% Mizar ND problem: t7_altcat_1,altcat_1,118,28 
fof(dh_c1_8__altcat_1,definition,
    ( ! [A,B] : 
        ( m1_pboole(B,k2_zfmisc_1(A,c1_8__altcat_1))
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(c1_8__altcat_1))
           => ! [D] : 
                ( m1_subset_1(D,k1_zfmisc_1(A))
               => ! [E,F] : 
                    ( ( r2_hidden(E,C)
                      & r2_hidden(F,D) )
                   => k1_binop_1(B,F,E) = k1_binop_1(k7_relat_1(B,k12_mcart_1(A,c1_8__altcat_1,D,C)),F,E) ) ) ) )
   => ! [G,H,I] : 
        ( m1_pboole(I,k2_zfmisc_1(H,G))
       => ! [J] : 
            ( m1_subset_1(J,k1_zfmisc_1(G))
           => ! [K] : 
                ( m1_subset_1(K,k1_zfmisc_1(H))
               => ! [L,M] : 
                    ( ( r2_hidden(L,J)
                      & r2_hidden(M,K) )
                   => k1_binop_1(I,M,L) = k1_binop_1(k7_relat_1(I,k12_mcart_1(H,G,K,J)),M,L) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_8__altcat_1),file(altcat_1,c1_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c1_8__altcat_1)]).

fof(dh_c2_8__altcat_1,definition,
    ( ! [A] : 
        ( m1_pboole(A,k2_zfmisc_1(c2_8__altcat_1,c1_8__altcat_1))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(c1_8__altcat_1))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(c2_8__altcat_1))
               => ! [D,E] : 
                    ( ( r2_hidden(D,B)
                      & r2_hidden(E,C) )
                   => k1_binop_1(A,E,D) = k1_binop_1(k7_relat_1(A,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,C,B)),E,D) ) ) ) )
   => ! [F,G] : 
        ( m1_pboole(G,k2_zfmisc_1(F,c1_8__altcat_1))
       => ! [H] : 
            ( m1_subset_1(H,k1_zfmisc_1(c1_8__altcat_1))
           => ! [I] : 
                ( m1_subset_1(I,k1_zfmisc_1(F))
               => ! [J,K] : 
                    ( ( r2_hidden(J,H)
                      & r2_hidden(K,I) )
                   => k1_binop_1(G,K,J) = k1_binop_1(k7_relat_1(G,k12_mcart_1(F,c1_8__altcat_1,I,H)),K,J) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_8__altcat_1),file(altcat_1,c2_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c2_8__altcat_1)]).

fof(dh_c3_8__altcat_1,definition,
    ( ( m1_pboole(c3_8__altcat_1,k2_zfmisc_1(c2_8__altcat_1,c1_8__altcat_1))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c1_8__altcat_1))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(c2_8__altcat_1))
             => ! [C,D] : 
                  ( ( r2_hidden(C,A)
                    & r2_hidden(D,B) )
                 => k1_binop_1(c3_8__altcat_1,D,C) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,B,A)),D,C) ) ) ) )
   => ! [E] : 
        ( m1_pboole(E,k2_zfmisc_1(c2_8__altcat_1,c1_8__altcat_1))
       => ! [F] : 
            ( m1_subset_1(F,k1_zfmisc_1(c1_8__altcat_1))
           => ! [G] : 
                ( m1_subset_1(G,k1_zfmisc_1(c2_8__altcat_1))
               => ! [H,I] : 
                    ( ( r2_hidden(H,F)
                      & r2_hidden(I,G) )
                   => k1_binop_1(E,I,H) = k1_binop_1(k7_relat_1(E,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,G,F)),I,H) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_8__altcat_1),file(altcat_1,c3_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c3_8__altcat_1)]).

fof(dh_c4_8__altcat_1,definition,
    ( ( m1_subset_1(c4_8__altcat_1,k1_zfmisc_1(c1_8__altcat_1))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(c2_8__altcat_1))
         => ! [B,C] : 
              ( ( r2_hidden(B,c4_8__altcat_1)
                & r2_hidden(C,A) )
             => k1_binop_1(c3_8__altcat_1,C,B) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,A,c4_8__altcat_1)),C,B) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,k1_zfmisc_1(c1_8__altcat_1))
       => ! [E] : 
            ( m1_subset_1(E,k1_zfmisc_1(c2_8__altcat_1))
           => ! [F,G] : 
                ( ( r2_hidden(F,D)
                  & r2_hidden(G,E) )
               => k1_binop_1(c3_8__altcat_1,G,F) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,E,D)),G,F) ) ) ) ),
    introduced(definition,[new_symbol(c4_8__altcat_1),file(altcat_1,c4_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c4_8__altcat_1)]).

