% Mizar problem: t51_algspec1,algspec1,1154,48 
fof(t51_algspec1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_msualg_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ! [F] : 
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ! [G] : 
                              ( ( v1_relat_1(G)
                                & v1_funct_1(G) )
                             => ( ( r1_partfun1(D,F)
                                  & r3_pua2mss1(A,C,D,E)
                                  & r3_pua2mss1(B,C,F,G) )
                               => r3_pua2mss1(k3_circcomb(A,B),C,k1_funct_4(D,F),k1_funct_4(E,G)) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_msualg_1,antisymmetry_r2_hidden,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_instalg1,cc3_instalg1,cc4_instalg1,cc5_instalg1,commutativity_k2_xboole_0,d11_finseq_1,d13_pua2mss1,d1_funct_2,d1_funct_4,d2_circcomb,d2_xboole_0,d4_finseq_1,d5_funct_1,dt_g1_msualg_1,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_funct_4,dt_k1_numbers,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_circcomb,dt_k3_finseq_2,dt_k4_relset_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_relset_1,dt_l1_msualg_1,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,existence_l1_msualg_1,existence_l1_struct_0,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,fc10_relat_1,fc12_relat_1,fc1_algspec1,fc1_funct_1,fc1_struct_0,fc1_xboole_0,fc2_relat_1,fc2_xboole_0,fc3_circcomb,fc3_msafree,fc3_msualg_2,fc3_xboole_0,fc4_circcomb,fc4_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,free_g1_msualg_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,rc1_circcomb,rc1_funct_1,rc1_instalg1,rc1_msualg_1,rc1_pboole,rc1_relat_1,rc1_xboole_0,rc2_catalg_1,rc2_funct_1,rc2_msualg_1,rc2_relat_1,rc2_xboole_0,rc3_funct_1,rc3_msualg_1,rc3_relat_1,rc3_struct_0,rc4_funct_1,rc5_struct_0,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,reflexivity_r1_partfun1,reflexivity_r1_tarski,symmetry_r1_partfun1,t10_funct_7,t11_funct_7,t12_funct_4,t14_funct_4,t18_funct_4,t1_boole,t1_subset,t1_xboole_1,t20_funct_4,t2_subset,t35_funct_4,t3_subset,t44_relat_1,t46_relat_1,t4_subset,t5_subset,t6_boole,t73_funct_4,t7_boole,t8_boole,t8_xboole_1]),
    [file(algspec1,t51_algspec1)]).

fof(abstractness_v1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_msualg_1(A)
       => A = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ),
    file(msualg_1,v1_msualg_1),
    []).

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

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

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

fof(cc1_relset_1,axiom,(
    ! [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),
    []).

fof(cc2_funct_1,axiom,(
    ! [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),
    []).

fof(cc2_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( ~ v3_struct_0(A)
       => v1_instalg1(A) ) ) ),
    file(instalg1,cc2_instalg1),
    []).

fof(cc3_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
       => v1_instalg1(A) ) ) ),
    file(instalg1,cc3_instalg1),
    []).

fof(cc4_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( ( v3_struct_0(A)
          & v1_instalg1(A) )
       => v2_msualg_1(A) ) ) ),
    file(instalg1,cc4_instalg1),
    []).

fof(cc5_instalg1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( ( ~ v2_msualg_1(A)
          & v1_instalg1(A) )
       => ~ v3_struct_0(A) ) ) ),
    file(instalg1,cc5_instalg1),
    []).

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

fof(d11_finseq_1,axiom,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    []).

fof(d13_pua2mss1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ! [B] : 
          ( l1_msualg_1(B)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r3_pua2mss1(A,B,C,D)
                  <=> ( k1_relat_1(C) = u1_struct_0(A)
                      & k1_relat_1(D) = u1_msualg_1(A)
                      & r1_tarski(k2_relat_1(C),u1_struct_0(B))
                      & r1_tarski(k2_relat_1(D),u1_msualg_1(B))
                      & k5_relat_1(u3_msualg_1(A),C) = k5_relat_1(D,u3_msualg_1(B))
                      & ! [E,F] : 
                          ( ( v1_relat_1(F)
                            & v1_funct_1(F) )
                         => ( ( r2_hidden(E,u1_msualg_1(A))
                              & F = k1_funct_1(u2_msualg_1(A),E) )
                           => k5_relat_1(F,C) = k1_funct_1(u2_msualg_1(B),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ),
    file(pua2mss1,d13_pua2mss1),
    []).

