assumption,(
    $true ),
    introduced(assumption,[file(axioms,c1_5_1_2_1_1_2_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_1__axioms)]).

fof(dh_c1_5_1_2_1_1_2_1__axioms,definition,
    ( ~ ( r2_hidden(c1_5_1_2_1_1_2_1__axioms,a_1_1_axioms(c2_5__axioms))
        & ~ r2_hidden(c1_5_1_2_1_1_2_1__axioms,k2_arytm_2) )
   => ! [A] : 
        ~ ( r2_hidden(A,a_1_1_axioms(c2_5__axioms))
          & ~ r2_hidden(A,k2_arytm_2) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_2_1__axioms),file(axioms,c1_5_1_2_1_1_2_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_1__axioms)]).

fof(e1_5_1_2_1_1_2_1__axioms,assumption,(
    r2_hidden(c1_5_1_2_1_1_2_1__axioms,a_1_1_axioms(c2_5__axioms)) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_2_1__axioms)]).

fof(e2_5_1_2_1_1_2_1__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & c1_5_1_2_1_1_2_1__axioms = A
      & r2_hidden(k4_tarski(0,A),c2_5__axioms) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_1__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_1__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c1_5_1_2_1_1_2_1__axioms,dt_c2_5__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,t2_tarski,fraenkel_a_1_1_axioms,d5_tarski,spc0_boole,spc0_numerals,e1_5_1_2_1_1_2_1__axioms]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_2_1__axioms),[file(axioms,e2_5_1_2_1_1_2_1__axioms)]]).

fof(e3_5_1_2_1_1_2_1__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2_1__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_1__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_1__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c1_5_1_2_1_1_2_1__axioms,dt_c2_5__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e2_5_1_2_1_1_2_1__axioms]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_2_1__axioms),[file(axioms,e3_5_1_2_1_1_2_1__axioms)]]).

fof(i3_5_1_2_1_1_2_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_2_1_1_2_1__axioms)]),
    [interesting(0.02),trivial,file(axioms,i3_5_1_2_1_1_2_1__axioms)]).

fof(i2_5_1_2_1_1_2_1__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2_1__axioms,k2_arytm_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_1__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_1__axioms])],[e3_5_1_2_1_1_2_1__axioms,i3_5_1_2_1_1_2_1__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_2_1__axioms),[file(axioms,i2_5_1_2_1_1_2_1__axioms)]]).

fof(i1_5_1_2_1_1_2_1__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_2_1__axioms,a_1_1_axioms(c2_5__axioms))
      & ~ r2_hidden(c1_5_1_2_1_1_2_1__axioms,k2_arytm_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_1__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2_1__axioms])],[e1_5_1_2_1_1_2_1__axioms,i2_5_1_2_1_1_2_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_1__axioms),[file(axioms,i1_5_1_2_1_1_2_1__axioms)]]).

fof(i1_5_1_2_1_1_2_1_tmp__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_2_1__axioms,a_1_1_axioms(c2_5__axioms))
      & ~ r2_hidden(c1_5_1_2_1_1_2_1__axioms,k2_arytm_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_5__axioms]),discharge_asm(discharge,[dt_c1_5_1_2_1_1_2_1__axioms])],[dt_c1_5_1_2_1_1_2_1__axioms,i1_5_1_2_1_1_2_1__axioms]),
    [interesting(0.05),e13_5_1_2_1_1_2__axioms]).

fof(e13_5_1_2_1_1_2__axioms,plain,(
    r1_tarski(a_1_1_axioms(c2_5__axioms),k2_arytm_2) ),
    inference(let,[status(thm),assumptions([dt_c2_5__axioms])],[i1_5_1_2_1_1_2_1_tmp__axioms,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_m2_subset_1,rc1_xcmplx_0,rc2_xcmplx_0,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,cc1_xcmplx_0,fc1_numbers,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,spc0_boole,spc0_numerals,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_arytm_2,dt_c2_5__axioms,fc2_arytm_2,t2_tarski,fraenkel_a_1_1_axioms,d3_tarski,dh_c1_5_1_2_1_1_2_1__axioms]),
    [interesting(0.05),file(axioms,e13_5_1_2_1_1_2__axioms),[file(axioms,e13_5_1_2_1_1_2__axioms)]]).

fof(e14_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(a_1_1_axioms(c2_5__axioms),k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,antisymmetry_r2_hidden,dt_k1_numbers,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,spc0_boole,t1_subset,t2_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d5_tarski,spc0_boole,spc0_numerals,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5__axioms,fc2_arytm_2,t3_subset,t2_tarski,fraenkel_a_1_1_axioms,e13_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e14_5_1_2_1_1_2__axioms),[file(axioms,e14_5_1_2_1_1_2__axioms)]]).

fof(dt_c6_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c6_5_1_2_1_1_2__axioms,k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_numbers,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_zfmisc_1,rc1_xboole_0,rc2_xboole_0,spc0_boole,t1_subset,t2_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole,d5_tarski,spc0_boole,spc0_numerals,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5__axioms,fc2_arytm_2,t3_subset,t2_tarski,fraenkel_a_1_1_axioms,de_c6_5_1_2_1_1_2__axioms,e14_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c6_5_1_2_1_1_2__axioms),[file(axioms,c6_5_1_2_1_1_2__axioms)]]).

fof(de_c9_5_1_2_1_1_2__axioms,definition,(
    c9_5_1_2_1_1_2__axioms = c8_5_1_2_1_1_2__axioms ),
    introduced(definition,[new_symbol(c9_5_1_2_1_1_2__axioms),file(axioms,c9_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c9_5_1_2_1_1_2__axioms)]).

fof(e21_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c8_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c7_5_1_2_1_1_2__axioms,dh_c8_5_1_2_1_1_2__axioms,e19_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e21_5_1_2_1_1_2__axioms),[file(axioms,e21_5_1_2_1_1_2__axioms)]]).

fof(e23_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c8_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c8_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,e21_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e23_5_1_2_1_1_2__axioms),[file(axioms,e23_5_1_2_1_1_2__axioms)]]).

fof(dt_c9_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c9_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c8_5_1_2_1_1_2__axioms,fc2_arytm_2,de_c9_5_1_2_1_1_2__axioms,e23_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c9_5_1_2_1_1_2__axioms),[file(axioms,c9_5_1_2_1_1_2__axioms)]]).

fof(dh_c1_5_1_2_1_1_2_4__axioms,definition,
    ( ( m1_subset_1(c1_5_1_2_1_1_2_4__axioms,k2_arytm_2)
     => ! [A] : 
          ( m1_subset_1(A,k2_arytm_2)
         => ( ( r2_hidden(c1_5_1_2_1_1_2_4__axioms,c6_5_1_2_1_1_2__axioms)
              & r2_hidden(A,c10_5_1_2_1_1_2__axioms) )
           => r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,A) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k2_arytm_2)
       => ! [C] : 
            ( m1_subset_1(C,k2_arytm_2)
           => ( ( r2_hidden(B,c6_5_1_2_1_1_2__axioms)
                & r2_hidden(C,c10_5_1_2_1_1_2__axioms) )
             => r1_arytm_2(B,C) ) ) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_2_4__axioms),file(axioms,c1_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_4__axioms)]).

fof(dh_c2_5_1_2_1_1_2_4__axioms,definition,
    ( ( m1_subset_1(c2_5_1_2_1_1_2_4__axioms,k2_arytm_2)
     => ( ( r2_hidden(c1_5_1_2_1_1_2_4__axioms,c6_5_1_2_1_1_2__axioms)
          & r2_hidden(c2_5_1_2_1_1_2_4__axioms,c10_5_1_2_1_1_2__axioms) )
       => r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,c2_5_1_2_1_1_2_4__axioms) ) )
   => ! [A] : 
        ( m1_subset_1(A,k2_arytm_2)
       => ( ( r2_hidden(c1_5_1_2_1_1_2_4__axioms,c6_5_1_2_1_1_2__axioms)
            & r2_hidden(A,c10_5_1_2_1_1_2__axioms) )
         => r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,A) ) ) ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_2_4__axioms),file(axioms,c2_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c2_5_1_2_1_1_2_4__axioms)]).

fof(e1_5_1_2_1_1_2_4__axioms,assumption,(
    r2_hidden(c1_5_1_2_1_1_2_4__axioms,c6_5_1_2_1_1_2__axioms) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_2_4__axioms)]).

fof(e5_5_1_2_1_1_2_4__axioms,assumption,(
    r2_hidden(c2_5_1_2_1_1_2_4__axioms,c10_5_1_2_1_1_2__axioms) ),
    introduced(assumption,[file(axioms,e5_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,e5_5_1_2_1_1_2_4__axioms)]).

fof(dt_c1_5_1_2_1_1_2_4__axioms,assumption,(
    m1_subset_1(c1_5_1_2_1_1_2_4__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,c1_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_4__axioms)]).

fof(dt_c2_5_1_2_1_1_2_4__axioms,assumption,(
    m1_subset_1(c2_5_1_2_1_1_2_4__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,c2_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c2_5_1_2_1_1_2_4__axioms)]).

fof(dh_c7_5_1_2_1_1_2_4__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & ? [B] : 
            ( m1_subset_1(B,k2_arytm_2)
            & c5_5_1_2_1_1_2_4__axioms = k4_tarski(0,A)
            & c6_5_1_2_1_1_2_4__axioms = k4_tarski(0,B)
            & r1_arytm_2(B,A) ) )
   => ( m1_subset_1(c7_5_1_2_1_1_2_4__axioms,k2_arytm_2)
      & ? [C] : 
          ( m1_subset_1(C,k2_arytm_2)
          & c5_5_1_2_1_1_2_4__axioms = k4_tarski(0,c7_5_1_2_1_1_2_4__axioms)
          & c6_5_1_2_1_1_2_4__axioms = k4_tarski(0,C)
          & r1_arytm_2(C,c7_5_1_2_1_1_2_4__axioms) ) ) ),
    introduced(definition,[new_symbol(c7_5_1_2_1_1_2_4__axioms),file(axioms,c7_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c7_5_1_2_1_1_2_4__axioms)]).

fof(de_c5_5_1_2_1_1_2_4__axioms,definition,(
    c5_5_1_2_1_1_2_4__axioms = k4_tarski(0,c2_5_1_2_1_1_2_4__axioms) ),
    introduced(definition,[new_symbol(c5_5_1_2_1_1_2_4__axioms),file(axioms,c5_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c5_5_1_2_1_1_2_4__axioms)]).

fof(dh_c3_5_1_2_1_1_2_4__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & c1_5_1_2_1_1_2_4__axioms = A
        & r2_hidden(k4_tarski(0,A),c2_5__axioms) )
   => ( m1_subset_1(c3_5_1_2_1_1_2_4__axioms,k2_arytm_2)
      & c1_5_1_2_1_1_2_4__axioms = c3_5_1_2_1_1_2_4__axioms
      & r2_hidden(k4_tarski(0,c3_5_1_2_1_1_2_4__axioms),c2_5__axioms) ) ),
    introduced(definition,[new_symbol(c3_5_1_2_1_1_2_4__axioms),file(axioms,c3_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c3_5_1_2_1_1_2_4__axioms)]).

fof(e2_5_1_2_1_1_2_4__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & c1_5_1_2_1_1_2_4__axioms = A
      & r2_hidden(k4_tarski(0,A),c2_5__axioms) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,dt_c6_5_1_2_1_1_2__axioms,de_c6_5_1_2_1_1_2__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e1_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_2_4__axioms),[file(axioms,e2_5_1_2_1_1_2_4__axioms)]]).

fof(dt_c3_5_1_2_1_1_2_4__axioms,plain,(
    m1_subset_1(c3_5_1_2_1_1_2_4__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms])],[dh_c3_5_1_2_1_1_2_4__axioms,e2_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,c3_5_1_2_1_1_2_4__axioms),[file(axioms,c3_5_1_2_1_1_2_4__axioms)]]).

fof(dh_c4_5_1_2_1_1_2_4__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & c2_5_1_2_1_1_2_4__axioms = A
        & r2_hidden(k4_tarski(0,A),c1_5__axioms) )
   => ( m1_subset_1(c4_5_1_2_1_1_2_4__axioms,k2_arytm_2)
      & c2_5_1_2_1_1_2_4__axioms = c4_5_1_2_1_1_2_4__axioms
      & r2_hidden(k4_tarski(0,c4_5_1_2_1_1_2_4__axioms),c1_5__axioms) ) ),
    introduced(definition,[new_symbol(c4_5_1_2_1_1_2_4__axioms),file(axioms,c4_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c4_5_1_2_1_1_2_4__axioms)]).

fof(e6_5_1_2_1_1_2_4__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & c2_5_1_2_1_1_2_4__axioms = A
      & r2_hidden(k4_tarski(0,A),c1_5__axioms) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c10_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,de_c10_5_1_2_1_1_2__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e5_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e6_5_1_2_1_1_2_4__axioms),[file(axioms,e6_5_1_2_1_1_2_4__axioms)]]).

fof(dt_c4_5_1_2_1_1_2_4__axioms,plain,(
    m1_subset_1(c4_5_1_2_1_1_2_4__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c4_5_1_2_1_1_2_4__axioms,e6_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,c4_5_1_2_1_1_2_4__axioms),[file(axioms,c4_5_1_2_1_1_2_4__axioms)]]).

fof(e3_5_1_2_1_1_2_4__axioms,plain,(
    c1_5_1_2_1_1_2_4__axioms = c3_5_1_2_1_1_2_4__axioms ),
    inference(consider,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms])],[dh_c3_5_1_2_1_1_2_4__axioms,e2_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_2_4__axioms),[file(axioms,e3_5_1_2_1_1_2_4__axioms)]]).

fof(e4_5_1_2_1_1_2_4__axioms,plain,(
    r2_hidden(k4_tarski(0,c3_5_1_2_1_1_2_4__axioms),c2_5__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms])],[dh_c3_5_1_2_1_1_2_4__axioms,e2_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_2_4__axioms),[file(axioms,e4_5_1_2_1_1_2_4__axioms)]]).

fof(e7_5_1_2_1_1_2_4__axioms,plain,(
    c2_5_1_2_1_1_2_4__axioms = c4_5_1_2_1_1_2_4__axioms ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c4_5_1_2_1_1_2_4__axioms,e6_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e7_5_1_2_1_1_2_4__axioms),[file(axioms,e7_5_1_2_1_1_2_4__axioms)]]).

fof(e8_5_1_2_1_1_2_4__axioms,plain,(
    r2_hidden(k4_tarski(0,c4_5_1_2_1_1_2_4__axioms),c1_5__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c4_5_1_2_1_1_2_4__axioms,e6_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e8_5_1_2_1_1_2_4__axioms),[file(axioms,e8_5_1_2_1_1_2_4__axioms)]]).

fof(e9_5_1_2_1_1_2_4__axioms,plain,
    ( v1_xreal_0(k4_tarski(0,c2_5_1_2_1_1_2_4__axioms))
    & v1_xreal_0(k4_tarski(0,c1_5_1_2_1_1_2_4__axioms)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_k4_tarski,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,dt_c3_5_1_2_1_1_2_4__axioms,dt_c4_5_1_2_1_1_2_4__axioms,cc2_xreal_0,fc1_numbers,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e3_5_1_2_1_1_2_4__axioms,e4_5_1_2_1_1_2_4__axioms,e7_5_1_2_1_1_2_4__axioms,e8_5_1_2_1_1_2_4__axioms,d1_xreal_0]),
    [interesting(0.02),file(axioms,e9_5_1_2_1_1_2_4__axioms),[file(axioms,e9_5_1_2_1_1_2_4__axioms)]]).

fof(dt_c5_5_1_2_1_1_2_4__axioms,plain,(
    v1_xreal_0(c5_5_1_2_1_1_2_4__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,dt_k4_tarski,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms,cc2_xreal_0,fc1_zfmisc_1,d5_tarski,spc0_boole,spc0_numerals,de_c5_5_1_2_1_1_2_4__axioms,e9_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,c5_5_1_2_1_1_2_4__axioms),[file(axioms,c5_5_1_2_1_1_2_4__axioms)]]).

fof(de_c6_5_1_2_1_1_2_4__axioms,definition,(
    c6_5_1_2_1_1_2_4__axioms = k4_tarski(0,c1_5_1_2_1_1_2_4__axioms) ),
    introduced(definition,[new_symbol(c6_5_1_2_1_1_2_4__axioms),file(axioms,c6_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c6_5_1_2_1_1_2_4__axioms)]).

fof(dt_c6_5_1_2_1_1_2_4__axioms,plain,(
    v1_xreal_0(c6_5_1_2_1_1_2_4__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,dt_k4_tarski,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms,cc2_xreal_0,fc1_zfmisc_1,d5_tarski,spc0_boole,spc0_numerals,de_c6_5_1_2_1_1_2_4__axioms,e9_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,c6_5_1_2_1_1_2_4__axioms),[file(axioms,c6_5_1_2_1_1_2_4__axioms)]]).