fof(dh_c5_8__altcat_1,definition,
    ( ( m1_subset_1(c5_8__altcat_1,k1_zfmisc_1(c2_8__altcat_1))
     => ! [A,B] : 
          ( ( r2_hidden(A,c4_8__altcat_1)
            & r2_hidden(B,c5_8__altcat_1) )
         => k1_binop_1(c3_8__altcat_1,B,A) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),B,A) ) )
   => ! [C] : 
        ( m1_subset_1(C,k1_zfmisc_1(c2_8__altcat_1))
       => ! [D,E] : 
            ( ( r2_hidden(D,c4_8__altcat_1)
              & r2_hidden(E,C) )
           => k1_binop_1(c3_8__altcat_1,E,D) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,C,c4_8__altcat_1)),E,D) ) ) ),
    introduced(definition,[new_symbol(c5_8__altcat_1),file(altcat_1,c5_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c5_8__altcat_1)]).

fof(dh_c6_8__altcat_1,definition,
    ( ! [A] : 
        ( ( r2_hidden(c6_8__altcat_1,c4_8__altcat_1)
          & r2_hidden(A,c5_8__altcat_1) )
       => k1_binop_1(c3_8__altcat_1,A,c6_8__altcat_1) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),A,c6_8__altcat_1) )
   => ! [B,C] : 
        ( ( r2_hidden(B,c4_8__altcat_1)
          & r2_hidden(C,c5_8__altcat_1) )
       => k1_binop_1(c3_8__altcat_1,C,B) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),C,B) ) ),
    introduced(definition,[new_symbol(c6_8__altcat_1),file(altcat_1,c6_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c6_8__altcat_1)]).

fof(dh_c7_8__altcat_1,definition,
    ( ( ( r2_hidden(c6_8__altcat_1,c4_8__altcat_1)
        & r2_hidden(c7_8__altcat_1,c5_8__altcat_1) )
     => k1_binop_1(c3_8__altcat_1,c7_8__altcat_1,c6_8__altcat_1) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),c7_8__altcat_1,c6_8__altcat_1) )
   => ! [A] : 
        ( ( r2_hidden(c6_8__altcat_1,c4_8__altcat_1)
          & r2_hidden(A,c5_8__altcat_1) )
       => k1_binop_1(c3_8__altcat_1,A,c6_8__altcat_1) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),A,c6_8__altcat_1) ) ),
    introduced(definition,[new_symbol(c7_8__altcat_1),file(altcat_1,c7_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c7_8__altcat_1)]).

fof(e1_8__altcat_1,assumption,
    ( r2_hidden(c6_8__altcat_1,c4_8__altcat_1)
    & r2_hidden(c7_8__altcat_1,c5_8__altcat_1) ),
    introduced(assumption,[file(altcat_1,e1_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,e1_8__altcat_1)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc1_fraenkel,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,cc1_fraenkel)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

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(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_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_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(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(fc4_subset_1,theorem,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]).

fof(rc1_fraenkel,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    [interesting(0.9),axiom,file(fraenkel,rc1_fraenkel)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc1_tex_2,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(tex_2,rc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc1_tex_2)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

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(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(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(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(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    [interesting(0.9),axiom,file(pboole,m1_pboole)]).

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

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

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_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    [interesting(0.9),axiom,file(pboole,m1_pboole)]).

fof(dt_c1_8__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c1_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c1_8__altcat_1)]).

fof(dt_c2_8__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c2_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c2_8__altcat_1)]).

fof(fc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_realset1(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(tex_2,fc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,fc1_tex_2)]).

fof(fc2_altcat_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v1_fraenkel(k1_tarski(A))
        & v1_realset1(k1_tarski(A)) ) ) ),
    file(altcat_1,fc2_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,fc2_altcat_1)]).

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(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(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    [interesting(0.9),axiom,file(binop_1,k1_binop_1)]).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

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

fof(dt_c3_8__altcat_1,assumption,(
    m1_pboole(c3_8__altcat_1,k2_zfmisc_1(c2_8__altcat_1,c1_8__altcat_1)) ),
    introduced(assumption,[file(altcat_1,c3_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c3_8__altcat_1)]).

fof(dt_c6_8__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c6_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c6_8__altcat_1)]).

fof(dt_c7_8__altcat_1,assumption,(
    $true ),
    introduced(assumption,[file(altcat_1,c7_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c7_8__altcat_1)]).

fof(d1_binop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    [interesting(0.9),axiom,file(binop_1,d1_binop_1)]).

