% Mizar problem: t9_osafree,osafree,1334,31 
fof(t9_osafree,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),C) = a_3_0_osafree(A,B,C) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_dtconstr,cc1_osalg_1,cc1_pboole,cc1_relset_1,cc2_pboole,cc3_pboole,cc4_trees_3,cc5_trees_3,commutativity_k2_tarski,commutativity_k2_xboole_0,d11_osafree,d5_osafree,d5_tarski,d7_osafree,d8_osafree,dt_g1_lang1,dt_g3_msualg_1,dt_k13_finseq_1,dt_k1_funct_1,dt_k1_osafree,dt_k1_osalg_1,dt_k1_tarski,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_3,dt_k2_msualg_1,dt_k2_osafree,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_finseq_2,dt_k3_msafree,dt_k4_dtconstr,dt_k4_osafree,dt_k4_tarski,dt_k5_osafree,dt_k5_relat_1,dt_k5_trees_3,dt_k6_pboole,dt_k7_osafree,dt_k7_pboole,dt_k8_osafree,dt_k8_pboole,dt_l1_lang1,dt_l1_msualg_1,dt_l1_orders_2,dt_l1_osalg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l2_osalg_1,dt_l3_msualg_1,dt_l3_osalg_1,dt_m1_dtconstr,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m3_pboole,dt_m3_trees_2,dt_m4_trees_3,dt_m5_trees_3,dt_u1_lang1,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_lang1,existence_l1_msualg_1,existence_l1_orders_2,existence_l1_osalg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l2_osalg_1,existence_l3_msualg_1,existence_l3_osalg_1,existence_m1_dtconstr,existence_m1_finseq_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m3_pboole,existence_m3_trees_2,existence_m4_trees_3,existence_m5_trees_3,fc1_dtconstr,fc1_msafree,fc1_msualg_1,fc1_osafree,fc1_pboole,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_dtconstr,fc2_msafree,fc2_osafree,fc2_pboole,fc2_subset_1,fc2_xboole_0,fc3_dtconstr,fc3_msafree,fc3_osafree,fc3_subset_1,fc3_xboole_0,fc4_osafree,fc4_subset_1,fc5_osafree,fc6_trees_3,fc7_funcop_1,fc8_funcop_1,fraenkel_a_3_0_osafree,free_g1_lang1,free_g3_msualg_1,idempotence_k2_xboole_0,rc10_osalg_1,rc11_osalg_1,rc12_osalg_1,rc1_dtconstr,rc1_funcop_1,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_partfun1,rc2_pboole,rc2_subset_1,rc2_xboole_0,rc3_pboole,rc3_struct_0,rc4_pboole,rc5_msualg_1,rc5_osalg_1,rc5_struct_0,rc6_msualg_1,redefinition_k1_osalg_1,redefinition_k3_finseq_2,redefinition_k3_msafree,redefinition_k7_pboole,redefinition_k8_pboole,redefinition_m1_dtconstr,redefinition_m2_relset_1,redefinition_m5_trees_3,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t1_boole,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(osafree,t9_osafree)]).

fof(abstractness_v1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => ( v1_lang1(A)
       => A = g1_lang1(u1_struct_0(A),u1_lang1(A)) ) ) ),
    file(lang1,v1_lang1),
    []).

fof(abstractness_v4_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => ( v4_msualg_1(B,A)
       => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ),
    file(msualg_1,v4_msualg_1),
    []).

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

fof(cc1_dtconstr,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k3_finseq_2(A))
     => v1_finseq_1(B) ) ),
    file(dtconstr,cc1_dtconstr),
    []).

fof(cc1_osalg_1,axiom,(
    ! [A] : 
      ( l3_osalg_1(A)
     => ( v4_osalg_1(A)
       => ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A) ) ) ) ),
    file(osalg_1,cc1_osalg_1),
    []).

