% Mizar ND problem: t29_supinf_1,supinf_1,321,61 
fof(dh_c1_25__supinf_1,definition,
    ( ( m1_subset_1(c1_25__supinf_1,k3_supinf_1)
     => ! [A] : 
          ( m1_subset_1(A,k3_supinf_1)
         => ! [B] : 
              ( m1_subset_1(B,k3_supinf_1)
             => ( ( r1_supinf_1(c1_25__supinf_1,A)
                  & r1_supinf_1(A,B) )
               => r1_supinf_1(c1_25__supinf_1,B) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,k3_supinf_1)
       => ! [D] : 
            ( m1_subset_1(D,k3_supinf_1)
           => ! [E] : 
                ( m1_subset_1(E,k3_supinf_1)
               => ( ( r1_supinf_1(C,D)
                    & r1_supinf_1(D,E) )
                 => r1_supinf_1(C,E) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_25__supinf_1),file(supinf_1,c1_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,c1_25__supinf_1)]).

fof(dh_c2_25__supinf_1,definition,
    ( ( m1_subset_1(c2_25__supinf_1,k3_supinf_1)
     => ! [A] : 
          ( m1_subset_1(A,k3_supinf_1)
         => ( ( r1_supinf_1(c1_25__supinf_1,c2_25__supinf_1)
              & r1_supinf_1(c2_25__supinf_1,A) )
           => r1_supinf_1(c1_25__supinf_1,A) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k3_supinf_1)
       => ! [C] : 
            ( m1_subset_1(C,k3_supinf_1)
           => ( ( r1_supinf_1(c1_25__supinf_1,B)
                & r1_supinf_1(B,C) )
             => r1_supinf_1(c1_25__supinf_1,C) ) ) ) ),
    introduced(definition,[new_symbol(c2_25__supinf_1),file(supinf_1,c2_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,c2_25__supinf_1)]).

fof(dh_c3_25__supinf_1,definition,
    ( ( m1_subset_1(c3_25__supinf_1,k3_supinf_1)
     => ( ( r1_supinf_1(c1_25__supinf_1,c2_25__supinf_1)
          & r1_supinf_1(c2_25__supinf_1,c3_25__supinf_1) )
       => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ) )
   => ! [A] : 
        ( m1_subset_1(A,k3_supinf_1)
       => ( ( r1_supinf_1(c1_25__supinf_1,c2_25__supinf_1)
            & r1_supinf_1(c2_25__supinf_1,A) )
         => r1_supinf_1(c1_25__supinf_1,A) ) ) ),
    introduced(definition,[new_symbol(c3_25__supinf_1),file(supinf_1,c3_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,c3_25__supinf_1)]).

fof(e1_25__supinf_1,assumption,(
    r1_supinf_1(c1_25__supinf_1,c2_25__supinf_1) ),
    introduced(assumption,[file(supinf_1,e1_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,e1_25__supinf_1)]).

fof(e2_25__supinf_1,assumption,(
    r1_supinf_1(c2_25__supinf_1,c3_25__supinf_1) ),
    introduced(assumption,[file(supinf_1,e2_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,e2_25__supinf_1)]).

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(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(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(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(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(fc10_membered,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc14_membered,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    [interesting(0.9),axiom,file(membered,fc14_membered)]).

fof(fc15_membered,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    [interesting(0.9),axiom,file(membered,fc15_membered)]).

fof(fc16_membered,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    [interesting(0.9),axiom,file(membered,fc16_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

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(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_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(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

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(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

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(fc12_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    [interesting(0.9),axiom,file(membered,fc12_membered)]).

fof(fc13_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    [interesting(0.9),axiom,file(membered,fc13_membered)]).

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(fc24_membered,theorem,(
    ! [A,B] : 
      ( ( v3_membered(A)
        & v3_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc24_membered),
    [interesting(0.9),axiom,file(membered,fc24_membered)]).

fof(fc25_membered,theorem,(
    ! [A,B] : 
      ( ( v4_membered(A)
        & v4_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc25_membered),
    [interesting(0.9),axiom,file(membered,fc25_membered)]).

fof(fc26_membered,theorem,(
    ! [A,B] : 
      ( ( v5_membered(A)
        & v5_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B))
        & v3_membered(k2_xboole_0(A,B))
        & v4_membered(k2_xboole_0(A,B))
        & v5_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc26_membered),
    [interesting(0.9),axiom,file(membered,fc26_membered)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(fc7_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

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(rc3_supinf_1,theorem,(
    ? [A] : v3_supinf_1(A) ),
    file(supinf_1,rc3_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,rc3_supinf_1)]).

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(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(dt_k1_supinf_1,axiom,(
    $true ),
    file(supinf_1,k1_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,k1_supinf_1)]).

fof(dt_k2_supinf_1,axiom,(
    $true ),
    file(supinf_1,k2_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,k2_supinf_1)]).

fof(dt_k3_supinf_1,axiom,(
    $true ),
    file(supinf_1,k3_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,k3_supinf_1)]).