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(e1_8_1__altcat_1,plain,(
    k1_binop_1(c3_8__altcat_1,c7_8__altcat_1,c6_8__altcat_1) = k1_funct_1(c3_8__altcat_1,k4_tarski(c7_8__altcat_1,c6_8__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1])],[existence_m1_subset_1,dt_m1_subset_1,cc1_fraenkel,rc3_relat_1,rc4_funct_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc4_relat_1,rc3_funct_1,t1_subset,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc4_subset_1,rc1_fraenkel,rc1_relat_1,rc1_tex_2,rc2_funct_1,rc2_relat_1,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,existence_m1_pboole,dt_k1_tarski,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_pboole,dt_c1_8__altcat_1,dt_c2_8__altcat_1,fc1_tex_2,fc2_altcat_1,fc2_subset_1,fc3_subset_1,rc1_funct_1,dt_k1_binop_1,dt_k1_funct_1,dt_k4_tarski,dt_c3_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1,d1_binop_1,d5_tarski]),
    [interesting(0.65),file(altcat_1,e1_8_1__altcat_1),[file(altcat_1,e1_8_1__altcat_1)]]).

fof(fc13_relat_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v3_relat_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v3_relat_1(k7_relat_1(A,B)) ) ) ),
    file(relat_1,fc13_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc13_relat_1)]).

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

fof(cc1_altcat_1,theorem,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    [interesting(0.9),axiom,file(altcat_1,cc1_altcat_1)]).

fof(cc1_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_tex_2(B,k1_zfmisc_1(A))
           => ~ v1_xboole_0(B) ) ) ) ),
    file(tex_2,cc1_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc1_tex_2)]).

fof(cc3_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_tex_2(B,k1_zfmisc_1(A))
           => ( v1_xboole_0(B)
              & v1_membered(B)
              & v2_membered(B)
              & v3_membered(B)
              & v4_membered(B)
              & v5_membered(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc3_tex_2)]).

fof(cc4_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ~ v1_xboole_0(B)
           => ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc4_tex_2)]).

fof(cc5_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & v1_realset1(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc5_tex_2)]).

fof(cc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & v1_realset1(B) )
           => ( ~ v1_xboole_0(B)
              & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ) ),
    file(tex_2,cc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc6_tex_2)]).

fof(cc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( ( ~ v1_xboole_0(B)
              & ~ v1_tex_2(B,k1_zfmisc_1(A)) )
           => ( ~ v1_xboole_0(B)
              & ~ v1_realset1(B) ) ) ) ) ),
    file(tex_2,cc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc7_tex_2)]).

fof(rc2_tex_2,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ),
    file(tex_2,rc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc2_tex_2)]).

fof(rc3_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc3_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc3_tex_2)]).

fof(rc4_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc4_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc4_tex_2)]).

fof(rc5_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B) ) ) ),
    file(tex_2,rc5_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc5_tex_2)]).

fof(rc6_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_realset1(B)
          & v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc6_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc6_tex_2)]).

fof(rc7_tex_2,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & ~ v1_realset1(B)
          & ~ v1_tex_2(B,k1_zfmisc_1(A)) ) ) ),
    file(tex_2,rc7_tex_2),
    [interesting(0.9),axiom,file(tex_2,rc7_tex_2)]).

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

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(cc2_tex_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_xboole_0(B)
           => v1_tex_2(B,k1_zfmisc_1(A)) ) ) ) ),
    file(tex_2,cc2_tex_2),
    [interesting(0.9),axiom,file(tex_2,cc2_tex_2)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

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(redefinition_k12_mcart_1,definition,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ),
    file(mcart_1,k12_mcart_1),
    [interesting(0.9),axiom,file(mcart_1,k12_mcart_1)]).

fof(dt_k12_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k1_zfmisc_1(A))
        & m1_subset_1(D,k1_zfmisc_1(B)) )
     => m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(mcart_1,k12_mcart_1),
    [interesting(0.9),axiom,file(mcart_1,k12_mcart_1)]).

fof(dt_k7_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k7_relat_1(A,B)) ) ),
    file(relat_1,k7_relat_1),
    [interesting(0.9),axiom,file(relat_1,k7_relat_1)]).

