% Mizar ND problem: t1_altcat_2,altcat_2,34,52 
fof(dh_c1_1__altcat_2,definition,
    ( ! [A,B,C] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,B),k2_funcop_1(A,C)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,A),k4_tarski(B,C))
   => ! [D,E,F,G] : k15_funct_3(k2_funcop_1(D,F),k2_funcop_1(E,G)) = k2_funcop_1(k2_zfmisc_1(D,E),k4_tarski(F,G)) ),
    introduced(definition,[new_symbol(c1_1__altcat_2),file(altcat_2,c1_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c1_1__altcat_2)]).

fof(dh_c2_1__altcat_2,definition,
    ( ! [A,B] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,A),k2_funcop_1(c2_1__altcat_2,B)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(A,B))
   => ! [C,D,E] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,D),k2_funcop_1(C,E)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,C),k4_tarski(D,E)) ),
    introduced(definition,[new_symbol(c2_1__altcat_2),file(altcat_2,c2_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c2_1__altcat_2)]).

fof(dh_c3_1__altcat_2,definition,
    ( ! [A] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),k2_funcop_1(c2_1__altcat_2,A)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,A))
   => ! [B,C] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,B),k2_funcop_1(c2_1__altcat_2,C)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(B,C)) ),
    introduced(definition,[new_symbol(c3_1__altcat_2),file(altcat_2,c3_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c3_1__altcat_2)]).

fof(dh_c4_1__altcat_2,definition,
    ( k15_funct_3(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2))
   => ! [A] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),k2_funcop_1(c2_1__altcat_2,A)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,A)) ),
    introduced(definition,[new_symbol(c4_1__altcat_2),file(altcat_2,c4_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c4_1__altcat_2)]).

fof(rc1_pboole,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    [interesting(0.9),axiom,file(pboole,rc1_pboole)]).

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

fof(cc1_realset1,theorem,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    [interesting(0.9),axiom,file(realset1,cc1_realset1)]).

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(fc2_funcop_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc2_funcop_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(rc1_realset1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    [interesting(0.9),axiom,file(realset1,rc1_realset1)]).

fof(rc2_realset1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    [interesting(0.9),axiom,file(realset1,rc2_realset1)]).

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(rc5_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc5_funct_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(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_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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

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(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_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc3_funcop_1)]).

fof(fc3_realset1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    [interesting(0.9),axiom,file(realset1,fc3_realset1)]).

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(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(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(fc9_funcop_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc9_funcop_1)]).

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(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(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(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_k15_funct_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k15_funct_3(A,B))
        & v1_funct_1(k15_funct_3(A,B)) ) ) ),
    file(funct_3,k15_funct_3),
    [interesting(0.9),axiom,file(funct_3,k15_funct_3)]).

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_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k2_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,k2_funcop_1)]).

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

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

fof(dt_c1_1__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c1_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c1_1__altcat_2)]).

fof(dt_c2_1__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c2_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c2_1__altcat_2)]).

fof(dt_c3_1__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c3_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c3_1__altcat_2)]).

fof(dt_c4_1__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c4_1__altcat_2)]),
    [interesting(0.8),axiom,file(altcat_2,c4_1__altcat_2)]).

fof(fc1_funcop_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc1_funcop_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(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(d2_funcop_1,definition,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ),
    file(funcop_1,d2_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,d2_funcop_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(dh_c1_1_1__altcat_2,definition,
    ( ! [A] : 
        ( ( r2_hidden(c1_1_1__altcat_2,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
          & r2_hidden(A,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) )
       => k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(c1_1_1__altcat_2,A)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),A)) )
   => ! [B,C] : 
        ( ( r2_hidden(B,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
          & r2_hidden(C,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) )
       => k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(B,C)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),B),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),C)) ) ),
    introduced(definition,[new_symbol(c1_1_1__altcat_2),file(altcat_2,c1_1_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c1_1_1__altcat_2)]).

fof(dh_c2_1_1__altcat_2,definition,
    ( ( ( r2_hidden(c1_1_1__altcat_2,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
        & r2_hidden(c2_1_1__altcat_2,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) )
     => k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(c1_1_1__altcat_2,c2_1_1__altcat_2)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),c2_1_1__altcat_2)) )
   => ! [A] : 
        ( ( r2_hidden(c1_1_1__altcat_2,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
          & r2_hidden(A,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) )
       => k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(c1_1_1__altcat_2,A)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),A)) ) ),
    introduced(definition,[new_symbol(c2_1_1__altcat_2),file(altcat_2,c2_1_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c2_1_1__altcat_2)]).

