% Mizar ND problem: t5_extens_1,extens_1,80,12 
fof(dh_c1_3__extens_1,definition,
    ( ! [A] : 
        ( m1_pboole(A,c1_3__extens_1)
       => ! [B] : 
            ( ( v2_relat_1(B)
              & m1_pboole(B,c1_3__extens_1) )
           => ! [C] : 
                ( m3_pboole(C,c1_3__extens_1,A,B)
               => ! [D] : 
                    ( m4_pboole(D,c1_3__extens_1,A)
                   => ( r2_pboole(c1_3__extens_1,A,D)
                     => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,A,B,D,C),C) ) ) ) ) )
   => ! [E,F] : 
        ( m1_pboole(F,E)
       => ! [G] : 
            ( ( v2_relat_1(G)
              & m1_pboole(G,E) )
           => ! [H] : 
                ( m3_pboole(H,E,F,G)
               => ! [I] : 
                    ( m4_pboole(I,E,F)
                   => ( r2_pboole(E,F,I)
                     => r6_pboole(E,k1_msafree(E,F,G,I,H),H) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_3__extens_1),file(extens_1,c1_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c1_3__extens_1)]).

fof(dh_c2_3__extens_1,definition,
    ( ( m1_pboole(c2_3__extens_1,c1_3__extens_1)
     => ! [A] : 
          ( ( v2_relat_1(A)
            & m1_pboole(A,c1_3__extens_1) )
         => ! [B] : 
              ( m3_pboole(B,c1_3__extens_1,c2_3__extens_1,A)
             => ! [C] : 
                  ( m4_pboole(C,c1_3__extens_1,c2_3__extens_1)
                 => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,C)
                   => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,A,C,B),B) ) ) ) ) )
   => ! [D] : 
        ( m1_pboole(D,c1_3__extens_1)
       => ! [E] : 
            ( ( v2_relat_1(E)
              & m1_pboole(E,c1_3__extens_1) )
           => ! [F] : 
                ( m3_pboole(F,c1_3__extens_1,D,E)
               => ! [G] : 
                    ( m4_pboole(G,c1_3__extens_1,D)
                   => ( r2_pboole(c1_3__extens_1,D,G)
                     => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,D,E,G,F),F) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_3__extens_1),file(extens_1,c2_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c2_3__extens_1)]).

fof(dh_c3_3__extens_1,definition,
    ( ( ( v2_relat_1(c3_3__extens_1)
        & m1_pboole(c3_3__extens_1,c1_3__extens_1) )
     => ! [A] : 
          ( m3_pboole(A,c1_3__extens_1,c2_3__extens_1,c3_3__extens_1)
         => ! [B] : 
              ( m4_pboole(B,c1_3__extens_1,c2_3__extens_1)
             => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,B)
               => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,B,A),A) ) ) ) )
   => ! [C] : 
        ( ( v2_relat_1(C)
          & m1_pboole(C,c1_3__extens_1) )
       => ! [D] : 
            ( m3_pboole(D,c1_3__extens_1,c2_3__extens_1,C)
           => ! [E] : 
                ( m4_pboole(E,c1_3__extens_1,c2_3__extens_1)
               => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,E)
                 => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,C,E,D),D) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_3__extens_1),file(extens_1,c3_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c3_3__extens_1)]).

fof(dh_c4_3__extens_1,definition,
    ( ( m3_pboole(c4_3__extens_1,c1_3__extens_1,c2_3__extens_1,c3_3__extens_1)
     => ! [A] : 
          ( m4_pboole(A,c1_3__extens_1,c2_3__extens_1)
         => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,A)
           => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,A,c4_3__extens_1),c4_3__extens_1) ) ) )
   => ! [B] : 
        ( m3_pboole(B,c1_3__extens_1,c2_3__extens_1,c3_3__extens_1)
       => ! [C] : 
            ( m4_pboole(C,c1_3__extens_1,c2_3__extens_1)
           => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,C)
             => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,C,B),B) ) ) ) ),
    introduced(definition,[new_symbol(c4_3__extens_1),file(extens_1,c4_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c4_3__extens_1)]).