fof(d1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    []).

fof(d1_funct_4,axiom,(
    ! [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 = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    []).

fof(d2_circcomb,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v1_msualg_1(C)
                & l1_msualg_1(C) )
             => ( C = k3_circcomb(A,B)
              <=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
                  & u1_msualg_1(C) = k2_xboole_0(u1_msualg_1(A),u1_msualg_1(B))
                  & u2_msualg_1(C) = k1_funct_4(u2_msualg_1(A),u2_msualg_1(B))
                  & u3_msualg_1(C) = k1_funct_4(u3_msualg_1(A),u3_msualg_1(B)) ) ) ) ) ) ),
    file(circcomb,d2_circcomb),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d4_finseq_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    []).

fof(d5_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    []).

fof(dt_g1_msualg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( v1_msualg_1(g1_msualg_1(A,B,C,D))
        & l1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ),
    file(msualg_1,g1_msualg_1),
    []).

fof(dt_k13_finseq_1,axiom,(
    $true ),
    file(finseq_1,k13_finseq_1),
    []).

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

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    []).

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

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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

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

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

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

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

fof(dt_k3_circcomb,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ( ~ v3_struct_0(k3_circcomb(A,B))
        & v1_msualg_1(k3_circcomb(A,B))
        & l1_msualg_1(k3_circcomb(A,B)) ) ) ),
    file(circcomb,k3_circcomb),
    []).

fof(dt_k3_finseq_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k3_finseq_2(A))
      & m1_finseq_2(k3_finseq_2(A),A) ) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(dt_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(relset_1,k4_relset_1),
    []).

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

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

fof(dt_k5_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k5_relat_1(A,B)) ) ),
    file(relat_1,k5_relat_1),
    []).

fof(dt_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(dt_l1_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) ),
    file(msualg_1,l1_msualg_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_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),
    []).

fof(dt_u1_msualg_1,axiom,(
    $true ),
    file(msualg_1,u1_msualg_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_funct_1(u2_msualg_1(A))
        & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)))
        & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ),
    file(msualg_1,u2_msualg_1),
    []).

fof(dt_u3_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v1_funct_1(u3_msualg_1(A))
        & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A))
        & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ),
    file(msualg_1,u3_msualg_1),
    []).

fof(existence_l1_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

fof(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc10_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(B,A))
        & v1_relat_1(k5_relat_1(B,A)) ) ) ),
    file(relat_1,fc10_relat_1),
    []).

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

fof(fc1_algspec1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( v1_msualg_1(g1_msualg_1(A,B,C,D))
        & ~ v2_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ),
    file(algspec1,fc1_algspec1),
    []).

fof(fc1_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(A,B))
        & v1_funct_1(k5_relat_1(A,B)) ) ) ),
    file(funct_1,fc1_funct_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

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

fof(fc3_circcomb,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ( ~ v3_struct_0(k3_circcomb(A,B))
        & v1_msualg_1(k3_circcomb(A,B))
        & ~ v2_msualg_1(k3_circcomb(A,B)) ) ) ),
    file(circcomb,fc3_circcomb),
    []).

fof(fc3_msafree,axiom,(
    ! [A] : 
      ( ( ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ~ v1_xboole_0(u1_msualg_1(A)) ) ),
    file(msafree,fc3_msafree),
    []).

fof(fc3_msualg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ( ~ v3_struct_0(g1_msualg_1(A,B,C,D))
        & v1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ),
    file(msualg_2,fc3_msualg_2),
    []).

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

fof(fc4_circcomb,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ( ~ v3_struct_0(k3_circcomb(B,A))
        & v1_msualg_1(k3_circcomb(B,A))
        & ~ v2_msualg_1(k3_circcomb(B,A)) ) ) ),
    file(circcomb,fc4_circcomb),
    []).

