% Mizar problem: t17_lmod_5,lmod_5,476,30 
fof(t17_lmod_5,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => k1_lmod_5(A,B,k4_subset_1(u1_struct_0(B),C,D)) = k1_vectsp_5(A,B,k1_lmod_5(A,B,C),k1_lmod_5(A,B,D)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v11_vectsp_1,antisymmetry_r2_hidden,cc1_finset_1,cc1_funct_1,cc1_relset_1,cc1_vectsp_1,cc2_finset_1,cc2_funct_1,cc2_vectsp_1,cc3_vectsp_1,cc4_vectsp_1,cc5_vectsp_1,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k4_rlvect_1,commutativity_k4_subset_1,commutativity_k5_subset_1,d10_vectsp_6,d11_vectsp_6,d2_xboole_0,d3_tarski,d3_xboole_0,d4_vectsp_6,d4_xboole_0,d5_vectsp_6,d7_vectsp_6,dt_g4_vectsp_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_lmod_5,dt_k1_rlvect_1,dt_k1_vectsp_5,dt_k1_vectsp_6,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_rlvect_1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_xboole_0,dt_k4_rlvect_1,dt_k4_subset_1,dt_k4_vectsp_6,dt_k4_xboole_0,dt_k5_subset_1,dt_k5_vectsp_6,dt_k6_subset_1,dt_k8_funct_2,dt_l1_group_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_l4_vectsp_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_subset_1,dt_m1_vectsp_4,dt_m1_vectsp_6,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_vectsp_6,dt_u1_rlvect_1,dt_u1_struct_0,dt_u2_struct_0,dt_u2_vectsp_1,existence_l1_group_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_l4_vectsp_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_subset_1,existence_m1_vectsp_4,existence_m1_vectsp_6,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_vectsp_6,fc10_finset_1,fc11_finset_1,fc12_finset_1,fc14_finset_1,fc1_struct_0,fc1_xboole_0,fc2_xboole_0,fc3_xboole_0,fc6_vectsp_1,fc9_finset_1,fraenkel_a_3_0_vectsp_6,fraenkel_a_3_1_lmod_5,free_g4_vectsp_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,rc11_vectsp_1,rc12_vectsp_1,rc13_vectsp_1,rc1_finset_1,rc1_funct_1,rc1_vectsp_4,rc1_xboole_0,rc2_funct_1,rc2_xboole_0,rc3_finset_1,rc3_funct_1,rc3_struct_0,rc4_finset_1,rc4_struct_0,rc5_struct_0,rc8_vectsp_1,rc9_vectsp_1,redefinition_k1_fraenkel,redefinition_k4_rlvect_1,redefinition_k4_subset_1,redefinition_k5_subset_1,redefinition_k6_subset_1,redefinition_k8_funct_2,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_r1_vectsp_6,reflexivity_r1_tarski,reflexivity_r1_vectsp_6,s9_funct_2__e5_18_1__lmod_5,s9_funct_2__e9_18_1__lmod_5,symmetry_r1_vectsp_6,t10_rlvect_1,t11_funct_2,t15_lmod_5,t17_xboole_1,t1_boole,t1_subset,t1_xboole_1,t2_boole,t2_subset,t2_tarski,t33_vectsp_4,t36_vectsp_4,t3_boole,t3_subset,t40_vectsp_5,t4_boole,t4_subset,t5_subset,t5_vectsp_5,t6_boole,t77_vectsp_6,t7_boole,t7_xboole_1,t8_boole,t9_lmod_5]),
    [file(lmod_5,t17_lmod_5)]).

fof(abstractness_v11_vectsp_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l4_vectsp_1(B,A) )
     => ( v11_vectsp_1(B,A)
       => B = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) ) ) ),
    file(vectsp_1,v11_vectsp_1),
    []).

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

fof(cc1_finset_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    []).

fof(cc1_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_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(cc1_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc1_vectsp_1),
    []).

fof(cc2_finset_1,axiom,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_finset_1(B) ) ) ),
    file(finset_1,cc2_finset_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_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc2_vectsp_1),
    []).

fof(cc3_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc3_vectsp_1),
    []).

fof(cc4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(vectsp_1,cc4_vectsp_1),
    []).

fof(cc5_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc5_vectsp_1),
    []).