fof(dh_c5_3__extens_1,definition,
    ( ( m4_pboole(c5_3__extens_1,c1_3__extens_1,c2_3__extens_1)
     => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,c5_3__extens_1)
       => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c4_3__extens_1) ) )
   => ! [A] : 
        ( m4_pboole(A,c1_3__extens_1,c2_3__extens_1)
       => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,A)
         => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,A,c4_3__extens_1),c4_3__extens_1) ) ) ),
    introduced(definition,[new_symbol(c5_3__extens_1),file(extens_1,c5_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c5_3__extens_1)]).

fof(e1_3__extens_1,assumption,(
    r2_pboole(c1_3__extens_1,c2_3__extens_1,c5_3__extens_1) ),
    introduced(assumption,[file(extens_1,e1_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,e1_3__extens_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(cc2_pboole,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    [interesting(0.9),axiom,file(pboole,cc2_pboole)]).

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(fc7_funcop_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,fc7_funcop_1)]).

fof(rc1_funcop_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    [interesting(0.9),axiom,file(funcop_1,rc1_funcop_1)]).

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(rc2_pboole,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    [interesting(0.9),axiom,file(pboole,rc2_pboole)]).

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(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(rc4_pboole,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    [interesting(0.9),axiom,file(pboole,rc4_pboole)]).

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

fof(existence_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    [interesting(0.9),axiom,file(pboole,m3_pboole)]).

fof(existence_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : m4_pboole(C,A,B) ) ),
    file(pboole,m4_pboole),
    [interesting(0.9),axiom,file(pboole,m4_pboole)]).

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

fof(dt_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    [interesting(0.9),axiom,file(pboole,m3_pboole)]).

fof(dt_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pboole,m4_pboole),
    [interesting(0.9),axiom,file(pboole,m4_pboole)]).

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_pboole,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    [interesting(0.9),axiom,file(pboole,cc1_pboole)]).

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(cc3_pboole,theorem,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) ),
    file(pboole,cc3_pboole),
    [interesting(0.9),axiom,file(pboole,cc3_pboole)]).

fof(fc2_pboole,theorem,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    [interesting(0.9),axiom,file(pboole,fc2_pboole)]).

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(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_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_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(rc3_pboole,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    [interesting(0.9),axiom,file(pboole,rc3_pboole)]).

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(rc5_pboole,theorem,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(pboole,rc5_pboole),
    [interesting(0.9),axiom,file(pboole,rc5_pboole)]).

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(symmetry_r6_pboole,theorem,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    [interesting(0.9),axiom,file(pboole,r6_pboole)]).

fof(reflexivity_r6_pboole,theorem,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    [interesting(0.9),axiom,file(pboole,r6_pboole)]).

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

fof(redefinition_r6_pboole,definition,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    [interesting(0.9),axiom,file(pboole,r6_pboole)]).

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_msafree,axiom,(
    ! [A,B,C,D,E] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A)
        & m4_pboole(D,A,B)
        & m3_pboole(E,A,B,C) )
     => m3_pboole(k1_msafree(A,B,C,D,E),A,D,C) ) ),
    file(msafree,k1_msafree),
    [interesting(0.9),axiom,file(msafree,k1_msafree)]).

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_3__extens_1,assumption,(
    $true ),
    introduced(assumption,[file(extens_1,c1_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c1_3__extens_1)]).

fof(dt_c2_3__extens_1,assumption,(
    m1_pboole(c2_3__extens_1,c1_3__extens_1) ),
    introduced(assumption,[file(extens_1,c2_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c2_3__extens_1)]).

fof(dt_c3_3__extens_1,assumption,
    ( v2_relat_1(c3_3__extens_1)
    & m1_pboole(c3_3__extens_1,c1_3__extens_1) ),
    introduced(assumption,[file(extens_1,c3_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c3_3__extens_1)]).

fof(dt_c4_3__extens_1,assumption,(
    m3_pboole(c4_3__extens_1,c1_3__extens_1,c2_3__extens_1,c3_3__extens_1) ),
    introduced(assumption,[file(extens_1,c4_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c4_3__extens_1)]).

