% Mizar problem: t30_pralg_3,pralg_3,1252,50 
fof(t30_pralg_3,conjecture,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( ( v5_msualg_1(D,B)
                    & l3_msualg_1(D,B) )
                 => ! [E] : 
                      ( ( v1_funcop_1(E)
                        & m1_pboole(E,A) )
                     => ~ ( ! [F] : 
                              ( m1_subset_1(F,A)
                             => ? [G] : 
                                  ( m3_pboole(G,u1_struct_0(B),u4_msualg_1(B,D),u4_msualg_1(B,k6_pralg_2(A,B,C,F)))
                                  & G = k1_funct_1(E,F)
                                  & r1_msualg_3(B,D,k6_pralg_2(A,B,C,F),G) ) )
                          & ! [F] : 
                              ( m3_pboole(F,u1_struct_0(B),u4_msualg_1(B,D),u4_msualg_1(B,k15_pralg_2(A,B,C)))
                             => ~ ( r1_msualg_3(B,D,k15_pralg_2(A,B,C),F)
                                  & ! [G] : 
                                      ( m1_subset_1(G,A)
                                     => k3_msualg_3(u1_struct_0(B),u4_msualg_1(B,D),u4_msualg_1(B,k15_pralg_2(A,B,C)),u4_msualg_1(B,k6_pralg_2(A,B,C,G)),F,k4_pralg_3(A,B,C,G)) = k1_funct_1(E,G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_msualg_1,cc1_pboole,cc1_relat_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_msualg_1,cc2_pboole,cc3_pboole,commutativity_k3_xboole_0,d11_msualg_1,d15_funct_1,d16_pralg_2,d17_pralg_1,d17_pralg_2,d18_pboole,d19_pralg_2,d1_cqc_lang,d1_funct_2,d1_pralg_3,d1_tarski,d20_pralg_2,d21_pralg_2,d24_pboole,d2_funct_2,d2_pralg_3,d3_pboole,d3_pralg_3,d3_tarski,d4_finseq_4,d5_funct_1,d6_pralg_2,d7_msualg_3,d8_pralg_2,d9_msualg_3,dt_g3_msualg_1,dt_k10_funct_6,dt_k10_pralg_2,dt_k11_pralg_2,dt_k12_pralg_2,dt_k13_finseq_1,dt_k13_pboole,dt_k13_pralg_2,dt_k14_pralg_2,dt_k15_pralg_1,dt_k15_pralg_2,dt_k1_cqc_lang,dt_k1_funct_1,dt_k1_funct_2,dt_k1_msualg_1,dt_k1_msualg_3,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funct_6,dt_k2_msualg_1,dt_k2_pralg_2,dt_k2_pralg_3,dt_k2_relat_1,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k3_msualg_1,dt_k3_msualg_3,dt_k3_pralg_2,dt_k3_pralg_3,dt_k3_tarski,dt_k3_xboole_0,dt_k4_card_3,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_msualg_1,dt_k4_pralg_3,dt_k4_relset_1,dt_k5_msualg_1,dt_k5_msualg_3,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_relset_1,dt_k6_msualg_3,dt_k6_pboole,dt_k6_pralg_2,dt_k7_funct_2,dt_k7_funct_6,dt_k7_pboole,dt_k8_funct_2,dt_k8_pboole,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_pralg_2,dt_m2_relset_1,dt_m3_pboole,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_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_pralg_2,existence_m2_relset_1,existence_m3_pboole,fc10_relat_1,fc12_relat_1,fc1_fraenkel,fc1_funct_1,fc1_msualg_1,fc1_msualg_3,fc1_pboole,fc1_pralg_2,fc1_pralg_3,fc1_relat_1,fc1_struct_0,fc1_subset_1,fc2_pboole,fc2_setfam_1,fc2_subset_1,fc3_msafree,fc3_pralg_3,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc6_funct_1,fc6_pralg_2,fc6_relat_1,fc7_funcop_1,fc7_pralg_2,fc7_relat_1,fc8_funcop_1,fc8_pralg_2,fc8_relat_1,fc9_relat_1,fraenkel_a_3_1_pralg_3,fraenkel_a_4_1_pralg_3,free_g3_msualg_1,idempotence_k3_xboole_0,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_partfun1,rc1_pboole,rc1_pralg_2,rc1_relat_1,rc1_setfam_1,rc1_subset_1,rc2_funct_1,rc2_partfun1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_funct_1,rc3_pboole,rc3_relat_1,rc3_struct_0,rc4_funct_1,rc4_pboole,rc5_funct_1,rc5_msualg_1,rc5_struct_0,rc6_msualg_1,redefinition_k1_msualg_3,redefinition_k3_finseq_2,redefinition_k3_msualg_3,redefinition_k3_pralg_2,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k6_msualg_3,redefinition_k6_pralg_2,redefinition_k7_funct_2,redefinition_k7_pboole,redefinition_k8_funct_2,redefinition_k8_pboole,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,reflexivity_r1_tarski,s5_pboole__e2_37__pralg_3,t10_pralg_2,t10_pralg_3,t11_pralg_2,t11_relset_1,t12_pralg_3,t13_pralg_3,t14_pralg_3,t15_pralg_2,t15_pralg_3,t16_pralg_2,t18_card_3,t18_pralg_3,t19_pralg_3,t1_subset,t22_funct_1,t23_pralg_3,t26_finseq_1,t27_pralg_3,t28_pralg_3,t29_pralg_3,t2_boole,t2_subset,t2_tarski,t3_subset,t46_relat_1,t4_subset,t5_subset,t6_boole,t7_boole,t85_funct_6,t86_funct_6,t8_boole,t9_funct_1,t9_pralg_3]),
    [file(pralg_3,t30_pralg_3)]).