fof(e11_5_1_2_1_1_2_4__axioms,plain,(
    r1_xreal_0(c5_5_1_2_1_1_2_4__axioms,c6_5_1_2_1_1_2_4__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_k4_tarski,dt_c1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,dt_c3_5_1_2_1_1_2_4__axioms,dt_c4_5_1_2_1_1_2_4__axioms,dt_c5_5_1_2_1_1_2_4__axioms,dt_c6_5_1_2_1_1_2_4__axioms,de_c5_5_1_2_1_1_2_4__axioms,de_c6_5_1_2_1_1_2_4__axioms,cc2_xreal_0,fc1_zfmisc_1,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e1_5__axioms,e3_5_1_2_1_1_2_4__axioms,e4_5_1_2_1_1_2_4__axioms,e7_5_1_2_1_1_2_4__axioms,e8_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e11_5_1_2_1_1_2_4__axioms),[file(axioms,e11_5_1_2_1_1_2_4__axioms)]]).

fof(e10_5_1_2_1_1_2_4__axioms,plain,
    ( r2_hidden(c5_5_1_2_1_1_2_4__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
    & r2_hidden(c6_5_1_2_1_1_2_4__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c5_5_1_2_1_1_2_4__axioms,dt_c6_5_1_2_1_1_2_4__axioms,de_c5_5_1_2_1_1_2_4__axioms,de_c6_5_1_2_1_1_2_4__axioms,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t6_boole,t7_boole,d5_tarski,spc0_boole,spc0_numerals,l24_axioms,t106_zfmisc_1]),
    [interesting(0.02),file(axioms,e10_5_1_2_1_1_2_4__axioms),[file(axioms,e10_5_1_2_1_1_2_4__axioms)]]).

fof(e12_5_1_2_1_1_2_4__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & ? [B] : 
          ( m1_subset_1(B,k2_arytm_2)
          & c5_5_1_2_1_1_2_4__axioms = k4_tarski(0,A)
          & c6_5_1_2_1_1_2_4__axioms = k4_tarski(0,B)
          & r1_arytm_2(B,A) ) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c5_5_1_2_1_1_2_4__axioms,dt_c6_5_1_2_1_1_2_4__axioms,de_c5_5_1_2_1_1_2_4__axioms,de_c6_5_1_2_1_1_2_4__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e11_5_1_2_1_1_2_4__axioms,e10_5_1_2_1_1_2_4__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e12_5_1_2_1_1_2_4__axioms),[file(axioms,e12_5_1_2_1_1_2_4__axioms)]]).

fof(dt_c7_5_1_2_1_1_2_4__axioms,plain,(
    m1_subset_1(c7_5_1_2_1_1_2_4__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c7_5_1_2_1_1_2_4__axioms,e12_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,c7_5_1_2_1_1_2_4__axioms),[file(axioms,c7_5_1_2_1_1_2_4__axioms)]]).

fof(dh_c8_5_1_2_1_1_2_4__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & c5_5_1_2_1_1_2_4__axioms = k4_tarski(0,c7_5_1_2_1_1_2_4__axioms)
        & c6_5_1_2_1_1_2_4__axioms = k4_tarski(0,A)
        & r1_arytm_2(A,c7_5_1_2_1_1_2_4__axioms) )
   => ( m1_subset_1(c8_5_1_2_1_1_2_4__axioms,k2_arytm_2)
      & c5_5_1_2_1_1_2_4__axioms = k4_tarski(0,c7_5_1_2_1_1_2_4__axioms)
      & c6_5_1_2_1_1_2_4__axioms = k4_tarski(0,c8_5_1_2_1_1_2_4__axioms)
      & r1_arytm_2(c8_5_1_2_1_1_2_4__axioms,c7_5_1_2_1_1_2_4__axioms) ) ),
    introduced(definition,[new_symbol(c8_5_1_2_1_1_2_4__axioms),file(axioms,c8_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),axiom,file(axioms,c8_5_1_2_1_1_2_4__axioms)]).

fof(dt_c8_5_1_2_1_1_2_4__axioms,plain,(
    m1_subset_1(c8_5_1_2_1_1_2_4__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c7_5_1_2_1_1_2_4__axioms,dh_c8_5_1_2_1_1_2_4__axioms,e12_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,c8_5_1_2_1_1_2_4__axioms),[file(axioms,c8_5_1_2_1_1_2_4__axioms)]]).

fof(e13_5_1_2_1_1_2_4__axioms,plain,(
    c5_5_1_2_1_1_2_4__axioms = k4_tarski(0,c7_5_1_2_1_1_2_4__axioms) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c7_5_1_2_1_1_2_4__axioms,dh_c8_5_1_2_1_1_2_4__axioms,e12_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e13_5_1_2_1_1_2_4__axioms),[file(axioms,e13_5_1_2_1_1_2_4__axioms)]]).

fof(e14_5_1_2_1_1_2_4__axioms,plain,(
    c6_5_1_2_1_1_2_4__axioms = k4_tarski(0,c8_5_1_2_1_1_2_4__axioms) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c7_5_1_2_1_1_2_4__axioms,dh_c8_5_1_2_1_1_2_4__axioms,e12_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e14_5_1_2_1_1_2_4__axioms),[file(axioms,e14_5_1_2_1_1_2_4__axioms)]]).

fof(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t33_zfmisc_1)]).

fof(e16_5_1_2_1_1_2_4__axioms,plain,
    ( c2_5_1_2_1_1_2_4__axioms = c7_5_1_2_1_1_2_4__axioms
    & c1_5_1_2_1_1_2_4__axioms = c8_5_1_2_1_1_2_4__axioms ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,dt_k4_tarski,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms,dt_c5_5_1_2_1_1_2_4__axioms,dt_c6_5_1_2_1_1_2_4__axioms,dt_c7_5_1_2_1_1_2_4__axioms,dt_c8_5_1_2_1_1_2_4__axioms,de_c5_5_1_2_1_1_2_4__axioms,de_c6_5_1_2_1_1_2_4__axioms,fc1_zfmisc_1,d5_tarski,spc0_boole,spc0_numerals,e13_5_1_2_1_1_2_4__axioms,e14_5_1_2_1_1_2_4__axioms,t33_zfmisc_1]),
    [interesting(0.02),file(axioms,e16_5_1_2_1_1_2_4__axioms),[file(axioms,e16_5_1_2_1_1_2_4__axioms)]]).

fof(e15_5_1_2_1_1_2_4__axioms,plain,(
    r1_arytm_2(c8_5_1_2_1_1_2_4__axioms,c7_5_1_2_1_1_2_4__axioms) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[dh_c7_5_1_2_1_1_2_4__axioms,dh_c8_5_1_2_1_1_2_4__axioms,e12_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e15_5_1_2_1_1_2_4__axioms),[file(axioms,e15_5_1_2_1_1_2_4__axioms)]]).

fof(e17_5_1_2_1_1_2_4__axioms,plain,(
    r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,c2_5_1_2_1_1_2_4__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,fc2_arytm_2,connectedness_r1_arytm_2,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms,dt_c7_5_1_2_1_1_2_4__axioms,dt_c8_5_1_2_1_1_2_4__axioms,e16_5_1_2_1_1_2_4__axioms,e15_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,e17_5_1_2_1_1_2_4__axioms),[file(axioms,e17_5_1_2_1_1_2_4__axioms)]]).

fof(i4_5_1_2_1_1_2_4__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i4_5_1_2_1_1_2_4__axioms)]),
    [interesting(0.02),trivial,file(axioms,i4_5_1_2_1_1_2_4__axioms)]).

fof(i3_5_1_2_1_1_2_4__axioms,plain,(
    r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,c2_5_1_2_1_1_2_4__axioms) ),
    inference(conclusion,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms,e5_5_1_2_1_1_2_4__axioms])],[e17_5_1_2_1_1_2_4__axioms,i4_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,i3_5_1_2_1_1_2_4__axioms),[file(axioms,i3_5_1_2_1_1_2_4__axioms)]]).

fof(i2_5_1_2_1_1_2_4__axioms,plain,(
    ~ ( r2_hidden(c2_5_1_2_1_1_2_4__axioms,c10_5_1_2_1_1_2__axioms)
      & ~ r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,c2_5_1_2_1_1_2_4__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2_4__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms]),discharge_asm(discharge,[e5_5_1_2_1_1_2_4__axioms])],[e5_5_1_2_1_1_2_4__axioms,i3_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_2_4__axioms),[file(axioms,i2_5_1_2_1_1_2_4__axioms)]]).

fof(i1_5_1_2_1_1_2_4__axioms,plain,
    ( ( r2_hidden(c1_5_1_2_1_1_2_4__axioms,c6_5_1_2_1_1_2__axioms)
      & r2_hidden(c2_5_1_2_1_1_2_4__axioms,c10_5_1_2_1_1_2__axioms) )
   => r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,c2_5_1_2_1_1_2_4__axioms) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5__axioms,dt_c1_5__axioms,dt_c2_5_1_2_1_1_2_4__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2_4__axioms])],[e1_5_1_2_1_1_2_4__axioms,i2_5_1_2_1_1_2_4__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_4__axioms),[file(axioms,i1_5_1_2_1_1_2_4__axioms)]]).

fof(i1_5_1_2_1_1_2_4_tmp__axioms,plain,
    ( ( m1_subset_1(c1_5_1_2_1_1_2_4__axioms,k2_arytm_2)
      & m1_subset_1(c2_5_1_2_1_1_2_4__axioms,k2_arytm_2) )
   => ( ( r2_hidden(c1_5_1_2_1_1_2_4__axioms,c6_5_1_2_1_1_2__axioms)
        & r2_hidden(c2_5_1_2_1_1_2_4__axioms,c10_5_1_2_1_1_2__axioms) )
     => r1_arytm_2(c1_5_1_2_1_1_2_4__axioms,c2_5_1_2_1_1_2_4__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,dt_c1_5__axioms]),discharge_asm(discharge,[dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms])],[dt_c1_5_1_2_1_1_2_4__axioms,dt_c2_5_1_2_1_1_2_4__axioms,i1_5_1_2_1_1_2_4__axioms]),
    [interesting(0.05),e28_5_1_2_1_1_2__axioms]).

fof(e28_5_1_2_1_1_2__axioms,plain,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( r2_hidden(A,c6_5_1_2_1_1_2__axioms)
              & r2_hidden(B,c10_5_1_2_1_1_2__axioms) )
           => r1_arytm_2(A,B) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,dt_c1_5__axioms])],[i1_5_1_2_1_1_2_4_tmp__axioms,dh_c1_5_1_2_1_1_2_4__axioms,dh_c2_5_1_2_1_1_2_4__axioms]),
    [interesting(0.05),file(axioms,e28_5_1_2_1_1_2__axioms),[file(axioms,e28_5_1_2_1_1_2__axioms)]]).

fof(e17_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c4_5_1_2_1_1_2__axioms,c6_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_numerals,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c3_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,fc1_zfmisc_1,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,spc0_boole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,d5_tarski,spc0_boole,spc0_numerals,antisymmetry_r2_hidden,dt_c2_5__axioms,dt_c4_5_1_2_1_1_2__axioms,dt_c5_5_1_2_1_1_2__axioms,dt_c6_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,de_c5_5_1_2_1_1_2__axioms,de_c6_5_1_2_1_1_2__axioms,t1_subset,t7_boole,e16_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e17_5_1_2_1_1_2__axioms),[file(axioms,e17_5_1_2_1_1_2__axioms)]]).

fof(dt_c7_5_1_2_1_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c7_5_1_2_1_1_2__axioms,e19_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c7_5_1_2_1_1_2__axioms),[file(axioms,c7_5_1_2_1_1_2__axioms)]]).

fof(e20_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c7_5_1_2_1_1_2__axioms,k1_tarski(0)) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c7_5_1_2_1_1_2__axioms,dh_c8_5_1_2_1_1_2__axioms,e19_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e20_5_1_2_1_1_2__axioms),[file(axioms,e20_5_1_2_1_1_2__axioms)]]).

fof(e22_5_1_2_1_1_2__axioms,plain,(
    c1_5_1_2__axioms = k4_tarski(c7_5_1_2_1_1_2__axioms,c8_5_1_2_1_1_2__axioms) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c7_5_1_2_1_1_2__axioms,dh_c8_5_1_2_1_1_2__axioms,e19_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e22_5_1_2_1_1_2__axioms),[file(axioms,e22_5_1_2_1_1_2__axioms)]]).

fof(e24_5_1_2_1_1_2__axioms,plain,(
    c1_5_1_2__axioms = k4_tarski(0,c9_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k4_tarski,dt_c1_5_1_2__axioms,dt_c7_5_1_2_1_1_2__axioms,dt_c8_5_1_2_1_1_2__axioms,dt_c9_5_1_2_1_1_2__axioms,de_c9_5_1_2_1_1_2__axioms,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e20_5_1_2_1_1_2__axioms,e22_5_1_2_1_1_2__axioms,d1_tarski]),
    [interesting(0.05),file(axioms,e24_5_1_2_1_1_2__axioms),[file(axioms,e24_5_1_2_1_1_2__axioms)]]).

fof(e27_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c9_5_1_2_1_1_2__axioms,c10_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c8_5_1_2_1_1_2__axioms,cc1_xcmplx_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,antisymmetry_r2_hidden,dt_k4_tarski,dt_c10_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c1_5_1_2__axioms,dt_c9_5_1_2_1_1_2__axioms,de_c10_5_1_2_1_1_2__axioms,de_c9_5_1_2_1_1_2__axioms,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e4_5_1_2__axioms,e24_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e27_5_1_2_1_1_2__axioms),[file(axioms,e27_5_1_2_1_1_2__axioms)]]).

fof(t9_arytm_2,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k2_arytm_2))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k2_arytm_2))
         => ~ ( ? [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                  & r2_hidden(C,A) )
              & ? [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                  & r2_hidden(C,B) )
              & ! [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                 => ! [D] : 
                      ( m1_subset_1(D,k2_arytm_2)
                     => ( ( r2_hidden(C,A)
                          & r2_hidden(D,B) )
                       => r1_arytm_2(C,D) ) ) )
              & ! [C] : 
                  ( m1_subset_1(C,k2_arytm_2)
                 => ? [D] : 
                      ( m1_subset_1(D,k2_arytm_2)
                      & ? [E] : 
                          ( m1_subset_1(E,k2_arytm_2)
                          & r2_hidden(D,A)
                          & r2_hidden(E,B)
                          & ~ ( r1_arytm_2(D,C)
                              & r1_arytm_2(C,E) ) ) ) ) ) ) ) ),
    file(arytm_2,t9_arytm_2),
    [interesting(0.9),axiom,file(arytm_2,t9_arytm_2)]).

fof(e29_5_1_2_1_1_2__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ( ( r2_hidden(B,c6_5_1_2_1_1_2__axioms)
                  & r2_hidden(C,c10_5_1_2_1_1_2__axioms) )
               => ( r1_arytm_2(B,A)
                  & r1_arytm_2(A,C) ) ) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,dt_k1_numbers,dt_k1_xboole_0,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_xboole_0,fc1_zfmisc_1,spc0_boole,d5_tarski,spc0_boole,spc0_numerals,reflexivity_r1_tarski,dt_c1_5__axioms,dt_c2_5__axioms,dt_c3_5_1_2_1_1_2__axioms,dt_c8_5_1_2_1_1_2__axioms,rc1_xboole_0,rc2_xboole_0,t2_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,connectedness_r1_arytm_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c10_5_1_2_1_1_2__axioms,dt_c4_5_1_2_1_1_2__axioms,dt_c6_5_1_2_1_1_2__axioms,dt_c9_5_1_2_1_1_2__axioms,de_c10_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,de_c6_5_1_2_1_1_2__axioms,de_c9_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t3_subset,t4_subset,t7_boole,e28_5_1_2_1_1_2__axioms,e17_5_1_2_1_1_2__axioms,e27_5_1_2_1_1_2__axioms,t9_arytm_2]),
    [interesting(0.05),file(axioms,e29_5_1_2_1_1_2__axioms),[file(axioms,e29_5_1_2_1_1_2__axioms)]]).

fof(dt_c11_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c11_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c11_5_1_2_1_1_2__axioms,e29_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c11_5_1_2_1_1_2__axioms),[file(axioms,c11_5_1_2_1_1_2__axioms)]]).

fof(de_c12_5_1_2_1_1_2__axioms,definition,(
    c12_5_1_2_1_1_2__axioms = k4_tarski(0,c11_5_1_2_1_1_2__axioms) ),
    introduced(definition,[new_symbol(c12_5_1_2_1_1_2__axioms),file(axioms,c12_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c12_5_1_2_1_1_2__axioms)]).

fof(e30_5_1_2_1_1_2__axioms,plain,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( r2_hidden(A,c6_5_1_2_1_1_2__axioms)
              & r2_hidden(B,c10_5_1_2_1_1_2__axioms) )
           => ( r1_arytm_2(A,c11_5_1_2_1_1_2__axioms)
              & r1_arytm_2(c11_5_1_2_1_1_2__axioms,B) ) ) ) ) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[dh_c11_5_1_2_1_1_2__axioms,e29_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e30_5_1_2_1_1_2__axioms),[file(axioms,e30_5_1_2_1_1_2__axioms)]]).