fof(dt_c5_3__extens_1,assumption,(
    m4_pboole(c5_3__extens_1,c1_3__extens_1,c2_3__extens_1) ),
    introduced(assumption,[file(extens_1,c5_3__extens_1)]),
    [interesting(0.8),axiom,file(extens_1,c5_3__extens_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(dh_c1_3_1__extens_1,definition,
    ( ( r2_hidden(c1_3_1__extens_1,c1_3__extens_1)
     => k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c1_3_1__extens_1) = k1_funct_1(c4_3__extens_1,c1_3_1__extens_1) )
   => ! [A] : 
        ( r2_hidden(A,c1_3__extens_1)
       => k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),A) = k1_funct_1(c4_3__extens_1,A) ) ),
    introduced(definition,[new_symbol(c1_3_1__extens_1),file(extens_1,c1_3_1__extens_1)]),
    [interesting(0.65),axiom,file(extens_1,c1_3_1__extens_1)]).

fof(e1_3_1__extens_1,assumption,(
    r2_hidden(c1_3_1__extens_1,c1_3__extens_1) ),
    introduced(assumption,[file(extens_1,e1_3_1__extens_1)]),
    [interesting(0.65),axiom,file(extens_1,e1_3_1__extens_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(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_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_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_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(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(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(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_k8_relset_1,definition,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(relset_1,k8_relset_1),
    [interesting(0.9),axiom,file(relset_1,k8_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_k8_relset_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_relset_1(C,A,B)
     => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ),
    file(relset_1,k8_relset_1),
    [interesting(0.9),axiom,file(relset_1,k8_relset_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_c1_3_1__extens_1,assumption,(
    $true ),
    introduced(assumption,[file(extens_1,c1_3_1__extens_1)]),
    [interesting(0.65),axiom,file(extens_1,c1_3_1__extens_1)]).

fof(de_c2_3_1__extens_1,definition,(
    c2_3_1__extens_1 = k1_funct_1(c4_3__extens_1,c1_3_1__extens_1) ),
    introduced(definition,[new_symbol(c2_3_1__extens_1),file(extens_1,c2_3_1__extens_1)]),
    [interesting(0.65),axiom,file(extens_1,c2_3_1__extens_1)]).

fof(d18_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( m3_pboole(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => ( v1_funct_1(k1_funct_1(D,E))
                      & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))
                      & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(pboole,d18_pboole),
    [interesting(0.9),axiom,file(pboole,d18_pboole)]).

fof(e2_3_1__extens_1,plain,
    ( v1_funct_1(k1_funct_1(c4_3__extens_1,c1_3_1__extens_1))
    & v1_funct_2(k1_funct_1(c4_3__extens_1,c1_3_1__extens_1),k1_funct_1(c2_3__extens_1,c1_3_1__extens_1),k1_funct_1(c3_3__extens_1,c1_3_1__extens_1))
    & m2_relset_1(k1_funct_1(c4_3__extens_1,c1_3_1__extens_1),k1_funct_1(c2_3__extens_1,c1_3_1__extens_1),k1_funct_1(c3_3__extens_1,c1_3_1__extens_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,e1_3_1__extens_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc2_pboole,fc1_xboole_0,rc1_pboole,rc2_pboole,rc3_funct_1,rc4_funct_1,t8_boole,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_1,cc1_pboole,cc1_relset_1,cc2_funct_1,fc2_pboole,fc7_funcop_1,rc1_funcop_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_pboole,rc4_pboole,rc5_funct_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_m1_pboole,existence_m2_relset_1,existence_m3_pboole,redefinition_m2_relset_1,dt_k1_funct_1,dt_m1_pboole,dt_m2_relset_1,dt_m3_pboole,dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,cc3_pboole,t1_subset,t7_boole,e1_3_1__extens_1,d18_pboole]),
    [interesting(0.65),file(extens_1,e2_3_1__extens_1),[file(extens_1,e2_3_1__extens_1)]]).

fof(dt_c2_3_1__extens_1,plain,
    ( v1_funct_1(c2_3_1__extens_1)
    & v1_funct_2(c2_3_1__extens_1,k1_funct_1(c2_3__extens_1,c1_3_1__extens_1),k1_funct_1(c3_3__extens_1,c1_3_1__extens_1))
    & m2_relset_1(c2_3_1__extens_1,k1_funct_1(c2_3__extens_1,c1_3_1__extens_1),k1_funct_1(c3_3__extens_1,c1_3_1__extens_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,e1_3_1__extens_1])],[reflexivity_r1_tarski,fc7_funcop_1,rc1_funcop_1,rc4_pboole,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m3_pboole,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m3_pboole,dt_c1_3__extens_1,cc1_relset_1,cc3_pboole,rc1_funct_1,rc3_pboole,rc5_funct_1,t3_subset,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_m2_relset_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,de_c2_3_1__extens_1,e2_3_1__extens_1]),
    [interesting(0.65),file(extens_1,c2_3_1__extens_1),[file(extens_1,c2_3_1__extens_1)]]).