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_fraenkel,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B) ) ) ) ),
    file(fraenkel,cc1_fraenkel),
    []).

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

fof(cc1_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] : 
          ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
         => ~ v1_xboole_0(C) ) ) ),
    file(msualg_1,cc1_msualg_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_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc1_setfam_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_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_msualg_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A) )
     => ! [C] : 
          ( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))))
         => ~ v1_xboole_0(C) ) ) ),
    file(msualg_1,cc2_msualg_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(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d11_msualg_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) ),
    file(msualg_1,d11_msualg_1),
    []).

fof(d15_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_relat_1(A)
      <=> ! [B] : ~ ( r2_hidden(B,k1_relat_1(A))
            & v1_xboole_0(k1_funct_1(A,B)) ) ) ) ),
    file(funct_1,d15_funct_1),
    []).

fof(d16_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] : 
              ( m2_pralg_2(D,A,B)
             => ! [E] : 
                  ( m1_pboole(E,A)
                 => ( ( A != k1_xboole_0
                     => ( E = k10_pralg_2(A,B,C,D)
                      <=> ! [F] : ~ ( r2_hidden(F,A)
                            & ! [G] : 
                                ( l3_msualg_1(G,B)
                               => ~ ( G = k1_funct_1(D,F)
                                    & k1_funct_1(E,F) = k1_funct_1(u4_msualg_1(B,G),C) ) ) ) ) )
                    & ( A = k1_xboole_0
                     => ( E = k10_pralg_2(A,B,C,D)
                      <=> E = k1_xboole_0 ) ) ) ) ) ) ) ),
    file(pralg_2,d16_pralg_2),
    []).

fof(d17_pralg_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k15_pralg_1(A,B)
              <=> ( k1_relat_1(C) = k1_relat_1(A)
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(A))
                     => k1_funct_1(C,D) = k1_funct_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pralg_1,d17_pralg_1),
    []).

fof(d17_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ! [C] : 
          ( m2_pralg_2(C,A,B)
         => ! [D] : 
              ( m1_pboole(D,u1_struct_0(B))
             => ( D = k11_pralg_2(A,B,C)
              <=> ! [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                   => k1_funct_1(D,E) = k4_card_3(k10_pralg_2(A,B,E,C)) ) ) ) ) ) ),
    file(pralg_2,d17_pralg_2),
    []).

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

fof(d19_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B) )
     => ! [C] : 
          ( m2_pralg_2(C,A,B)
         => ! [D] : 
              ( m1_subset_1(D,u1_msualg_1(B))
             => k13_pralg_2(A,B,C,D) = k1_funct_1(k10_funct_6(k12_pralg_2(A,B,C)),D) ) ) ) ),
    file(pralg_2,d19_pralg_2),
    []).

fof(d1_cqc_lang,axiom,(
    ! [A,B,C,D] : 
      ( ( A = B
       => k1_cqc_lang(A,B,C,D) = C )
      & ( A != B
       => k1_cqc_lang(A,B,C,D) = D ) ) ),
    file(cqc_lang,d1_cqc_lang),
    []).

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

fof(d1_pralg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => k2_pralg_3(A,B,C) = k1_funct_1(k5_msualg_1(A,C,B),k1_xboole_0) ) ) ) ),
    file(pralg_3,d1_pralg_3),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d20_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B) )
     => ! [C] : 
          ( m2_pralg_2(C,A,B)
         => ! [D] : 
              ( m3_pboole(D,u1_msualg_1(B),k8_pboole(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),k6_pboole(u1_struct_0(B),k11_pralg_2(A,B,C))),k8_pboole(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),k11_pralg_2(A,B,C)))
             => ( ( A != k1_xboole_0
                 => ( D = k14_pralg_2(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_msualg_1(B))
                       => k1_funct_1(D,E) = k1_cqc_lang(k1_msualg_1(B,E),k1_xboole_0,k10_funct_6(k13_pralg_2(A,B,C,E)),k2_pralg_2(k3_pralg_2(k13_pralg_2(A,B,C,E)))) ) ) )
                & ( A = k1_xboole_0
                 => D = k14_pralg_2(A,B,C) ) ) ) ) ) ),
    file(pralg_2,d20_pralg_2),
    []).