fof(e32_5_1_2_1_1_2__axioms,plain,(
    r1_arytm_2(c4_5_1_2_1_1_2__axioms,c11_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e1_5_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_xboole_0,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_xboole_0,fc1_zfmisc_1,spc0_boole,d5_tarski,spc0_boole,spc0_numerals,dt_k1_zfmisc_1,dt_c1_5__axioms,dt_c2_5__axioms,dt_c3_5_1_2_1_1_2__axioms,dt_c8_5_1_2_1_1_2__axioms,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,connectedness_r1_arytm_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c10_5_1_2_1_1_2__axioms,dt_c11_5_1_2_1_1_2__axioms,dt_c4_5_1_2_1_1_2__axioms,dt_c6_5_1_2_1_1_2__axioms,dt_c9_5_1_2_1_1_2__axioms,de_c10_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,de_c6_5_1_2_1_1_2__axioms,de_c9_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,e17_5_1_2_1_1_2__axioms,e27_5_1_2_1_1_2__axioms,e30_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e32_5_1_2_1_1_2__axioms),[file(axioms,e32_5_1_2_1_1_2__axioms)]]).

fof(t3_arytm_0,theorem,(
    ! [A] : 
      ~ ( r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers)
        & A = k12_arytm_3 ) ),
    file(arytm_0,t3_arytm_0),
    [interesting(0.9),axiom,file(arytm_0,t3_arytm_0)]).

fof(e31_5_1_2_1_1_2__axioms,plain,(
    c4_5_1_2_1_1_2__axioms != 0 ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc4_arytm_3,rc1_arytm_3,rc2_arytm_3,rc3_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,rc1_xcmplx_0,rc2_xcmplx_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_k6_arytm_3,dt_m1_subset_1,dt_m2_subset_1,dt_c3_5_1_2_1_1_2__axioms,cc1_xcmplx_0,fc1_xboole_0,fc2_arytm_2,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_numbers,dt_k4_tarski,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,fc1_numbers,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e11_5_1_2_1_1_2__axioms,t3_arytm_0]),
    [interesting(0.05),file(axioms,e31_5_1_2_1_1_2__axioms),[file(axioms,e31_5_1_2_1_1_2__axioms)]]).

fof(t5_arytm_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( r1_arytm_2(A,B)
              & B = k1_xboole_0 )
           => A = k1_xboole_0 ) ) ) ),
    file(arytm_1,t5_arytm_1),
    [interesting(0.9),axiom,file(arytm_1,t5_arytm_1)]).

fof(e33_5_1_2_1_1_2__axioms,plain,(
    c11_5_1_2_1_1_2__axioms != 0 ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t3_subset,t4_subset,t5_subset,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c3_5_1_2_1_1_2__axioms,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t7_boole,t8_boole,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k1_xboole_0,dt_k2_arytm_2,dt_m1_subset_1,dt_c11_5_1_2_1_1_2__axioms,dt_c4_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,fc1_xboole_0,fc2_arytm_2,t6_boole,spc0_boole,spc0_numerals,e32_5_1_2_1_1_2__axioms,e31_5_1_2_1_1_2__axioms,t5_arytm_1]),
    [interesting(0.05),file(axioms,e33_5_1_2_1_1_2__axioms),[file(axioms,e33_5_1_2_1_1_2__axioms)]]).

fof(t2_arytm_0,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ( A != k12_arytm_3
       => r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers) ) ) ),
    file(arytm_0,t2_arytm_0),
    [interesting(0.9),axiom,file(arytm_0,t2_arytm_0)]).

fof(e34_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(k4_tarski(0,c11_5_1_2_1_1_2__axioms),k1_numbers) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc4_arytm_3,rc1_arytm_3,rc2_arytm_3,rc3_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k5_numbers,dt_k6_arytm_3,dt_m2_subset_1,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc1_xcmplx_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k12_arytm_3,dt_k12_arytm_3,dt_k1_numbers,dt_k2_arytm_2,dt_k4_tarski,dt_m1_subset_1,dt_c11_5_1_2_1_1_2__axioms,cc1_xcmplx_0,fc1_numbers,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e33_5_1_2_1_1_2__axioms,t2_arytm_0]),
    [interesting(0.05),file(axioms,e34_5_1_2_1_1_2__axioms),[file(axioms,e34_5_1_2_1_1_2__axioms)]]).

fof(e35_5_1_2_1_1_2__axioms,plain,(
    v1_xreal_0(k4_tarski(0,c11_5_1_2_1_1_2__axioms)) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_k4_tarski,dt_c11_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_numbers,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e34_5_1_2_1_1_2__axioms,d1_xreal_0]),
    [interesting(0.05),file(axioms,e35_5_1_2_1_1_2__axioms),[file(axioms,e35_5_1_2_1_1_2__axioms)]]).

fof(dt_c12_5_1_2_1_1_2__axioms,plain,(
    v1_xreal_0(c12_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,dt_k4_tarski,dt_c11_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_zfmisc_1,d5_tarski,spc0_boole,spc0_numerals,de_c12_5_1_2_1_1_2__axioms,e35_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c12_5_1_2_1_1_2__axioms),[file(axioms,c12_5_1_2_1_1_2__axioms)]]).

fof(dh_c13_5_1_2_1_1_2__axioms,definition,
    ( ( v1_xreal_0(c13_5_1_2_1_1_2__axioms)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ( ( r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms)
              & r2_hidden(A,c2_5__axioms) )
           => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
              & r1_xreal_0(c12_5_1_2_1_1_2__axioms,A) ) ) ) )
   => ! [B] : 
        ( v1_xreal_0(B)
       => ! [C] : 
            ( v1_xreal_0(C)
           => ( ( r2_hidden(B,c1_5__axioms)
                & r2_hidden(C,c2_5__axioms) )
             => ( r1_xreal_0(B,c12_5_1_2_1_1_2__axioms)
                & r1_xreal_0(c12_5_1_2_1_1_2__axioms,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c13_5_1_2_1_1_2__axioms),file(axioms,c13_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c13_5_1_2_1_1_2__axioms)]).

fof(dh_c14_5_1_2_1_1_2__axioms,definition,
    ( ( v1_xreal_0(c14_5_1_2_1_1_2__axioms)
     => ( ( r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms)
          & r2_hidden(c14_5_1_2_1_1_2__axioms,c2_5__axioms) )
       => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
          & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ) ) )
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ( r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms)
            & r2_hidden(A,c2_5__axioms) )
         => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
            & r1_xreal_0(c12_5_1_2_1_1_2__axioms,A) ) ) ) ),
    introduced(definition,[new_symbol(c14_5_1_2_1_1_2__axioms),file(axioms,c14_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c14_5_1_2_1_1_2__axioms)]).

fof(e37_5_1_2_1_1_2__axioms,assumption,(
    r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms) ),
    introduced(assumption,[file(axioms,e37_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,e37_5_1_2_1_1_2__axioms)]).

fof(e38_5_1_2_1_1_2__axioms,assumption,(
    r2_hidden(c14_5_1_2_1_1_2__axioms,c2_5__axioms) ),
    introduced(assumption,[file(axioms,e38_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,e38_5_1_2_1_1_2__axioms)]).

fof(dt_c13_5_1_2_1_1_2__axioms,assumption,(
    v1_xreal_0(c13_5_1_2_1_1_2__axioms) ),
    introduced(assumption,[file(axioms,c13_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c13_5_1_2_1_1_2__axioms)]).

fof(dt_c14_5_1_2_1_1_2__axioms,assumption,(
    v1_xreal_0(c14_5_1_2_1_1_2__axioms) ),
    introduced(assumption,[file(axioms,c14_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c14_5_1_2_1_1_2__axioms)]).

fof(e1_5_1_2_1_1_2_5_1_1__axioms,assumption,(
    r2_hidden(c14_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2_5_1_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_2_5_1_1__axioms)]).

fof(dh_c15_5_1_2_1_1_2__axioms,definition,
    ( ? [A,B] : 
        ( r2_hidden(A,k1_tarski(0))
        & r2_hidden(B,k2_arytm_2)
        & c13_5_1_2_1_1_2__axioms = k4_tarski(A,B) )
   => ? [C] : 
        ( r2_hidden(c15_5_1_2_1_1_2__axioms,k1_tarski(0))
        & r2_hidden(C,k2_arytm_2)
        & c13_5_1_2_1_1_2__axioms = k4_tarski(c15_5_1_2_1_1_2__axioms,C) ) ),
    introduced(definition,[new_symbol(c15_5_1_2_1_1_2__axioms),file(axioms,c15_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c15_5_1_2_1_1_2__axioms)]).

fof(dh_c16_5_1_2_1_1_2__axioms,definition,
    ( ? [A] : 
        ( r2_hidden(c15_5_1_2_1_1_2__axioms,k1_tarski(0))
        & r2_hidden(A,k2_arytm_2)
        & c13_5_1_2_1_1_2__axioms = k4_tarski(c15_5_1_2_1_1_2__axioms,A) )
   => ( r2_hidden(c15_5_1_2_1_1_2__axioms,k1_tarski(0))
      & r2_hidden(c16_5_1_2_1_1_2__axioms,k2_arytm_2)
      & c13_5_1_2_1_1_2__axioms = k4_tarski(c15_5_1_2_1_1_2__axioms,c16_5_1_2_1_1_2__axioms) ) ),
    introduced(definition,[new_symbol(c16_5_1_2_1_1_2__axioms),file(axioms,c16_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c16_5_1_2_1_1_2__axioms)]).

fof(e39_5_1_2_1_1_2__axioms,plain,(
    ? [A,B] : 
      ( r2_hidden(A,k1_tarski(0))
      & r2_hidden(B,k2_arytm_2)
      & c13_5_1_2_1_1_2__axioms = k4_tarski(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c13_5_1_2_1_1_2__axioms,dt_c1_5__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t3_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e18_5_1_2_1_1_2__axioms,e37_5_1_2_1_1_2__axioms,t103_zfmisc_1]),
    [interesting(0.05),file(axioms,e39_5_1_2_1_1_2__axioms),[file(axioms,e39_5_1_2_1_1_2__axioms)]]).

fof(dt_c16_5_1_2_1_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[dh_c15_5_1_2_1_1_2__axioms,dh_c16_5_1_2_1_1_2__axioms,e39_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c16_5_1_2_1_1_2__axioms),[file(axioms,c16_5_1_2_1_1_2__axioms)]]).

fof(de_c17_5_1_2_1_1_2__axioms,definition,(
    c17_5_1_2_1_1_2__axioms = c16_5_1_2_1_1_2__axioms ),
    introduced(definition,[new_symbol(c17_5_1_2_1_1_2__axioms),file(axioms,c17_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),axiom,file(axioms,c17_5_1_2_1_1_2__axioms)]).

fof(e41_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c16_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[dh_c15_5_1_2_1_1_2__axioms,dh_c16_5_1_2_1_1_2__axioms,e39_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e41_5_1_2_1_1_2__axioms),[file(axioms,e41_5_1_2_1_1_2__axioms)]]).

fof(e43_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c16_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c16_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,e41_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e43_5_1_2_1_1_2__axioms),[file(axioms,e43_5_1_2_1_1_2__axioms)]]).

fof(dt_c17_5_1_2_1_1_2__axioms,plain,(
    m1_subset_1(c17_5_1_2_1_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c16_5_1_2_1_1_2__axioms,fc2_arytm_2,de_c17_5_1_2_1_1_2__axioms,e43_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c17_5_1_2_1_1_2__axioms),[file(axioms,c17_5_1_2_1_1_2__axioms)]]).

fof(dt_c15_5_1_2_1_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[dh_c15_5_1_2_1_1_2__axioms,e39_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,c15_5_1_2_1_1_2__axioms),[file(axioms,c15_5_1_2_1_1_2__axioms)]]).

fof(e40_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c15_5_1_2_1_1_2__axioms,k1_tarski(0)) ),
    inference(consider,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[dh_c15_5_1_2_1_1_2__axioms,dh_c16_5_1_2_1_1_2__axioms,e39_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e40_5_1_2_1_1_2__axioms),[file(axioms,e40_5_1_2_1_1_2__axioms)]]).

fof(e42_5_1_2_1_1_2__axioms,plain,(
    c13_5_1_2_1_1_2__axioms = k4_tarski(c15_5_1_2_1_1_2__axioms,c16_5_1_2_1_1_2__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[dh_c15_5_1_2_1_1_2__axioms,dh_c16_5_1_2_1_1_2__axioms,e39_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e42_5_1_2_1_1_2__axioms),[file(axioms,e42_5_1_2_1_1_2__axioms)]]).

fof(e44_5_1_2_1_1_2__axioms,plain,(
    c13_5_1_2_1_1_2__axioms = k4_tarski(0,c17_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k4_tarski,dt_c13_5_1_2_1_1_2__axioms,dt_c15_5_1_2_1_1_2__axioms,dt_c16_5_1_2_1_1_2__axioms,dt_c17_5_1_2_1_1_2__axioms,de_c17_5_1_2_1_1_2__axioms,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e40_5_1_2_1_1_2__axioms,e42_5_1_2_1_1_2__axioms,d1_tarski]),
    [interesting(0.05),file(axioms,e44_5_1_2_1_1_2__axioms),[file(axioms,e44_5_1_2_1_1_2__axioms)]]).

fof(e45_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c17_5_1_2_1_1_2__axioms,c10_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c16_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,antisymmetry_r2_hidden,dt_k4_tarski,dt_c10_5_1_2_1_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,dt_c17_5_1_2_1_1_2__axioms,dt_c1_5__axioms,de_c10_5_1_2_1_1_2__axioms,de_c17_5_1_2_1_1_2__axioms,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e44_5_1_2_1_1_2__axioms,e37_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e45_5_1_2_1_1_2__axioms),[file(axioms,e45_5_1_2_1_1_2__axioms)]]).

fof(e2_5_1_2_1_1_2_5_1_1__axioms,plain,
    ( r1_arytm_2(c4_5_1_2_1_1_2__axioms,c11_5_1_2_1_1_2__axioms)
    & r1_arytm_2(c11_5_1_2_1_1_2__axioms,c17_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_xboole_0,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_xboole_0,fc1_zfmisc_1,spc0_boole,d5_tarski,spc0_boole,spc0_numerals,dt_k1_zfmisc_1,dt_c16_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms,dt_c3_5_1_2_1_1_2__axioms,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,connectedness_r1_arytm_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c10_5_1_2_1_1_2__axioms,dt_c11_5_1_2_1_1_2__axioms,dt_c17_5_1_2_1_1_2__axioms,dt_c4_5_1_2_1_1_2__axioms,dt_c6_5_1_2_1_1_2__axioms,de_c10_5_1_2_1_1_2__axioms,de_c17_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,de_c6_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,e17_5_1_2_1_1_2__axioms,e30_5_1_2_1_1_2__axioms,e45_5_1_2_1_1_2__axioms]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_2_5_1_1__axioms),[file(axioms,e2_5_1_2_1_1_2_5_1_1__axioms)]]).

fof(e36_5_1_2_1_1_2__axioms,plain,(
    r2_hidden(c12_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c11_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c12_5_1_2_1_1_2__axioms,de_c12_5_1_2_1_1_2__axioms,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t6_boole,t7_boole,d5_tarski,spc0_boole,spc0_numerals,l24_axioms,t106_zfmisc_1]),
    [interesting(0.05),file(axioms,e36_5_1_2_1_1_2__axioms),[file(axioms,e36_5_1_2_1_1_2__axioms)]]).

fof(e3_5_1_2_1_1_2_5_1_1__axioms,plain,(
    r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c16_5_1_2_1_1_2__axioms,dt_c3_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c11_5_1_2_1_1_2__axioms,dt_c12_5_1_2_1_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,dt_c17_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c4_5_1_2_1_1_2__axioms,de_c12_5_1_2_1_1_2__axioms,de_c17_5_1_2_1_1_2__axioms,de_c4_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t3_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e2_5_1_2_1_1_2_5_1_1__axioms,e18_5_1_2_1_1_2__axioms,e36_5_1_2_1_1_2__axioms,e37_5_1_2_1_1_2__axioms,e44_5_1_2_1_1_2__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_2_5_1_1__axioms),[file(axioms,e3_5_1_2_1_1_2_5_1_1__axioms)]]).

fof(e4_5_1_2_1_1_2_5_1_1__axioms,plain,
    ( ~ r2_hidden(c12_5_1_2_1_1_2__axioms,k2_arytm_2)
    & ~ r2_hidden(c14_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc4_arytm_3,rc1_arytm_3,rc2_arytm_3,rc3_arytm_3,commutativity_k2_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k4_tarski,dt_k5_numbers,dt_k6_arytm_3,dt_m1_subset_1,dt_m2_subset_1,dt_c11_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc1_xboole_0,fc1_zfmisc_1,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,d5_tarski,symmetry_r1_subset_1,irreflexivity_r1_subset_1,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k12_arytm_3,redefinition_r1_subset_1,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c12_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,de_c12_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,spc0_boole,spc0_numerals,e36_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_1__axioms,t5_arytm_0,t3_xboole_0]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_2_5_1_1__axioms),[file(axioms,e4_5_1_2_1_1_2_5_1_1__axioms)]]).