fof(d1_msafree,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,B)
             => ! [E] : 
                  ( m3_pboole(E,A,B,C)
                 => ! [F] : 
                      ( m3_pboole(F,A,D,C)
                     => ( F = k1_msafree(A,B,C,D,E)
                      <=> ! [G] : 
                            ( r2_hidden(G,A)
                           => ! [H] : 
                                ( ( v1_funct_1(H)
                                  & v1_funct_2(H,k1_funct_1(B,G),k1_funct_1(C,G))
                                  & m2_relset_1(H,k1_funct_1(B,G),k1_funct_1(C,G)) )
                               => ( H = k1_funct_1(E,G)
                                 => k1_funct_1(F,G) = k8_relset_1(k1_funct_1(B,G),k1_funct_1(C,G),H,k1_funct_1(D,G)) ) ) ) ) ) ) ) ) ) ),
    file(msafree,d1_msafree),
    [interesting(0.9),axiom,file(msafree,d1_msafree)]).

fof(e1_3_1_1__extens_1,plain,(
    k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c1_3_1__extens_1) = k8_relset_1(k1_funct_1(c2_3__extens_1,c1_3_1__extens_1),k1_funct_1(c3_3__extens_1,c1_3_1__extens_1),c2_3_1__extens_1,k1_funct_1(c5_3__extens_1,c1_3_1__extens_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c5_3__extens_1,e1_3_1__extens_1])],[reflexivity_r1_tarski,dt_k1_xboole_0,cc2_pboole,fc1_xboole_0,rc1_pboole,rc2_pboole,rc3_funct_1,rc4_funct_1,existence_m1_relset_1,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k7_relat_1,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_1,cc1_pboole,cc1_relset_1,cc2_funct_1,fc2_pboole,fc4_funct_1,fc7_funcop_1,rc1_funcop_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_pboole,rc4_pboole,rc5_funct_1,rc5_pboole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m1_pboole,existence_m2_relset_1,existence_m3_pboole,existence_m4_pboole,redefinition_k8_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k1_msafree,dt_k8_relset_1,dt_m1_pboole,dt_m2_relset_1,dt_m3_pboole,dt_m4_pboole,dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c2_3_1__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c5_3__extens_1,de_c2_3_1__extens_1,cc3_pboole,t1_subset,t7_boole,e1_3_1__extens_1,d1_msafree]),
    [interesting(0.5),file(extens_1,e1_3_1_1__extens_1),[file(extens_1,e1_3_1_1__extens_1)]]).

fof(redefinition_k2_partfun1,definition,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ),
    file(partfun1,k2_partfun1),
    [interesting(0.9),axiom,file(partfun1,k2_partfun1)]).

fof(dt_k2_partfun1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => ( v1_funct_1(k2_partfun1(A,B,C,D))
        & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ),
    file(partfun1,k2_partfun1),
    [interesting(0.9),axiom,file(partfun1,k2_partfun1)]).

fof(reflexivity_r2_pboole,theorem,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) ),
    file(pboole,r2_pboole),
    [interesting(0.9),axiom,file(pboole,r2_pboole)]).

fof(d5_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ),
    file(pboole,d5_pboole),
    [interesting(0.9),axiom,file(pboole,d5_pboole)]).

fof(e3_3_1__extens_1,plain,(
    r1_tarski(k1_funct_1(c2_3__extens_1,c1_3_1__extens_1),k1_funct_1(c5_3__extens_1,c1_3_1__extens_1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1,e1_3_1__extens_1])],[dt_k1_xboole_0,fc1_xboole_0,rc3_funct_1,t8_boole,existence_m1_subset_1,existence_m4_pboole,dt_k1_zfmisc_1,dt_m1_subset_1,dt_m4_pboole,cc1_funct_1,cc2_funct_1,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,t2_subset,t4_subset,t5_subset,t6_boole,reflexivity_r1_tarski,antisymmetry_r2_hidden,reflexivity_r2_pboole,existence_m1_pboole,dt_k1_funct_1,dt_m1_pboole,dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,t1_subset,t3_subset,t7_boole,e1_3__extens_1,e1_3_1__extens_1,d5_pboole]),
    [interesting(0.65),file(extens_1,e3_3_1__extens_1),[file(extens_1,e3_3_1__extens_1)]]).