fof(d21_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B) )
     => ! [C] : 
          ( m2_pralg_2(C,A,B)
         => k15_pralg_2(A,B,C) = g3_msualg_1(B,k11_pralg_2(A,B,C),k14_pralg_2(A,B,C)) ) ) ),
    file(pralg_2,d21_pralg_2),
    []).

fof(d24_pboole,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_funcop_1(C) )
             => ( C = k13_pboole(A,B)
              <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ),
    file(pboole,d24_pboole),
    []).

fof(d2_funct_2,axiom,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    []).

fof(d2_pralg_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( C = k3_pralg_3(A,B)
          <=> ( k1_relat_1(C) = k4_card_3(A)
              & ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r2_hidden(D,k1_relat_1(C))
                   => k1_funct_1(C,D) = k1_funct_1(D,B) ) ) ) ) ) ) ),
    file(pralg_3,d2_pralg_3),
    []).

fof(d3_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    []).

fof(d3_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(B),u4_msualg_1(B,k15_pralg_2(A,B,C)),u4_msualg_1(B,k6_pralg_2(A,B,C,D)))
                     => ( E = k4_pralg_3(A,B,C,D)
                      <=> ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(B))
                           => k1_msualg_3(u1_struct_0(B),u4_msualg_1(B,k15_pralg_2(A,B,C)),u4_msualg_1(B,k6_pralg_2(A,B,C,D)),E,F) = k3_pralg_3(k10_pralg_2(A,B,F,C),D) ) ) ) ) ) ) ) ),
    file(pralg_3,d3_pralg_3),
    []).

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

fof(d4_finseq_4,axiom,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    []).

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

fof(d6_pralg_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k2_pralg_2(A)
          <=> ( ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                <=> ? [D] : 
                      ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & r2_hidden(D,k1_relat_1(A))
                      & C = k10_funct_6(D) ) )
              & ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C) )
                 => ( r2_hidden(C,k1_relat_1(B))
                   => k1_funct_1(B,C) = k1_funct_1(A,k10_funct_6(C)) ) ) ) ) ) ) ),
    file(pralg_2,d6_pralg_2),
    []).

fof(d7_msualg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                     => ! [F] : 
                          ( m1_subset_1(F,k3_msualg_1(A,D,B))
                         => ~ ( k3_msualg_1(A,D,B) != k1_xboole_0
                              & k3_msualg_1(A,D,C) != k1_xboole_0
                              & k5_msualg_3(A,B,C,D,E,F) != k1_funct_1(k3_pralg_2(k5_relat_1(k1_msualg_1(A,D),E)),F) ) ) ) ) ) ) ) ),
    file(msualg_3,d7_msualg_3),
    []).

fof(d8_pralg_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] : 
          ( ( v1_funcop_1(B)
            & m1_pboole(B,k4_card_3(k2_funct_6(A))) )
         => ( B = k3_pralg_2(A)
          <=> ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C) )
               => ( r2_hidden(C,k4_card_3(k2_funct_6(A)))
                 => k1_funct_1(B,C) = k15_pralg_1(A,C) ) ) ) ) ) ),
    file(pralg_2,d8_pralg_2),
    []).

fof(d9_msualg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                 => ( r1_msualg_3(A,B,C,D)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_msualg_1(A))
                       => ( k3_msualg_1(A,E,B) != k1_xboole_0
                         => ! [F] : 
                              ( m1_subset_1(F,k3_msualg_1(A,E,B))
                             => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,B),F)) = k1_funct_1(k5_msualg_1(A,E,C),k5_msualg_3(A,B,C,E,D,F)) ) ) ) ) ) ) ) ) ),
    file(msualg_3,d9_msualg_3),
    []).

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_k10_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k10_funct_6(A))
        & v1_funct_1(k10_funct_6(A))
        & v1_funcop_1(k10_funct_6(A)) ) ) ),
    file(funct_6,k10_funct_6),
    []).

fof(dt_k10_pralg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m2_pralg_2(D,A,B) )
     => m1_pboole(k10_pralg_2(A,B,C,D),A) ) ),
    file(pralg_2,k10_pralg_2),
    []).

fof(dt_k11_pralg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B) )
     => m1_pboole(k11_pralg_2(A,B,C),u1_struct_0(B)) ) ),
    file(pralg_2,k11_pralg_2),
    []).

fof(dt_k12_pralg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B) )
     => ( v1_funcop_1(k12_pralg_2(A,B,C))
        & m1_pboole(k12_pralg_2(A,B,C),A) ) ) ),
    file(pralg_2,k12_pralg_2),
    []).