fof(dt_c4_8__altcat_1,assumption,(
    m1_subset_1(c4_8__altcat_1,k1_zfmisc_1(c1_8__altcat_1)) ),
    introduced(assumption,[file(altcat_1,c4_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c4_8__altcat_1)]).

fof(dt_c5_8__altcat_1,assumption,(
    m1_subset_1(c5_8__altcat_1,k1_zfmisc_1(c2_8__altcat_1)) ),
    introduced(assumption,[file(altcat_1,c5_8__altcat_1)]),
    [interesting(0.8),axiom,file(altcat_1,c5_8__altcat_1)]).

fof(fc4_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_funct_1(k7_relat_1(A,B)) ) ) ),
    file(funct_1,fc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc4_funct_1)]).

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(e2_8__altcat_1,plain,(
    r2_hidden(k4_tarski(c7_8__altcat_1,c6_8__altcat_1),k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1,e1_8__altcat_1])],[cc1_altcat_1,cc1_fraenkel,rc1_fraenkel,rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_tex_2,cc2_funct_1,cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,fc12_relat_1,fc2_altcat_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc1_tex_2,rc2_funct_1,rc2_relat_1,rc2_tex_2,rc3_tex_2,rc4_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_tex_2,fc1_subset_1,fc1_tex_2,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_mcart_1,dt_k12_mcart_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1,t1_subset,t7_boole,d5_tarski,e1_8__altcat_1,t106_zfmisc_1]),
    [interesting(0.8),file(altcat_1,e2_8__altcat_1),[file(altcat_1,e2_8__altcat_1)]]).

fof(t72_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    [interesting(0.9),axiom,file(funct_1,t72_funct_1)]).

fof(e2_8_1__altcat_1,plain,(
    k1_funct_1(c3_8__altcat_1,k4_tarski(c7_8__altcat_1,c6_8__altcat_1)) = k1_funct_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),k4_tarski(c7_8__altcat_1,c6_8__altcat_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_8__altcat_1,dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1,e1_8__altcat_1])],[fc13_relat_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_altcat_1,cc1_fraenkel,cc1_tex_2,cc3_tex_2,cc4_tex_2,cc5_tex_2,cc6_tex_2,cc7_tex_2,fc12_relat_1,fc4_relat_1,rc1_fraenkel,rc1_tex_2,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,rc5_tex_2,rc6_tex_2,rc7_tex_2,commutativity_k2_tarski,existence_m1_pboole,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_pboole,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_tex_2,fc1_subset_1,fc1_tex_2,fc2_altcat_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k12_mcart_1,dt_k12_mcart_1,dt_k1_funct_1,dt_k4_tarski,dt_k7_relat_1,dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1,fc4_funct_1,rc1_funct_1,t1_subset,t7_boole,d5_tarski,e2_8__altcat_1,t72_funct_1]),
    [interesting(0.65),file(altcat_1,e2_8_1__altcat_1),[file(altcat_1,e2_8_1__altcat_1)]]).

fof(e3_8_1__altcat_1,plain,(
    k1_funct_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),k4_tarski(c7_8__altcat_1,c6_8__altcat_1)) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),c7_8__altcat_1,c6_8__altcat_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1])],[fc13_relat_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_tex_2,cc3_tex_2,cc5_tex_2,cc7_tex_2,fc12_relat_1,fc4_relat_1,rc2_tex_2,rc3_funct_1,rc3_tex_2,rc4_tex_2,rc6_tex_2,rc7_tex_2,t1_subset,t4_subset,t5_subset,reflexivity_r1_tarski,cc1_altcat_1,cc1_fraenkel,cc1_funct_1,cc1_relat_1,cc2_funct_1,cc2_tex_2,cc4_tex_2,cc6_tex_2,fc4_subset_1,rc1_fraenkel,rc1_relat_1,rc1_subset_1,rc1_tex_2,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc5_tex_2,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,existence_m1_pboole,existence_m1_subset_1,dt_k1_tarski,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_m1_pboole,dt_m1_subset_1,cc1_relset_1,fc1_subset_1,fc1_tex_2,fc2_altcat_1,fc2_subset_1,fc3_subset_1,fc4_funct_1,rc1_funct_1,t3_subset,redefinition_k12_mcart_1,dt_k12_mcart_1,dt_k1_binop_1,dt_k1_funct_1,dt_k4_tarski,dt_k7_relat_1,dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1,d1_binop_1,d5_tarski]),
    [interesting(0.65),file(altcat_1,e3_8_1__altcat_1),[file(altcat_1,e3_8_1__altcat_1)]]).