fof(t40_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(A,C)
       => k2_partfun1(A,B,D,C) = D ) ) ),
    file(funct_2,t40_funct_2),
    [interesting(0.9),axiom,file(funct_2,t40_funct_2)]).

fof(e2_3_1_1__extens_1,plain,(
    k8_relset_1(k1_funct_1(c2_3__extens_1,c1_3_1__extens_1),k1_funct_1(c3_3__extens_1,c1_3_1__extens_1),c2_3_1__extens_1,k1_funct_1(c5_3__extens_1,c1_3_1__extens_1)) = k1_funct_1(c4_3__extens_1,c1_3_1__extens_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1,e1_3_1__extens_1])],[fc7_funcop_1,rc1_funcop_1,rc4_pboole,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m3_pboole,existence_m4_pboole,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k7_relat_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m3_pboole,dt_m4_pboole,dt_c1_3__extens_1,cc1_relset_1,cc3_pboole,fc4_funct_1,rc1_funct_1,rc3_pboole,rc5_funct_1,rc5_pboole,reflexivity_r1_tarski,existence_m2_relset_1,redefinition_k2_partfun1,redefinition_k8_relset_1,redefinition_m2_relset_1,dt_k1_funct_1,dt_k2_partfun1,dt_k8_relset_1,dt_m2_relset_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c2_3_1__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c5_3__extens_1,de_c2_3_1__extens_1,t3_subset,e3_3_1__extens_1,t40_funct_2]),
    [interesting(0.5),file(extens_1,e2_3_1_1__extens_1),[file(extens_1,e2_3_1_1__extens_1)]]).

fof(e4_3_1__extens_1,plain,(
    k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c1_3_1__extens_1) = k1_funct_1(c4_3__extens_1,c1_3_1__extens_1) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1,e1_3_1__extens_1])],[e1_3_1_1__extens_1,e2_3_1_1__extens_1]),
    [interesting(0.65),file(extens_1,e4_3_1__extens_1),[file(extens_1,e4_3_1__extens_1)]]).

fof(i3_3_1__extens_1,theorem,(
    $true ),
    introduced(tautology,[file(extens_1,i3_3_1__extens_1)]),
    [interesting(0.65),trivial,file(extens_1,i3_3_1__extens_1)]).

fof(i2_3_1__extens_1,plain,(
    k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c1_3_1__extens_1) = k1_funct_1(c4_3__extens_1,c1_3_1__extens_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1,e1_3_1__extens_1])],[e4_3_1__extens_1,i3_3_1__extens_1]),
    [interesting(0.65),file(extens_1,i2_3_1__extens_1),[file(extens_1,i2_3_1__extens_1)]]).

fof(i1_3_1__extens_1,plain,
    ( r2_hidden(c1_3_1__extens_1,c1_3__extens_1)
   => k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c1_3_1__extens_1) = k1_funct_1(c4_3__extens_1,c1_3_1__extens_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c1_3_1__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1]),discharge_asm(discharge,[e1_3_1__extens_1])],[e1_3_1__extens_1,i2_3_1__extens_1]),
    [interesting(0.65),file(extens_1,i1_3_1__extens_1),[file(extens_1,i1_3_1__extens_1)]]).

fof(i1_3_1_tmp__extens_1,plain,
    ( r2_hidden(c1_3_1__extens_1,c1_3__extens_1)
   => k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c1_3_1__extens_1) = k1_funct_1(c4_3__extens_1,c1_3_1__extens_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1]),discharge_asm(discharge,[dt_c1_3_1__extens_1])],[dt_c1_3_1__extens_1,i1_3_1__extens_1]),
    [interesting(0.8),e2_3__extens_1]).

fof(e2_3__extens_1,plain,(
    ! [A] : 
      ( r2_hidden(A,c1_3__extens_1)
     => k1_funct_1(k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),A) = k1_funct_1(c4_3__extens_1,A) ) ),
    inference(let,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1])],[i1_3_1_tmp__extens_1,dh_c1_3_1__extens_1]),
    [interesting(0.8),file(extens_1,e2_3__extens_1),[file(extens_1,e2_3__extens_1)]]).