fof(e5_5_1_2_1_1_2_5_1_1__axioms,plain,(
    r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c11_5_1_2_1_1_2__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c12_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,de_c12_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e4_5_1_2_1_1_2_5_1_1__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e5_5_1_2_1_1_2_5_1_1__axioms),[file(axioms,e5_5_1_2_1_1_2_5_1_1__axioms)]]).

fof(i3_5_1_2_1_1_2_5_1_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_2_1_1_2_5_1_1__axioms)]),
    [interesting(0.02),trivial,file(axioms,i3_5_1_2_1_1_2_5_1_1__axioms)]).

fof(i2_5_1_2_1_1_2_5_1_1__axioms,plain,(
    r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_1__axioms])],[e5_5_1_2_1_1_2_5_1_1__axioms,i3_5_1_2_1_1_2_5_1_1__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_2_5_1_1__axioms),[file(axioms,i2_5_1_2_1_1_2_5_1_1__axioms)]]).

fof(i1_5_1_2_1_1_2_5_1_1__axioms,plain,
    ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
    & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_1__axioms])],[e3_5_1_2_1_1_2_5_1_1__axioms,i2_5_1_2_1_1_2_5_1_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_5_1_1__axioms),[file(axioms,i1_5_1_2_1_1_2_5_1_1__axioms)]]).

fof(i1_5_1_2_1_1_2_5_1__axioms,plain,
    ( r2_hidden(c14_5_1_2_1_1_2__axioms,k2_arytm_2)
   => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
      & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c13_5_1_2_1_1_2__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2_5_1_1__axioms])],[e1_5_1_2_1_1_2_5_1_1__axioms,i1_5_1_2_1_1_2_5_1_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_5_1__axioms),[file(axioms,i1_5_1_2_1_1_2_5_1__axioms)]]).

fof(e1_5_1_2_1_1_2_5_1_2__axioms,assumption,(
    r2_hidden(c14_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_2_5_1_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_2_5_1_2__axioms)]).

fof(dh_c1_5_1_2_1_1_2_5_1_2__axioms,definition,
    ( ? [A,B] : 
        ( r2_hidden(A,k1_tarski(0))
        & r2_hidden(B,k2_arytm_2)
        & c14_5_1_2_1_1_2__axioms = k4_tarski(A,B) )
   => ? [C] : 
        ( r2_hidden(c1_5_1_2_1_1_2_5_1_2__axioms,k1_tarski(0))
        & r2_hidden(C,k2_arytm_2)
        & c14_5_1_2_1_1_2__axioms = k4_tarski(c1_5_1_2_1_1_2_5_1_2__axioms,C) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_2_5_1_2__axioms),file(axioms,c1_5_1_2_1_1_2_5_1_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_2_5_1_2__axioms)]).

fof(dh_c2_5_1_2_1_1_2_5_1_2__axioms,definition,
    ( ? [A] : 
        ( r2_hidden(c1_5_1_2_1_1_2_5_1_2__axioms,k1_tarski(0))
        & r2_hidden(A,k2_arytm_2)
        & c14_5_1_2_1_1_2__axioms = k4_tarski(c1_5_1_2_1_1_2_5_1_2__axioms,A) )
   => ( r2_hidden(c1_5_1_2_1_1_2_5_1_2__axioms,k1_tarski(0))
      & r2_hidden(c2_5_1_2_1_1_2_5_1_2__axioms,k2_arytm_2)
      & c14_5_1_2_1_1_2__axioms = k4_tarski(c1_5_1_2_1_1_2_5_1_2__axioms,c2_5_1_2_1_1_2_5_1_2__axioms) ) ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_2_5_1_2__axioms),file(axioms,c2_5_1_2_1_1_2_5_1_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c2_5_1_2_1_1_2_5_1_2__axioms)]).

fof(e2_5_1_2_1_1_2_5_1_2__axioms,plain,(
    ? [A,B] : 
      ( r2_hidden(A,k1_tarski(0))
      & r2_hidden(B,k2_arytm_2)
      & c14_5_1_2_1_1_2__axioms = k4_tarski(A,B) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_c14_5_1_2_1_1_2__axioms,fc1_zfmisc_1,fc2_arytm_2,t1_subset,t3_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e1_5_1_2_1_1_2_5_1_2__axioms,t103_zfmisc_1]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e2_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(dt_c2_5_1_2_1_1_2_5_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[dh_c1_5_1_2_1_1_2_5_1_2__axioms,dh_c2_5_1_2_1_1_2_5_1_2__axioms,e2_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,c2_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,c2_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(de_c3_5_1_2_1_1_2_5_1_2__axioms,definition,(
    c3_5_1_2_1_1_2_5_1_2__axioms = c2_5_1_2_1_1_2_5_1_2__axioms ),
    introduced(definition,[new_symbol(c3_5_1_2_1_1_2_5_1_2__axioms),file(axioms,c3_5_1_2_1_1_2_5_1_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c3_5_1_2_1_1_2_5_1_2__axioms)]).

fof(e4_5_1_2_1_1_2_5_1_2__axioms,plain,(
    r2_hidden(c2_5_1_2_1_1_2_5_1_2__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[dh_c1_5_1_2_1_1_2_5_1_2__axioms,dh_c2_5_1_2_1_1_2_5_1_2__axioms,e2_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e4_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(e6_5_1_2_1_1_2_5_1_2__axioms,plain,(
    m1_subset_1(c2_5_1_2_1_1_2_5_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5_1_2_1_1_2_5_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,e4_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,e6_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e6_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(dt_c3_5_1_2_1_1_2_5_1_2__axioms,plain,(
    m1_subset_1(c3_5_1_2_1_1_2_5_1_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5_1_2_1_1_2_5_1_2__axioms,fc2_arytm_2,de_c3_5_1_2_1_1_2_5_1_2__axioms,e6_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,c3_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,c3_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(dt_c1_5_1_2_1_1_2_5_1_2__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[dh_c1_5_1_2_1_1_2_5_1_2__axioms,e2_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,c1_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,c1_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(e3_5_1_2_1_1_2_5_1_2__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_2_5_1_2__axioms,k1_tarski(0)) ),
    inference(consider,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[dh_c1_5_1_2_1_1_2_5_1_2__axioms,dh_c2_5_1_2_1_1_2_5_1_2__axioms,e2_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e3_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(e5_5_1_2_1_1_2_5_1_2__axioms,plain,(
    c14_5_1_2_1_1_2__axioms = k4_tarski(c1_5_1_2_1_1_2_5_1_2__axioms,c2_5_1_2_1_1_2_5_1_2__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[dh_c1_5_1_2_1_1_2_5_1_2__axioms,dh_c2_5_1_2_1_1_2_5_1_2__axioms,e2_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,e5_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e5_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(e7_5_1_2_1_1_2_5_1_2__axioms,plain,(
    c14_5_1_2_1_1_2__axioms = k4_tarski(0,c3_5_1_2_1_1_2_5_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_tarski,dt_k4_tarski,dt_c14_5_1_2_1_1_2__axioms,dt_c1_5_1_2_1_1_2_5_1_2__axioms,dt_c2_5_1_2_1_1_2_5_1_2__axioms,dt_c3_5_1_2_1_1_2_5_1_2__axioms,de_c3_5_1_2_1_1_2_5_1_2__axioms,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e3_5_1_2_1_1_2_5_1_2__axioms,e5_5_1_2_1_1_2_5_1_2__axioms,d1_tarski]),
    [interesting(0.02),file(axioms,e7_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e7_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(e8_5_1_2_1_1_2_5_1_2__axioms,plain,(
    r2_hidden(c3_5_1_2_1_1_2_5_1_2__axioms,c6_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms,e38_5_1_2_1_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c2_5_1_2_1_1_2_5_1_2__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,antisymmetry_r2_hidden,dt_k4_tarski,dt_c14_5_1_2_1_1_2__axioms,dt_c2_5__axioms,dt_c3_5_1_2_1_1_2_5_1_2__axioms,dt_c6_5_1_2_1_1_2__axioms,de_c3_5_1_2_1_1_2_5_1_2__axioms,de_c6_5_1_2_1_1_2__axioms,fc1_zfmisc_1,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e7_5_1_2_1_1_2_5_1_2__axioms,e38_5_1_2_1_1_2__axioms]),
    [interesting(0.02),file(axioms,e8_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e8_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(e9_5_1_2_1_1_2_5_1_2__axioms,plain,
    ( r1_arytm_2(c3_5_1_2_1_1_2_5_1_2__axioms,c11_5_1_2_1_1_2__axioms)
    & r1_arytm_2(c11_5_1_2_1_1_2__axioms,c17_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms,e38_5_1_2_1_1_2__axioms,e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_tarski,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,rc1_xcmplx_0,rc2_xcmplx_0,t1_numerals,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_xboole_0,dt_k4_tarski,cc1_xcmplx_0,fc1_numbers,fc1_xboole_0,fc1_zfmisc_1,spc0_boole,d5_tarski,spc0_boole,spc0_numerals,dt_k1_zfmisc_1,dt_c16_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_2_5_1_2__axioms,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,t2_tarski,fraenkel_a_1_1_axioms,connectedness_r1_arytm_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c10_5_1_2_1_1_2__axioms,dt_c11_5_1_2_1_1_2__axioms,dt_c17_5_1_2_1_1_2__axioms,dt_c3_5_1_2_1_1_2_5_1_2__axioms,dt_c6_5_1_2_1_1_2__axioms,de_c10_5_1_2_1_1_2__axioms,de_c17_5_1_2_1_1_2__axioms,de_c3_5_1_2_1_1_2_5_1_2__axioms,de_c6_5_1_2_1_1_2__axioms,fc2_arytm_2,t1_subset,t7_boole,e8_5_1_2_1_1_2_5_1_2__axioms,e30_5_1_2_1_1_2__axioms,e45_5_1_2_1_1_2__axioms]),
    [interesting(0.02),file(axioms,e9_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e9_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(e10_5_1_2_1_1_2_5_1_2__axioms,plain,
    ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
    & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e38_5_1_2_1_1_2__axioms,e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c16_5_1_2_1_1_2__axioms,dt_c2_5_1_2_1_1_2_5_1_2__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c11_5_1_2_1_1_2__axioms,dt_c12_5_1_2_1_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,dt_c17_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c3_5_1_2_1_1_2_5_1_2__axioms,de_c12_5_1_2_1_1_2__axioms,de_c17_5_1_2_1_1_2__axioms,de_c3_5_1_2_1_1_2_5_1_2__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t3_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e9_5_1_2_1_1_2_5_1_2__axioms,e18_5_1_2_1_1_2__axioms,e36_5_1_2_1_1_2__axioms,e37_5_1_2_1_1_2__axioms,e44_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms,e7_5_1_2_1_1_2_5_1_2__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e10_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,e10_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(i2_5_1_2_1_1_2_5_1_2__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i2_5_1_2_1_1_2_5_1_2__axioms)]),
    [interesting(0.02),trivial,file(axioms,i2_5_1_2_1_1_2_5_1_2__axioms)]).

fof(i1_5_1_2_1_1_2_5_1_2__axioms,plain,
    ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
    & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(conclusion,[status(thm),assumptions([e38_5_1_2_1_1_2__axioms,e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,e1_5_1_2_1_1_2_5_1_2__axioms])],[e10_5_1_2_1_1_2_5_1_2__axioms,i2_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_2_5_1_2__axioms),[file(axioms,i1_5_1_2_1_1_2_5_1_2__axioms)]]).

fof(i2_5_1_2_1_1_2_5_1__axioms,plain,
    ( r2_hidden(c14_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
   => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
      & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([e38_5_1_2_1_1_2__axioms,e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2_5_1_2__axioms])],[e1_5_1_2_1_1_2_5_1_2__axioms,i1_5_1_2_1_1_2_5_1_2__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_2_5_1__axioms),[file(axioms,i2_5_1_2_1_1_2_5_1__axioms)]]).

fof(e1_5_1_2_1_1_2_5_1__axioms,plain,
    ( r2_hidden(c14_5_1_2_1_1_2__axioms,k2_arytm_2)
    | r2_hidden(c14_5_1_2_1_1_2__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c14_5_1_2_1_1_2__axioms,dt_c2_5__axioms,e38_5_1_2_1_1_2__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c14_5_1_2_1_1_2__axioms,dt_c2_5__axioms,fc2_arytm_2,t1_subset,t3_subset,t7_boole,spc0_boole,spc0_numerals,e9_5_1_2__axioms,e38_5_1_2_1_1_2__axioms,d2_xboole_0]),
    [interesting(0.02),file(axioms,e1_5_1_2_1_1_2_5_1__axioms),[file(axioms,e1_5_1_2_1_1_2_5_1__axioms)]]).

fof(e46_5_1_2_1_1_2__axioms,plain,
    ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
    & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(percases,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,dt_c2_5__axioms,e38_5_1_2_1_1_2__axioms])],[i1_5_1_2_1_1_2_5_1__axioms,i2_5_1_2_1_1_2_5_1__axioms,e1_5_1_2_1_1_2_5_1__axioms]),
    [interesting(0.05),file(axioms,e46_5_1_2_1_1_2__axioms),[file(axioms,e46_5_1_2_1_1_2__axioms)]]).

fof(e47_5_1_2_1_1_2__axioms,plain,
    ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
    & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,dt_c2_5__axioms,e38_5_1_2_1_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_tarski,dt_k2_arytm_2,dt_k2_tarski,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,dt_k4_tarski,dt_c11_5_1_2_1_1_2__axioms,cc2_xreal_0,fc1_zfmisc_1,rqLessOrEqual__r1_xreal_0__r0_r0,d5_tarski,spc0_boole,spc0_numerals,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c12_5_1_2_1_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,de_c12_5_1_2_1_1_2__axioms,e46_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,e47_5_1_2_1_1_2__axioms),[file(axioms,e47_5_1_2_1_1_2__axioms)]]).

fof(i6_5_1_2_1_1_2__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i6_5_1_2_1_1_2__axioms)]),
    [interesting(0.05),trivial,file(axioms,i6_5_1_2_1_1_2__axioms)]).

fof(i5_5_1_2_1_1_2__axioms,plain,
    ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
    & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ),
    inference(conclusion,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,e37_5_1_2_1_1_2__axioms,dt_c14_5_1_2_1_1_2__axioms,dt_c2_5__axioms,e38_5_1_2_1_1_2__axioms])],[e47_5_1_2_1_1_2__axioms,i6_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,i5_5_1_2_1_1_2__axioms),[file(axioms,i5_5_1_2_1_1_2__axioms)]]).

fof(i4_5_1_2_1_1_2__axioms,plain,
    ( ( r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms)
      & r2_hidden(c14_5_1_2_1_1_2__axioms,c2_5__axioms) )
   => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
      & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c14_5_1_2_1_1_2__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e37_5_1_2_1_1_2__axioms,e38_5_1_2_1_1_2__axioms])],[e37_5_1_2_1_1_2__axioms,e38_5_1_2_1_1_2__axioms,i5_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,i4_5_1_2_1_1_2__axioms),[file(axioms,i4_5_1_2_1_1_2__axioms)]]).

fof(i4_5_1_2_1_1_2_tmp__axioms,plain,
    ( v1_xreal_0(c14_5_1_2_1_1_2__axioms)
   => ( ( r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms)
        & r2_hidden(c14_5_1_2_1_1_2__axioms,c2_5__axioms) )
     => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
        & r1_xreal_0(c12_5_1_2_1_1_2__axioms,c14_5_1_2_1_1_2__axioms) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[dt_c14_5_1_2_1_1_2__axioms])],[dt_c14_5_1_2_1_1_2__axioms,i4_5_1_2_1_1_2__axioms]),
    [interesting(0.05),i3_5_1_2_1_1_2__axioms]).

fof(i3_5_1_2_1_1_2__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ( r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms)
          & r2_hidden(A,c2_5__axioms) )
       => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
          & r1_xreal_0(c12_5_1_2_1_1_2__axioms,A) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_5_1_2__axioms,dt_c13_5_1_2_1_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms])],[i4_5_1_2_1_1_2_tmp__axioms,dh_c14_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,i3_5_1_2_1_1_2__axioms),[file(axioms,i3_5_1_2_1_1_2__axioms)]]).

fof(i3_5_1_2_1_1_2_tmp__axioms,plain,
    ( v1_xreal_0(c13_5_1_2_1_1_2__axioms)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ( r2_hidden(c13_5_1_2_1_1_2__axioms,c1_5__axioms)
            & r2_hidden(A,c2_5__axioms) )
         => ( r1_xreal_0(c13_5_1_2_1_1_2__axioms,c12_5_1_2_1_1_2__axioms)
            & r1_xreal_0(c12_5_1_2_1_1_2__axioms,A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[dt_c13_5_1_2_1_1_2__axioms])],[dt_c13_5_1_2_1_1_2__axioms,i3_5_1_2_1_1_2__axioms]),
    [interesting(0.05),i2_5_1_2_1_1_2__axioms]).

