% Mizar problem: t25_latsubgr,latsubgr,526,34 
fof(t25_latsubgr,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_group_3(A))) )
         => ( r2_hidden(k5_group_2(A),B)
           => r1_group_2(A,k2_latsubgr(A,B),k5_group_2(A)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_group_1,antisymmetry_r2_hidden,cc1_funct_2,cc1_relset_1,cc5_funct_2,cc6_funct_2,d10_xboole_0,d1_group_3,d1_latsubgr,d2_latsubgr,d5_group_2,d7_group_2,dt_g1_group_1,dt_k18_group_2,dt_k1_funct_1,dt_k1_group_3,dt_k1_latsubgr,dt_k1_realset1,dt_k1_setfam_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funct_2,dt_k2_group_1,dt_k2_latsubgr,dt_k2_zfmisc_1,dt_k5_finsub_1,dt_k5_group_2,dt_k6_domain_1,dt_k6_setfam_1,dt_k8_funct_2,dt_k9_relat_1,dt_l1_group_1,dt_l1_struct_0,dt_m1_group_2,dt_m1_group_6,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_group_1,dt_u1_struct_0,existence_l1_group_1,existence_l1_struct_0,existence_m1_group_2,existence_m1_group_6,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_group_3,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_subset_1,fc4_subset_1,free_g1_group_1,rc1_funct_2,rc1_subset_1,rc1_xboole_0,rc2_partfun1,rc2_subset_1,rc2_xboole_0,rc3_struct_0,rc5_struct_0,redefinition_k18_group_2,redefinition_k2_funct_2,redefinition_k6_domain_1,redefinition_k6_setfam_1,redefinition_k8_funct_2,redefinition_m1_group_6,redefinition_m2_relset_1,redefinition_r1_group_2,reflexivity_r1_group_2,reflexivity_r1_tarski,symmetry_r1_group_2,t1_subset,t2_subset,t3_subset,t43_funct_2,t4_setfam_1,t4_subset,t5_subset,t6_boole,t77_group_2,t7_boole,t8_boole]),
    [file(latsubgr,t25_latsubgr)]).

fof(abstractness_v1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_group_1(A)
       => A = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ),
    file(group_1,v1_group_1),
    []).

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

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

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(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d1_group_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( B = k1_group_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ( v1_group_1(C)
                & m1_group_2(C,A) ) ) ) ) ),
    file(group_3,d1_group_3),
    []).

fof(d1_latsubgr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
            & m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = k1_latsubgr(A)
          <=> ! [C] : 
                ( ( v1_group_1(C)
                  & m1_group_2(C,A) )
               => k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ) ),
    file(latsubgr,d1_latsubgr),
    []).

fof(d2_latsubgr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(k1_group_3(A))) )
         => ! [C] : 
              ( ( v1_group_1(C)
                & m1_group_2(C,A) )
             => ( C = k2_latsubgr(A,B)
              <=> u1_struct_0(C) = k6_setfam_1(u1_struct_0(A),k2_funct_2(k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)),k1_latsubgr(A),B)) ) ) ) ) ),
    file(latsubgr,d2_latsubgr),
    []).

fof(d5_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) )
         => ( m1_group_2(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & u1_group_1(B) = k1_realset1(u1_group_1(A),u1_struct_0(B)) ) ) ) ) ),
    file(group_2,d5_group_2),
    []).

fof(d7_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( ( v1_group_1(B)
            & m1_group_2(B,A) )
         => ( B = k5_group_2(A)
          <=> u1_struct_0(B) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) ),
    file(group_2,d7_group_2),
    []).

fof(dt_g1_group_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_group_1(g1_group_1(A,B))
        & l1_group_1(g1_group_1(A,B)) ) ) ),
    file(group_1,g1_group_1),
    []).

fof(dt_k18_group_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k18_group_2(A,B),k5_finsub_1(A)) ) ),
    file(group_2,k18_group_2),
    []).

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

fof(dt_k1_group_3,axiom,(
    $true ),
    file(group_3,k1_group_3),
    []).

fof(dt_k1_latsubgr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_funct_1(k1_latsubgr(A))
        & v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
        & m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ),
    file(latsubgr,k1_latsubgr),
    []).

fof(dt_k1_realset1,axiom,(
    $true ),
    file(realset1,k1_realset1),
    []).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    []).