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

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_supinf_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => v3_supinf_1(A) ) ),
    file(supinf_1,cc1_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,cc1_supinf_1)]).

fof(cc2_supinf_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & v3_supinf_1(A) ) ) ),
    file(supinf_1,cc2_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,cc2_supinf_1)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(fc22_membered,theorem,(
    ! [A,B] : 
      ( ( v1_membered(A)
        & v1_membered(B) )
     => v1_membered(k2_xboole_0(A,B)) ) ),
    file(membered,fc22_membered),
    [interesting(0.9),axiom,file(membered,fc22_membered)]).

fof(fc23_membered,theorem,(
    ! [A,B] : 
      ( ( v2_membered(A)
        & v2_membered(B) )
     => ( v1_membered(k2_xboole_0(A,B))
        & v2_membered(k2_xboole_0(A,B)) ) ) ),
    file(membered,fc23_membered),
    [interesting(0.9),axiom,file(membered,fc23_membered)]).

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(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(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(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(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(d1_supinf_1,definition,(
    k1_supinf_1 = k1_numbers ),
    file(supinf_1,d1_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,d1_supinf_1)]).

fof(d3_supinf_1,definition,(
    k2_supinf_1 = k1_tarski(k1_numbers) ),
    file(supinf_1,d3_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,d3_supinf_1)]).

fof(d6_supinf_1,definition,(
    k3_supinf_1 = k2_xboole_0(k1_numbers,k2_tarski(k2_supinf_1,k1_supinf_1)) ),
    file(supinf_1,d6_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,d6_supinf_1)]).

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(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(reflexivity_r1_supinf_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => r1_supinf_1(A,A) ) ),
    file(supinf_1,r1_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,r1_supinf_1)]).

fof(connectedness_r1_supinf_1,theorem,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => ( r1_supinf_1(A,B)
        | r1_supinf_1(B,A) ) ) ),
    file(supinf_1,r1_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,r1_supinf_1)]).

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(redefinition_k4_supinf_1,definition,(
    k4_supinf_1 = k1_supinf_1 ),
    file(supinf_1,k4_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,k4_supinf_1)]).

fof(redefinition_k5_supinf_1,definition,(
    k5_supinf_1 = k2_supinf_1 ),
    file(supinf_1,k5_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,k5_supinf_1)]).

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

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

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

fof(dt_k4_supinf_1,axiom,(
    m1_subset_1(k4_supinf_1,k3_supinf_1) ),
    file(supinf_1,k4_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,k4_supinf_1)]).

fof(dt_k5_supinf_1,axiom,(
    m1_subset_1(k5_supinf_1,k3_supinf_1) ),
    file(supinf_1,k5_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,k5_supinf_1)]).

fof(dt_c1_25__supinf_1,assumption,(
    m1_subset_1(c1_25__supinf_1,k3_supinf_1) ),
    introduced(assumption,[file(supinf_1,c1_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,c1_25__supinf_1)]).

fof(dt_c2_25__supinf_1,assumption,(
    m1_subset_1(c2_25__supinf_1,k3_supinf_1) ),
    introduced(assumption,[file(supinf_1,c2_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,c2_25__supinf_1)]).

fof(dt_c3_25__supinf_1,assumption,(
    m1_subset_1(c3_25__supinf_1,k3_supinf_1) ),
    introduced(assumption,[file(supinf_1,c3_25__supinf_1)]),
    [interesting(0.8),axiom,file(supinf_1,c3_25__supinf_1)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(fc3_subset_1,theorem,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]).

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(e1_25_8__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) ),
    introduced(assumption,[file(supinf_1,e1_25_8__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_8__supinf_1)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.9),axiom,file(tarski,d2_tarski)]).

fof(e2_25_8__supinf_1,plain,(
    ~ ( ~ ( c1_25__supinf_1 = k4_supinf_1
          & c2_25__supinf_1 = k5_supinf_1
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( c1_25__supinf_1 = k4_supinf_1
          & c2_25__supinf_1 = k5_supinf_1
          & c3_25__supinf_1 = k4_supinf_1 )
      & ~ ( c1_25__supinf_1 = k4_supinf_1
          & c2_25__supinf_1 = k4_supinf_1
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( c1_25__supinf_1 = k4_supinf_1
          & c2_25__supinf_1 = k4_supinf_1
          & c3_25__supinf_1 = k4_supinf_1 )
      & ~ ( c1_25__supinf_1 = k5_supinf_1
          & c2_25__supinf_1 = k5_supinf_1
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( c1_25__supinf_1 = k5_supinf_1
          & c2_25__supinf_1 = k5_supinf_1
          & c3_25__supinf_1 = k4_supinf_1 )
      & ~ ( c1_25__supinf_1 = k5_supinf_1
          & c2_25__supinf_1 = k4_supinf_1
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( c1_25__supinf_1 = k5_supinf_1
          & c2_25__supinf_1 = k4_supinf_1
          & c3_25__supinf_1 = k4_supinf_1 ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_8__supinf_1])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_xreal_0,cc7_xreal_0,fc10_membered,fc11_membered,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc7_membered,fc8_membered,fc9_membered,rc1_xreal_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_supinf_1,cc3_membered,cc4_membered,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_membered,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc6_membered,rc1_membered,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc15_membered,cc1_supinf_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k2_tarski,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc3_subset_1,t1_subset,t7_boole,e1_25_8__supinf_1,d2_tarski]),
    [interesting(0.65),file(supinf_1,e2_25_8__supinf_1),[file(supinf_1,e2_25_8__supinf_1)]]).