fof(i2_5_1_2_1_1_2__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r2_hidden(A,c1_5__axioms)
              & r2_hidden(B,c2_5__axioms) )
           => ( r1_xreal_0(A,c12_5_1_2_1_1_2__axioms)
              & r1_xreal_0(c12_5_1_2_1_1_2__axioms,B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_5_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms])],[i3_5_1_2_1_1_2_tmp__axioms,dh_c13_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,i2_5_1_2_1_1_2__axioms),[file(axioms,i2_5_1_2_1_1_2__axioms)]]).

fof(i1_5_1_2_1_1_2__axioms,plain,(
    ? [A] : 
      ( v1_xreal_0(A)
      & ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms) )
               => ( r1_xreal_0(B,A)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(take,[status(thm),assumptions([e1_5_1_2__axioms,e1_5__axioms,e1_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,dt_k1_numbers,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xcmplx_0,rc1_xreal_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c12_5_1_2_1_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms,cc2_xreal_0,i2_5_1_2_1_1_2__axioms]),
    [interesting(0.05),file(axioms,i1_5_1_2_1_1_2__axioms),[file(axioms,i1_5_1_2_1_1_2__axioms)]]).

fof(i2_5_1_2_1_1__axioms,plain,(
    ~ ( ~ r1_xboole_0(c2_5__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
      & ! [A] : 
          ( v1_xreal_0(A)
         => ? [B] : 
              ( v1_xreal_0(B)
              & ? [C] : 
                  ( v1_xreal_0(C)
                  & r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms)
                  & ~ ( r1_xreal_0(B,A)
                      & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5_1_2__axioms,e1_5__axioms,dt_c1_5__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_2__axioms])],[e1_5_1_2_1_1_2__axioms,i1_5_1_2_1_1_2__axioms]),
    [interesting(0.2),file(axioms,i2_5_1_2_1_1__axioms),[file(axioms,i2_5_1_2_1_1__axioms)]]).

fof(e1_5_1_2_1_1_3__axioms,assumption,(
    ~ r1_xboole_0(c1_5__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,e1_5_1_2_1_1_3__axioms)]).

fof(dh_c6_5_1_2_1_1_3__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k2_arytm_2)
        & ! [B] : 
            ( m1_subset_1(B,k2_arytm_2)
           => ! [C] : 
                ( m1_subset_1(C,k2_arytm_2)
               => ( ( r2_hidden(B,c4_5_1_2_1_1_3__axioms)
                    & r2_hidden(C,c5_5_1_2_1_1_3__axioms) )
                 => ( r1_arytm_2(B,A)
                    & r1_arytm_2(A,C) ) ) ) ) )
   => ( m1_subset_1(c6_5_1_2_1_1_3__axioms,k2_arytm_2)
      & ! [D] : 
          ( m1_subset_1(D,k2_arytm_2)
         => ! [E] : 
              ( m1_subset_1(E,k2_arytm_2)
             => ( ( r2_hidden(D,c4_5_1_2_1_1_3__axioms)
                  & r2_hidden(E,c5_5_1_2_1_1_3__axioms) )
               => ( r1_arytm_2(D,c6_5_1_2_1_1_3__axioms)
                  & r1_arytm_2(c6_5_1_2_1_1_3__axioms,E) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c6_5_1_2_1_1_3__axioms),file(axioms,c6_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c6_5_1_2_1_1_3__axioms)]).

fof(dh_c1_5_1_2_1_1_3__axioms,definition,
    ( ? [A] : 
        ( r2_hidden(A,c1_5__axioms)
        & r2_hidden(A,k2_arytm_2) )
   => ( r2_hidden(c1_5_1_2_1_1_3__axioms,c1_5__axioms)
      & r2_hidden(c1_5_1_2_1_1_3__axioms,k2_arytm_2) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_3__axioms),file(axioms,c1_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c1_5_1_2_1_1_3__axioms)]).

fof(e2_5_1_2_1_1_3__axioms,plain,(
    ? [A] : 
      ( r2_hidden(A,c1_5__axioms)
      & r2_hidden(A,k2_arytm_2) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t8_boole,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,symmetry_r1_xboole_0,antisymmetry_r2_hidden,dt_k2_arytm_2,dt_c1_5__axioms,fc2_arytm_2,t1_subset,t7_boole,e1_5_1_2_1_1_3__axioms,t3_xboole_0]),
    [interesting(0.05),file(axioms,e2_5_1_2_1_1_3__axioms),[file(axioms,e2_5_1_2_1_1_3__axioms)]]).

fof(dt_c1_5_1_2_1_1_3__axioms,plain,(
    $true ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dh_c1_5_1_2_1_1_3__axioms,e2_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c1_5_1_2_1_1_3__axioms),[file(axioms,c1_5_1_2_1_1_3__axioms)]]).

fof(t2_boole,theorem,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    [interesting(0.9),axiom,file(boole,t2_boole)]).

fof(commutativity_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(idempotence_k3_xboole_0,theorem,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]).

fof(de_c2_5_1_2_1_1_3__axioms,definition,(
    c2_5_1_2_1_1_3__axioms = c1_5_1_2_1_1_3__axioms ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_3__axioms),file(axioms,c2_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c2_5_1_2_1_1_3__axioms)]).

fof(e4_5_1_2_1_1_3__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dh_c1_5_1_2_1_1_3__axioms,e2_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,e4_5_1_2_1_1_3__axioms),[file(axioms,e4_5_1_2_1_1_3__axioms)]]).

fof(e5_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c1_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c1_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole,e4_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,e5_5_1_2_1_1_3__axioms),[file(axioms,e5_5_1_2_1_1_3__axioms)]]).

fof(dt_c2_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c2_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c1_5_1_2_1_1_3__axioms,fc2_arytm_2,de_c2_5_1_2_1_1_3__axioms,e5_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c2_5_1_2_1_1_3__axioms),[file(axioms,c2_5_1_2_1_1_3__axioms)]]).

fof(dh_c2_5_1_2__axioms,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & r2_hidden(A,c2_5__axioms) )
   => ( m1_subset_1(c2_5_1_2__axioms,k1_numbers)
      & r2_hidden(c2_5_1_2__axioms,c2_5__axioms) ) ),
    introduced(definition,[new_symbol(c2_5_1_2__axioms),file(axioms,c2_5_1_2__axioms)]),
    [interesting(0.5),axiom,file(axioms,c2_5_1_2__axioms)]).

fof(e5_5_1_2__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & r2_hidden(A,c2_5__axioms) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c2_5__axioms,e2_5_1_2__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,reflexivity_r1_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k5_numbers,dt_m2_subset_1,rc1_xboole_0,rc1_xcmplx_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t5_subset,t8_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c2_5__axioms,cc1_xcmplx_0,fc1_numbers,fc1_xboole_0,t1_subset,t3_subset,t4_subset,t6_boole,t7_boole,spc0_boole,spc0_numerals,e2_5_1_2__axioms,t10_subset_1]),
    [interesting(0.5),file(axioms,e5_5_1_2__axioms),[file(axioms,e5_5_1_2__axioms)]]).

fof(dt_c2_5_1_2__axioms,plain,(
    m1_subset_1(c2_5_1_2__axioms,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e2_5_1_2__axioms])],[dh_c2_5_1_2__axioms,e5_5_1_2__axioms]),
    [interesting(0.5),file(axioms,c2_5_1_2__axioms),[file(axioms,c2_5_1_2__axioms)]]).

fof(de_c3_5_1_2_1_1_3__axioms,definition,(
    c3_5_1_2_1_1_3__axioms = c2_5_1_2_1_1_3__axioms ),
    introduced(definition,[new_symbol(c3_5_1_2_1_1_3__axioms),file(axioms,c3_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c3_5_1_2_1_1_3__axioms)]).

fof(e6_5_1_2_1_1_3__axioms,plain,(
    r2_hidden(c2_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dt_k1_xboole_0,fc1_xboole_0,existence_m1_subset_1,dt_m1_subset_1,dt_c1_5_1_2_1_1_3__axioms,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k2_arytm_2,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole]),
    [interesting(0.05),file(axioms,e6_5_1_2_1_1_3__axioms),[file(axioms,e6_5_1_2_1_1_3__axioms)]]).

fof(t1_arytm_0,theorem,(
    r1_tarski(k2_arytm_2,k1_numbers) ),
    file(arytm_0,t1_arytm_0),
    [interesting(0.9),axiom,file(arytm_0,t1_arytm_0)]).

fof(e7_5_1_2_1_1_3__axioms,plain,(
    v1_xreal_0(c2_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c1_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc7_xreal_0,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_numbers,dt_k2_arytm_2,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,cc2_xreal_0,fc1_numbers,fc2_arytm_2,t1_subset,t3_subset,t7_boole,e6_5_1_2_1_1_3__axioms,t1_arytm_0,d1_xreal_0]),
    [interesting(0.05),file(axioms,e7_5_1_2_1_1_3__axioms),[file(axioms,e7_5_1_2_1_1_3__axioms)]]).

fof(dt_c3_5_1_2_1_1_3__axioms,plain,(
    v1_xreal_0(c3_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c1_5_1_2_1_1_3__axioms,fc2_arytm_2,rc1_xcmplx_0,rc1_xreal_0,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,cc2_xreal_0,de_c3_5_1_2_1_1_3__axioms,e7_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c3_5_1_2_1_1_3__axioms),[file(axioms,c3_5_1_2_1_1_3__axioms)]]).

fof(de_c4_5_1_2_1_1_3__axioms,definition,(
    c4_5_1_2_1_1_3__axioms = k3_xboole_0(c1_5__axioms,k2_arytm_2) ),
    introduced(definition,[new_symbol(c4_5_1_2_1_1_3__axioms),file(axioms,c4_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c4_5_1_2_1_1_3__axioms)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.9),axiom,file(xboole_1,t17_xboole_1)]).

fof(e8_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(k3_xboole_0(c1_5__axioms,k2_arytm_2),k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t2_boole,t4_subset,t5_subset,dt_k1_numbers,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k3_xboole_0,dt_m1_subset_1,dt_c1_5__axioms,fc2_arytm_2,t3_subset,t17_xboole_1]),
    [interesting(0.05),file(axioms,e8_5_1_2_1_1_3__axioms),[file(axioms,e8_5_1_2_1_1_3__axioms)]]).

fof(dt_c4_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c4_5_1_2_1_1_3__axioms,k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t2_boole,t4_subset,t5_subset,reflexivity_r1_tarski,dt_k1_numbers,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k3_xboole_0,dt_m1_subset_1,dt_c1_5__axioms,fc2_arytm_2,t3_subset,de_c4_5_1_2_1_1_3__axioms,e8_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c4_5_1_2_1_1_3__axioms),[file(axioms,c4_5_1_2_1_1_3__axioms)]]).

fof(de_c5_5_1_2_1_1_3__axioms,definition,(
    c5_5_1_2_1_1_3__axioms = c2_5__axioms ),
    introduced(definition,[new_symbol(c5_5_1_2_1_1_3__axioms),file(axioms,c5_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c5_5_1_2_1_1_3__axioms)]).

fof(dt_c1_5_1_2_1_1_3_1__axioms,assumption,(
    $true ),
    introduced(assumption,[file(axioms,c1_5_1_2_1_1_3_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_3_1__axioms)]).

fof(dh_c1_5_1_2_1_1_3_1__axioms,definition,
    ( ~ ( r2_hidden(c1_5_1_2_1_1_3_1__axioms,c2_5__axioms)
        & ~ r2_hidden(c1_5_1_2_1_1_3_1__axioms,k2_arytm_2) )
   => ! [A] : 
        ~ ( r2_hidden(A,c2_5__axioms)
          & ~ r2_hidden(A,k2_arytm_2) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_3_1__axioms),file(axioms,c1_5_1_2_1_1_3_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_3_1__axioms)]).

fof(e1_5_1_2_1_1_3_1__axioms,assumption,(
    r2_hidden(c1_5_1_2_1_1_3_1__axioms,c2_5__axioms) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_3_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_3_1__axioms)]).

fof(de_c2_5_1_2_1_1_3_1__axioms,definition,(
    c2_5_1_2_1_1_3_1__axioms = c1_5_1_2_1_1_3_1__axioms ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_3_1__axioms),file(axioms,c2_5_1_2_1_1_3_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,c2_5_1_2_1_1_3_1__axioms)]).

fof(e2_5_1_2_1_1_3_1__axioms,plain,(
    v1_xreal_0(c1_5_1_2_1_1_3_1__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_3_1__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,cc7_xreal_0,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,dt_k1_numbers,dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,cc2_xreal_0,fc1_numbers,t1_subset,t7_boole,e1_5_1_2_1_1_3_1__axioms,d1_xreal_0]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_3_1__axioms),[file(axioms,e2_5_1_2_1_1_3_1__axioms)]]).

fof(dt_c2_5_1_2_1_1_3_1__axioms,plain,(
    v1_xreal_0(c2_5_1_2_1_1_3_1__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_3_1__axioms])],[rc1_xcmplx_0,rc1_xreal_0,dt_c1_5_1_2_1_1_3_1__axioms,cc2_xreal_0,de_c2_5_1_2_1_1_3_1__axioms,e2_5_1_2_1_1_3_1__axioms]),
    [interesting(0.02),file(axioms,c2_5_1_2_1_1_3_1__axioms),[file(axioms,c2_5_1_2_1_1_3_1__axioms)]]).

fof(e1_5_1_2_1_1_3_1_1__axioms,assumption,(
    r2_hidden(c2_5_1_2_1_1_3_1__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_3_1_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_3_1_1__axioms)]).

fof(e3_5_1_2_1_1_3_1_1__axioms,plain,
    ( ~ r2_hidden(c2_5_1_2_1_1_3_1__axioms,k2_arytm_2)
    & ~ r2_hidden(c3_5_1_2_1_1_3__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_3_1__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_1_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc4_arytm_3,rc1_arytm_3,rc2_arytm_3,rc3_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_c1_5_1_2_1_1_3__axioms,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k5_numbers,dt_k6_arytm_3,dt_m1_subset_1,dt_m2_subset_1,dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,symmetry_r1_subset_1,irreflexivity_r1_subset_1,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k12_arytm_3,redefinition_r1_subset_1,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c2_5_1_2_1_1_3_1__axioms,dt_c3_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3_1__axioms,de_c3_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole,spc0_boole,spc0_numerals,e1_5_1_2_1_1_3_1_1__axioms,t5_arytm_0,t3_xboole_0]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_3_1_1__axioms),[file(axioms,e3_5_1_2_1_1_3_1_1__axioms)]]).

fof(e3_5_1_2_1_1_3__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_3__axioms,c1_5__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dh_c1_5_1_2_1_1_3__axioms,e2_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,e3_5_1_2_1_1_3__axioms),[file(axioms,e3_5_1_2_1_1_3__axioms)]]).

fof(e2_5_1_2_1_1_3_1_1__axioms,plain,(
    r1_xreal_0(c3_5_1_2_1_1_3__axioms,c2_5_1_2_1_1_3_1__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_1__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_arytm_2,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc2_arytm_2,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_m1_subset_1,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c1_5__axioms,dt_c1_5_1_2_1_1_3__axioms,dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_3_1__axioms,dt_c3_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3_1__axioms,de_c3_5_1_2_1_1_3__axioms,cc2_xreal_0,t1_subset,t7_boole,e1_5__axioms,e3_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_1__axioms]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_3_1_1__axioms),[file(axioms,e2_5_1_2_1_1_3_1_1__axioms)]]).

fof(e4_5_1_2_1_1_3_1_1__axioms,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2_1_1_3_1_1__axioms,dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_1__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_c1_5_1_2_1_1_3__axioms,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c2_5_1_2_1_1_3_1__axioms,dt_c3_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3_1__axioms,de_c3_5_1_2_1_1_3__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e3_5_1_2_1_1_3_1_1__axioms,e2_5_1_2_1_1_3_1_1__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_3_1_1__axioms),[file(axioms,e4_5_1_2_1_1_3_1_1__axioms)]]).

fof(i2_5_1_2_1_1_3_1_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i2_5_1_2_1_1_3_1_1__axioms)]),
    [interesting(0.02),trivial,file(axioms,i2_5_1_2_1_1_3_1_1__axioms)]).

fof(i1_5_1_2_1_1_3_1_1__axioms,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([e1_5_1_2_1_1_3_1_1__axioms,dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_1__axioms])],[e4_5_1_2_1_1_3_1_1__axioms,i2_5_1_2_1_1_3_1_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_3_1_1__axioms),[file(axioms,i1_5_1_2_1_1_3_1_1__axioms)]]).

fof(e3_5_1_2_1_1_3_1__axioms,plain,(
    ~ r2_hidden(c2_5_1_2_1_1_3_1__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_1__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_3_1_1__axioms])],[e1_5_1_2_1_1_3_1_1__axioms,i1_5_1_2_1_1_3_1_1__axioms]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_3_1__axioms),[file(axioms,e3_5_1_2_1_1_3_1__axioms)]]).