fof(e3_8__altcat_1,plain,(
    k1_binop_1(c3_8__altcat_1,c7_8__altcat_1,c6_8__altcat_1) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),c7_8__altcat_1,c6_8__altcat_1) ),
    inference(iterative_eq,[status(thm),assumptions([e1_8__altcat_1,dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1])],[e1_8_1__altcat_1,e2_8_1__altcat_1,e3_8_1__altcat_1]),
    [interesting(0.8),file(altcat_1,e3_8__altcat_1),[file(altcat_1,e3_8__altcat_1)]]).

fof(i7_8__altcat_1,theorem,(
    $true ),
    introduced(tautology,[file(altcat_1,i7_8__altcat_1)]),
    [interesting(0.8),trivial,file(altcat_1,i7_8__altcat_1)]).

fof(i6_8__altcat_1,plain,(
    k1_binop_1(c3_8__altcat_1,c7_8__altcat_1,c6_8__altcat_1) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),c7_8__altcat_1,c6_8__altcat_1) ),
    inference(conclusion,[status(thm),assumptions([e1_8__altcat_1,dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1])],[e3_8__altcat_1,i7_8__altcat_1]),
    [interesting(0.8),file(altcat_1,i6_8__altcat_1),[file(altcat_1,i6_8__altcat_1)]]).

fof(i5_8__altcat_1,plain,
    ( ( r2_hidden(c6_8__altcat_1,c4_8__altcat_1)
      & r2_hidden(c7_8__altcat_1,c5_8__altcat_1) )
   => k1_binop_1(c3_8__altcat_1,c7_8__altcat_1,c6_8__altcat_1) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),c7_8__altcat_1,c6_8__altcat_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1,dt_c6_8__altcat_1,dt_c7_8__altcat_1]),discharge_asm(discharge,[e1_8__altcat_1])],[e1_8__altcat_1,i6_8__altcat_1]),
    [interesting(0.8),file(altcat_1,i5_8__altcat_1),[file(altcat_1,i5_8__altcat_1)]]).

fof(i5_8_tmp__altcat_1,plain,
    ( ( r2_hidden(c6_8__altcat_1,c4_8__altcat_1)
      & r2_hidden(c7_8__altcat_1,c5_8__altcat_1) )
   => k1_binop_1(c3_8__altcat_1,c7_8__altcat_1,c6_8__altcat_1) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),c7_8__altcat_1,c6_8__altcat_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1]),discharge_asm(discharge,[dt_c6_8__altcat_1,dt_c7_8__altcat_1])],[dt_c6_8__altcat_1,dt_c7_8__altcat_1,i5_8__altcat_1]),
    [interesting(0.8),i4_8__altcat_1]).

fof(i4_8__altcat_1,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,c4_8__altcat_1)
        & r2_hidden(B,c5_8__altcat_1) )
     => k1_binop_1(c3_8__altcat_1,B,A) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),B,A) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1,dt_c5_8__altcat_1])],[i5_8_tmp__altcat_1,dh_c6_8__altcat_1,dh_c7_8__altcat_1]),
    [interesting(0.8),file(altcat_1,i4_8__altcat_1),[file(altcat_1,i4_8__altcat_1)]]).

fof(i4_8_tmp__altcat_1,plain,
    ( m1_subset_1(c5_8__altcat_1,k1_zfmisc_1(c2_8__altcat_1))
   => ! [A,B] : 
        ( ( r2_hidden(A,c4_8__altcat_1)
          & r2_hidden(B,c5_8__altcat_1) )
       => k1_binop_1(c3_8__altcat_1,B,A) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,c5_8__altcat_1,c4_8__altcat_1)),B,A) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1]),discharge_asm(discharge,[dt_c5_8__altcat_1])],[dt_c5_8__altcat_1,i4_8__altcat_1]),
    [interesting(0.8),i3_8__altcat_1]).

fof(i3_8__altcat_1,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c2_8__altcat_1))
     => ! [B,C] : 
          ( ( r2_hidden(B,c4_8__altcat_1)
            & r2_hidden(C,A) )
         => k1_binop_1(c3_8__altcat_1,C,B) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,A,c4_8__altcat_1)),C,B) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1,dt_c4_8__altcat_1])],[i4_8_tmp__altcat_1,dh_c5_8__altcat_1]),
    [interesting(0.8),file(altcat_1,i3_8__altcat_1),[file(altcat_1,i3_8__altcat_1)]]).