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

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_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(cc3_pboole,axiom,(
    ! [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),
    []).

fof(cc4_trees_3,axiom,(
    ! [A] : 
      ( v3_trees_3(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v3_trees_3(B) ) ) ),
    file(trees_3,cc4_trees_3),
    []).

fof(cc5_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m4_trees_3(B,A)
         => v3_trees_3(B) ) ) ),
    file(trees_3,cc5_trees_3),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

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_osafree,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k8_osafree(A,B) = g3_msualg_1(A,k5_osafree(A,B),k7_osafree(A,B)) ) ) ),
    file(osafree,d11_osafree),
    []).

fof(d5_osafree,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => k2_osafree(A,B) = g1_lang1(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k1_osafree(A,B)) ) ) ),
    file(osafree,d5_osafree),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d7_osafree,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k4_osafree(A,B,C) = a_3_0_osafree(A,B,C) ) ) ) ),
    file(osafree,d7_osafree),
    []).

fof(d8_osafree,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( ( v11_osalg_1(C,A)
                & m1_pboole(C,u1_struct_0(A)) )
             => ( C = k5_osafree(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k4_osafree(A,B,D) ) ) ) ) ) ),
    file(osafree,d8_osafree),
    []).

fof(dt_g1_lang1,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k3_finseq_2(A))
     => ( v1_lang1(g1_lang1(A,B))
        & l1_lang1(g1_lang1(A,B)) ) ) ),
    file(lang1,g1_lang1),
    []).

fof(dt_g3_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ( v4_msualg_1(g3_msualg_1(A,B,C),A)
        & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ),
    file(msualg_1,g3_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_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => m2_relset_1(k1_osafree(A,B),k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))) ) ),
    file(osafree,k1_osafree),
    []).

fof(dt_k1_osalg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => m1_subset_1(k1_osalg_1(A,B),u1_struct_0(A)) ) ),
    file(osalg_1,k1_osalg_1),
    []).

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

fof(dt_k1_trees_4,axiom,(
    ! [A] : 
      ( v1_relat_1(k1_trees_4(A))
      & v1_funct_1(k1_trees_4(A))
      & v3_trees_2(k1_trees_4(A)) ) ),
    file(trees_4,k1_trees_4),
    []).

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_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_card_3(A))
        & v1_funct_1(k2_card_3(A)) ) ) ),
    file(card_3,k2_card_3),
    []).

fof(dt_k2_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)) ) ),
    file(msualg_1,k2_msualg_1),
    []).

fof(dt_k2_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => l1_lang1(k2_osafree(A,B)) ) ),
    file(osafree,k2_osafree),
    []).

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

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_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    []).

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_k3_msafree,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_pboole(k3_msafree(A,B),A) ) ),
    file(msafree,k3_msafree),
    []).

fof(dt_k4_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => m1_subset_1(k4_dtconstr(A),k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) ) ),
    file(dtconstr,k4_dtconstr),
    []).

fof(dt_k4_osafree,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_osafree(A,B,C),k1_zfmisc_1(k4_dtconstr(k2_osafree(A,B)))) ) ),
    file(osafree,k4_osafree),
    []).

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

fof(dt_k5_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v11_osalg_1(k5_osafree(A,B),A)
        & m1_pboole(k5_osafree(A,B),u1_struct_0(A)) ) ) ),
    file(osafree,k5_osafree),
    []).

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_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => m4_trees_3(k5_trees_3(A),A) ) ),
    file(trees_3,k5_trees_3),
    []).

fof(dt_k6_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ),
    file(pboole,k6_pboole),
    []).

fof(dt_k7_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => m3_pboole(k7_osafree(A,B),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B))) ) ),
    file(osafree,k7_osafree),
    []).

fof(dt_k7_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => m1_pboole(k7_pboole(A,B,C,D),A) ) ),
    file(pboole,k7_pboole),
    []).

fof(dt_k8_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v12_osalg_1(k8_osafree(A,B),A)
        & l3_msualg_1(k8_osafree(A,B),A) ) ) ),
    file(osafree,k8_osafree),
    []).

fof(dt_k8_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & v2_relat_1(D)
        & m1_pboole(D,B) )
     => ( v2_relat_1(k8_pboole(A,B,C,D))
        & m1_pboole(k8_pboole(A,B,C,D),A) ) ) ),
    file(pboole,k8_pboole),
    []).

fof(dt_l1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => l1_struct_0(A) ) ),
    file(lang1,l1_lang1),
    []).

