fof(t14_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => m2_finseq_1(u5_msualg_1(A,B),k4_partfun1(k3_finseq_2(k11_msualg_1(A,B)),k11_msualg_1(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d12_msualg_1,d2_finseq_1,d3_tarski,d4_finseq_1,d5_funct_1,d1_funct_2,t7_funct_2,t151_pboole,t13_msualg_1,t23_funct_1,d17_msualg_1,d18_pboole,t30_partfun1,t119_partfun1]),
    [file(msualg_1,t14_msualg_1),interesting(1.00)]).

fof(t13_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_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) )
             => r1_tarski(k3_msualg_1(A,B,C),k3_finseq_2(k11_msualg_1(A,C))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_msualg_1,t12_msualg_1]),
    [file(msualg_1,t13_msualg_1),interesting(0.93)]).

fof(t9_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ~ v1_xboole_0(k3_unialg_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,d11_unialg_1,t25_finseq_1]),
    [file(msualg_1,t9_msualg_1),interesting(0.79)]).

fof(t6_msualg_1,theorem,(
    ! [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) )
             => ~ v1_xboole_0(k5_msualg_1(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t60_relat_1]),
    [file(msualg_1,t6_msualg_1),interesting(0.77)]).

fof(l18_msualg_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & ~ v1_xboole_0(B)
            & v1_unialg_1(B,A)
            & v2_unialg_1(B,A)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => k1_relat_1(B) = k4_finseq_2(k2_unialg_1(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_relset_1,d3_tarski,d11_finseq_1,d10_unialg_1,t110_finseq_2,d10_xboole_0,d3_tarski,t64_relat_1,d11_finseq_1,d10_unialg_1,t109_finseq_2,d2_unialg_1]),
    [file(msualg_1,l18_msualg_1),interesting(0.77)]).

fof(t12_msualg_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[s10_fraenkel,d4_finseq_2]),
    [file(msualg_1,t12_msualg_1),interesting(0.76)]).

fof(t8_msualg_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & ~ v1_xboole_0(B)
            & v1_unialg_1(B,A)
            & v2_unialg_1(B,A)
            & m2_relset_1(B,k3_finseq_2(A),A) )
         => k1_relat_1(B) = k1_funct_2(k2_finseq_1(k2_unialg_1(A,B)),A) ) ) ),
    inference(mizar_proof,[status(thm)],[l18_msualg_1,t111_finseq_2]),
    [file(msualg_1,t8_msualg_1),interesting(0.75)]).

fof(t11_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & ~ v2_msualg_1(A)
        & v6_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) )
             => k3_msualg_1(A,B,C) = k4_finseq_2(k3_finseq_1(k1_msualg_1(A,B)),k11_msualg_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_msualg_1,d1_funct_2,t23_funct_1,d19_pboole,d2_finseq_1,d4_finseq_1,d3_pboole,t46_relat_1,d3_tarski,d5_card_3,d2_finseq_1,d3_tarski,d5_funct_1,t23_funct_1,d5_funct_1,t151_pboole,d17_msualg_1,d4_finseq_1,t31_finseq_3,t110_finseq_2,d10_xboole_0,d3_tarski,t111_finseq_2,d2_funct_2,d3_finseq_1,d5_funct_1,d5_funct_1,t151_pboole,d17_msualg_1,t23_funct_1,t18_card_3]),
    [file(msualg_1,t11_msualg_1),interesting(0.74)]).

fof(t7_msualg_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ! [D] : 
              ( ( v1_funct_1(D)
                & m2_relset_1(D,A,B) )
             => ! [E] : 
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ( v1_funct_1(k1_partfun1(A,B,B,C,D,E))
                    & v1_funct_2(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C)
                    & m2_relset_1(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,t46_relat_1,t12_relset_1,d1_funct_2,t11_relset_1]),
    [file(msualg_1,t7_msualg_1),interesting(0.69)]).

fof(t10_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_msualg_1(A) )
     => ( v3_realset2(A)
       => ! [B] : 
            ( l3_msualg_1(B,A)
           => ! [C] : 
                ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B)))
               => ! [D] : 
                    ( m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B)))
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t150_pboole,t150_pboole,d7_realset2]),
    [file(msualg_1,t10_msualg_1),interesting(0.64)]).

fof(t15_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_unialg_1(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => A = k13_msualg_1(k7_msualg_1(A),k10_msualg_1(A)) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t14_funcop_1,d17_msualg_1]),
    [file(msualg_1,t15_msualg_1),interesting(0.63)]).

fof(t16_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(0)))
            & m2_relset_1(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(0))) )
         => ( B = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(0)),k6_msualg_1(A),k9_pboole(0))
           => k7_msualg_1(A) = g1_msualg_1(k1_tarski(0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),0)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_msualg_1]),
    [file(msualg_1,t16_msualg_1),interesting(0.18)]).