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

fof(dt_k13_pboole,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_funcop_1(B) )
     => ( v1_relat_1(k13_pboole(A,B))
        & v1_funct_1(k13_pboole(A,B))
        & v1_funcop_1(k13_pboole(A,B)) ) ) ),
    file(pboole,k13_pboole),
    []).

fof(dt_k13_pralg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B)
        & m1_subset_1(D,u1_msualg_1(B)) )
     => ( v1_funcop_1(k13_pralg_2(A,B,C,D))
        & m1_pboole(k13_pralg_2(A,B,C,D),A) ) ) ),
    file(pralg_2,k13_pralg_2),
    []).

fof(dt_k14_pralg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B) )
     => m3_pboole(k14_pralg_2(A,B,C),u1_msualg_1(B),k8_pboole(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),k6_pboole(u1_struct_0(B),k11_pralg_2(A,B,C))),k8_pboole(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),k11_pralg_2(A,B,C))) ) ),
    file(pralg_2,k14_pralg_2),
    []).

fof(dt_k15_pralg_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(k15_pralg_1(A,B))
        & v1_funct_1(k15_pralg_1(A,B)) ) ) ),
    file(pralg_1,k15_pralg_1),
    []).

fof(dt_k15_pralg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B) )
     => l3_msualg_1(k15_pralg_2(A,B,C),B) ) ),
    file(pralg_2,k15_pralg_2),
    []).

fof(dt_k1_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k1_cqc_lang),
    []).

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_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)) )
     => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ),
    file(msualg_1,k1_msualg_1),
    []).

fof(dt_k1_msualg_3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m3_pboole(D,A,B,C)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k1_msualg_3(A,B,C,D,E))
        & v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E))
        & m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ),
    file(msualg_3,k1_msualg_3),
    []).

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

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

fof(dt_k1_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_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_6(A))
        & v1_funct_1(k2_funct_6(A)) ) ) ),
    file(funct_6,k2_funct_6),
    []).

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_pralg_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_pralg_2(A))
        & v1_funct_1(k2_pralg_2(A)) ) ) ),
    file(pralg_2,k2_pralg_2),
    []).

fof(dt_k2_pralg_3,axiom,(
    $true ),
    file(pralg_3,k2_pralg_3),
    []).

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

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

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_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & l3_msualg_1(C,A) )
     => m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))) ) ),
    file(msualg_1,k3_msualg_1),
    []).

fof(dt_k3_msualg_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & v2_relat_1(D)
        & m1_pboole(D,A)
        & m3_pboole(E,A,B,C)
        & m3_pboole(F,A,C,D) )
     => m3_pboole(k3_msualg_3(A,B,C,D,E,F),A,B,D) ) ),
    file(msualg_3,k3_msualg_3),
    []).

fof(dt_k3_pralg_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_funcop_1(k3_pralg_2(A))
        & m1_pboole(k3_pralg_2(A),k4_card_3(k2_funct_6(A))) ) ) ),
    file(pralg_2,k3_pralg_2),
    []).

fof(dt_k3_pralg_3,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_pralg_3(A,B))
        & v1_funct_1(k3_pralg_3(A,B)) ) ) ),
    file(pralg_3,k3_pralg_3),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k4_card_3,axiom,(
    $true ),
    file(card_3,k4_card_3),
    []).

fof(dt_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    []).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    []).

fof(dt_k4_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & l3_msualg_1(C,A) )
     => m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))) ) ),
    file(msualg_1,k4_msualg_1),
    []).

fof(dt_k4_pralg_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B)
        & m1_subset_1(D,A) )
     => m3_pboole(k4_pralg_3(A,B,C,D),u1_struct_0(B),u4_msualg_1(B,k15_pralg_2(A,B,C)),u4_msualg_1(B,k6_pralg_2(A,B,C,D))) ) ),
    file(pralg_3,k4_pralg_3),
    []).

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

fof(dt_k5_msualg_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & m1_subset_1(B,u1_msualg_1(A))
        & l3_msualg_1(C,A) )
     => ( v1_funct_1(k5_msualg_1(A,B,C))
        & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C))
        & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) ) ) ),
    file(msualg_1,k5_msualg_1),
    []).

fof(dt_k5_msualg_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & l3_msualg_1(B,A)
        & l3_msualg_1(C,A)
        & m1_subset_1(D,u1_msualg_1(A))
        & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(F,k3_msualg_1(A,D,B)) )
     => m1_subset_1(k5_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ),
    file(msualg_3,k5_msualg_3),
    []).

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

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

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

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

fof(dt_k6_msualg_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m1_subset_1(D,u1_msualg_1(A))
        & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(F,k3_msualg_1(A,D,B)) )
     => m1_subset_1(k6_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ),
    file(msualg_3,k6_msualg_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_k6_pralg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B)
        & m1_subset_1(D,A) )
     => ( v5_msualg_1(k6_pralg_2(A,B,C,D),B)
        & l3_msualg_1(k6_pralg_2(A,B,C,D),B) ) ) ),
    file(pralg_2,k6_pralg_2),
    []).

fof(dt_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => ( v1_funct_1(k7_funct_2(A,B,C,D,E))
        & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C)
        & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ),
    file(funct_2,k7_funct_2),
    []).

fof(dt_k7_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k7_funct_6(A))
        & v1_funct_1(k7_funct_6(A)) ) ) ),
    file(funct_6,k7_funct_6),
    []).