fof(e3_25_8__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_8__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,t1_subset,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_xboole_0,fc7_membered,fc8_membered,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_numbers,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,cc2_supinf_1,fc2_membered,fc2_subset_1,fc3_subset_1,rc3_supinf_1,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc1_supinf_1,d1_supinf_1,d3_supinf_1,d6_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25_8__supinf_1,e1_25__supinf_1,e2_25__supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_8__supinf_1),[file(supinf_1,e3_25_8__supinf_1)]]).

fof(i2_25_8__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_8__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_8__supinf_1)]).

fof(i1_25_8__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_8__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[e3_25_8__supinf_1,i2_25_8__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_8__supinf_1),[file(supinf_1,i1_25_8__supinf_1)]]).

fof(e10_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25__supinf_1,e2_25__supinf_1]),discharge_asm(discharge,[e1_25_8__supinf_1])],[e1_25_8__supinf_1,i1_25_8__supinf_1]),
    [interesting(0.8),file(supinf_1,e10_25__supinf_1),[file(supinf_1,e10_25__supinf_1)]]).

fof(e1_25_1__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k1_numbers)
    & r2_hidden(c2_25__supinf_1,k1_numbers)
    & r2_hidden(c3_25__supinf_1,k1_numbers) ),
    introduced(assumption,[file(supinf_1,e1_25_1__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_1__supinf_1)]).

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(dh_c1_25_1__supinf_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & ? [B] : 
            ( m1_subset_1(B,k1_numbers)
            & c1_25__supinf_1 = A
            & c2_25__supinf_1 = B
            & r1_xreal_0(A,B) ) )
   => ( m1_subset_1(c1_25_1__supinf_1,k1_numbers)
      & ? [C] : 
          ( m1_subset_1(C,k1_numbers)
          & c1_25__supinf_1 = c1_25_1__supinf_1
          & c2_25__supinf_1 = C
          & r1_xreal_0(c1_25_1__supinf_1,C) ) ) ),
    introduced(definition,[new_symbol(c1_25_1__supinf_1),file(supinf_1,c1_25_1__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,c1_25_1__supinf_1)]).

fof(d7_supinf_1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( ( r2_hidden(A,k1_numbers)
                & r2_hidden(B,k1_numbers) )
             => ( r1_supinf_1(A,B)
              <=> ? [C] : 
                    ( m1_subset_1(C,k1_numbers)
                    & ? [D] : 
                        ( m1_subset_1(D,k1_numbers)
                        & C = A
                        & D = B
                        & r1_xreal_0(C,D) ) ) ) )
            & ( ~ ( r2_hidden(A,k1_numbers)
                  & r2_hidden(B,k1_numbers) )
             => ( r1_supinf_1(A,B)
              <=> ( A = k5_supinf_1
                  | B = k4_supinf_1 ) ) ) ) ) ) ),
    file(supinf_1,d7_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,d7_supinf_1)]).

fof(e2_25_1__supinf_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ? [B] : 
          ( m1_subset_1(B,k1_numbers)
          & c1_25__supinf_1 = A
          & c2_25__supinf_1 = B
          & r1_xreal_0(A,B) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_1__supinf_1,e1_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_supinf_1,dt_k2_supinf_1,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d6_supinf_1,e1_25_1__supinf_1,e1_25__supinf_1,d7_supinf_1]),
    [interesting(0.65),file(supinf_1,e2_25_1__supinf_1),[file(supinf_1,e2_25_1__supinf_1)]]).

fof(dt_c1_25_1__supinf_1,plain,(
    m1_subset_1(c1_25_1__supinf_1,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_1__supinf_1,e1_25__supinf_1])],[dh_c1_25_1__supinf_1,e2_25_1__supinf_1]),
    [interesting(0.65),file(supinf_1,c1_25_1__supinf_1),[file(supinf_1,c1_25_1__supinf_1)]]).

fof(dh_c2_25_1__supinf_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & c1_25__supinf_1 = c1_25_1__supinf_1
        & c2_25__supinf_1 = A
        & r1_xreal_0(c1_25_1__supinf_1,A) )
   => ( m1_subset_1(c2_25_1__supinf_1,k1_numbers)
      & c1_25__supinf_1 = c1_25_1__supinf_1
      & c2_25__supinf_1 = c2_25_1__supinf_1
      & r1_xreal_0(c1_25_1__supinf_1,c2_25_1__supinf_1) ) ),
    introduced(definition,[new_symbol(c2_25_1__supinf_1),file(supinf_1,c2_25_1__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,c2_25_1__supinf_1)]).

fof(dt_c2_25_1__supinf_1,plain,(
    m1_subset_1(c2_25_1__supinf_1,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_1__supinf_1,e1_25__supinf_1])],[dh_c1_25_1__supinf_1,dh_c2_25_1__supinf_1,e2_25_1__supinf_1]),
    [interesting(0.65),file(supinf_1,c2_25_1__supinf_1),[file(supinf_1,c2_25_1__supinf_1)]]).