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(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(commutativity_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(commutativity_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(commutativity_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(d10_vectsp_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_6(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => ( r1_vectsp_6(A,B,C,D)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(B))
                       => k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) ) ) ) ) ) ) ),
    file(vectsp_6,d10_vectsp_6),
    []).

fof(d11_vectsp_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_6(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => ! [E] : 
                      ( m1_vectsp_6(E,A,B)
                     => ( E = k5_vectsp_6(A,B,C,D)
                      <=> ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(B))
                           => k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,F) = k4_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F)) ) ) ) ) ) ) ) ),
    file(vectsp_6,d11_vectsp_6),
    []).

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(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_vectsp_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A)))
             => ( m1_vectsp_6(C,A,B)
              <=> ? [D] : 
                    ( v1_finset_1(D)
                    & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                    & ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( ~ r2_hidden(E,D)
                         => k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E) = k1_rlvect_1(A) ) ) ) ) ) ) ) ),
    file(vectsp_6,d4_vectsp_6),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_vectsp_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_6(C,A,B)
             => k1_vectsp_6(A,B,C) = a_3_0_vectsp_6(A,B,C) ) ) ) ),
    file(vectsp_6,d5_vectsp_6),
    []).

fof(d7_vectsp_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => ( m2_vectsp_6(D,A,B,C)
                  <=> r1_tarski(k1_vectsp_6(A,B,D),C) ) ) ) ) ) ),
    file(vectsp_6,d7_vectsp_6),
    []).

fof(dt_g4_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B)
        & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) )
     => ( v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A)
        & l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) ) ) ),
    file(vectsp_1,g4_vectsp_1),
    []).

fof(dt_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

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

fof(dt_k1_funct_2,axiom,(
    $true ),
    file(funct_2,k1_funct_2),
    []).

fof(dt_k1_lmod_5,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ( v11_vectsp_1(k1_lmod_5(A,B,C),A)
        & m1_vectsp_4(k1_lmod_5(A,B,C),A,B) ) ) ),
    file(lmod_5,k1_lmod_5),
    []).

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    []).

fof(dt_k1_vectsp_5,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_vectsp_4(C,A,B)
        & m1_vectsp_4(D,A,B) )
     => ( v11_vectsp_1(k1_vectsp_5(A,B,C,D),A)
        & m1_vectsp_4(k1_vectsp_5(A,B,C,D),A,B) ) ) ),
    file(vectsp_5,k1_vectsp_5),
    []).

fof(dt_k1_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B) )
     => ( v1_finset_1(k1_vectsp_6(A,B,C))
        & m1_subset_1(k1_vectsp_6(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ) ),
    file(vectsp_6,k1_vectsp_6),
    []).

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_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k2_rlvect_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_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(dt_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(dt_k4_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B) )
     => m1_subset_1(k4_vectsp_6(A,B,C),u1_struct_0(B)) ) ),
    file(vectsp_6,k4_vectsp_6),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(dt_k5_vectsp_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B)
        & m1_vectsp_6(D,A,B) )
     => m1_vectsp_6(k5_vectsp_6(A,B,C,D),A,B) ) ),
    file(vectsp_6,k5_vectsp_6),
    []).

fof(dt_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(dt_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

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

fof(dt_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(dt_l4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ! [B] : 
          ( l4_vectsp_1(B,A)
         => l1_rlvect_1(B) ) ) ),
    file(vectsp_1,l4_vectsp_1),
    []).

fof(dt_m1_fraenkel,axiom,(
    ! [A,B,C] : 
      ( m1_fraenkel(C,A,B)
     => ( ~ v1_xboole_0(C)
        & v1_fraenkel(C) ) ) ),
    file(fraenkel,m1_fraenkel),
    []).

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_m1_vectsp_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A) )
     => ! [C] : 
          ( m1_vectsp_4(C,A,B)
         => ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v12_vectsp_1(C,A)
            & l4_vectsp_1(C,A) ) ) ) ),
    file(vectsp_4,m1_vectsp_4),
    []).

fof(dt_m1_vectsp_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ! [C] : 
          ( m1_vectsp_6(C,A,B)
         => m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A))) ) ) ),
    file(vectsp_6,m1_vectsp_6),
    []).

fof(dt_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
         => ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B) ) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_m2_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ! [D] : 
          ( m2_vectsp_6(D,A,B,C)
         => m1_vectsp_6(D,A,B) ) ) ),
    file(vectsp_6,m2_vectsp_6),
    []).

fof(dt_u1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( v1_funct_1(u1_rlvect_1(A))
        & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(rlvect_1,u1_rlvect_1),
    []).