fof(t3_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    [interesting(0.9),axiom,file(pboole,t3_pboole)]).

fof(e3_3__extens_1,plain,(
    r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c4_3__extens_1) ),
    inference(mizar_by,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1])],[dt_k1_xboole_0,cc2_pboole,fc1_xboole_0,fc7_funcop_1,rc1_funcop_1,rc1_pboole,rc2_pboole,rc3_funct_1,rc4_funct_1,rc4_pboole,existence_m1_subset_1,existence_m3_pboole,existence_m4_pboole,dt_m1_subset_1,dt_m3_pboole,dt_m4_pboole,cc1_funct_1,cc1_pboole,cc2_funct_1,cc3_pboole,fc2_pboole,rc1_funct_1,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_pboole,rc5_funct_1,rc5_pboole,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,symmetry_r6_pboole,reflexivity_r6_pboole,existence_m1_pboole,redefinition_r6_pboole,dt_k1_funct_1,dt_k1_msafree,dt_m1_pboole,dt_c1_3__extens_1,dt_c2_3__extens_1,dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c5_3__extens_1,t1_subset,t7_boole,e2_3__extens_1,t3_pboole]),
    [interesting(0.8),file(extens_1,e3_3__extens_1),[file(extens_1,e3_3__extens_1)]]).

fof(i7_3__extens_1,theorem,(
    $true ),
    introduced(tautology,[file(extens_1,i7_3__extens_1)]),
    [interesting(0.8),trivial,file(extens_1,i7_3__extens_1)]).

fof(i6_3__extens_1,plain,(
    r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c4_3__extens_1) ),
    inference(conclusion,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1,e1_3__extens_1])],[e3_3__extens_1,i7_3__extens_1]),
    [interesting(0.8),file(extens_1,i6_3__extens_1),[file(extens_1,i6_3__extens_1)]]).

fof(i5_3__extens_1,plain,
    ( r2_pboole(c1_3__extens_1,c2_3__extens_1,c5_3__extens_1)
   => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c4_3__extens_1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1,dt_c5_3__extens_1]),discharge_asm(discharge,[e1_3__extens_1])],[e1_3__extens_1,i6_3__extens_1]),
    [interesting(0.8),file(extens_1,i5_3__extens_1),[file(extens_1,i5_3__extens_1)]]).

fof(i5_3_tmp__extens_1,plain,
    ( m4_pboole(c5_3__extens_1,c1_3__extens_1,c2_3__extens_1)
   => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,c5_3__extens_1)
     => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,c5_3__extens_1,c4_3__extens_1),c4_3__extens_1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1]),discharge_asm(discharge,[dt_c5_3__extens_1])],[dt_c5_3__extens_1,i5_3__extens_1]),
    [interesting(0.8),i4_3__extens_1]).

fof(i4_3__extens_1,plain,(
    ! [A] : 
      ( m4_pboole(A,c1_3__extens_1,c2_3__extens_1)
     => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,A)
       => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,A,c4_3__extens_1),c4_3__extens_1) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_3__extens_1,dt_c4_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1])],[i5_3_tmp__extens_1,dh_c5_3__extens_1]),
    [interesting(0.8),file(extens_1,i4_3__extens_1),[file(extens_1,i4_3__extens_1)]]).

fof(i4_3_tmp__extens_1,plain,
    ( m3_pboole(c4_3__extens_1,c1_3__extens_1,c2_3__extens_1,c3_3__extens_1)
   => ! [A] : 
        ( m4_pboole(A,c1_3__extens_1,c2_3__extens_1)
       => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,A)
         => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,A,c4_3__extens_1),c4_3__extens_1) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c3_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1]),discharge_asm(discharge,[dt_c4_3__extens_1])],[dt_c4_3__extens_1,i4_3__extens_1]),
    [interesting(0.8),i3_3__extens_1]).

fof(i3_3__extens_1,plain,(
    ! [A] : 
      ( m3_pboole(A,c1_3__extens_1,c2_3__extens_1,c3_3__extens_1)
     => ! [B] : 
          ( m4_pboole(B,c1_3__extens_1,c2_3__extens_1)
         => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,B)
           => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,B,A),A) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c3_3__extens_1,dt_c1_3__extens_1,dt_c2_3__extens_1])],[i4_3_tmp__extens_1,dh_c4_3__extens_1]),
    [interesting(0.8),file(extens_1,i3_3__extens_1),[file(extens_1,i3_3__extens_1)]]).