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

fof(dt_l1_orders_2,axiom,(
    ! [A] : 
      ( l1_orders_2(A)
     => l1_struct_0(A) ) ),
    file(orders_2,l1_orders_2),
    []).

fof(dt_l1_osalg_1,axiom,(
    ! [A] : 
      ( l1_osalg_1(A)
     => l1_msualg_1(A) ) ),
    file(osalg_1,l1_osalg_1),
    []).

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

fof(dt_l2_msualg_1,axiom,(
    $true ),
    file(msualg_1,l2_msualg_1),
    []).

fof(dt_l2_osalg_1,axiom,(
    ! [A] : 
      ( l2_osalg_1(A)
     => ( l1_msualg_1(A)
        & l1_orders_2(A) ) ) ),
    file(osalg_1,l2_osalg_1),
    []).

fof(dt_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => l2_msualg_1(B,A) ) ) ),
    file(msualg_1,l3_msualg_1),
    []).

fof(dt_l3_osalg_1,axiom,(
    ! [A] : 
      ( l3_osalg_1(A)
     => ( l1_osalg_1(A)
        & l2_osalg_1(A) ) ) ),
    file(osalg_1,l3_osalg_1),
    []).

fof(dt_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] : 
          ( m1_dtconstr(D,A,B,C)
         => m5_trees_3(D,A,B) ) ) ),
    file(dtconstr,m1_dtconstr),
    []).

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

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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_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_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),
    []).

fof(dt_m3_trees_2,axiom,(
    ! [A,B] : 
      ( m3_trees_2(B,A)
     => v1_relat_1(B) ) ),
    file(trees_2,m3_trees_2),
    []).

fof(dt_m4_trees_3,axiom,(
    $true ),
    file(trees_3,m4_trees_3),
    []).

fof(dt_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] : 
          ( m5_trees_3(C,A,B)
         => ( v1_funct_1(C)
            & v3_trees_2(C)
            & m3_trees_2(C,A) ) ) ) ),
    file(trees_3,m5_trees_3),
    []).

fof(dt_u1_lang1,axiom,(
    ! [A] : 
      ( l1_lang1(A)
     => m2_relset_1(u1_lang1(A),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ),
    file(lang1,u1_lang1),
    []).

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(dt_u4_msualg_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l2_msualg_1(B,A) )
     => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ),
    file(msualg_1,u4_msualg_1),
    []).

fof(dt_u5_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A) )
     => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ),
    file(msualg_1,u5_msualg_1),
    []).

fof(existence_l1_lang1,axiom,(
    ? [A] : l1_lang1(A) ),
    file(lang1,l1_lang1),
    []).

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

fof(existence_l1_orders_2,axiom,(
    ? [A] : l1_orders_2(A) ),
    file(orders_2,l1_orders_2),
    []).

fof(existence_l1_osalg_1,axiom,(
    ? [A] : l1_osalg_1(A) ),
    file(osalg_1,l1_osalg_1),
    []).

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

fof(existence_l2_msualg_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l2_msualg_1(B,A) ) ),
    file(msualg_1,l2_msualg_1),
    []).

fof(existence_l2_osalg_1,axiom,(
    ? [A] : l2_osalg_1(A) ),
    file(osalg_1,l2_osalg_1),
    []).

fof(existence_l3_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : l3_msualg_1(B,A) ) ),
    file(msualg_1,l3_msualg_1),
    []).

fof(existence_l3_osalg_1,axiom,(
    ? [A] : l3_osalg_1(A) ),
    file(osalg_1,l3_osalg_1),
    []).

fof(existence_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ? [D] : m1_dtconstr(D,A,B,C) ) ),
    file(dtconstr,m1_dtconstr),
    []).