fof(e4_5_1_2_1_1_3_1__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_3_1__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_3_1__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c1_5_1_2_1_1_3_1__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_3_1__axioms,de_c2_5_1_2_1_1_3_1__axioms,fc2_arytm_2,t1_subset,t3_subset,t7_boole,spc0_boole,spc0_numerals,e3_5_1_2_1_1_3_1__axioms,e9_5_1_2__axioms,e1_5_1_2_1_1_3_1__axioms,d2_xboole_0]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_3_1__axioms),[file(axioms,e4_5_1_2_1_1_3_1__axioms)]]).

fof(i3_5_1_2_1_1_3_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_2_1_1_3_1__axioms)]),
    [interesting(0.02),trivial,file(axioms,i3_5_1_2_1_1_3_1__axioms)]).

fof(i2_5_1_2_1_1_3_1__axioms,plain,(
    r2_hidden(c1_5_1_2_1_1_3_1__axioms,k2_arytm_2) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,e1_5_1_2_1_1_3_1__axioms])],[e4_5_1_2_1_1_3_1__axioms,i3_5_1_2_1_1_3_1__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_3_1__axioms),[file(axioms,i2_5_1_2_1_1_3_1__axioms)]]).

fof(i1_5_1_2_1_1_3_1__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_3_1__axioms,c2_5__axioms)
      & ~ r2_hidden(c1_5_1_2_1_1_3_1__axioms,k2_arytm_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_1__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_3_1__axioms])],[e1_5_1_2_1_1_3_1__axioms,i2_5_1_2_1_1_3_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_3_1__axioms),[file(axioms,i1_5_1_2_1_1_3_1__axioms)]]).

fof(i1_5_1_2_1_1_3_1_tmp__axioms,plain,(
    ~ ( r2_hidden(c1_5_1_2_1_1_3_1__axioms,c2_5__axioms)
      & ~ r2_hidden(c1_5_1_2_1_1_3_1__axioms,k2_arytm_2) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[dt_c1_5_1_2_1_1_3_1__axioms])],[dt_c1_5_1_2_1_1_3_1__axioms,i1_5_1_2_1_1_3_1__axioms]),
    [interesting(0.05),e10_5_1_2_1_1_3__axioms]).

fof(e10_5_1_2_1_1_3__axioms,plain,(
    r1_tarski(c2_5__axioms,k2_arytm_2) ),
    inference(let,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms])],[i1_5_1_2_1_1_3_1_tmp__axioms,rc1_xcmplx_0,rc2_xcmplx_0,dt_k1_numbers,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k2_arytm_2,dt_c2_5__axioms,fc2_arytm_2,d3_tarski,dh_c1_5_1_2_1_1_3_1__axioms]),
    [interesting(0.05),file(axioms,e10_5_1_2_1_1_3__axioms),[file(axioms,e10_5_1_2_1_1_3__axioms)]]).

fof(e11_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c2_5__axioms,k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t4_subset,t5_subset,t8_boole,dt_k1_numbers,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5__axioms,fc2_arytm_2,t3_subset,e10_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,e11_5_1_2_1_1_3__axioms),[file(axioms,e11_5_1_2_1_1_3__axioms)]]).

fof(dt_c5_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c5_5_1_2_1_1_3__axioms,k1_zfmisc_1(k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,dt_k1_numbers,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5__axioms,fc2_arytm_2,t3_subset,de_c5_5_1_2_1_1_3__axioms,e11_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c5_5_1_2_1_1_3__axioms),[file(axioms,c5_5_1_2_1_1_3__axioms)]]).

fof(dh_c1_5_1_2_1_1_3_2__axioms,definition,
    ( ( m1_subset_1(c1_5_1_2_1_1_3_2__axioms,k2_arytm_2)
     => ! [A] : 
          ( m1_subset_1(A,k2_arytm_2)
         => ( ( r2_hidden(c1_5_1_2_1_1_3_2__axioms,c4_5_1_2_1_1_3__axioms)
              & r2_hidden(A,c5_5_1_2_1_1_3__axioms) )
           => r1_arytm_2(c1_5_1_2_1_1_3_2__axioms,A) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k2_arytm_2)
       => ! [C] : 
            ( m1_subset_1(C,k2_arytm_2)
           => ( ( r2_hidden(B,c4_5_1_2_1_1_3__axioms)
                & r2_hidden(C,c5_5_1_2_1_1_3__axioms) )
             => r1_arytm_2(B,C) ) ) ) ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_3_2__axioms),file(axioms,c1_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_3_2__axioms)]).

fof(dh_c2_5_1_2_1_1_3_2__axioms,definition,
    ( ( m1_subset_1(c2_5_1_2_1_1_3_2__axioms,k2_arytm_2)
     => ( ( r2_hidden(c1_5_1_2_1_1_3_2__axioms,c4_5_1_2_1_1_3__axioms)
          & r2_hidden(c2_5_1_2_1_1_3_2__axioms,c5_5_1_2_1_1_3__axioms) )
       => r1_arytm_2(c1_5_1_2_1_1_3_2__axioms,c2_5_1_2_1_1_3_2__axioms) ) )
   => ! [A] : 
        ( m1_subset_1(A,k2_arytm_2)
       => ( ( r2_hidden(c1_5_1_2_1_1_3_2__axioms,c4_5_1_2_1_1_3__axioms)
            & r2_hidden(A,c5_5_1_2_1_1_3__axioms) )
         => r1_arytm_2(c1_5_1_2_1_1_3_2__axioms,A) ) ) ),
    introduced(definition,[new_symbol(c2_5_1_2_1_1_3_2__axioms),file(axioms,c2_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c2_5_1_2_1_1_3_2__axioms)]).

fof(e1_5_1_2_1_1_3_2__axioms,assumption,
    ( r2_hidden(c1_5_1_2_1_1_3_2__axioms,c4_5_1_2_1_1_3__axioms)
    & r2_hidden(c2_5_1_2_1_1_3_2__axioms,c5_5_1_2_1_1_3__axioms) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_3_2__axioms)]).

fof(dt_c1_5_1_2_1_1_3_2__axioms,assumption,(
    m1_subset_1(c1_5_1_2_1_1_3_2__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,c1_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_3_2__axioms)]).

fof(dt_c2_5_1_2_1_1_3_2__axioms,assumption,(
    m1_subset_1(c2_5_1_2_1_1_3_2__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,c2_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c2_5_1_2_1_1_3_2__axioms)]).

fof(de_c3_5_1_2_1_1_3_2__axioms,definition,(
    c3_5_1_2_1_1_3_2__axioms = c1_5_1_2_1_1_3_2__axioms ),
    introduced(definition,[new_symbol(c3_5_1_2_1_1_3_2__axioms),file(axioms,c3_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c3_5_1_2_1_1_3_2__axioms)]).

fof(e2_5_1_2_1_1_3_2__axioms,plain,
    ( r2_hidden(c1_5_1_2_1_1_3_2__axioms,k2_arytm_2)
    & r2_hidden(c2_5_1_2_1_1_3_2__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k2_arytm_2,dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,fc2_arytm_2,t1_subset,t7_boole]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_3_2__axioms),[file(axioms,e2_5_1_2_1_1_3_2__axioms)]]).

fof(e3_5_1_2_1_1_3_2__axioms,plain,
    ( v1_xreal_0(c1_5_1_2_1_1_3_2__axioms)
    & v1_xreal_0(c2_5_1_2_1_1_3_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms])],[dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,cc7_xreal_0,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_numbers,dt_k2_arytm_2,dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,cc2_xreal_0,fc1_numbers,fc2_arytm_2,t1_subset,t3_subset,t7_boole,e2_5_1_2_1_1_3_2__axioms,t1_arytm_0,d1_xreal_0]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_3_2__axioms),[file(axioms,e3_5_1_2_1_1_3_2__axioms)]]).

fof(dt_c3_5_1_2_1_1_3_2__axioms,plain,(
    v1_xreal_0(c3_5_1_2_1_1_3_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,fc2_arytm_2,rc1_xcmplx_0,rc1_xreal_0,dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,cc2_xreal_0,de_c3_5_1_2_1_1_3_2__axioms,e3_5_1_2_1_1_3_2__axioms]),
    [interesting(0.02),file(axioms,c3_5_1_2_1_1_3_2__axioms),[file(axioms,c3_5_1_2_1_1_3_2__axioms)]]).

fof(de_c4_5_1_2_1_1_3_2__axioms,definition,(
    c4_5_1_2_1_1_3_2__axioms = c2_5_1_2_1_1_3_2__axioms ),
    introduced(definition,[new_symbol(c4_5_1_2_1_1_3_2__axioms),file(axioms,c4_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,c4_5_1_2_1_1_3_2__axioms)]).

fof(dt_c4_5_1_2_1_1_3_2__axioms,plain,(
    v1_xreal_0(c4_5_1_2_1_1_3_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,fc2_arytm_2,rc1_xcmplx_0,rc1_xreal_0,dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,cc2_xreal_0,de_c4_5_1_2_1_1_3_2__axioms,e3_5_1_2_1_1_3_2__axioms]),
    [interesting(0.02),file(axioms,c4_5_1_2_1_1_3_2__axioms),[file(axioms,c4_5_1_2_1_1_3_2__axioms)]]).

fof(e4_5_1_2_1_1_3_2__axioms,plain,(
    r1_tarski(c4_5_1_2_1_1_3__axioms,c1_5__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t2_boole,t4_subset,t5_subset,rc1_xboole_0,rc1_xcmplx_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,cc1_xcmplx_0,fc1_numbers,fc2_arytm_2,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,dt_k3_xboole_0,dt_c1_5__axioms,dt_c4_5_1_2_1_1_3__axioms,de_c4_5_1_2_1_1_3__axioms,t3_subset,t17_xboole_1]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_3_2__axioms),[file(axioms,e4_5_1_2_1_1_3_2__axioms)]]).

fof(e5_5_1_2_1_1_3_2__axioms,plain,(
    r1_xreal_0(c3_5_1_2_1_1_3_2__axioms,c4_5_1_2_1_1_3_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c1_5__axioms,e1_5__axioms,e1_5_1_2_1_1_3_2__axioms])],[dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k3_xboole_0,dt_m1_subset_1,cc1_xcmplx_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c1_5__axioms,dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_3_2__axioms,dt_c3_5_1_2_1_1_3_2__axioms,dt_c4_5_1_2_1_1_3__axioms,dt_c4_5_1_2_1_1_3_2__axioms,dt_c5_5_1_2_1_1_3__axioms,de_c3_5_1_2_1_1_3_2__axioms,de_c4_5_1_2_1_1_3__axioms,de_c4_5_1_2_1_1_3_2__axioms,de_c5_5_1_2_1_1_3__axioms,cc2_xreal_0,t1_subset,t3_subset,t7_boole,e4_5_1_2_1_1_3_2__axioms,e1_5__axioms,e1_5_1_2_1_1_3_2__axioms]),
    [interesting(0.02),file(axioms,e5_5_1_2_1_1_3_2__axioms),[file(axioms,e5_5_1_2_1_1_3_2__axioms)]]).

fof(e6_5_1_2_1_1_3_2__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & ? [B] : 
          ( m1_subset_1(B,k2_arytm_2)
          & c3_5_1_2_1_1_3_2__axioms = A
          & c4_5_1_2_1_1_3_2__axioms = B
          & r1_arytm_2(A,B) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c1_5__axioms,e1_5__axioms,e1_5_1_2_1_1_3_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c3_5_1_2_1_1_3_2__axioms,dt_c4_5_1_2_1_1_3_2__axioms,de_c3_5_1_2_1_1_3_2__axioms,de_c4_5_1_2_1_1_3_2__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e5_5_1_2_1_1_3_2__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e6_5_1_2_1_1_3_2__axioms),[file(axioms,e6_5_1_2_1_1_3_2__axioms)]]).

fof(e7_5_1_2_1_1_3_2__axioms,plain,(
    r1_arytm_2(c1_5_1_2_1_1_3_2__axioms,c2_5_1_2_1_1_3_2__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c1_5__axioms,e1_5__axioms,e1_5_1_2_1_1_3_2__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc2_xreal_0,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,connectedness_r1_arytm_2,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,dt_c3_5_1_2_1_1_3_2__axioms,dt_c4_5_1_2_1_1_3_2__axioms,de_c3_5_1_2_1_1_3_2__axioms,de_c4_5_1_2_1_1_3_2__axioms,fc2_arytm_2,e6_5_1_2_1_1_3_2__axioms]),
    [interesting(0.02),file(axioms,e7_5_1_2_1_1_3_2__axioms),[file(axioms,e7_5_1_2_1_1_3_2__axioms)]]).

fof(i3_5_1_2_1_1_3_2__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_2_1_1_3_2__axioms)]),
    [interesting(0.02),trivial,file(axioms,i3_5_1_2_1_1_3_2__axioms)]).

fof(i2_5_1_2_1_1_3_2__axioms,plain,(
    r1_arytm_2(c1_5_1_2_1_1_3_2__axioms,c2_5_1_2_1_1_3_2__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c1_5__axioms,e1_5__axioms,e1_5_1_2_1_1_3_2__axioms])],[e7_5_1_2_1_1_3_2__axioms,i3_5_1_2_1_1_3_2__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_3_2__axioms),[file(axioms,i2_5_1_2_1_1_3_2__axioms)]]).

fof(i1_5_1_2_1_1_3_2__axioms,plain,
    ( ( r2_hidden(c1_5_1_2_1_1_3_2__axioms,c4_5_1_2_1_1_3__axioms)
      & r2_hidden(c2_5_1_2_1_1_3_2__axioms,c5_5_1_2_1_1_3__axioms) )
   => r1_arytm_2(c1_5_1_2_1_1_3_2__axioms,c2_5_1_2_1_1_3_2__axioms) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c1_5__axioms,e1_5__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_3_2__axioms])],[e1_5_1_2_1_1_3_2__axioms,i2_5_1_2_1_1_3_2__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_3_2__axioms),[file(axioms,i1_5_1_2_1_1_3_2__axioms)]]).

fof(i1_5_1_2_1_1_3_2_tmp__axioms,plain,
    ( ( m1_subset_1(c1_5_1_2_1_1_3_2__axioms,k2_arytm_2)
      & m1_subset_1(c2_5_1_2_1_1_3_2__axioms,k2_arytm_2) )
   => ( ( r2_hidden(c1_5_1_2_1_1_3_2__axioms,c4_5_1_2_1_1_3__axioms)
        & r2_hidden(c2_5_1_2_1_1_3_2__axioms,c5_5_1_2_1_1_3__axioms) )
     => r1_arytm_2(c1_5_1_2_1_1_3_2__axioms,c2_5_1_2_1_1_3_2__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c1_5__axioms,e1_5__axioms]),discharge_asm(discharge,[dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms])],[dt_c1_5_1_2_1_1_3_2__axioms,dt_c2_5_1_2_1_1_3_2__axioms,i1_5_1_2_1_1_3_2__axioms]),
    [interesting(0.05),e12_5_1_2_1_1_3__axioms]).

fof(e12_5_1_2_1_1_3__axioms,plain,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( r2_hidden(A,c4_5_1_2_1_1_3__axioms)
              & r2_hidden(B,c5_5_1_2_1_1_3__axioms) )
           => r1_arytm_2(A,B) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c1_5__axioms,e1_5__axioms])],[i1_5_1_2_1_1_3_2_tmp__axioms,dh_c1_5_1_2_1_1_3_2__axioms,dh_c2_5_1_2_1_1_3_2__axioms]),
    [interesting(0.05),file(axioms,e12_5_1_2_1_1_3__axioms),[file(axioms,e12_5_1_2_1_1_3__axioms)]]).

fof(e6_5_1_2__axioms,plain,(
    r2_hidden(c2_5_1_2__axioms,c2_5__axioms) ),
    inference(consider,[status(thm),assumptions([dt_c2_5__axioms,e2_5_1_2__axioms])],[dh_c2_5_1_2__axioms,e5_5_1_2__axioms]),
    [interesting(0.5),file(axioms,e6_5_1_2__axioms),[file(axioms,e6_5_1_2__axioms)]]).