fof(dh_c3_25_1__supinf_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & ? [B] : 
            ( m1_subset_1(B,k1_numbers)
            & c2_25__supinf_1 = A
            & c3_25__supinf_1 = B
            & r1_xreal_0(A,B) ) )
   => ( m1_subset_1(c3_25_1__supinf_1,k1_numbers)
      & ? [C] : 
          ( m1_subset_1(C,k1_numbers)
          & c2_25__supinf_1 = c3_25_1__supinf_1
          & c3_25__supinf_1 = C
          & r1_xreal_0(c3_25_1__supinf_1,C) ) ) ),
    introduced(definition,[new_symbol(c3_25_1__supinf_1),file(supinf_1,c3_25_1__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,c3_25_1__supinf_1)]).

fof(e4_25_1__supinf_1,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_numbers)
      & ? [B] : 
          ( m1_subset_1(B,k1_numbers)
          & c2_25__supinf_1 = A
          & c3_25__supinf_1 = B
          & r1_xreal_0(A,B) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1,e1_25_1__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_supinf_1,dt_k2_supinf_1,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d6_supinf_1,e2_25__supinf_1,e1_25_1__supinf_1,d7_supinf_1]),
    [interesting(0.65),file(supinf_1,e4_25_1__supinf_1),[file(supinf_1,e4_25_1__supinf_1)]]).

fof(dt_c3_25_1__supinf_1,plain,(
    m1_subset_1(c3_25_1__supinf_1,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1,e1_25_1__supinf_1])],[dh_c3_25_1__supinf_1,e4_25_1__supinf_1]),
    [interesting(0.65),file(supinf_1,c3_25_1__supinf_1),[file(supinf_1,c3_25_1__supinf_1)]]).

fof(dh_c4_25_1__supinf_1,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_numbers)
        & c2_25__supinf_1 = c3_25_1__supinf_1
        & c3_25__supinf_1 = A
        & r1_xreal_0(c3_25_1__supinf_1,A) )
   => ( m1_subset_1(c4_25_1__supinf_1,k1_numbers)
      & c2_25__supinf_1 = c3_25_1__supinf_1
      & c3_25__supinf_1 = c4_25_1__supinf_1
      & r1_xreal_0(c3_25_1__supinf_1,c4_25_1__supinf_1) ) ),
    introduced(definition,[new_symbol(c4_25_1__supinf_1),file(supinf_1,c4_25_1__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,c4_25_1__supinf_1)]).

fof(dt_c4_25_1__supinf_1,plain,(
    m1_subset_1(c4_25_1__supinf_1,k1_numbers) ),
    inference(consider,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1,e1_25_1__supinf_1])],[dh_c3_25_1__supinf_1,dh_c4_25_1__supinf_1,e4_25_1__supinf_1]),
    [interesting(0.65),file(supinf_1,c4_25_1__supinf_1),[file(supinf_1,c4_25_1__supinf_1)]]).

fof(e3_25_1__supinf_1,plain,
    ( c1_25__supinf_1 = c1_25_1__supinf_1
    & c2_25__supinf_1 = c2_25_1__supinf_1
    & r1_xreal_0(c1_25_1__supinf_1,c2_25_1__supinf_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_1__supinf_1,e1_25__supinf_1])],[dh_c1_25_1__supinf_1,dh_c2_25_1__supinf_1,e2_25_1__supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_1__supinf_1),[file(supinf_1,e3_25_1__supinf_1)]]).

fof(e5_25_1__supinf_1,plain,
    ( c2_25__supinf_1 = c3_25_1__supinf_1
    & c3_25__supinf_1 = c4_25_1__supinf_1
    & r1_xreal_0(c3_25_1__supinf_1,c4_25_1__supinf_1) ),
    inference(consider,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1,e1_25_1__supinf_1])],[dh_c3_25_1__supinf_1,dh_c4_25_1__supinf_1,e4_25_1__supinf_1]),
    [interesting(0.65),file(supinf_1,e5_25_1__supinf_1),[file(supinf_1,e5_25_1__supinf_1)]]).

fof(t2_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    [interesting(0.9),axiom,file(xreal_1,t2_xreal_1)]).

fof(e6_25_1__supinf_1,plain,(
    r1_xreal_0(c1_25_1__supinf_1,c4_25_1__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_25__supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1,e1_25_1__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,antisymmetry_r2_hidden,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,t1_subset,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_supinf_1,dt_k2_supinf_1,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t7_boole,t8_boole,d1_supinf_1,d3_supinf_1,existence_m1_subset_1,dt_k1_numbers,dt_k3_supinf_1,dt_m1_subset_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,rc1_xreal_0,d6_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,dt_c1_25__supinf_1,dt_c1_25_1__supinf_1,dt_c2_25__supinf_1,dt_c2_25_1__supinf_1,dt_c3_25__supinf_1,dt_c3_25_1__supinf_1,dt_c4_25_1__supinf_1,cc2_xreal_0,e3_25_1__supinf_1,e5_25_1__supinf_1,t2_xreal_1]),
    [interesting(0.65),file(supinf_1,e6_25_1__supinf_1),[file(supinf_1,e6_25_1__supinf_1)]]).