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

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

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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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),
    []).

fof(existence_m3_trees_2,axiom,(
    ! [A] : 
    ? [B] : m3_trees_2(B,A) ),
    file(trees_2,m3_trees_2),
    []).

fof(existence_m4_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : m4_trees_3(B,A) ) ),
    file(trees_3,m4_trees_3),
    []).

fof(existence_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ? [C] : m5_trees_3(C,A,B) ) ),
    file(trees_3,m5_trees_3),
    []).

fof(fc1_dtconstr,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,k3_finseq_2(A)) )
     => ( ~ v3_struct_0(g1_lang1(A,B))
        & v1_lang1(g1_lang1(A,B)) ) ) ),
    file(dtconstr,fc1_dtconstr),
    []).

fof(fc1_msafree,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k2_card_3(B))
        & v2_relat_1(k2_card_3(B))
        & v1_funct_1(k2_card_3(B)) ) ) ),
    file(msafree,fc1_msafree),
    []).

fof(fc1_msualg_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & v5_msualg_1(B,A)
        & l2_msualg_1(B,A) )
     => ( v1_relat_1(u4_msualg_1(A,B))
        & v2_relat_1(u4_msualg_1(A,B))
        & v1_funct_1(u4_msualg_1(A,B)) ) ) ),
    file(msualg_1,fc1_msualg_1),
    []).

fof(fc1_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_osafree(A,B))
        & v1_lang1(k2_osafree(A,B)) ) ) ),
    file(osafree,fc1_osafree),
    []).

fof(fc1_pboole,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( v1_relat_1(k6_pboole(A,B))
        & v2_relat_1(k6_pboole(A,B))
        & ~ v3_relat_1(k6_pboole(A,B))
        & v1_funct_1(k6_pboole(A,B)) ) ) ),
    file(pboole,fc1_pboole),
    []).

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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

fof(fc2_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & l1_lang1(A) )
     => ( ~ v1_xboole_0(k4_dtconstr(A))
        & v3_trees_3(k4_dtconstr(A)) ) ) ),
    file(dtconstr,fc2_dtconstr),
    []).

fof(fc2_msafree,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A) )
     => ~ v1_xboole_0(k3_card_3(B)) ) ),
    file(msafree,fc2_msafree),
    []).

fof(fc2_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k2_osafree(A,B))
        & v1_lang1(k2_osafree(A,B))
        & v1_dtconstr(k2_osafree(A,B))
        & v2_dtconstr(k2_osafree(A,B))
        & v3_dtconstr(k2_osafree(A,B)) ) ) ),
    file(osafree,fc2_osafree),
    []).

fof(fc2_pboole,axiom,(
    ! [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),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_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_dtconstr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_dtconstr(A)
        & l1_lang1(A) )
     => ( ~ v1_xboole_0(k4_dtconstr(A))
        & v3_trees_3(k4_dtconstr(A)) ) ) ),
    file(dtconstr,fc3_dtconstr),
    []).

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_osafree,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v1_xboole_0(k4_osafree(A,B,C))
        & v3_trees_3(k4_osafree(A,B,C)) ) ) ),
    file(osafree,fc3_osafree),
    []).

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

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_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v1_relat_1(k5_osafree(A,B))
        & v2_relat_1(k5_osafree(A,B))
        & ~ v3_relat_1(k5_osafree(A,B))
        & v1_funct_1(k5_osafree(A,B))
        & v11_osalg_1(k5_osafree(A,B),A) ) ) ),
    file(osafree,fc4_osafree),
    []).

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

fof(fc5_osafree,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A)
        & v2_relat_1(B)
        & m1_pboole(B,u1_struct_0(A)) )
     => ( v4_msualg_1(k8_osafree(A,B),A)
        & v5_msualg_1(k8_osafree(A,B),A)
        & v12_osalg_1(k8_osafree(A,B),A) ) ) ),
    file(osafree,fc5_osafree),
    []).

fof(fc6_trees_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k5_trees_3(A))
        & v3_trees_3(k5_trees_3(A)) ) ) ),
    file(trees_3,fc6_trees_3),
    []).

fof(fc7_funcop_1,axiom,(
    ! [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),
    []).

fof(fc8_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k5_relat_1(B,A))
        & v1_funct_1(k5_relat_1(B,A))
        & v1_funcop_1(k5_relat_1(B,A)) ) ) ),
    file(funcop_1,fc8_funcop_1),
    []).