fof(i3_3_tmp__extens_1,plain,
    ( ( v2_relat_1(c3_3__extens_1)
      & m1_pboole(c3_3__extens_1,c1_3__extens_1) )
   => ! [A] : 
        ( m3_pboole(A,c1_3__extens_1,c2_3__extens_1,c3_3__extens_1)
       => ! [B] : 
            ( m4_pboole(B,c1_3__extens_1,c2_3__extens_1)
           => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,B)
             => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,c3_3__extens_1,B,A),A) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__extens_1,dt_c2_3__extens_1]),discharge_asm(discharge,[dt_c3_3__extens_1])],[dt_c3_3__extens_1,i3_3__extens_1]),
    [interesting(0.8),i2_3__extens_1]).

fof(i2_3__extens_1,plain,(
    ! [A] : 
      ( ( v2_relat_1(A)
        & m1_pboole(A,c1_3__extens_1) )
     => ! [B] : 
          ( m3_pboole(B,c1_3__extens_1,c2_3__extens_1,A)
         => ! [C] : 
              ( m4_pboole(C,c1_3__extens_1,c2_3__extens_1)
             => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,C)
               => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,A,C,B),B) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__extens_1,dt_c2_3__extens_1])],[i3_3_tmp__extens_1,dh_c3_3__extens_1]),
    [interesting(0.8),file(extens_1,i2_3__extens_1),[file(extens_1,i2_3__extens_1)]]).

fof(i2_3_tmp__extens_1,plain,
    ( m1_pboole(c2_3__extens_1,c1_3__extens_1)
   => ! [A] : 
        ( ( v2_relat_1(A)
          & m1_pboole(A,c1_3__extens_1) )
       => ! [B] : 
            ( m3_pboole(B,c1_3__extens_1,c2_3__extens_1,A)
           => ! [C] : 
                ( m4_pboole(C,c1_3__extens_1,c2_3__extens_1)
               => ( r2_pboole(c1_3__extens_1,c2_3__extens_1,C)
                 => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,c2_3__extens_1,A,C,B),B) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_3__extens_1]),discharge_asm(discharge,[dt_c2_3__extens_1])],[dt_c2_3__extens_1,i2_3__extens_1]),
    [interesting(0.8),i1_3__extens_1]).

fof(i1_3__extens_1,plain,(
    ! [A] : 
      ( m1_pboole(A,c1_3__extens_1)
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,c1_3__extens_1) )
         => ! [C] : 
              ( m3_pboole(C,c1_3__extens_1,A,B)
             => ! [D] : 
                  ( m4_pboole(D,c1_3__extens_1,A)
                 => ( r2_pboole(c1_3__extens_1,A,D)
                   => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,A,B,D,C),C) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_3__extens_1])],[i2_3_tmp__extens_1,dh_c2_3__extens_1]),
    [interesting(0.8),file(extens_1,i1_3__extens_1),[file(extens_1,i1_3__extens_1)]]).

fof(i1_3_tmp__extens_1,plain,(
    ! [A] : 
      ( m1_pboole(A,c1_3__extens_1)
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,c1_3__extens_1) )
         => ! [C] : 
              ( m3_pboole(C,c1_3__extens_1,A,B)
             => ! [D] : 
                  ( m4_pboole(D,c1_3__extens_1,A)
                 => ( r2_pboole(c1_3__extens_1,A,D)
                   => r6_pboole(c1_3__extens_1,k1_msafree(c1_3__extens_1,A,B,D,C),C) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_3__extens_1])],[dt_c1_3__extens_1,i1_3__extens_1]),
    [interesting(1),t5_extens_1]).

fof(t5_extens_1,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( ( v2_relat_1(C)
            & m1_pboole(C,A) )
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ! [E] : 
                  ( m4_pboole(E,A,B)
                 => ( r2_pboole(A,B,E)
                   => r6_pboole(A,k1_msafree(A,B,C,E,D),D) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_3_tmp__extens_1,dh_c1_3__extens_1]),
    [interesting(1),file(extens_1,t5_extens_1),[file(extens_1,t5_extens_1)]]).