fof(i3_8_tmp__altcat_1,plain,
    ( m1_subset_1(c4_8__altcat_1,k1_zfmisc_1(c1_8__altcat_1))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c2_8__altcat_1))
       => ! [B,C] : 
            ( ( r2_hidden(B,c4_8__altcat_1)
              & r2_hidden(C,A) )
           => k1_binop_1(c3_8__altcat_1,C,B) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,A,c4_8__altcat_1)),C,B) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1]),discharge_asm(discharge,[dt_c4_8__altcat_1])],[dt_c4_8__altcat_1,i3_8__altcat_1]),
    [interesting(0.8),i2_8__altcat_1]).

fof(i2_8__altcat_1,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(c1_8__altcat_1))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c2_8__altcat_1))
         => ! [C,D] : 
              ( ( r2_hidden(C,A)
                & r2_hidden(D,B) )
             => k1_binop_1(c3_8__altcat_1,D,C) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,B,A)),D,C) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1,dt_c3_8__altcat_1])],[i3_8_tmp__altcat_1,dh_c4_8__altcat_1]),
    [interesting(0.8),file(altcat_1,i2_8__altcat_1),[file(altcat_1,i2_8__altcat_1)]]).

fof(i2_8_tmp__altcat_1,plain,
    ( m1_pboole(c3_8__altcat_1,k2_zfmisc_1(c2_8__altcat_1,c1_8__altcat_1))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(c1_8__altcat_1))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(c2_8__altcat_1))
           => ! [C,D] : 
                ( ( r2_hidden(C,A)
                  & r2_hidden(D,B) )
               => k1_binop_1(c3_8__altcat_1,D,C) = k1_binop_1(k7_relat_1(c3_8__altcat_1,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,B,A)),D,C) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1]),discharge_asm(discharge,[dt_c3_8__altcat_1])],[dt_c3_8__altcat_1,i2_8__altcat_1]),
    [interesting(0.8),i1_8__altcat_1]).

fof(i1_8__altcat_1,plain,(
    ! [A] : 
      ( m1_pboole(A,k2_zfmisc_1(c2_8__altcat_1,c1_8__altcat_1))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c1_8__altcat_1))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(c2_8__altcat_1))
             => ! [D,E] : 
                  ( ( r2_hidden(D,B)
                    & r2_hidden(E,C) )
                 => k1_binop_1(A,E,D) = k1_binop_1(k7_relat_1(A,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,C,B)),E,D) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_8__altcat_1,dt_c2_8__altcat_1])],[i2_8_tmp__altcat_1,dh_c3_8__altcat_1]),
    [interesting(0.8),file(altcat_1,i1_8__altcat_1),[file(altcat_1,i1_8__altcat_1)]]).

fof(i1_8_tmp__altcat_1,plain,(
    ! [A] : 
      ( m1_pboole(A,k2_zfmisc_1(c2_8__altcat_1,c1_8__altcat_1))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(c1_8__altcat_1))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(c2_8__altcat_1))
             => ! [D,E] : 
                  ( ( r2_hidden(D,B)
                    & r2_hidden(E,C) )
                 => k1_binop_1(A,E,D) = k1_binop_1(k7_relat_1(A,k12_mcart_1(c2_8__altcat_1,c1_8__altcat_1,C,B)),E,D) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_8__altcat_1,dt_c2_8__altcat_1])],[dt_c1_8__altcat_1,dt_c2_8__altcat_1,i1_8__altcat_1]),
    [interesting(1),t7_altcat_1]).

fof(t7_altcat_1,theorem,(
    ! [A,B,C] : 
      ( m1_pboole(C,k2_zfmisc_1(B,A))
     => ! [D] : 
          ( m1_subset_1(D,k1_zfmisc_1(A))
         => ! [E] : 
              ( m1_subset_1(E,k1_zfmisc_1(B))
             => ! [F,G] : 
                  ( ( r2_hidden(F,D)
                    & r2_hidden(G,E) )
                 => k1_binop_1(C,G,F) = k1_binop_1(k7_relat_1(C,k12_mcart_1(B,A,E,D)),G,F) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_8_tmp__altcat_1,dh_c1_8__altcat_1,dh_c2_8__altcat_1]),
    [interesting(1),file(altcat_1,t7_altcat_1),[file(altcat_1,t7_altcat_1)]]).