fof(e1_1_1__altcat_2,assumption,
    ( r2_hidden(c1_1_1__altcat_2,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
    & r2_hidden(c2_1_1__altcat_2,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) ),
    introduced(assumption,[file(altcat_2,e1_1_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,e1_1_1__altcat_2)]).

fof(dt_c1_1_1__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c1_1_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c1_1_1__altcat_2)]).

fof(dt_c2_1_1__altcat_2,assumption,(
    $true ),
    introduced(assumption,[file(altcat_2,c2_1_1__altcat_2)]),
    [interesting(0.65),axiom,file(altcat_2,c2_1_1__altcat_2)]).

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(fc6_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => v1_setfam_1(k2_relat_1(A)) ) ),
    file(funct_1,fc6_funct_1),
    [interesting(0.9),axiom,file(funct_1,fc6_funct_1)]).

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(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(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_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(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(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_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(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t19_funcop_1)]).

fof(e1_1__altcat_2,plain,
    ( k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)) = c1_1__altcat_2
    & k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2)) = c2_1__altcat_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[rc1_pboole,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_altcat_1,fc12_relat_1,fc2_funcop_1,fc4_relat_1,fc6_funct_1,rc3_funct_1,rc5_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_realset1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc2_altcat_1,fc3_funcop_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_funcop_1,rc1_funct_1,rc1_realset1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_realset1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,fc1_funcop_1,fc2_subset_1,fc3_realset1,t3_subset,d2_funcop_1,t19_funcop_1]),
    [interesting(0.8),file(altcat_2,e1_1__altcat_2),[file(altcat_2,e1_1__altcat_2)]]).

fof(e2_1__altcat_2,plain,(
    k1_relat_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2))) = k2_zfmisc_1(k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)),k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[rc1_pboole,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,cc1_altcat_1,fc12_relat_1,fc2_funcop_1,fc4_relat_1,fc6_funct_1,rc3_funct_1,rc5_funct_1,t1_subset,t4_subset,t5_subset,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_realset1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc2_altcat_1,fc3_funcop_1,fc3_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_funcop_1,rc1_funct_1,rc1_realset1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_realset1,rc2_relat_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,fc1_funcop_1,fc2_subset_1,fc3_realset1,t3_subset,d2_funcop_1,d5_tarski,e1_1__altcat_2,t19_funcop_1]),
    [interesting(0.8),file(altcat_2,e2_1__altcat_2),[file(altcat_2,e2_1__altcat_2)]]).

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(e3_1_1__altcat_2,plain,(
    r2_hidden(k4_tarski(c1_1_1__altcat_2,c2_1_1__altcat_2),k1_relat_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,e1_1_1__altcat_2])],[rc1_pboole,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_realset1,fc12_relat_1,fc2_funcop_1,fc4_relat_1,rc1_realset1,rc2_realset1,rc3_funct_1,rc5_funct_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_altcat_1,fc2_subset_1,fc3_funcop_1,fc3_realset1,fc3_subset_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_funcop_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_1__altcat_2,dt_c1_1_1__altcat_2,dt_c2_1__altcat_2,dt_c2_1_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,fc1_funcop_1,t1_subset,t7_boole,d2_funcop_1,d5_tarski,e2_1__altcat_2,e1_1_1__altcat_2,t106_zfmisc_1]),
    [interesting(0.65),file(altcat_2,e3_1_1__altcat_2),[file(altcat_2,e3_1_1__altcat_2)]]).

fof(e4_1_1__altcat_2,plain,(
    r2_hidden(k4_tarski(c1_1_1__altcat_2,c2_1_1__altcat_2),k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,e1_1_1__altcat_2])],[rc1_pboole,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_altcat_1,fc12_relat_1,fc2_funcop_1,fc4_relat_1,fc6_funct_1,rc3_funct_1,rc5_funct_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_realset1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc1_subset_1,fc2_altcat_1,fc3_funcop_1,fc3_subset_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_funcop_1,rc1_funct_1,rc1_realset1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_realset1,rc2_relat_1,rc2_subset_1,t2_subset,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_relat_1,dt_k1_tarski,dt_k2_funcop_1,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_1__altcat_2,dt_c1_1_1__altcat_2,dt_c2_1__altcat_2,dt_c2_1_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,fc1_funcop_1,fc2_subset_1,fc3_realset1,t1_subset,t3_subset,t7_boole,d2_funcop_1,d5_tarski,e3_1_1__altcat_2,t19_funcop_1]),
    [interesting(0.65),file(altcat_2,e4_1_1__altcat_2),[file(altcat_2,e4_1_1__altcat_2)]]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,t13_funcop_1)]).