fof(e7_25_1__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([e1_25__supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1,e1_25_1__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_supinf_1,dt_k2_supinf_1,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c1_25_1__supinf_1,dt_c2_25__supinf_1,dt_c2_25_1__supinf_1,dt_c3_25__supinf_1,dt_c3_25_1__supinf_1,dt_c4_25_1__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d6_supinf_1,e6_25_1__supinf_1,e3_25_1__supinf_1,e5_25_1__supinf_1,d7_supinf_1]),
    [interesting(0.65),file(supinf_1,e7_25_1__supinf_1),[file(supinf_1,e7_25_1__supinf_1)]]).

fof(i2_25_1__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_1__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_1__supinf_1)]).

fof(i1_25_1__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([e1_25__supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1,e1_25_1__supinf_1])],[e7_25_1__supinf_1,i2_25_1__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_1__supinf_1),[file(supinf_1,i1_25_1__supinf_1)]]).

fof(e3_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & r2_hidden(c3_25__supinf_1,k1_numbers) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([e1_25__supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1]),discharge_asm(discharge,[e1_25_1__supinf_1])],[e1_25_1__supinf_1,i1_25_1__supinf_1]),
    [interesting(0.8),file(supinf_1,e3_25__supinf_1),[file(supinf_1,e3_25__supinf_1)]]).

fof(e1_25_2__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c2_25__supinf_1,k1_numbers)
    & r2_hidden(c3_25__supinf_1,k1_numbers) ),
    introduced(assumption,[file(supinf_1,e1_25_2__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_2__supinf_1)]).

fof(e2_25_2__supinf_1,plain,
    ( ( c1_25__supinf_1 = k4_supinf_1
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & r2_hidden(c3_25__supinf_1,k1_numbers) )
    | ( c1_25__supinf_1 = k5_supinf_1
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & r2_hidden(c3_25__supinf_1,k1_numbers) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_2__supinf_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_supinf_1,cc2_supinf_1,cc4_membered,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_tarski,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,e1_25_2__supinf_1,d2_tarski]),
    [interesting(0.65),file(supinf_1,e2_25_2__supinf_1),[file(supinf_1,e2_25_2__supinf_1)]]).

fof(t6_supinf_1,theorem,(
    ~ r2_hidden(k2_supinf_1,k1_numbers) ),
    file(supinf_1,t6_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,t6_supinf_1)]).

fof(t24_supinf_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ( r1_supinf_1(k4_supinf_1,A)
       => A = k4_supinf_1 ) ) ),
    file(supinf_1,t24_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,t24_supinf_1)]).

fof(e3_25_2__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_2__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_supinf_1,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,fc7_membered,fc8_membered,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d1_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_supinf_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d3_supinf_1,d6_supinf_1,e2_25_2__supinf_1,e1_25__supinf_1,e2_25__supinf_1,d7_supinf_1,t6_supinf_1,t24_supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_2__supinf_1),[file(supinf_1,e3_25_2__supinf_1)]]).

fof(i2_25_2__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_2__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_2__supinf_1)]).

fof(i1_25_2__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_2__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[e3_25_2__supinf_1,i2_25_2__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_2__supinf_1),[file(supinf_1,i1_25_2__supinf_1)]]).

fof(e4_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & r2_hidden(c3_25__supinf_1,k1_numbers) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25__supinf_1,e2_25__supinf_1]),discharge_asm(discharge,[e1_25_2__supinf_1])],[e1_25_2__supinf_1,i1_25_2__supinf_1]),
    [interesting(0.8),file(supinf_1,e4_25__supinf_1),[file(supinf_1,e4_25__supinf_1)]]).

fof(e1_25_3__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k1_numbers)
    & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c3_25__supinf_1,k1_numbers) ),
    introduced(assumption,[file(supinf_1,e1_25_3__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_3__supinf_1)]).

fof(t2_supinf_1,theorem,(
    ~ r2_hidden(k1_supinf_1,k1_numbers) ),
    file(supinf_1,t2_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,t2_supinf_1)]).

fof(e3_25_3__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & c2_25__supinf_1 = k4_supinf_1
      & r2_hidden(c3_25__supinf_1,k1_numbers) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k2_supinf_1,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d3_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,dt_k1_numbers,dt_k1_supinf_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d1_supinf_1,d6_supinf_1,e2_25__supinf_1,t2_supinf_1,t24_supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_3__supinf_1),[file(supinf_1,e3_25_3__supinf_1)]]).

fof(e2_25_3__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & c2_25__supinf_1 = k5_supinf_1
      & r2_hidden(c3_25__supinf_1,k1_numbers) )
    | ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & c2_25__supinf_1 = k4_supinf_1
      & r2_hidden(c3_25__supinf_1,k1_numbers) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_3__supinf_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_supinf_1,cc2_supinf_1,cc4_membered,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_tarski,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,e1_25_3__supinf_1,d2_tarski]),
    [interesting(0.65),file(supinf_1,e2_25_3__supinf_1),[file(supinf_1,e2_25_3__supinf_1)]]).