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

fof(dt_u2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ),
    file(struct_0,u2_struct_0),
    []).

fof(dt_u2_vectsp_1,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l4_vectsp_1(B,A) )
     => ( v1_funct_1(u2_vectsp_1(A,B))
        & v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B))
        & m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) ) ) ),
    file(vectsp_1,u2_vectsp_1),
    []).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

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

fof(existence_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(existence_l4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l4_vectsp_1(B,A) ) ),
    file(vectsp_1,l4_vectsp_1),
    []).

fof(existence_m1_fraenkel,axiom,(
    ! [A,B] : 
    ? [C] : m1_fraenkel(C,A,B) ),
    file(fraenkel,m1_fraenkel),
    []).

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_m1_vectsp_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A) )
     => ? [C] : m1_vectsp_4(C,A,B) ) ),
    file(vectsp_4,m1_vectsp_4),
    []).

fof(existence_m1_vectsp_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A) )
     => ? [C] : m1_vectsp_6(C,A,B) ) ),
    file(vectsp_6,m1_vectsp_6),
    []).

fof(existence_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ? [D] : m2_fraenkel(D,A,B,C) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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

fof(existence_m2_vectsp_6,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
     => ? [D] : m2_vectsp_6(D,A,B,C) ) ),
    file(vectsp_6,m2_vectsp_6),
    []).

fof(fc10_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(B)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc10_finset_1),
    []).

fof(fc11_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k3_xboole_0(A,B)) ) ),
    file(finset_1,fc11_finset_1),
    []).

fof(fc12_finset_1,axiom,(
    ! [A,B] : 
      ( v1_finset_1(A)
     => v1_finset_1(k4_xboole_0(A,B)) ) ),
    file(finset_1,fc12_finset_1),
    []).

fof(fc14_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_zfmisc_1(A,B)) ) ),
    file(finset_1,fc14_finset_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_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_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc6_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l1_struct_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B)
        & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) )
     => ( ~ v3_struct_0(g4_vectsp_1(A,B,C,D,E))
        & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) ) ) ),
    file(vectsp_1,fc6_vectsp_1),
    []).

fof(fc9_finset_1,axiom,(
    ! [A,B] : 
      ( ( v1_finset_1(A)
        & v1_finset_1(B) )
     => v1_finset_1(k2_xboole_0(A,B)) ) ),
    file(finset_1,fc9_finset_1),
    []).

fof(fraenkel_a_3_0_vectsp_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l2_struct_0(B)
        & ~ v3_struct_0(C)
        & l4_vectsp_1(C,B)
        & m1_vectsp_6(D,B,C) )
     => ( r2_hidden(A,a_3_0_vectsp_6(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(C))
            & A = E
            & k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) != k1_rlvect_1(B) ) ) ) ),
    file(vectsp_6,a_3_0_vectsp_6),
    []).

fof(fraenkel_a_3_1_lmod_5,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & ~ v10_vectsp_1(B)
        & v2_vectsp_2(B)
        & l3_vectsp_1(B)
        & ~ v3_struct_0(C)
        & v3_rlvect_1(C)
        & v4_rlvect_1(C)
        & v5_rlvect_1(C)
        & v6_rlvect_1(C)
        & v12_vectsp_1(C,B)
        & l4_vectsp_1(C,B)
        & m1_vectsp_6(D,B,C) )
     => ( r2_hidden(A,a_3_1_lmod_5(B,C,D))
      <=> ? [E] : 
            ( m1_subset_1(E,u1_struct_0(C))
            & A = E
            & k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) != k1_rlvect_1(B) ) ) ) ),
    file(lmod_5,a_3_1_lmod_5),
    []).

fof(free_g4_vectsp_1,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l1_struct_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(B,B),B)
        & m1_relset_1(C,k2_zfmisc_1(B,B),B)
        & m1_subset_1(D,B)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B)
        & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) )
     => ! [F,G,H,I,J] : 
          ( g4_vectsp_1(A,B,C,D,E) = g4_vectsp_1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) ),
    file(vectsp_1,g4_vectsp_1),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,B) = B ) ),
    file(subset_1,k4_subset_1),
    []).

fof(idempotence_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,B) = B ) ),
    file(subset_1,k5_subset_1),
    []).

fof(rc11_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l4_vectsp_1(B,A)
          & v11_vectsp_1(B,A) ) ) ),
    file(vectsp_1,rc11_vectsp_1),
    []).

fof(rc12_vectsp_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : 
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v11_vectsp_1(B,A) ) ) ),
    file(vectsp_1,rc12_vectsp_1),
    []).

fof(rc13_vectsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ? [B] : 
          ( l4_vectsp_1(B,A)
          & ~ v3_struct_0(B)
          & v3_rlvect_1(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & v11_vectsp_1(B,A)
          & v12_vectsp_1(B,A) ) ) ),
    file(vectsp_1,rc13_vectsp_1),
    []).

fof(rc1_finset_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    []).