fof(fraenkel_a_3_0_osafree,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & v4_osalg_1(B)
        & v5_osalg_1(B)
        & l3_osalg_1(B)
        & v2_relat_1(C)
        & m1_pboole(C,u1_struct_0(B))
        & m1_subset_1(D,u1_struct_0(B)) )
     => ( r2_hidden(A,a_3_0_osafree(B,C,D))
      <=> ? [E] : 
            ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C)))
            & A = E
            & ~ ( ! [F] : 
                    ( m1_subset_1(F,u1_struct_0(B))
                   => ! [G] : ~ ( r3_orders_2(B,F,D)
                        & r2_hidden(G,k1_funct_1(C,F))
                        & E = k1_trees_4(k4_tarski(G,F)) ) )
                & ! [F] : 
                    ( m1_subset_1(F,u1_msualg_1(B))
                   => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0)
                        & r3_orders_2(B,k1_osalg_1(B,F),D) ) ) ) ) ) ) ),
    file(osafree,a_3_0_osafree),
    []).

fof(free_g1_lang1,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,A,k3_finseq_2(A))
     => ! [C,D] : 
          ( g1_lang1(A,B) = g1_lang1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(lang1,g1_lang1),
    []).

fof(free_g3_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & m1_pboole(B,u1_struct_0(A))
        & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) )
     => ! [D,E,F] : 
          ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(msualg_1,g3_msualg_1),
    []).

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

fof(rc10_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A) ) ) ),
    file(osalg_1,rc10_osalg_1),
    []).

fof(rc11_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_pboole(B,u1_struct_0(A))
          & v1_relat_1(B)
          & v2_relat_1(B)
          & v1_funct_1(B)
          & v11_osalg_1(B,A) ) ) ),
    file(osalg_1,rc11_osalg_1),
    []).

fof(rc12_osalg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & v4_osalg_1(A)
        & v5_osalg_1(A)
        & l3_osalg_1(A) )
     => ? [B] : 
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A)
          & v5_msualg_1(B,A)
          & v12_osalg_1(B,A) ) ) ),
    file(osalg_1,rc12_osalg_1),
    []).

fof(rc1_dtconstr,axiom,(
    ? [A] : 
      ( l1_lang1(A)
      & ~ v3_struct_0(A)
      & v1_lang1(A)
      & v1_dtconstr(A)
      & v2_dtconstr(A)
      & v3_dtconstr(A) ) ),
    file(dtconstr,rc1_dtconstr),
    []).

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

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

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

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

fof(rc2_partfun1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C) ) ),
    file(partfun1,rc2_partfun1),
    []).

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

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

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

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

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

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

fof(rc5_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : 
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A) ) ) ),
    file(msualg_1,rc5_msualg_1),
    []).

fof(rc5_osalg_1,axiom,(
    ? [A] : 
      ( l1_osalg_1(A)
      & ~ v3_struct_0(A)
      & ~ v2_msualg_1(A) ) ),
    file(osalg_1,rc5_osalg_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(rc6_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ? [B] : 
          ( l3_msualg_1(B,A)
          & v4_msualg_1(B,A)
          & v5_msualg_1(B,A) ) ) ),
    file(msualg_1,rc6_msualg_1),
    []).

fof(redefinition_k1_osalg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A)) )
     => k1_osalg_1(A,B) = k2_msualg_1(A,B) ) ),
    file(osalg_1,k1_osalg_1),
    []).

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

fof(redefinition_k3_msafree,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k3_msafree(A,B) = k2_card_3(B) ) ),
    file(msafree,k3_msafree),
    []).

fof(redefinition_k7_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,B) )
     => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(pboole,k7_pboole),
    []).

fof(redefinition_k8_pboole,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & v2_relat_1(D)
        & m1_pboole(D,B) )
     => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ),
    file(pboole,k8_pboole),
    []).

fof(redefinition_m1_dtconstr,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(B)) )
     => ! [D] : 
          ( m1_dtconstr(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(dtconstr,m1_dtconstr),
    []).

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(redefinition_m5_trees_3,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] : 
          ( m5_trees_3(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(trees_3,m5_trees_3),
    []).

fof(redefinition_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_orders_2(A,B,C)
      <=> r1_orders_2(A,B,C) ) ) ),
    file(orders_2,r3_orders_2),
    []).

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

fof(reflexivity_r3_orders_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r3_orders_2(A,B,B) ) ),
    file(orders_2,r3_orders_2),
    []).

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

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

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

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(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),
    []).