fof(e4_25_3__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([e2_25__supinf_1,e1_25__supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_3__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_supinf_1,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,fc7_membered,fc8_membered,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d1_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_supinf_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d3_supinf_1,d6_supinf_1,e3_25_3__supinf_1,e1_25__supinf_1,e2_25_3__supinf_1,d7_supinf_1,t6_supinf_1]),
    [interesting(0.65),file(supinf_1,e4_25_3__supinf_1),[file(supinf_1,e4_25_3__supinf_1)]]).

fof(i2_25_3__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_3__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_3__supinf_1)]).

fof(i1_25_3__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([e2_25__supinf_1,e1_25__supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_3__supinf_1])],[e4_25_3__supinf_1,i2_25_3__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_3__supinf_1),[file(supinf_1,i1_25_3__supinf_1)]]).

fof(e5_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c3_25__supinf_1,k1_numbers) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([e2_25__supinf_1,e1_25__supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1]),discharge_asm(discharge,[e1_25_3__supinf_1])],[e1_25_3__supinf_1,i1_25_3__supinf_1]),
    [interesting(0.8),file(supinf_1,e5_25__supinf_1),[file(supinf_1,e5_25__supinf_1)]]).

fof(e1_25_4__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c3_25__supinf_1,k1_numbers) ),
    introduced(assumption,[file(supinf_1,e1_25_4__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_4__supinf_1)]).

fof(e2_25_4__supinf_1,plain,(
    ~ ( ~ ( c1_25__supinf_1 = k5_supinf_1
          & c2_25__supinf_1 = k5_supinf_1
          & r2_hidden(c3_25__supinf_1,k1_numbers) )
      & ~ ( c1_25__supinf_1 = k5_supinf_1
          & c2_25__supinf_1 = k4_supinf_1
          & r2_hidden(c3_25__supinf_1,k1_numbers) )
      & ~ ( c1_25__supinf_1 = k4_supinf_1
          & c2_25__supinf_1 = k5_supinf_1
          & r2_hidden(c3_25__supinf_1,k1_numbers) )
      & ~ ( c1_25__supinf_1 = k4_supinf_1
          & c2_25__supinf_1 = k4_supinf_1
          & r2_hidden(c3_25__supinf_1,k1_numbers) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_4__supinf_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_supinf_1,cc2_supinf_1,cc4_membered,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_tarski,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,e1_25_4__supinf_1,d2_tarski]),
    [interesting(0.65),file(supinf_1,e2_25_4__supinf_1),[file(supinf_1,e2_25_4__supinf_1)]]).

fof(e3_25_4__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_4__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k2_supinf_1,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d3_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k1_supinf_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d1_supinf_1,d6_supinf_1,e2_25_4__supinf_1,e1_25__supinf_1,e2_25__supinf_1,d7_supinf_1,t2_supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_4__supinf_1),[file(supinf_1,e3_25_4__supinf_1)]]).

fof(i2_25_4__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_4__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_4__supinf_1)]).

fof(i1_25_4__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_4__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[e3_25_4__supinf_1,i2_25_4__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_4__supinf_1),[file(supinf_1,i1_25_4__supinf_1)]]).

fof(e6_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c3_25__supinf_1,k1_numbers) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25__supinf_1,e2_25__supinf_1]),discharge_asm(discharge,[e1_25_4__supinf_1])],[e1_25_4__supinf_1,i1_25_4__supinf_1]),
    [interesting(0.8),file(supinf_1,e6_25__supinf_1),[file(supinf_1,e6_25__supinf_1)]]).

fof(e1_25_5__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k1_numbers)
    & r2_hidden(c2_25__supinf_1,k1_numbers)
    & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) ),
    introduced(assumption,[file(supinf_1,e1_25_5__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_5__supinf_1)]).

fof(e2_25_5__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & c3_25__supinf_1 = k5_supinf_1 )
    | ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & c3_25__supinf_1 = k4_supinf_1 ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_5__supinf_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_supinf_1,cc2_supinf_1,cc4_membered,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_tarski,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,e1_25_5__supinf_1,d2_tarski]),
    [interesting(0.65),file(supinf_1,e2_25_5__supinf_1),[file(supinf_1,e2_25_5__supinf_1)]]).

fof(t14_supinf_1,theorem,(
    k5_supinf_1 != k4_supinf_1 ),
    file(supinf_1,t14_supinf_1),
    [interesting(0.9),axiom,file(supinf_1,t14_supinf_1)]).

fof(e3_25_5__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_5__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,fc7_membered,fc8_membered,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,e2_25_5__supinf_1,e2_25__supinf_1,d7_supinf_1,t2_supinf_1,t6_supinf_1,t14_supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_5__supinf_1),[file(supinf_1,e3_25_5__supinf_1)]]).

fof(i2_25_5__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_5__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_5__supinf_1)]).