fof(d1_struct_0,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_struct_0(A)
      <=> v1_xboole_0(u1_struct_0(A)) ) ) ),
    file(struct_0,d1_struct_0),
    [interesting(0.00)]).

fof(t25_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k3_finseq_1(A) = 0
      <=> A = k1_xboole_0 ) ) ),
    file(finseq_1,t25_finseq_1),
    [interesting(0.00)]).

fof(d11_unialg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( B = k3_unialg_1(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(u1_unialg_1(A))
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => ! [D] : 
                        ( ( ~ v1_xboole_0(D)
                          & v1_funct_1(D)
                          & v1_unialg_1(D,u1_struct_0(A))
                          & m2_relset_1(D,k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) )
                       => ( D = k1_funct_1(u1_unialg_1(A),C)
                         => k1_funct_1(B,C) = k2_unialg_1(u1_struct_0(A),D) ) ) ) ) ) ) ) ) ),
    file(unialg_1,d11_unialg_1),
    [interesting(0.00)]).

fof(t64_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( ( k1_relat_1(A) = k1_xboole_0
          | k2_relat_1(A) = k1_xboole_0 )
       => A = k1_xboole_0 ) ) ),
    file(relat_1,t64_relat_1),
    [interesting(0.00)]).

fof(d12_msualg_1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v6_msualg_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & u1_msualg_1(A) = k2_finseq_1(B) ) ) ) ),
    file(msualg_1,d12_msualg_1),
    [interesting(0.00)]).

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    [interesting(0.00)]).

fof(d5_msualg_1,definition,(
    ! [A] : 
      ( l1_msualg_1(A)
     => ( v2_msualg_1(A)
      <=> u1_msualg_1(A) = k1_xboole_0 ) ) ),
    file(msualg_1,d5_msualg_1),
    [interesting(0.00)]).

fof(d5_realset2,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_realset2(A)
      <=> v1_realset1(u1_struct_0(A)) ) ) ),
    file(realset2,d5_realset2),
    [interesting(0.00)]).

fof(l24_msualg_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(0)))
            & m2_relset_1(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(0))) )
         => ( B = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(0)),k6_msualg_1(A),k9_pboole(0))
           => ( ~ v3_struct_0(g1_msualg_1(k1_tarski(0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),0)))
              & v6_msualg_1(g1_msualg_1(k1_tarski(0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),0)))
              & v3_realset2(g1_msualg_1(k1_tarski(0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),0)))
              & ~ v2_msualg_1(g1_msualg_1(k1_tarski(0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),0)))
              & v1_msualg_1(g1_msualg_1(k1_tarski(0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),0))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_struct_0,t9_msualg_1,t64_relat_1,d12_msualg_1,d3_finseq_1,d5_msualg_1,d5_realset2]),
    [file(msualg_1,l24_msualg_1),interesting(0.00)]).

fof(t150_pboole,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k2_relat_1(B))
             => ? [D] : 
                  ( r2_hidden(D,A)
                  & C = k1_funct_1(B,D) ) ) ) ) ),
    file(pboole,t150_pboole),
    [interesting(0.00)]).

fof(d7_realset2,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_realset2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) ) ),
    file(realset2,d7_realset2),
    [interesting(0.00)]).

fof(d3_pboole,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( m1_pboole(B,A)
      <=> k1_relat_1(B) = A ) ) ),
    file(pboole,d3_pboole),
    [interesting(0.00)]).

fof(d2_finseq_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finseq_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k1_relat_1(A) = k2_finseq_1(B) ) ) ) ),
    file(finseq_1,d2_finseq_1),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d4_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [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),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [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),
    [interesting(0.00)]).

fof(t7_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    [interesting(0.00)]).

fof(t151_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( r2_hidden(C,A)
         => m1_subset_1(k1_funct_1(B,C),k2_relat_1(B)) ) ) ),
    file(pboole,t151_pboole),
    [interesting(0.00)]).

fof(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.00)]).

fof(d19_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,k3_finseq_2(A))
         => ( C = k6_pboole(A,B)
          <=> ! [D] : 
                ( m2_finseq_2(D,A,k3_finseq_2(A))
               => k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)) ) ) ) ) ),
    file(pboole,d19_pboole),
    [interesting(0.00)]).

fof(t46_relat_1,theorem,(
    ! [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),
    [interesting(0.00)]).

fof(d5_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k4_card_3(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & C = D
                  & k1_relat_1(D) = k1_relat_1(A)
                  & ! [E] : 
                      ( r2_hidden(E,k1_relat_1(A))
                     => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ),
    file(card_3,d5_card_3),
    [interesting(0.00)]).

fof(d17_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_realset2(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( C = k11_msualg_1(A,B)
            <=> m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) ) ) ) ),
    file(msualg_1,d17_msualg_1),
    [interesting(0.00)]).