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

fof(rc1_vectsp_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A) )
     => ? [C] : 
          ( m1_vectsp_4(C,A,B)
          & ~ v3_struct_0(C)
          & v3_rlvect_1(C)
          & v4_rlvect_1(C)
          & v5_rlvect_1(C)
          & v6_rlvect_1(C)
          & v11_vectsp_1(C,A)
          & v12_vectsp_1(C,A) ) ) ),
    file(vectsp_4,rc1_vectsp_4),
    []).

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

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_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc3_finset_1),
    []).

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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_finset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B)
          & v1_finset_1(B) ) ) ),
    file(finset_1,rc4_finset_1),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

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(rc8_vectsp_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v4_group_1(A)
      & v7_group_1(A) ) ),
    file(vectsp_1,rc8_vectsp_1),
    []).

fof(rc9_vectsp_1,axiom,(
    ? [A] : 
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v6_vectsp_1(A)
      & v8_vectsp_1(A) ) ),
    file(vectsp_1,rc9_vectsp_1),
    []).

fof(redefinition_k1_fraenkel,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ),
    file(fraenkel,k1_fraenkel),
    []).

fof(redefinition_k4_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ),
    file(rlvect_1,k4_rlvect_1),
    []).

fof(redefinition_k4_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(subset_1,k4_subset_1),
    []).

fof(redefinition_k5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ),
    file(subset_1,k5_subset_1),
    []).

fof(redefinition_k6_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k1_zfmisc_1(A))
        & m1_subset_1(C,k1_zfmisc_1(A)) )
     => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ),
    file(subset_1,k6_subset_1),
    []).

fof(redefinition_k8_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_subset_1(D,A) )
     => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(funct_2,k8_funct_2),
    []).

fof(redefinition_m2_fraenkel,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(B)
        & m1_fraenkel(C,A,B) )
     => ! [D] : 
          ( m2_fraenkel(D,A,B,C)
        <=> m1_subset_1(D,C) ) ) ),
    file(fraenkel,m2_fraenkel),
    []).

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_r1_vectsp_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B)
        & m1_vectsp_6(D,A,B) )
     => ( r1_vectsp_6(A,B,C,D)
      <=> C = D ) ) ),
    file(vectsp_6,r1_vectsp_6),
    []).

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

fof(reflexivity_r1_vectsp_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B)
        & m1_vectsp_6(D,A,B) )
     => r1_vectsp_6(A,B,C,C) ) ),
    file(vectsp_6,r1_vectsp_6),
    []).

fof(s9_funct_2__e5_18_1__lmod_5,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
        & m2_vectsp_6(E,A,B,k4_subset_1(u1_struct_0(B),C,D)) )
     => ( ! [F] : 
            ( r2_hidden(F,u1_struct_0(B))
           => ( ( r2_hidden(F,k5_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
               => r2_hidden(k1_funct_1(E,F),u1_struct_0(A)) )
              & ( ~ r2_hidden(F,k5_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
               => r2_hidden(k1_rlvect_1(A),u1_struct_0(A)) ) ) )
       => ? [F] : 
            ( v1_funct_1(F)
            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(A))
            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A))
            & ! [G] : 
                ( r2_hidden(G,u1_struct_0(B))
               => ( ( r2_hidden(G,k5_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
                   => k1_funct_1(F,G) = k1_funct_1(E,G) )
                  & ( ~ r2_hidden(G,k5_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
                   => k1_funct_1(F,G) = k1_rlvect_1(A) ) ) ) ) ) ) ),
    file(lmod_5,s9_funct_2__e5_18_1__lmod_5),
    []).

fof(s9_funct_2__e9_18_1__lmod_5,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v12_vectsp_1(B,A)
        & l4_vectsp_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
        & m2_vectsp_6(E,A,B,k4_subset_1(u1_struct_0(B),C,D)) )
     => ( ! [F] : 
            ( r2_hidden(F,u1_struct_0(B))
           => ( ( r2_hidden(F,k6_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
               => r2_hidden(k1_funct_1(E,F),u1_struct_0(A)) )
              & ( ~ r2_hidden(F,k6_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
               => r2_hidden(k1_rlvect_1(A),u1_struct_0(A)) ) ) )
       => ? [F] : 
            ( v1_funct_1(F)
            & v1_funct_2(F,u1_struct_0(B),u1_struct_0(A))
            & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A))
            & ! [G] : 
                ( r2_hidden(G,u1_struct_0(B))
               => ( ( r2_hidden(G,k6_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
                   => k1_funct_1(F,G) = k1_funct_1(E,G) )
                  & ( ~ r2_hidden(G,k6_subset_1(u1_struct_0(B),k1_vectsp_6(A,B,E),C))
                   => k1_funct_1(F,G) = k1_rlvect_1(A) ) ) ) ) ) ) ),
    file(lmod_5,s9_funct_2__e9_18_1__lmod_5),
    []).