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

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_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ),
    file(funct_2,k2_funct_2),
    []).

fof(dt_k2_group_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => m1_subset_1(k2_group_1(A),u1_struct_0(A)) ) ),
    file(group_1,k2_group_1),
    []).

fof(dt_k2_latsubgr,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(k1_group_3(A))) )
     => ( v1_group_1(k2_latsubgr(A,B))
        & m1_group_2(k2_latsubgr(A,B),A) ) ) ),
    file(latsubgr,k2_latsubgr),
    []).

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

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_k5_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ( v1_group_1(k5_group_2(A))
        & m1_group_2(k5_group_2(A),A) ) ) ),
    file(group_2,k5_group_2),
    []).

fof(dt_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(dt_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ),
    file(setfam_1,k6_setfam_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_k9_relat_1,axiom,(
    $true ),
    file(relat_1,k9_relat_1),
    []).

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

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

fof(dt_m1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => ( ~ v3_struct_0(B)
            & v3_group_1(B)
            & l1_group_1(B) ) ) ) ),
    file(group_2,m1_group_2),
    []).

fof(dt_m1_group_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ! [C] : 
          ( m1_group_6(C,A,B)
         => m1_group_2(C,A) ) ) ),
    file(group_6,m1_group_6),
    []).

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_u1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => ( v1_funct_1(u1_group_1(A))
        & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(group_1,u1_group_1),
    []).

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

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

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

fof(existence_m1_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & l1_group_1(A) )
     => ? [B] : m1_group_2(B,A) ) ),
    file(group_2,m1_group_2),
    []).

fof(existence_m1_group_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ? [C] : m1_group_6(C,A,B) ) ),
    file(group_6,m1_group_6),
    []).

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(fc1_group_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ~ v1_xboole_0(k1_group_3(A)) ) ),
    file(group_3,fc1_group_3),
    []).

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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

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(free_g1_group_1,axiom,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] : 
          ( g1_group_1(A,B) = g1_group_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(group_1,g1_group_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

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_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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_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(redefinition_k18_group_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k18_group_2(A,B) = k1_tarski(B) ) ),
    file(group_2,k18_group_2),
    []).

fof(redefinition_k2_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B) )
     => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ),
    file(funct_2,k2_funct_2),
    []).

fof(redefinition_k6_domain_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A) )
     => k6_domain_1(A,B) = k1_tarski(B) ) ),
    file(domain_1,k6_domain_1),
    []).

fof(redefinition_k6_setfam_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => k6_setfam_1(A,B) = k1_setfam_1(B) ) ),
    file(setfam_1,k6_setfam_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_m1_group_6,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & m1_group_2(B,A) )
     => ! [C] : 
          ( m1_group_6(C,A,B)
        <=> m1_group_2(C,B) ) ) ),
    file(group_6,m1_group_6),
    []).

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_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
      <=> B = C ) ) ),
    file(group_2,r1_group_2),
    []).

fof(reflexivity_r1_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => r1_group_2(A,B,B) ) ),
    file(group_2,r1_group_2),
    []).

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

fof(symmetry_r1_group_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A)
        & v1_group_1(B)
        & m1_group_2(B,A)
        & v1_group_1(C)
        & m1_group_2(C,A) )
     => ( r1_group_2(A,B,C)
       => r1_group_2(A,C,B) ) ) ),
    file(group_2,r1_group_2),
    []).

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

fof(t43_funct_2,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( ? [F] : 
                ( r2_hidden(F,A)
                & r2_hidden(F,C)
                & E = k1_funct_1(D,F) )
           => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ),
    file(funct_2,t43_funct_2),
    []).

fof(t4_setfam_1,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(k1_setfam_1(B),A) ) ),
    file(setfam_1,t4_setfam_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(t77_group_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_group_1(A)
        & v4_group_1(A)
        & l1_group_1(A) )
     => ! [B] : 
          ( m1_group_2(B,A)
         => m1_group_2(k5_group_2(A),B) ) ) ),
    file(group_2,t77_group_2),
    []).

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),
    []).