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_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_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_msualg_1,axiom,(
    ! [A] : 
      ( l1_msualg_1(A)
     => l1_struct_0(A) ) ),
    file(msualg_1,l1_msualg_1),
    []).

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

fof(dt_l2_msualg_1,axiom,(
    $true ),
    file(msualg_1,l2_msualg_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_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    []).

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

fof(dt_m1_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_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(dt_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

fof(dt_m2_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ! [C] : 
          ( m2_pralg_2(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pralg_2,m2_pralg_2),
    []).

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_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_msualg_1,axiom,(
    ? [A] : l1_msualg_1(A) ),
    file(msualg_1,l1_msualg_1),
    []).

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

fof(existence_l2_msualg_1,axiom,(
    ! [A] : 
      ( l1_struct_0(A)
     => ? [B] : l2_msualg_1(B,A) ) ),
    file(msualg_1,l2_msualg_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_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    []).

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

fof(existence_m1_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_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(existence_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    []).

fof(existence_m2_pralg_2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B) )
     => ? [C] : m2_pralg_2(C,A,B) ) ),
    file(pralg_2,m2_pralg_2),
    []).

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

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

fof(fc1_fraenkel,axiom,(
    ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ),
    file(fraenkel,fc1_fraenkel),
    []).

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

fof(fc1_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_msualg_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & m1_subset_1(C,u1_msualg_1(A)) )
     => ( ~ v1_xboole_0(k3_msualg_1(A,C,B))
        & v1_fraenkel(k3_msualg_1(A,C,B)) ) ) ),
    file(msualg_3,fc1_msualg_3),
    []).

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_pralg_2,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ( ~ v1_xboole_0(k4_card_3(B))
        & v1_fraenkel(k4_card_3(B))
        & v1_pralg_2(k4_card_3(B)) ) ) ),
    file(pralg_2,fc1_pralg_2),
    []).

fof(fc1_pralg_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B) )
     => ( v4_msualg_1(k15_pralg_2(A,B,C),B)
        & v5_msualg_1(k15_pralg_2(A,B,C),B) ) ) ),
    file(pralg_3,fc1_pralg_3),
    []).

fof(fc1_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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_setfam_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    []).

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

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_pralg_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,u1_msualg_1(A))
        & m2_pralg_2(D,B,A) )
     => ( v1_relat_1(k2_pralg_3(A,k15_pralg_2(B,A,D),C))
        & v1_funct_1(k2_pralg_3(A,k15_pralg_2(B,A,D),C)) ) ) ),
    file(pralg_3,fc3_pralg_3),
    []).

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_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(fc5_relat_1,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    []).

fof(fc6_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_relat_1(A)
        & v1_funct_1(A) )
     => v1_setfam_1(k2_relat_1(A)) ) ),
    file(funct_1,fc6_funct_1),
    []).

fof(fc6_pralg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m2_pralg_2(D,A,B) )
     => ( v1_relat_1(k10_pralg_2(A,B,C,D))
        & v2_relat_1(k10_pralg_2(A,B,C,D))
        & v1_funct_1(k10_pralg_2(A,B,C,D)) ) ) ),
    file(pralg_2,fc6_pralg_2),
    []).

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

fof(fc7_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(fc7_pralg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B) )
     => ( v1_relat_1(k11_pralg_2(A,B,C))
        & v2_relat_1(k11_pralg_2(A,B,C))
        & ~ v3_relat_1(k11_pralg_2(A,B,C))
        & v1_funct_1(k11_pralg_2(A,B,C)) ) ) ),
    file(pralg_2,fc7_pralg_2),
    []).

fof(fc7_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    []).

fof(fc8_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(fc8_pralg_2,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B) )
     => v4_msualg_1(k15_pralg_2(A,B,C),B) ) ),
    file(pralg_2,fc8_pralg_2),
    []).

fof(fc8_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    []).

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

fof(fraenkel_a_3_1_pralg_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & ~ v2_msualg_1(C)
        & l1_msualg_1(C)
        & m2_pralg_2(D,B,C) )
     => ( r2_hidden(A,a_3_1_pralg_3(B,C,D))
      <=> ? [E,F] : 
            ( m1_subset_1(E,B)
            & m1_subset_1(F,u1_struct_0(C))
            & A = k1_funct_1(u4_msualg_1(C,k6_pralg_2(B,C,D,E)),F) ) ) ) ),
    file(pralg_3,a_3_1_pralg_3),
    []).

fof(fraenkel_a_4_1_pralg_3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & ~ v3_struct_0(C)
        & ~ v2_msualg_1(C)
        & l1_msualg_1(C)
        & m2_pralg_2(D,B,C)
        & m1_subset_1(E,u1_msualg_1(C)) )
     => ( r2_hidden(A,a_4_1_pralg_3(B,C,D,E))
      <=> ? [F] : 
            ( m1_subset_1(F,B)
            & A = k4_msualg_1(C,E,k6_pralg_2(B,C,D,F)) ) ) ) ),
    file(pralg_3,a_4_1_pralg_3),
    []).