fof(symmetry_r1_vectsp_6,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l2_struct_0(A)
        & ~ v3_struct_0(B)
        & l4_vectsp_1(B,A)
        & m1_vectsp_6(C,A,B)
        & m1_vectsp_6(D,A,B) )
     => ( r1_vectsp_6(A,B,C,D)
       => r1_vectsp_6(A,B,D,C) ) ) ),
    file(vectsp_6,r1_vectsp_6),
    []).

fof(t10_rlvect_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    []).

fof(t11_funct_2,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => r2_hidden(C,k1_funct_2(A,B)) ) ) ),
    file(funct_2,t11_funct_2),
    []).

fof(t15_lmod_5,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( r1_tarski(C,D)
                   => m1_vectsp_4(k1_lmod_5(A,B,C),A,k1_lmod_5(A,B,D)) ) ) ) ) ) ),
    file(lmod_5,t15_lmod_5),
    []).

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

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(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t33_vectsp_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v11_vectsp_1(B,A)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v11_vectsp_1(C,A)
                & v12_vectsp_1(C,A)
                & l4_vectsp_1(C,A) )
             => ( ( m1_vectsp_4(C,A,B)
                  & m1_vectsp_4(B,A,C) )
               => C = B ) ) ) ) ),
    file(vectsp_4,t33_vectsp_4),
    []).

fof(t36_vectsp_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_4(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_4(D,A,B)
                 => ( ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r1_rlvect_1(C,E)
                         => r1_rlvect_1(D,E) ) )
                   => m1_vectsp_4(C,A,D) ) ) ) ) ) ),
    file(vectsp_4,t36_vectsp_4),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

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

fof(t40_vectsp_5,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_4(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] : 
                      ( m1_vectsp_4(E,A,B)
                     => ( ( m1_vectsp_4(C,A,D)
                          & m1_vectsp_4(E,A,D) )
                       => m1_vectsp_4(k1_vectsp_5(A,B,C,E),A,D) ) ) ) ) ) ) ),
    file(vectsp_5,t40_vectsp_5),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

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(t5_vectsp_5,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_4(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_4(D,A,B)
                 => ! [E] : 
                      ( r1_rlvect_1(k1_vectsp_5(A,B,C,D),E)
                    <=> ? [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                          & ? [G] : 
                              ( m1_subset_1(G,u1_struct_0(B))
                              & r1_rlvect_1(C,F)
                              & r1_rlvect_1(D,G)
                              & E = k4_rlvect_1(B,F,G) ) ) ) ) ) ) ) ),
    file(vectsp_5,t5_vectsp_5),
    []).

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

fof(t77_vectsp_6,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v12_vectsp_1(B,A)
            & l4_vectsp_1(B,A) )
         => ! [C] : 
              ( m1_vectsp_6(C,A,B)
             => ! [D] : 
                  ( m1_vectsp_6(D,A,B)
                 => k4_vectsp_6(A,B,k5_vectsp_6(A,B,C,D)) = k4_rlvect_1(B,k4_vectsp_6(A,B,C),k4_vectsp_6(A,B,D)) ) ) ) ) ),
    file(vectsp_6,t77_vectsp_6),
    []).

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

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

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

fof(t9_lmod_5,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v4_group_1(B)
        & v7_group_1(B)
        & v6_vectsp_1(B)
        & v7_vectsp_1(B)
        & v8_vectsp_1(B)
        & ~ v10_vectsp_1(B)
        & v2_vectsp_2(B)
        & l3_vectsp_1(B) )
     => ! [C] : 
          ( ( ~ v3_struct_0(C)
            & v3_rlvect_1(C)
            & v4_rlvect_1(C)
            & v5_rlvect_1(C)
            & v6_rlvect_1(C)
            & v12_vectsp_1(C,B)
            & l4_vectsp_1(C,B) )
         => ! [D] : 
              ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C)))
             => ( r1_rlvect_1(k1_lmod_5(B,C,D),A)
              <=> ? [E] : 
                    ( m2_vectsp_6(E,B,C,D)
                    & A = k4_vectsp_6(B,C,E) ) ) ) ) ) ),
    file(lmod_5,t9_lmod_5),
    []).