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(0.9),axiom,file(xboole_0,d3_xboole_0)]).

fof(e9_5_1_2_1_1_3__axioms,plain,(
    r2_hidden(c3_5_1_2_1_1_3__axioms,c4_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_boole,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k3_xboole_0,dt_c1_5__axioms,dt_c1_5_1_2_1_1_3__axioms,dt_c3_5_1_2_1_1_3__axioms,dt_c4_5_1_2_1_1_3__axioms,de_c3_5_1_2_1_1_3__axioms,de_c4_5_1_2_1_1_3__axioms,t1_subset,t7_boole,e3_5_1_2_1_1_3__axioms,d3_xboole_0]),
    [interesting(0.05),file(axioms,e9_5_1_2_1_1_3__axioms),[file(axioms,e9_5_1_2_1_1_3__axioms)]]).

fof(e13_5_1_2_1_1_3__axioms,plain,(
    ? [A] : 
      ( m1_subset_1(A,k2_arytm_2)
      & ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ! [C] : 
              ( m1_subset_1(C,k2_arytm_2)
             => ( ( r2_hidden(B,c4_5_1_2_1_1_3__axioms)
                  & r2_hidden(C,c5_5_1_2_1_1_3__axioms) )
               => ( r1_arytm_2(B,A)
                  & r1_arytm_2(A,C) ) ) ) ) ) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dt_k1_xboole_0,dt_c1_5_1_2_1_1_3__axioms,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,dt_k1_numbers,dt_k3_xboole_0,dt_c1_5__axioms,dt_c2_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t5_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5__axioms,dt_c2_5_1_2__axioms,dt_c3_5_1_2_1_1_3__axioms,dt_c4_5_1_2_1_1_3__axioms,dt_c5_5_1_2_1_1_3__axioms,de_c3_5_1_2_1_1_3__axioms,de_c4_5_1_2_1_1_3__axioms,de_c5_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t3_subset,t4_subset,t7_boole,e12_5_1_2_1_1_3__axioms,e6_5_1_2__axioms,e9_5_1_2_1_1_3__axioms,t9_arytm_2]),
    [interesting(0.05),file(axioms,e13_5_1_2_1_1_3__axioms),[file(axioms,e13_5_1_2_1_1_3__axioms)]]).

fof(dt_c6_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c6_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dh_c6_5_1_2_1_1_3__axioms,e13_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c6_5_1_2_1_1_3__axioms),[file(axioms,c6_5_1_2_1_1_3__axioms)]]).

fof(de_c7_5_1_2_1_1_3__axioms,definition,(
    c7_5_1_2_1_1_3__axioms = c6_5_1_2_1_1_3__axioms ),
    introduced(definition,[new_symbol(c7_5_1_2_1_1_3__axioms),file(axioms,c7_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c7_5_1_2_1_1_3__axioms)]).

fof(e15_5_1_2_1_1_3__axioms,plain,(
    r2_hidden(c6_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,existence_m1_subset_1,dt_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,dt_k2_arytm_2,dt_c6_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole]),
    [interesting(0.05),file(axioms,e15_5_1_2_1_1_3__axioms),[file(axioms,e15_5_1_2_1_1_3__axioms)]]).

fof(e16_5_1_2_1_1_3__axioms,plain,(
    v1_xreal_0(c6_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,cc7_xreal_0,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_numbers,dt_k2_arytm_2,dt_c6_5_1_2_1_1_3__axioms,cc2_xreal_0,fc1_numbers,fc2_arytm_2,t1_subset,t3_subset,t7_boole,e15_5_1_2_1_1_3__axioms,t1_arytm_0,d1_xreal_0]),
    [interesting(0.05),file(axioms,e16_5_1_2_1_1_3__axioms),[file(axioms,e16_5_1_2_1_1_3__axioms)]]).

fof(dt_c7_5_1_2_1_1_3__axioms,plain,(
    v1_xreal_0(c7_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,fc2_arytm_2,rc1_xcmplx_0,rc1_xreal_0,dt_c6_5_1_2_1_1_3__axioms,cc2_xreal_0,de_c7_5_1_2_1_1_3__axioms,e16_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c7_5_1_2_1_1_3__axioms),[file(axioms,c7_5_1_2_1_1_3__axioms)]]).

fof(dh_c8_5_1_2_1_1_3__axioms,definition,
    ( ( v1_xreal_0(c8_5_1_2_1_1_3__axioms)
     => ! [A] : 
          ( v1_xreal_0(A)
         => ( ( r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms)
              & r2_hidden(A,c2_5__axioms) )
           => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
              & r1_xreal_0(c7_5_1_2_1_1_3__axioms,A) ) ) ) )
   => ! [B] : 
        ( v1_xreal_0(B)
       => ! [C] : 
            ( v1_xreal_0(C)
           => ( ( r2_hidden(B,c1_5__axioms)
                & r2_hidden(C,c2_5__axioms) )
             => ( r1_xreal_0(B,c7_5_1_2_1_1_3__axioms)
                & r1_xreal_0(c7_5_1_2_1_1_3__axioms,C) ) ) ) ) ),
    introduced(definition,[new_symbol(c8_5_1_2_1_1_3__axioms),file(axioms,c8_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c8_5_1_2_1_1_3__axioms)]).

fof(dh_c9_5_1_2_1_1_3__axioms,definition,
    ( ( v1_xreal_0(c9_5_1_2_1_1_3__axioms)
     => ( ( r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms)
          & r2_hidden(c9_5_1_2_1_1_3__axioms,c2_5__axioms) )
       => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
          & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ) ) )
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ( r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms)
            & r2_hidden(A,c2_5__axioms) )
         => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
            & r1_xreal_0(c7_5_1_2_1_1_3__axioms,A) ) ) ) ),
    introduced(definition,[new_symbol(c9_5_1_2_1_1_3__axioms),file(axioms,c9_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c9_5_1_2_1_1_3__axioms)]).

fof(e17_5_1_2_1_1_3__axioms,assumption,(
    r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms) ),
    introduced(assumption,[file(axioms,e17_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,e17_5_1_2_1_1_3__axioms)]).

fof(e18_5_1_2_1_1_3__axioms,assumption,(
    r2_hidden(c9_5_1_2_1_1_3__axioms,c2_5__axioms) ),
    introduced(assumption,[file(axioms,e18_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,e18_5_1_2_1_1_3__axioms)]).

fof(dt_c8_5_1_2_1_1_3__axioms,assumption,(
    v1_xreal_0(c8_5_1_2_1_1_3__axioms) ),
    introduced(assumption,[file(axioms,c8_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c8_5_1_2_1_1_3__axioms)]).

fof(dt_c9_5_1_2_1_1_3__axioms,assumption,(
    v1_xreal_0(c9_5_1_2_1_1_3__axioms) ),
    introduced(assumption,[file(axioms,c9_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c9_5_1_2_1_1_3__axioms)]).

fof(e1_5_1_2_1_1_3_3_1_1__axioms,assumption,(
    r2_hidden(c8_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_3_3_1_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_3_3_1_1__axioms)]).

fof(de_c10_5_1_2_1_1_3__axioms,definition,(
    c10_5_1_2_1_1_3__axioms = c9_5_1_2_1_1_3__axioms ),
    introduced(definition,[new_symbol(c10_5_1_2_1_1_3__axioms),file(axioms,c10_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),axiom,file(axioms,c10_5_1_2_1_1_3__axioms)]).

fof(e19_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c9_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,e18_5_1_2_1_1_3__axioms])],[dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,dt_k1_numbers,dt_k1_zfmisc_1,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c2_5__axioms,dt_c9_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t3_subset,t7_boole,e10_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,e19_5_1_2_1_1_3__axioms),[file(axioms,e19_5_1_2_1_1_3__axioms)]]).

fof(dt_c10_5_1_2_1_1_3__axioms,plain,(
    m1_subset_1(c10_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,e18_5_1_2_1_1_3__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc2_xreal_0,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c9_5_1_2_1_1_3__axioms,fc2_arytm_2,de_c10_5_1_2_1_1_3__axioms,e19_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,c10_5_1_2_1_1_3__axioms),[file(axioms,c10_5_1_2_1_1_3__axioms)]]).

fof(de_c1_5_1_2_1_1_3_3_1_1__axioms,definition,(
    c1_5_1_2_1_1_3_3_1_1__axioms = c8_5_1_2_1_1_3__axioms ),
    introduced(definition,[new_symbol(c1_5_1_2_1_1_3_3_1_1__axioms),file(axioms,c1_5_1_2_1_1_3_3_1_1__axioms)]),
    [interesting(0.02),axiom,file(axioms,c1_5_1_2_1_1_3_3_1_1__axioms)]).

fof(e2_5_1_2_1_1_3_3_1_1__axioms,plain,(
    m1_subset_1(c8_5_1_2_1_1_3__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c8_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_3_1_1__axioms])],[dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t8_boole,cc2_xreal_0,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c8_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole,e1_5_1_2_1_1_3_3_1_1__axioms]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_3_3_1_1__axioms),[file(axioms,e2_5_1_2_1_1_3_3_1_1__axioms)]]).

fof(dt_c1_5_1_2_1_1_3_3_1_1__axioms,plain,(
    m1_subset_1(c1_5_1_2_1_1_3_3_1_1__axioms,k2_arytm_2) ),
    inference(mizar_by,[status(thm),assumptions([dt_c8_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_3_1_1__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc2_xreal_0,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c8_5_1_2_1_1_3__axioms,fc2_arytm_2,de_c1_5_1_2_1_1_3_3_1_1__axioms,e2_5_1_2_1_1_3_3_1_1__axioms]),
    [interesting(0.02),file(axioms,c1_5_1_2_1_1_3_3_1_1__axioms),[file(axioms,c1_5_1_2_1_1_3_3_1_1__axioms)]]).

fof(e3_5_1_2_1_1_3_3_1_1__axioms,plain,
    ( r2_hidden(c1_5_1_2_1_1_3_3_1_1__axioms,c4_5_1_2_1_1_3__axioms)
    & r2_hidden(c10_5_1_2_1_1_3__axioms,c5_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2_1_1_3_3_1_1__axioms,e1_5__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_boole,existence_m1_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_m1_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,fc2_arytm_2,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,dt_k3_xboole_0,dt_c10_5_1_2_1_1_3__axioms,dt_c1_5__axioms,dt_c1_5_1_2_1_1_3_3_1_1__axioms,dt_c2_5__axioms,dt_c4_5_1_2_1_1_3__axioms,dt_c5_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,de_c10_5_1_2_1_1_3__axioms,de_c1_5_1_2_1_1_3_3_1_1__axioms,de_c4_5_1_2_1_1_3__axioms,de_c5_5_1_2_1_1_3__axioms,t1_subset,t7_boole,e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,d3_xboole_0]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_3_3_1_1__axioms),[file(axioms,e3_5_1_2_1_1_3_3_1_1__axioms)]]).

fof(e14_5_1_2_1_1_3__axioms,plain,(
    ! [A] : 
      ( m1_subset_1(A,k2_arytm_2)
     => ! [B] : 
          ( m1_subset_1(B,k2_arytm_2)
         => ( ( r2_hidden(A,c4_5_1_2_1_1_3__axioms)
              & r2_hidden(B,c5_5_1_2_1_1_3__axioms) )
           => ( r1_arytm_2(A,c6_5_1_2_1_1_3__axioms)
              & r1_arytm_2(c6_5_1_2_1_1_3__axioms,B) ) ) ) ) ),
    inference(consider,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[dh_c6_5_1_2_1_1_3__axioms,e13_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,e14_5_1_2_1_1_3__axioms),[file(axioms,e14_5_1_2_1_1_3__axioms)]]).

fof(e4_5_1_2_1_1_3_3_1_1__axioms,plain,
    ( r1_arytm_2(c1_5_1_2_1_1_3_3_1_1__axioms,c6_5_1_2_1_1_3__axioms)
    & r1_arytm_2(c6_5_1_2_1_1_3__axioms,c10_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2_1_1_3_3_1_1__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_xboole_0,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,fc1_xboole_0,t2_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_c1_5__axioms,dt_c2_5__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c10_5_1_2_1_1_3__axioms,dt_c1_5_1_2_1_1_3_3_1_1__axioms,dt_c4_5_1_2_1_1_3__axioms,dt_c5_5_1_2_1_1_3__axioms,dt_c6_5_1_2_1_1_3__axioms,de_c10_5_1_2_1_1_3__axioms,de_c1_5_1_2_1_1_3_3_1_1__axioms,de_c4_5_1_2_1_1_3__axioms,de_c5_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole,e3_5_1_2_1_1_3_3_1_1__axioms,e14_5_1_2_1_1_3__axioms]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_3_3_1_1__axioms),[file(axioms,e4_5_1_2_1_1_3_3_1_1__axioms)]]).

fof(e5_5_1_2_1_1_3_3_1_1__axioms,plain,
    ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
    & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5_1_2_1_1_3_3_1_1__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c10_5_1_2_1_1_3__axioms,dt_c1_5_1_2_1_1_3_3_1_1__axioms,dt_c6_5_1_2_1_1_3__axioms,dt_c7_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,de_c10_5_1_2_1_1_3__axioms,de_c1_5_1_2_1_1_3_3_1_1__axioms,de_c7_5_1_2_1_1_3__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e4_5_1_2_1_1_3_3_1_1__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e5_5_1_2_1_1_3_3_1_1__axioms),[file(axioms,e5_5_1_2_1_1_3_3_1_1__axioms)]]).

fof(i2_5_1_2_1_1_3_3_1_1__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i2_5_1_2_1_1_3_3_1_1__axioms)]),
    [interesting(0.02),trivial,file(axioms,i2_5_1_2_1_1_3_3_1_1__axioms)]).

fof(i1_5_1_2_1_1_3_3_1_1__axioms,plain,
    ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
    & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(conclusion,[status(thm),assumptions([e1_5_1_2_1_1_3_3_1_1__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms])],[e5_5_1_2_1_1_3_3_1_1__axioms,i2_5_1_2_1_1_3_3_1_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_3_3_1_1__axioms),[file(axioms,i1_5_1_2_1_1_3_3_1_1__axioms)]]).

fof(i1_5_1_2_1_1_3_3_1__axioms,plain,
    ( r2_hidden(c8_5_1_2_1_1_3__axioms,k2_arytm_2)
   => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
      & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_3_3_1_1__axioms])],[e1_5_1_2_1_1_3_3_1_1__axioms,i1_5_1_2_1_1_3_3_1_1__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_3_3_1__axioms),[file(axioms,i1_5_1_2_1_1_3_3_1__axioms)]]).

fof(e1_5_1_2_1_1_3_3_1_2__axioms,assumption,(
    r2_hidden(c8_5_1_2_1_1_3__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    introduced(assumption,[file(axioms,e1_5_1_2_1_1_3_3_1_2__axioms)]),
    [interesting(0.02),axiom,file(axioms,e1_5_1_2_1_1_3_3_1_2__axioms)]).

fof(e2_5_1_2_1_1_3_3_1_2__axioms,plain,
    ( ~ r2_hidden(c8_5_1_2_1_1_3__axioms,k2_arytm_2)
    & ~ r2_hidden(c7_5_1_2_1_1_3__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_3_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,cc4_arytm_3,rc1_arytm_3,rc2_arytm_3,rc3_arytm_3,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k5_numbers,dt_k6_arytm_3,dt_m1_subset_1,dt_m2_subset_1,dt_c6_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc1_xboole_0,fc8_arytm_3,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t6_boole,t8_boole,symmetry_r1_subset_1,irreflexivity_r1_subset_1,symmetry_r1_xboole_0,antisymmetry_r2_hidden,redefinition_k12_arytm_3,redefinition_r1_subset_1,dt_k12_arytm_3,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c7_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,de_c7_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole,spc0_boole,spc0_numerals,e1_5_1_2_1_1_3_3_1_2__axioms,t5_arytm_0,t3_xboole_0]),
    [interesting(0.02),file(axioms,e2_5_1_2_1_1_3_3_1_2__axioms),[file(axioms,e2_5_1_2_1_1_3_3_1_2__axioms)]]).

fof(e3_5_1_2_1_1_3_3_1_2__axioms,plain,(
    r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_3_1_2__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c6_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c7_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,de_c7_5_1_2_1_1_3__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e2_5_1_2_1_1_3_3_1_2__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e3_5_1_2_1_1_3_3_1_2__axioms),[file(axioms,e3_5_1_2_1_1_3_3_1_2__axioms)]]).

fof(e4_5_1_2_1_1_3_3_1_2__axioms,plain,
    ( r1_arytm_2(c2_5_1_2_1_1_3__axioms,c6_5_1_2_1_1_3__axioms)
    & r1_arytm_2(c6_5_1_2_1_1_3__axioms,c10_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t2_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_xboole_0,dt_c1_5__axioms,dt_c1_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc2_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,dt_c10_5_1_2_1_1_3__axioms,dt_c2_5__axioms,dt_c2_5_1_2_1_1_3__axioms,dt_c3_5_1_2_1_1_3__axioms,dt_c4_5_1_2_1_1_3__axioms,dt_c5_5_1_2_1_1_3__axioms,dt_c6_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,de_c10_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,de_c3_5_1_2_1_1_3__axioms,de_c4_5_1_2_1_1_3__axioms,de_c5_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t7_boole,e9_5_1_2_1_1_3__axioms,e14_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms]),
    [interesting(0.02),file(axioms,e4_5_1_2_1_1_3_3_1_2__axioms),[file(axioms,e4_5_1_2_1_1_3_3_1_2__axioms)]]).