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_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(rc1_fraenkel,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A) ) ),
    file(fraenkel,rc1_fraenkel),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_partfun1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    []).

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

fof(rc1_pralg_2,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A)
      & v1_pralg_2(A) ) ),
    file(pralg_2,rc1_pralg_2),
    []).

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

fof(rc1_setfam_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    []).

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(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_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_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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(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_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_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

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

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

fof(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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

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_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_msualg_3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,A)
        & m1_pboole(C,A)
        & m3_pboole(D,A,B,C)
        & m1_subset_1(E,A) )
     => k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) ),
    file(msualg_3,k1_msualg_3),
    []).

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

fof(redefinition_k3_msualg_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( m1_pboole(B,A)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & v2_relat_1(D)
        & m1_pboole(D,A)
        & m3_pboole(E,A,B,C)
        & m3_pboole(F,A,C,D) )
     => k3_msualg_3(A,B,C,D,E,F) = k13_pboole(E,F) ) ),
    file(msualg_3,k3_msualg_3),
    []).

fof(redefinition_k3_pralg_2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => k3_pralg_2(A) = k7_funct_6(A) ) ),
    file(pralg_2,k3_pralg_2),
    []).

fof(redefinition_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_1),
    []).

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

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

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

fof(redefinition_k6_msualg_3,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A)
        & v5_msualg_1(B,A)
        & l3_msualg_1(B,A)
        & v5_msualg_1(C,A)
        & l3_msualg_1(C,A)
        & m1_subset_1(D,u1_msualg_1(A))
        & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
        & m1_subset_1(F,k3_msualg_1(A,D,B)) )
     => k6_msualg_3(A,B,C,D,E,F) = k5_msualg_3(A,B,C,D,E,F) ) ),
    file(msualg_3,k6_msualg_3),
    []).

fof(redefinition_k6_pralg_2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & l1_msualg_1(B)
        & m2_pralg_2(C,A,B)
        & m1_subset_1(D,A) )
     => k6_pralg_2(A,B,C,D) = k1_funct_1(C,D) ) ),
    file(pralg_2,k6_pralg_2),
    []).

fof(redefinition_k7_funct_2,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B)
        & v1_funct_1(E)
        & v1_funct_2(E,B,C)
        & m1_relset_1(E,B,C) )
     => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ),
    file(funct_2,k7_funct_2),
    []).

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_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_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_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    []).

fof(redefinition_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_2),
    []).

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

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

fof(s5_pboole__e2_37__pralg_3,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v3_struct_0(B)
        & ~ v2_msualg_1(B)
        & l1_msualg_1(B)
        & v1_funcop_1(C)
        & m1_pboole(C,A) )
     => ? [D] : 
          ( m1_pboole(D,u1_struct_0(B))
          & ! [E] : 
              ( m1_subset_1(E,u1_struct_0(B))
             => k1_funct_1(D,E) = k10_funct_6(k1_funct_1(k10_funct_6(C),E)) ) ) ) ),
    file(pralg_3,s5_pboole__e2_37__pralg_3),
    []).

fof(t10_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( k3_msualg_1(A,C,B) = k4_card_3(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B)))
                & k1_relat_1(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))) = k1_relat_1(k1_msualg_1(A,C))
                & k4_msualg_1(A,C,B) = k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C)) ) ) ) ) ),
    file(pralg_2,t10_pralg_2),
    []).

fof(t10_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m2_pralg_2(D,A,B)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_msualg_1(B))
                     => ( k1_msualg_1(B,E) = k1_xboole_0
                       => k1_funct_1(k2_pralg_3(B,k15_pralg_2(A,B,D),E),C) = k2_pralg_3(B,k6_pralg_2(A,B,D,C),E) ) ) ) ) ) ) ),
    file(pralg_3,t10_pralg_3),
    []).

fof(t11_pralg_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ( k1_msualg_1(A,C) = k1_xboole_0
               => k3_msualg_1(A,C,B) = k1_tarski(k1_xboole_0) ) ) ) ) ),
    file(pralg_2,t11_pralg_2),
    []).

fof(t11_relset_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    []).

fof(t12_pralg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( l3_msualg_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k3_msualg_1(A,D,B))
                     => ( ( E = k1_xboole_0
                          & k1_msualg_1(A,D) = k1_xboole_0 )
                       => ( k3_msualg_1(A,D,B) = k1_xboole_0
                          | k3_msualg_1(A,D,C) = k1_xboole_0
                          | ! [F] : 
                              ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
                             => k5_msualg_3(A,B,C,D,F,E) = k1_xboole_0 ) ) ) ) ) ) ) ) ),
    file(pralg_3,t12_pralg_3),
    []).