fof(e2_1_1__altcat_2,plain,
    ( k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2) = c3_1__altcat_2
    & k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),c2_1_1__altcat_2) = c4_1__altcat_2 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2,e1_1_1__altcat_2,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[rc1_pboole,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_realset1,fc12_relat_1,fc2_funcop_1,fc4_relat_1,rc1_realset1,rc2_realset1,rc3_funct_1,rc5_funct_1,existence_m1_subset_1,dt_k1_tarski,dt_k2_zfmisc_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_altcat_1,fc2_subset_1,fc3_funcop_1,fc3_realset1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_funcop_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funcop_1,dt_c1_1__altcat_2,dt_c1_1_1__altcat_2,dt_c2_1__altcat_2,dt_c2_1_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,fc1_funcop_1,t1_subset,t7_boole,d2_funcop_1,e1_1_1__altcat_2,e1_1__altcat_2,t13_funcop_1]),
    [interesting(0.65),file(altcat_2,e2_1_1__altcat_2),[file(altcat_2,e2_1_1__altcat_2)]]).

fof(e5_1_1__altcat_2,plain,(
    k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(c1_1_1__altcat_2,c2_1_1__altcat_2)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),c2_1_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2,e1_1_1__altcat_2,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[rc1_pboole,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_realset1,fc12_relat_1,fc2_funcop_1,fc4_relat_1,rc1_realset1,rc2_realset1,rc3_funct_1,rc5_funct_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_altcat_1,fc2_subset_1,fc3_funcop_1,fc3_realset1,fc3_subset_1,fc4_subset_1,fc9_funcop_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_funct_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_1__altcat_2,dt_c1_1_1__altcat_2,dt_c2_1__altcat_2,dt_c2_1_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,fc1_funcop_1,t1_subset,t7_boole,d2_funcop_1,d5_tarski,e4_1_1__altcat_2,e2_1_1__altcat_2,t13_funcop_1]),
    [interesting(0.65),file(altcat_2,e5_1_1__altcat_2),[file(altcat_2,e5_1_1__altcat_2)]]).

fof(i3_1_1__altcat_2,theorem,(
    $true ),
    introduced(tautology,[file(altcat_2,i3_1_1__altcat_2)]),
    [interesting(0.65),trivial,file(altcat_2,i3_1_1__altcat_2)]).

fof(i2_1_1__altcat_2,plain,(
    k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(c1_1_1__altcat_2,c2_1_1__altcat_2)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),c2_1_1__altcat_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2,e1_1_1__altcat_2,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[e5_1_1__altcat_2,i3_1_1__altcat_2]),
    [interesting(0.65),file(altcat_2,i2_1_1__altcat_2),[file(altcat_2,i2_1_1__altcat_2)]]).

fof(i1_1_1__altcat_2,plain,
    ( ( r2_hidden(c1_1_1__altcat_2,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
      & r2_hidden(c2_1_1__altcat_2,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) )
   => k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(c1_1_1__altcat_2,c2_1_1__altcat_2)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),c2_1_1__altcat_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2]),discharge_asm(discharge,[e1_1_1__altcat_2])],[e1_1_1__altcat_2,i2_1_1__altcat_2]),
    [interesting(0.65),file(altcat_2,i1_1_1__altcat_2),[file(altcat_2,i1_1_1__altcat_2)]]).

fof(i1_1_1_tmp__altcat_2,plain,
    ( ( r2_hidden(c1_1_1__altcat_2,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
      & r2_hidden(c2_1_1__altcat_2,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) )
   => k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(c1_1_1__altcat_2,c2_1_1__altcat_2)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),c1_1_1__altcat_2),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),c2_1_1__altcat_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2]),discharge_asm(discharge,[dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2])],[dt_c1_1_1__altcat_2,dt_c2_1_1__altcat_2,i1_1_1__altcat_2]),
    [interesting(0.8),e3_1__altcat_2]).

fof(e3_1__altcat_2,plain,(
    ! [A,B] : 
      ( ( r2_hidden(A,k1_relat_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2)))
        & r2_hidden(B,k1_relat_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2))) )
     => k1_funct_1(k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)),k4_tarski(A,B)) = k4_tarski(k1_funct_1(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),A),k1_funct_1(k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2),B)) ) ),
    inference(let,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[i1_1_1_tmp__altcat_2,dh_c1_1_1__altcat_2,dh_c2_1_1__altcat_2]),
    [interesting(0.8),file(altcat_2,e3_1__altcat_2),[file(altcat_2,e3_1__altcat_2)]]).