fof(e5_5_1_2_1_1_3_3_1_2__axioms,plain,(
    r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms])],[reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k2_tarski,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1_2_1_1_3__axioms,cc1_xcmplx_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,rc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xboole_0,rc2_xcmplx_0,t1_numerals,t2_subset,t6_boole,t8_boole,connectedness_r1_arytm_2,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_k4_tarski,dt_m1_subset_1,dt_c10_5_1_2_1_1_3__axioms,dt_c2_5_1_2_1_1_3__axioms,dt_c6_5_1_2_1_1_3__axioms,dt_c7_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,de_c10_5_1_2_1_1_3__axioms,de_c2_5_1_2_1_1_3__axioms,de_c7_5_1_2_1_1_3__axioms,cc2_xreal_0,fc1_zfmisc_1,fc2_arytm_2,rqLessOrEqual__r1_xreal_0__r0_r0,t1_subset,t7_boole,d5_tarski,spc0_boole,spc0_numerals,e4_5_1_2_1_1_3_3_1_2__axioms,d2_xreal_0]),
    [interesting(0.02),file(axioms,e5_5_1_2_1_1_3_3_1_2__axioms),[file(axioms,e5_5_1_2_1_1_3_3_1_2__axioms)]]).

fof(i3_5_1_2_1_1_3_3_1_2__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i3_5_1_2_1_1_3_3_1_2__axioms)]),
    [interesting(0.02),trivial,file(axioms,i3_5_1_2_1_1_3_3_1_2__axioms)]).

fof(i2_5_1_2_1_1_3_3_1_2__axioms,plain,(
    r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms])],[e5_5_1_2_1_1_3_3_1_2__axioms,i3_5_1_2_1_1_3_3_1_2__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_3_3_1_2__axioms),[file(axioms,i2_5_1_2_1_1_3_3_1_2__axioms)]]).

fof(i1_5_1_2_1_1_3_3_1_2__axioms,plain,
    ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
    & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c8_5_1_2_1_1_3__axioms,e1_5_1_2_1_1_3_3_1_2__axioms,dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms])],[e3_5_1_2_1_1_3_3_1_2__axioms,i2_5_1_2_1_1_3_3_1_2__axioms]),
    [interesting(0.02),file(axioms,i1_5_1_2_1_1_3_3_1_2__axioms),[file(axioms,i1_5_1_2_1_1_3_3_1_2__axioms)]]).

fof(i2_5_1_2_1_1_3_3_1__axioms,plain,
    ( r2_hidden(c8_5_1_2_1_1_3__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
   => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
      & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_3_3_1_2__axioms])],[e1_5_1_2_1_1_3_3_1_2__axioms,i1_5_1_2_1_1_3_3_1_2__axioms]),
    [interesting(0.02),file(axioms,i2_5_1_2_1_1_3_3_1__axioms),[file(axioms,i2_5_1_2_1_1_3_3_1__axioms)]]).

fof(e1_5_1_2_1_1_3_3_1__axioms,plain,
    ( r2_hidden(c8_5_1_2_1_1_3__axioms,k2_arytm_2)
    | r2_hidden(c8_5_1_2_1_1_3__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c8_5_1_2_1_1_3__axioms,dt_c1_5__axioms,e17_5_1_2_1_1_3__axioms])],[cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc1_xreal_0,rc2_xcmplx_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc1_numbers,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_tarski,dt_k2_arytm_2,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_c1_5__axioms,dt_c8_5_1_2_1_1_3__axioms,fc2_arytm_2,t1_subset,t3_subset,t7_boole,spc0_boole,spc0_numerals,e8_5_1_2__axioms,e17_5_1_2_1_1_3__axioms,d2_xboole_0]),
    [interesting(0.02),file(axioms,e1_5_1_2_1_1_3_3_1__axioms),[file(axioms,e1_5_1_2_1_1_3_3_1__axioms)]]).

fof(e20_5_1_2_1_1_3__axioms,plain,
    ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
    & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(percases,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c1_5__axioms,e17_5_1_2_1_1_3__axioms])],[i1_5_1_2_1_1_3_3_1__axioms,i2_5_1_2_1_1_3_3_1__axioms,e1_5_1_2_1_1_3_3_1__axioms]),
    [interesting(0.05),file(axioms,e20_5_1_2_1_1_3__axioms),[file(axioms,e20_5_1_2_1_1_3__axioms)]]).

fof(e21_5_1_2_1_1_3__axioms,plain,
    ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
    & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(mizar_by,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c1_5__axioms,e17_5_1_2_1_1_3__axioms])],[antisymmetry_r2_hidden,dt_k1_xboole_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_subset,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_subset_1,dt_k2_arytm_2,dt_m1_subset_1,fc2_arytm_2,rc1_xcmplx_0,rc1_xreal_0,dt_c6_5_1_2_1_1_3__axioms,cc2_xreal_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c7_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c9_5_1_2_1_1_3__axioms,de_c7_5_1_2_1_1_3__axioms,e20_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,e21_5_1_2_1_1_3__axioms),[file(axioms,e21_5_1_2_1_1_3__axioms)]]).

fof(i6_5_1_2_1_1_3__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i6_5_1_2_1_1_3__axioms)]),
    [interesting(0.05),trivial,file(axioms,i6_5_1_2_1_1_3__axioms)]).

fof(i5_5_1_2_1_1_3__axioms,plain,
    ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
    & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ),
    inference(conclusion,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c1_5__axioms,e17_5_1_2_1_1_3__axioms])],[e21_5_1_2_1_1_3__axioms,i6_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,i5_5_1_2_1_1_3__axioms),[file(axioms,i5_5_1_2_1_1_3__axioms)]]).

fof(i4_5_1_2_1_1_3__axioms,plain,
    ( ( r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms)
      & r2_hidden(c9_5_1_2_1_1_3__axioms,c2_5__axioms) )
   => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
      & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c9_5_1_2_1_1_3__axioms,e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c1_5__axioms]),discharge_asm(discharge,[e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms])],[e17_5_1_2_1_1_3__axioms,e18_5_1_2_1_1_3__axioms,i5_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,i4_5_1_2_1_1_3__axioms),[file(axioms,i4_5_1_2_1_1_3__axioms)]]).

fof(i4_5_1_2_1_1_3_tmp__axioms,plain,
    ( v1_xreal_0(c9_5_1_2_1_1_3__axioms)
   => ( ( r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms)
        & r2_hidden(c9_5_1_2_1_1_3__axioms,c2_5__axioms) )
     => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
        & r1_xreal_0(c7_5_1_2_1_1_3__axioms,c9_5_1_2_1_1_3__axioms) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c1_5__axioms]),discharge_asm(discharge,[dt_c9_5_1_2_1_1_3__axioms])],[dt_c9_5_1_2_1_1_3__axioms,i4_5_1_2_1_1_3__axioms]),
    [interesting(0.05),i3_5_1_2_1_1_3__axioms]).

fof(i3_5_1_2_1_1_3__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( ( r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms)
          & r2_hidden(A,c2_5__axioms) )
       => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
          & r1_xreal_0(c7_5_1_2_1_1_3__axioms,A) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c8_5_1_2_1_1_3__axioms,dt_c1_5__axioms])],[i4_5_1_2_1_1_3_tmp__axioms,dh_c9_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,i3_5_1_2_1_1_3__axioms),[file(axioms,i3_5_1_2_1_1_3__axioms)]]).

fof(i3_5_1_2_1_1_3_tmp__axioms,plain,
    ( v1_xreal_0(c8_5_1_2_1_1_3__axioms)
   => ! [A] : 
        ( v1_xreal_0(A)
       => ( ( r2_hidden(c8_5_1_2_1_1_3__axioms,c1_5__axioms)
            & r2_hidden(A,c2_5__axioms) )
         => ( r1_xreal_0(c8_5_1_2_1_1_3__axioms,c7_5_1_2_1_1_3__axioms)
            & r1_xreal_0(c7_5_1_2_1_1_3__axioms,A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c1_5__axioms]),discharge_asm(discharge,[dt_c8_5_1_2_1_1_3__axioms])],[dt_c8_5_1_2_1_1_3__axioms,i3_5_1_2_1_1_3__axioms]),
    [interesting(0.05),i2_5_1_2_1_1_3__axioms]).

fof(i2_5_1_2_1_1_3__axioms,plain,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r2_hidden(A,c1_5__axioms)
              & r2_hidden(B,c2_5__axioms) )
           => ( r1_xreal_0(A,c7_5_1_2_1_1_3__axioms)
              & r1_xreal_0(c7_5_1_2_1_1_3__axioms,B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c1_5__axioms])],[i3_5_1_2_1_1_3_tmp__axioms,dh_c8_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,i2_5_1_2_1_1_3__axioms),[file(axioms,i2_5_1_2_1_1_3__axioms)]]).

fof(i1_5_1_2_1_1_3__axioms,plain,(
    ? [A] : 
      ( v1_xreal_0(A)
      & ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms) )
               => ( r1_xreal_0(B,A)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(take,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,e1_5_1_2_1_1_3__axioms,dt_c1_5__axioms])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc7_xreal_0,rc1_xboole_0,rc2_xboole_0,rc2_xcmplx_0,dt_k1_numbers,dt_k1_zfmisc_1,dt_m1_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xcmplx_0,rc1_xreal_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_c1_5__axioms,dt_c2_5__axioms,dt_c7_5_1_2_1_1_3__axioms,cc2_xreal_0,i2_5_1_2_1_1_3__axioms]),
    [interesting(0.05),file(axioms,i1_5_1_2_1_1_3__axioms),[file(axioms,i1_5_1_2_1_1_3__axioms)]]).

fof(i3_5_1_2_1_1__axioms,plain,(
    ~ ( ~ r1_xboole_0(c1_5__axioms,k2_arytm_2)
      & ! [A] : 
          ( v1_xreal_0(A)
         => ? [B] : 
              ( v1_xreal_0(B)
              & ? [C] : 
                  ( v1_xreal_0(C)
                  & r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms)
                  & ~ ( r1_xreal_0(B,A)
                      & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c2_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms]),discharge_asm(discharge,[e1_5_1_2_1_1_3__axioms])],[e1_5_1_2_1_1_3__axioms,i1_5_1_2_1_1_3__axioms]),
    [interesting(0.2),file(axioms,i3_5_1_2_1_1__axioms),[file(axioms,i3_5_1_2_1_1__axioms)]]).

fof(e1_5_1_2_1_1__axioms,plain,(
    ~ ( ~ ( r1_xboole_0(c1_5__axioms,k2_arytm_2)
          & r1_xboole_0(c2_5__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)) )
      & r1_xboole_0(c2_5__axioms,k2_zfmisc_1(k1_tarski(0),k2_arytm_2))
      & r1_xboole_0(c1_5__axioms,k2_arytm_2) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,symmetry_r1_xboole_0,dt_k1_tarski,dt_k2_arytm_2,dt_k2_zfmisc_1,dt_c1_5__axioms,dt_c2_5__axioms,fc2_arytm_2,spc0_boole,spc0_numerals]),
    [interesting(0.2),file(axioms,e1_5_1_2_1_1__axioms),[file(axioms,e1_5_1_2_1_1__axioms)]]).

fof(e10_5_1_2__axioms,plain,(
    ? [A] : 
      ( v1_xreal_0(A)
      & ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms) )
               => ( r1_xreal_0(B,A)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(percases,[status(thm),assumptions([e1_5_1_2__axioms,e1_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms])],[i1_5_1_2_1_1__axioms,i2_5_1_2_1_1__axioms,i3_5_1_2_1_1__axioms,e1_5_1_2_1_1__axioms]),
    [interesting(0.5),file(axioms,e10_5_1_2__axioms),[file(axioms,e10_5_1_2__axioms)]]).

fof(i2_5_1_2__axioms,theorem,(
    $true ),
    introduced(tautology,[file(axioms,i2_5_1_2__axioms)]),
    [interesting(0.5),trivial,file(axioms,i2_5_1_2__axioms)]).

fof(i1_5_1_2__axioms,plain,(
    ? [A] : 
      ( v1_xreal_0(A)
      & ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms) )
               => ( r1_xreal_0(B,A)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(conclusion,[status(thm),assumptions([e1_5_1_2__axioms,e1_5__axioms,e2_5_1_2__axioms,dt_c1_5__axioms,dt_c2_5__axioms])],[e10_5_1_2__axioms,i2_5_1_2__axioms]),
    [interesting(0.5),file(axioms,i1_5_1_2__axioms),[file(axioms,i1_5_1_2__axioms)]]).

fof(i2_5_1__axioms,plain,(
    ~ ( c1_5__axioms != 0
      & c2_5__axioms != 0
      & ! [A] : 
          ( v1_xreal_0(A)
         => ? [B] : 
              ( v1_xreal_0(B)
              & ? [C] : 
                  ( v1_xreal_0(C)
                  & r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms)
                  & ~ ( r1_xreal_0(B,A)
                      & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e1_5_1_2__axioms,e2_5_1_2__axioms])],[e1_5_1_2__axioms,e2_5_1_2__axioms,i1_5_1_2__axioms]),
    [interesting(0.65),file(axioms,i2_5_1__axioms),[file(axioms,i2_5_1__axioms)]]).

fof(e1_5_1__axioms,plain,(
    ~ ( c1_5__axioms != 0
      & c2_5__axioms != 0
      & ~ ( c1_5__axioms != 0
          & c2_5__axioms != 0 ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xcmplx_0,rc1_arytm_3,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc1_ordinal2,fc1_xboole_0,rc1_xcmplx_0,rc2_xcmplx_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_xcmplx_0,fc1_numbers,rc1_xboole_0,rc2_xboole_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,dt_c1_5__axioms,dt_c2_5__axioms,spc0_boole,spc0_numerals]),
    [interesting(0.65),file(axioms,e1_5_1__axioms),[file(axioms,e1_5_1__axioms)]]).

fof(i2_5__axioms,plain,(
    ? [A] : 
      ( v1_xreal_0(A)
      & ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms) )
               => ( r1_xreal_0(B,A)
                  & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(percases,[status(thm),assumptions([e1_5__axioms,dt_c1_5__axioms,dt_c2_5__axioms])],[i1_5_1__axioms,i2_5_1__axioms,e1_5_1__axioms]),
    [interesting(0.8),file(axioms,i2_5__axioms),[file(axioms,i2_5__axioms)]]).

fof(i1_5__axioms,plain,(
    ~ ( ! [A] : 
          ( v1_xreal_0(A)
         => ! [B] : 
              ( v1_xreal_0(B)
             => ( ( r2_hidden(A,c1_5__axioms)
                  & r2_hidden(B,c2_5__axioms) )
               => r1_xreal_0(A,B) ) ) )
      & ! [A] : 
          ( v1_xreal_0(A)
         => ? [B] : 
              ( v1_xreal_0(B)
              & ? [C] : 
                  ( v1_xreal_0(C)
                  & r2_hidden(B,c1_5__axioms)
                  & r2_hidden(C,c2_5__axioms)
                  & ~ ( r1_xreal_0(B,A)
                      & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_5__axioms,dt_c2_5__axioms]),discharge_asm(discharge,[e1_5__axioms])],[e1_5__axioms,i2_5__axioms]),
    [interesting(0.8),file(axioms,i1_5__axioms),[file(axioms,i1_5__axioms)]]).

fof(i1_5_tmp__axioms,plain,
    ( ( m1_subset_1(c1_5__axioms,k1_zfmisc_1(k1_numbers))
      & m1_subset_1(c2_5__axioms,k1_zfmisc_1(k1_numbers)) )
   => ~ ( ! [A] : 
            ( v1_xreal_0(A)
           => ! [B] : 
                ( v1_xreal_0(B)
               => ( ( r2_hidden(A,c1_5__axioms)
                    & r2_hidden(B,c2_5__axioms) )
                 => r1_xreal_0(A,B) ) ) )
        & ! [A] : 
            ( v1_xreal_0(A)
           => ? [B] : 
                ( v1_xreal_0(B)
                & ? [C] : 
                    ( v1_xreal_0(C)
                    & r2_hidden(B,c1_5__axioms)
                    & r2_hidden(C,c2_5__axioms)
                    & ~ ( r1_xreal_0(B,A)
                        & r1_xreal_0(A,C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__axioms,dt_c2_5__axioms])],[dt_c1_5__axioms,dt_c2_5__axioms,i1_5__axioms]),
    [interesting(1),t26_axioms]).

fof(t26_axioms,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
         => ~ ( ! [C] : 
                  ( v1_xreal_0(C)
                 => ! [D] : 
                      ( v1_xreal_0(D)
                     => ( ( r2_hidden(C,A)
                          & r2_hidden(D,B) )
                       => r1_xreal_0(C,D) ) ) )
              & ! [C] : 
                  ( v1_xreal_0(C)
                 => ? [D] : 
                      ( v1_xreal_0(D)
                      & ? [E] : 
                          ( v1_xreal_0(E)
                          & r2_hidden(D,A)
                          & r2_hidden(E,B)
                          & ~ ( r1_xreal_0(D,C)
                              & r1_xreal_0(C,E) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_5_tmp__axioms,dh_c1_5__axioms,dh_c2_5__axioms]),
    [interesting(1),file(axioms,t26_axioms),[file(axioms,t26_axioms)]]).