fof(t13_pralg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                     => ! [F] : 
                          ( m1_subset_1(F,k3_msualg_1(A,B,C))
                         => r2_hidden(F,k4_card_3(k2_funct_6(k5_relat_1(k1_msualg_1(A,B),E)))) ) ) ) ) ) ) ),
    file(pralg_3,t13_pralg_3),
    []).

fof(t14_pralg_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & l3_msualg_1(C,A) )
             => ! [D] : 
                  ( ( v5_msualg_1(D,A)
                    & l3_msualg_1(D,A) )
                 => ! [E] : 
                      ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                     => ! [F] : 
                          ( m1_subset_1(F,k3_msualg_1(A,B,C))
                         => ! [G] : 
                              ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,B)))
                             => k1_funct_1(k6_msualg_3(A,C,D,B,E,F),G) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G)),k1_funct_1(F,G)) ) ) ) ) ) ) ) ),
    file(pralg_3,t14_pralg_3),
    []).

fof(t15_pralg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(B))
                 => ! [E] : 
                      ( r2_hidden(E,k2_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D))))
                     => ( v1_relat_1(E)
                        & v1_funct_1(E) ) ) ) ) ) ) ),
    file(pralg_2,t15_pralg_2),
    []).

fof(t15_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(B))
                 => ! [E] : 
                      ( m1_subset_1(E,k3_msualg_1(B,D,k15_pralg_2(A,B,C)))
                     => r2_hidden(E,k1_funct_2(k4_finseq_1(k1_msualg_1(B,D)),k1_funct_2(A,k3_tarski(a_3_1_pralg_3(A,B,C))))) ) ) ) ) ) ),
    file(pralg_3,t15_pralg_3),
    []).

fof(t16_pralg_2,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(B))
                 => ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E) )
                     => ( r2_hidden(E,k2_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D))))
                       => ( k1_relat_1(E) = A
                          & ! [F] : 
                              ( m1_subset_1(F,A)
                             => r2_hidden(k1_funct_1(E,F),k4_msualg_1(B,D,k6_pralg_2(A,B,C,F))) ) ) ) ) ) ) ) ) ),
    file(pralg_2,t16_pralg_2),
    []).

fof(t18_card_3,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_hidden(A,k4_card_3(B))
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(B))
                 => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ),
    file(card_3,t18_card_3),
    []).

fof(t18_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(B))
                 => ! [E] : 
                      ( m1_subset_1(E,k3_msualg_1(B,D,k15_pralg_2(A,B,C)))
                     => ( k1_msualg_1(B,D) != k1_xboole_0
                       => r2_hidden(k10_funct_6(E),k4_card_3(k2_funct_6(k13_pralg_2(A,B,C,D)))) ) ) ) ) ) ) ),
    file(pralg_3,t18_pralg_3),
    []).

fof(t19_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(B))
                 => ! [E] : 
                      ( m1_subset_1(E,k3_msualg_1(B,D,k15_pralg_2(A,B,C)))
                     => ( k1_msualg_1(B,D) != k1_xboole_0
                       => r2_hidden(E,k1_relat_1(k2_pralg_2(k3_pralg_2(k13_pralg_2(A,B,C,D))))) ) ) ) ) ) ) ),
    file(pralg_3,t19_pralg_3),
    []).

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

fof(t22_funct_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))
           => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ),
    file(funct_1,t22_funct_1),
    []).

fof(t23_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(B))
                 => ( k1_msualg_1(B,D) != k1_xboole_0
                   => ! [E] : 
                        ( m1_subset_1(E,k3_msualg_1(B,D,k15_pralg_2(A,B,C)))
                       => ! [F] : 
                            ( m1_subset_1(F,A)
                           => ! [G] : 
                                ( ( v1_relat_1(G)
                                  & v1_funct_1(G) )
                               => ( G = k8_funct_2(k3_msualg_1(B,D,k15_pralg_2(A,B,C)),k4_msualg_1(B,D,k15_pralg_2(A,B,C)),k5_msualg_1(B,D,k15_pralg_2(A,B,C)),E)
                                 => k1_funct_1(G,F) = k1_funct_1(k5_msualg_1(B,D,k6_pralg_2(A,B,C,F)),k1_funct_1(k10_funct_6(E),F)) ) ) ) ) ) ) ) ) ) ),
    file(pralg_3,t23_pralg_3),
    []).

fof(t26_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( A = k1_xboole_0
      <=> k4_finseq_1(A) = k1_xboole_0 ) ) ),
    file(finseq_1,t26_finseq_1),
    []).