fof(d9_funct_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k15_funct_3(A,B)
              <=> ( k1_relat_1(C) = k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))
                  & ! [D,E] : 
                      ( ( r2_hidden(D,k1_relat_1(A))
                        & r2_hidden(E,k1_relat_1(B)) )
                     => k1_funct_1(C,k4_tarski(D,E)) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)) ) ) ) ) ) ) ),
    file(funct_3,d9_funct_3),
    [interesting(0.9),axiom,file(funct_3,d9_funct_3)]).

fof(e4_1__altcat_2,plain,(
    k15_funct_3(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[rc1_pboole,rc3_relat_1,rc4_funct_1,dt_k1_xboole_0,cc1_realset1,fc12_relat_1,fc2_funcop_1,fc4_relat_1,rc1_realset1,rc2_realset1,rc3_funct_1,rc5_funct_1,commutativity_k2_tarski,existence_m1_subset_1,dt_k1_tarski,dt_k2_tarski,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc2_altcat_1,fc2_subset_1,fc3_funcop_1,fc3_realset1,fc3_subset_1,fc4_subset_1,fc5_relat_1,fc7_relat_1,fc9_funcop_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k15_funct_3,dt_k1_funct_1,dt_k1_relat_1,dt_k2_funcop_1,dt_k2_zfmisc_1,dt_k4_tarski,dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2,fc1_funcop_1,rc1_funct_1,t1_subset,t7_boole,d2_funcop_1,d5_tarski,e3_1__altcat_2,e2_1__altcat_2,d9_funct_3]),
    [interesting(0.8),file(altcat_2,e4_1__altcat_2),[file(altcat_2,e4_1__altcat_2)]]).

fof(i3_1__altcat_2,theorem,(
    $true ),
    introduced(tautology,[file(altcat_2,i3_1__altcat_2)]),
    [interesting(0.8),trivial,file(altcat_2,i3_1__altcat_2)]).

fof(i2_1__altcat_2,plain,(
    k15_funct_3(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)) ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2,dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[e4_1__altcat_2,i3_1__altcat_2]),
    [interesting(0.8),file(altcat_2,i2_1__altcat_2),[file(altcat_2,i2_1__altcat_2)]]).

fof(i2_1_tmp__altcat_2,plain,(
    k15_funct_3(k2_funcop_1(c1_1__altcat_2,c3_1__altcat_2),k2_funcop_1(c2_1__altcat_2,c4_1__altcat_2)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(c3_1__altcat_2,c4_1__altcat_2)) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2]),discharge_asm(discharge,[dt_c3_1__altcat_2,dt_c4_1__altcat_2])],[dt_c3_1__altcat_2,dt_c4_1__altcat_2,i2_1__altcat_2]),
    [interesting(0.8),i1_1__altcat_2]).

fof(i1_1__altcat_2,plain,(
    ! [A,B] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,A),k2_funcop_1(c2_1__altcat_2,B)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(A,B)) ),
    inference(let,[status(thm),assumptions([dt_c1_1__altcat_2,dt_c2_1__altcat_2])],[i2_1_tmp__altcat_2,dh_c3_1__altcat_2,dh_c4_1__altcat_2]),
    [interesting(0.8),file(altcat_2,i1_1__altcat_2),[file(altcat_2,i1_1__altcat_2)]]).

fof(i1_1_tmp__altcat_2,plain,(
    ! [A,B] : k15_funct_3(k2_funcop_1(c1_1__altcat_2,A),k2_funcop_1(c2_1__altcat_2,B)) = k2_funcop_1(k2_zfmisc_1(c1_1__altcat_2,c2_1__altcat_2),k4_tarski(A,B)) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__altcat_2,dt_c2_1__altcat_2])],[dt_c1_1__altcat_2,dt_c2_1__altcat_2,i1_1__altcat_2]),
    [interesting(1),t1_altcat_2]).

fof(t1_altcat_2,theorem,(
    ! [A,B,C,D] : k15_funct_3(k2_funcop_1(A,C),k2_funcop_1(B,D)) = k2_funcop_1(k2_zfmisc_1(A,B),k4_tarski(C,D)) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__altcat_2,dh_c1_1__altcat_2,dh_c2_1__altcat_2]),
    [interesting(1),file(altcat_2,t1_altcat_2),[file(altcat_2,t1_altcat_2)]]).