fof(i1_25_5__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_5__supinf_1,e2_25__supinf_1])],[e3_25_5__supinf_1,i2_25_5__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_5__supinf_1),[file(supinf_1,i1_25_5__supinf_1)]]).

fof(e7_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1]),discharge_asm(discharge,[e1_25_5__supinf_1])],[e1_25_5__supinf_1,i1_25_5__supinf_1]),
    [interesting(0.8),file(supinf_1,e7_25__supinf_1),[file(supinf_1,e7_25__supinf_1)]]).

fof(e1_25_6__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c2_25__supinf_1,k1_numbers)
    & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) ),
    introduced(assumption,[file(supinf_1,e1_25_6__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_6__supinf_1)]).

fof(e2_25_6__supinf_1,plain,(
    ~ ( ~ ( c1_25__supinf_1 = k5_supinf_1
          & r2_hidden(c2_25__supinf_1,k1_numbers)
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( c1_25__supinf_1 = k5_supinf_1
          & r2_hidden(c2_25__supinf_1,k1_numbers)
          & c3_25__supinf_1 = k4_supinf_1 )
      & ~ ( c1_25__supinf_1 = k4_supinf_1
          & r2_hidden(c2_25__supinf_1,k1_numbers)
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( c1_25__supinf_1 = k4_supinf_1
          & r2_hidden(c2_25__supinf_1,k1_numbers)
          & c3_25__supinf_1 = k4_supinf_1 ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_6__supinf_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_supinf_1,cc2_supinf_1,cc4_membered,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_tarski,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,e1_25_6__supinf_1,d2_tarski]),
    [interesting(0.65),file(supinf_1,e2_25_6__supinf_1),[file(supinf_1,e2_25_6__supinf_1)]]).

fof(e3_25_6__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_6__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_supinf_1,dt_k1_tarski,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,fc7_membered,fc8_membered,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d1_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_supinf_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d3_supinf_1,d6_supinf_1,e2_25_6__supinf_1,e2_25__supinf_1,d7_supinf_1,t6_supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_6__supinf_1),[file(supinf_1,e3_25_6__supinf_1)]]).

fof(i2_25_6__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_6__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_6__supinf_1)]).

fof(i1_25_6__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_6__supinf_1,e2_25__supinf_1])],[e3_25_6__supinf_1,i2_25_6__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_6__supinf_1),[file(supinf_1,i1_25_6__supinf_1)]]).

fof(e8_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c2_25__supinf_1,k1_numbers)
      & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e2_25__supinf_1]),discharge_asm(discharge,[e1_25_6__supinf_1])],[e1_25_6__supinf_1,i1_25_6__supinf_1]),
    [interesting(0.8),file(supinf_1,e8_25__supinf_1),[file(supinf_1,e8_25__supinf_1)]]).

fof(e1_25_7__supinf_1,assumption,
    ( r2_hidden(c1_25__supinf_1,k1_numbers)
    & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
    & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) ),
    introduced(assumption,[file(supinf_1,e1_25_7__supinf_1)]),
    [interesting(0.65),axiom,file(supinf_1,e1_25_7__supinf_1)]).

fof(e2_25_7__supinf_1,plain,(
    ~ ( ~ ( r2_hidden(c1_25__supinf_1,k1_numbers)
          & c2_25__supinf_1 = k5_supinf_1
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( r2_hidden(c1_25__supinf_1,k1_numbers)
          & c2_25__supinf_1 = k5_supinf_1
          & c3_25__supinf_1 = k4_supinf_1 )
      & ~ ( r2_hidden(c1_25__supinf_1,k1_numbers)
          & c2_25__supinf_1 = k4_supinf_1
          & c3_25__supinf_1 = k5_supinf_1 )
      & ~ ( r2_hidden(c1_25__supinf_1,k1_numbers)
          & c2_25__supinf_1 = k4_supinf_1
          & c3_25__supinf_1 = k4_supinf_1 ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_7__supinf_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k1_tarski,dt_k1_xboole_0,dt_k2_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc1_xboole_0,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc2_xboole_0,fc3_xboole_0,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_supinf_1,cc2_supinf_1,cc4_membered,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_tarski,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,e1_25_7__supinf_1,d2_tarski]),
    [interesting(0.65),file(supinf_1,e2_25_7__supinf_1),[file(supinf_1,e2_25_7__supinf_1)]]).

fof(e3_25_7__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_7__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,t1_boole,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,dt_k2_supinf_1,dt_k2_tarski,dt_k2_xboole_0,cc10_membered,cc11_membered,cc15_membered,cc2_xreal_0,cc4_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,rc1_xboole_0,rc1_xreal_0,rc2_xboole_0,rc3_supinf_1,t2_subset,t6_boole,t8_boole,d3_supinf_1,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,existence_m1_subset_1,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k1_supinf_1,dt_k3_supinf_1,dt_k4_supinf_1,dt_k5_supinf_1,dt_m1_subset_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,cc1_supinf_1,cc2_supinf_1,fc2_membered,t1_subset,t7_boole,d1_supinf_1,d6_supinf_1,e2_25_7__supinf_1,e1_25__supinf_1,e2_25__supinf_1,d7_supinf_1,t2_supinf_1]),
    [interesting(0.65),file(supinf_1,e3_25_7__supinf_1),[file(supinf_1,e3_25_7__supinf_1)]]).