fof(t27_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] : 
                      ( ( v5_msualg_1(E,B)
                        & l3_msualg_1(E,B) )
                     => ! [F] : 
                          ( ( v1_funcop_1(F)
                            & m1_pboole(F,A) )
                         => ( ! [G] : 
                                ( m1_subset_1(G,A)
                               => ? [H] : 
                                    ( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,E),u4_msualg_1(B,k6_pralg_2(A,B,C,G)))
                                    & H = k1_funct_1(F,G)
                                    & r1_msualg_3(B,E,k6_pralg_2(A,B,C,G),H) ) )
                           => r2_hidden(k1_funct_1(k10_funct_6(F),D),k1_funct_2(A,k1_funct_2(k1_funct_1(u4_msualg_1(B,E),D),k3_tarski(a_3_1_pralg_3(A,B,C))))) ) ) ) ) ) ) ) ),
    file(pralg_3,t27_pralg_3),
    []).

fof(t28_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m2_pralg_2(D,A,B)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] : 
                          ( ( v5_msualg_1(F,B)
                            & l3_msualg_1(F,B) )
                         => ! [G] : 
                              ( ( v1_funcop_1(G)
                                & m1_pboole(G,A) )
                             => ( ! [H] : 
                                    ( m1_subset_1(H,A)
                                   => ? [I] : 
                                        ( m3_pboole(I,u1_struct_0(B),u4_msualg_1(B,F),u4_msualg_1(B,k6_pralg_2(A,B,D,H)))
                                        & I = k1_funct_1(G,H)
                                        & r1_msualg_3(B,F,k6_pralg_2(A,B,D,H),I) ) )
                               => ! [H] : 
                                    ( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,F),u4_msualg_1(B,k6_pralg_2(A,B,D,C)))
                                   => ( H = k1_funct_1(G,C)
                                     => ! [I] : 
                                          ( r2_hidden(I,k1_funct_1(u4_msualg_1(B,F),E))
                                         => ! [J] : 
                                              ( ( v1_relat_1(J)
                                                & v1_funct_1(J) )
                                             => ( J = k1_funct_1(k10_funct_6(k1_funct_1(k10_funct_6(G),E)),I)
                                               => k1_funct_1(J,C) = k1_funct_1(k1_msualg_3(u1_struct_0(B),u4_msualg_1(B,F),u4_msualg_1(B,k6_pralg_2(A,B,D,C)),H,E),I) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(pralg_3,t28_pralg_3),
    []).

fof(t29_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] : 
                      ( ( v5_msualg_1(E,B)
                        & l3_msualg_1(E,B) )
                     => ! [F] : 
                          ( ( v1_funcop_1(F)
                            & m1_pboole(F,A) )
                         => ( ! [G] : 
                                ( m1_subset_1(G,A)
                               => ? [H] : 
                                    ( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,E),u4_msualg_1(B,k6_pralg_2(A,B,C,G)))
                                    & H = k1_funct_1(F,G)
                                    & r1_msualg_3(B,E,k6_pralg_2(A,B,C,G),H) ) )
                           => ! [G] : 
                                ( r2_hidden(G,k1_funct_1(u4_msualg_1(B,E),D))
                               => r2_hidden(k1_funct_1(k10_funct_6(k1_funct_1(k10_funct_6(F),D)),G),k4_card_3(k10_pralg_2(A,B,D,C))) ) ) ) ) ) ) ) ) ),
    file(pralg_3,t29_pralg_3),
    []).

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

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

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

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

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

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

fof(t85_funct_6,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C)))
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | r2_hidden(k10_funct_6(D),k1_funct_2(B,k1_funct_2(A,C))) ) ) ) ),
    file(funct_6,t85_funct_6),
    []).

fof(t86_funct_6,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C)))
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | ! [E] : 
              ( ( v1_relat_1(E)
                & v1_funct_1(E) )
             => ! [F] : 
                  ( ( v1_relat_1(F)
                    & v1_funct_1(F) )
                 => ! [G,H] : 
                      ( ( r2_hidden(G,A)
                        & r2_hidden(H,B)
                        & k1_funct_1(D,G) = E
                        & k1_funct_1(k10_funct_6(D),H) = F )
                     => ( k1_funct_1(F,G) = k1_funct_1(E,H)
                        & k1_relat_1(F) = A
                        & k1_relat_1(E) = B
                        & r1_tarski(k2_relat_1(F),C)
                        & r1_tarski(k2_relat_1(E),C) ) ) ) ) ) ) ) ),
    file(funct_6,t86_funct_6),
    []).

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

fof(t9_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    []).

fof(t9_pralg_3,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & ~ v2_msualg_1(B)
            & l1_msualg_1(B) )
         => ! [C] : 
              ( m2_pralg_2(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_msualg_1(B))
                 => ( k1_msualg_1(B,D) = k1_xboole_0
                   => r2_hidden(k2_pralg_3(B,k15_pralg_2(A,B,C),D),k1_funct_2(A,k3_tarski(a_4_1_pralg_3(A,B,C,D)))) ) ) ) ) ) ),
    file(pralg_3,t9_pralg_3),
    []).