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

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

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

fof(fc7_relat_1,axiom,(
    ! [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),
    []).

fof(fc8_relat_1,axiom,(
    ! [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),
    []).

fof(fc9_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(B) )
     => ( v1_xboole_0(k5_relat_1(A,B))
        & v1_relat_1(k5_relat_1(A,B)) ) ) ),
    file(relat_1,fc9_relat_1),
    []).

fof(free_g1_msualg_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,B,k3_finseq_2(A))
        & m1_relset_1(C,B,k3_finseq_2(A))
        & v1_funct_1(D)
        & v1_funct_2(D,B,A)
        & m1_relset_1(D,B,A) )
     => ! [E,F,G,H] : 
          ( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(msualg_1,g1_msualg_1),
    []).

fof(idempotence_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    []).

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

fof(rc1_circcomb,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(circcomb,rc1_circcomb),
    []).

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

fof(rc1_instalg1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A)
      & v1_instalg1(A) ) ),
    file(instalg1,rc1_instalg1),
    []).

fof(rc1_msualg_1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & v1_msualg_1(A) ) ),
    file(msualg_1,rc1_msualg_1),
    []).

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

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

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

fof(rc2_catalg_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & ~ v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(catalg_1,rc2_catalg_1),
    []).

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

fof(rc2_msualg_1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & v2_msualg_1(A) ) ),
    file(msualg_1,rc2_msualg_1),
    []).

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

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

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

fof(rc3_msualg_1,axiom,(
    ? [A] : 
      ( l1_msualg_1(A)
      & ~ v3_struct_0(A)
      & v1_msualg_1(A)
      & ~ v2_msualg_1(A) ) ),
    file(msualg_1,rc3_msualg_1),
    []).

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

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

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

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k3_finseq_2,axiom,(
    ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ),
    file(finseq_2,k3_finseq_2),
    []).

fof(redefinition_k4_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k4_relset_1(A,B,C) = k1_relat_1(C) ) ),
    file(relset_1,k4_relset_1),
    []).

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

fof(redefinition_k5_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => k5_relset_1(A,B,C) = k2_relat_1(C) ) ),
    file(relset_1,k5_relset_1),
    []).

fof(redefinition_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

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

fof(reflexivity_r1_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_partfun1(A,A) ) ),
    file(partfun1,r1_partfun1),
    []).

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

fof(symmetry_r1_partfun1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_partfun1(A,B)
       => r1_partfun1(B,A) ) ) ),
    file(partfun1,r1_partfun1),
    []).

fof(t10_funct_7,axiom,(
    ! [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) )
             => ( ( r1_tarski(k2_relat_1(B),k1_relat_1(A))
                  & r1_tarski(k2_relat_1(C),k1_relat_1(A)) )
               => k5_relat_1(k1_funct_4(B,C),A) = k1_funct_4(k5_relat_1(B,A),k5_relat_1(C,A)) ) ) ) ) ),
    file(funct_7,t10_funct_7),
    []).

fof(t11_funct_7,axiom,(
    ! [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) )
             => k5_relat_1(A,k1_funct_4(B,C)) = k1_funct_4(k5_relat_1(A,B),k5_relat_1(A,C)) ) ) ) ),
    file(funct_7,t11_funct_7),
    []).

fof(t12_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    []).

fof(t14_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    []).

fof(t18_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(funct_4,t18_funct_4),
    []).

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

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t20_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_tarski(k1_relat_1(A),k1_relat_1(B))
           => k1_funct_4(A,B) = B ) ) ) ),
    file(funct_4,t20_funct_4),
    []).

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

fof(t35_funct_4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r1_partfun1(A,B)
          <=> k1_funct_4(A,B) = k1_funct_4(B,A) ) ) ) ),
    file(funct_4,t35_funct_4),
    []).

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

fof(t44_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)) ) ) ),
    file(relat_1,t44_relat_1),
    []).

fof(t46_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(k2_relat_1(A),k1_relat_1(B))
           => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ),
    file(relat_1,t46_relat_1),
    []).

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

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

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

fof(t73_funct_4,axiom,(
    ! [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) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( ( r1_tarski(k2_relat_1(C),k1_relat_1(A))
                      & r1_tarski(k2_relat_1(D),k1_relat_1(B))
                      & r1_partfun1(A,B) )
                   => k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B)) ) ) ) ) ) ),
    file(funct_4,t73_funct_4),
    []).

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

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

fof(t8_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    []).