fof(t31_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( k3_finseq_1(A) = k3_finseq_1(B)
          <=> k4_finseq_1(A) = k4_finseq_1(B) ) ) ) ),
    file(finseq_3,t31_finseq_3),
    [interesting(0.00)]).

fof(t110_finseq_2,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)) ) ),
    file(finseq_2,t110_finseq_2),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t111_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B) ) ) ),
    file(finseq_2,t111_finseq_2),
    [interesting(0.00)]).

fof(d2_funct_2,definition,(
    ! [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),
    [interesting(0.00)]).

fof(t18_card_3,theorem,(
    ! [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),
    [interesting(0.00)]).

fof(s10_fraenkel,theorem,(
    r1_tarski(a_0_18_fraenkel,f1_s10_fraenkel) ),
    file(fraenkel,s10_fraenkel),
    [interesting(0.00)]).

fof(d4_finseq_2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k4_finseq_2(A,B) = a_2_0_finseq_2(A,B) ) ),
    file(finseq_2,d4_finseq_2),
    [interesting(0.00)]).

fof(d18_pboole,definition,(
    ! [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),
    [interesting(0.00)]).

fof(t30_partfun1,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & m2_relset_1(D,A,B) )
     => ( r1_tarski(A,C)
       => ( v1_funct_1(D)
          & m2_relset_1(D,C,B) ) ) ) ),
    file(partfun1,t30_partfun1),
    [interesting(0.00)]).

fof(t119_partfun1,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => r2_hidden(C,k4_partfun1(A,B)) ) ),
    file(partfun1,t119_partfun1),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(t14_funcop_1,theorem,(
    ! [A,B] : 
      ( A != k1_xboole_0
     => k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B) ) ),
    file(funcop_1,t14_funcop_1),
    [interesting(0.00)]).

fof(d13_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_realset2(B)
            & v1_msualg_1(B)
            & ~ v2_msualg_1(B)
            & v6_msualg_1(B)
            & l1_msualg_1(B) )
         => ( B = k7_msualg_1(A)
          <=> ( u1_struct_0(B) = k1_tarski(0)
              & u1_msualg_1(B) = k4_finseq_1(k6_msualg_1(A))
              & u2_msualg_1(B) = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(0)),k6_msualg_1(A),k9_pboole(0))
              & u3_msualg_1(B) = k10_pboole(k4_finseq_1(k6_msualg_1(A)),0) ) ) ) ) ),
    file(msualg_1,d13_msualg_1),
    [interesting(0.00)]).

fof(t1_msualg_1,theorem,(
    $true ),
    file(msualg_1,t1_msualg_1),
    [interesting(0.00)]).

fof(t2_msualg_1,theorem,(
    $true ),
    file(msualg_1,t2_msualg_1),
    [interesting(0.00)]).

fof(t3_msualg_1,theorem,(
    $true ),
    file(msualg_1,t3_msualg_1),
    [interesting(0.00)]).

fof(t4_msualg_1,theorem,(
    $true ),
    file(msualg_1,t4_msualg_1),
    [interesting(0.00)]).

fof(t5_msualg_1,theorem,(
    $true ),
    file(msualg_1,t5_msualg_1),
    [interesting(0.00)]).

fof(t60_relat_1,theorem,
    ( k1_relat_1(k1_xboole_0) = k1_xboole_0
    & k2_relat_1(k1_xboole_0) = k1_xboole_0 ),
    file(relat_1,t60_relat_1),
    [interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [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),
    [interesting(0.00)]).

fof(d11_finseq_1,definition,(
    ! [A,B] : 
      ( B = k13_finseq_1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m2_finseq_1(C,A) ) ) ),
    file(finseq_1,d11_finseq_1),
    [interesting(0.00)]).

fof(d10_unialg_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_funct_1(B)
            & v1_unialg_1(B,A)
            & m2_relset_1(B,k13_finseq_1(A),A) )
         => ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( C = k2_unialg_1(A,B)
              <=> ! [D] : 
                    ( m2_finseq_1(D,A)
                   => ( r2_hidden(D,k1_relat_1(B))
                     => C = k3_finseq_1(D) ) ) ) ) ) ) ),
    file(unialg_1,d10_unialg_1),
    [interesting(0.00)]).

fof(t109_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k3_finseq_1(C) = A ) ) ) ),
    file(finseq_2,t109_finseq_2),
    [interesting(0.00)]).

fof(d2_unialg_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k13_finseq_1(A),A) )
     => ( v2_unialg_1(B,A)
      <=> ! [C] : 
            ( m2_finseq_1(C,A)
           => ! [D] : 
                ( m2_finseq_1(D,A)
               => ( ( k3_finseq_1(C) = k3_finseq_1(D)
                    & r2_hidden(C,k1_relat_1(B)) )
                 => r2_hidden(D,k1_relat_1(B)) ) ) ) ) ) ),
    file(unialg_1,d2_unialg_1),
    [interesting(0.00)]).