fof(i2_25_7__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i2_25_7__supinf_1)]),
    [interesting(0.65),trivial,file(supinf_1,i2_25_7__supinf_1)]).

fof(i1_25_7__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25_7__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[e3_25_7__supinf_1,i2_25_7__supinf_1]),
    [interesting(0.65),file(supinf_1,i1_25_7__supinf_1),[file(supinf_1,i1_25_7__supinf_1)]]).

fof(e9_25__supinf_1,plain,
    ( ( r2_hidden(c1_25__supinf_1,k1_numbers)
      & r2_hidden(c2_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1))
      & r2_hidden(c3_25__supinf_1,k2_tarski(k5_supinf_1,k4_supinf_1)) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25__supinf_1,e2_25__supinf_1]),discharge_asm(discharge,[e1_25_7__supinf_1])],[e1_25_7__supinf_1,i1_25_7__supinf_1]),
    [interesting(0.8),file(supinf_1,e9_25__supinf_1),[file(supinf_1,e9_25__supinf_1)]]).

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(e11_25__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[cc1_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,fc10_membered,fc11_membered,fc14_membered,fc15_membered,fc16_membered,fc9_membered,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,dt_k1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc12_membered,fc13_membered,fc1_xboole_0,fc24_membered,fc25_membered,fc26_membered,fc2_subset_1,fc6_membered,fc7_membered,fc8_membered,rc1_membered,rc1_xreal_0,rc3_supinf_1,t1_boole,existence_m1_subset_1,dt_k1_supinf_1,dt_k2_supinf_1,dt_k3_supinf_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_supinf_1,cc2_supinf_1,cc4_membered,fc22_membered,fc23_membered,fc2_xboole_0,fc3_xboole_0,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t8_boole,d1_supinf_1,d3_supinf_1,d6_supinf_1,commutativity_k2_tarski,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_supinf_1,connectedness_r1_supinf_1,antisymmetry_r2_hidden,redefinition_k4_supinf_1,redefinition_k5_supinf_1,dt_k1_numbers,dt_k2_tarski,dt_k2_xboole_0,dt_k4_supinf_1,dt_k5_supinf_1,dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,fc2_membered,fc3_subset_1,t1_subset,t7_boole,e10_25__supinf_1,e3_25__supinf_1,e4_25__supinf_1,e5_25__supinf_1,e6_25__supinf_1,e7_25__supinf_1,e8_25__supinf_1,e9_25__supinf_1,d2_xboole_0]),
    [interesting(0.8),file(supinf_1,e11_25__supinf_1),[file(supinf_1,e11_25__supinf_1)]]).

fof(i3_25__supinf_1,theorem,(
    $true ),
    introduced(tautology,[file(supinf_1,i3_25__supinf_1)]),
    [interesting(0.8),trivial,file(supinf_1,i3_25__supinf_1)]).

fof(i2_25__supinf_1,plain,(
    r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,e1_25__supinf_1,e2_25__supinf_1])],[e11_25__supinf_1,i3_25__supinf_1]),
    [interesting(0.8),file(supinf_1,i2_25__supinf_1),[file(supinf_1,i2_25__supinf_1)]]).

fof(i1_25__supinf_1,plain,
    ( ( r1_supinf_1(c1_25__supinf_1,c2_25__supinf_1)
      & r1_supinf_1(c2_25__supinf_1,c3_25__supinf_1) )
   => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1]),discharge_asm(discharge,[e1_25__supinf_1,e2_25__supinf_1])],[e1_25__supinf_1,e2_25__supinf_1,i2_25__supinf_1]),
    [interesting(0.8),file(supinf_1,i1_25__supinf_1),[file(supinf_1,i1_25__supinf_1)]]).

fof(i1_25_tmp__supinf_1,plain,
    ( ( m1_subset_1(c1_25__supinf_1,k3_supinf_1)
      & m1_subset_1(c2_25__supinf_1,k3_supinf_1)
      & m1_subset_1(c3_25__supinf_1,k3_supinf_1) )
   => ( ( r1_supinf_1(c1_25__supinf_1,c2_25__supinf_1)
        & r1_supinf_1(c2_25__supinf_1,c3_25__supinf_1) )
     => r1_supinf_1(c1_25__supinf_1,c3_25__supinf_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1])],[dt_c1_25__supinf_1,dt_c2_25__supinf_1,dt_c3_25__supinf_1,i1_25__supinf_1]),
    [interesting(1),t29_supinf_1]).

fof(t29_supinf_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ! [C] : 
              ( m1_subset_1(C,k3_supinf_1)
             => ( ( r1_supinf_1(A,B)
                  & r1_supinf_1(B,C) )
               => r1_supinf_1(A,C) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_25_tmp__supinf_1,dh_c1_25__supinf_1,dh_c2_25__supinf_1,dh_c3_25__supinf_1]),
    [interesting(1),file(supinf_1,t29_supinf_1),[file(supinf_1,t29_supinf_1)]]).