fof(t18_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v2_msafree(k11_msafree(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_msafree,t17_msafree]),
    [file(msafree,t18_msafree),interesting(1.00)]).

fof(t19_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ? [C] : 
              ( v4_msualg_1(C,A)
              & v5_msualg_1(C,A)
              & v2_msafree(C,A)
              & l3_msualg_1(C,A)
              & ? [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                  & r2_msualg_3(A,C,B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_msafree,d5_msafree,t18_msafree,d10_msualg_3,d3_msualg_3,d18_pboole,d1_msafree,t76_funct_1,t12_relset_1,d10_xboole_0,d3_tarski,t7_msafree,d20_msafree,d1_funct_2,t7_mcart_1,t14_msafree,d5_funct_1,d19_msafree,t7_mcart_1]),
    [file(msafree,t19_msafree),interesting(1.00)]).

fof(t17_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v1_msafree(k13_msafree(A,B),A,k11_msafree(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_msafree,s8_dtconstr,s3_funct_1,d3_pboole,d6_funcop_1,t7_msafree,t7_mcart_1,t14_msafree,d18_msafree,d1_funct_2,t12_relset_1,d5_funct_1,t72_funct_1,d21_msafree,d3_xboole_0,t4_xboole_0,t13_msafree,d6_msualg_1,d9_msualg_1,t1_msafree,t1_alg_1,d18_trees_3,d22_msafree,d4_finseq_1,d3_pboole,t46_relat_1,d1_lang1,t106_zfmisc_1,t5_msafree,d3_finseq_1,t5_msafree,t1_alg_1,d4_finseq_1,d5_funct_1,t10_msafree,t1_msafree,t18_card_3,t22_funct_1,d5_funct_1,d1_funct_2,t12_msafree,d3_pboole,d5_funct_1,t92_zfmisc_1,t91_relat_1,t70_funct_1,t22_funct_1,t18_card_3,d23_msafree,d1_funct_2,t12_relset_1,d5_funct_1,d3_pboole,t12_relset_1,d1_funct_2,t46_relat_1,d10_msualg_1,t22_funct_1,d7_msualg_1,d14_msafree,d1_funct_2,t12_relset_1,t10_msafree,d5_funct_1,t22_funct_1,d7_msualg_1,t72_funct_1,t3_xboole_0,t13_msafree,s7_dtconstr,d1_funct_2,t12_msafree,d3_pboole,d5_funct_1,t92_zfmisc_1,t91_relat_1,d3_tarski,d5_funct_1,d1_funct_2,t91_relat_1,d1_funct_2,t11_relset_1,d18_pboole,d9_msualg_3,d11_msualg_1,d15_msafree,d9_msualg_1,t8_msafree,t10_msafree,d14_msafree,d1_funct_2,d6_msualg_1,d22_msafree,t33_zfmisc_1,d3_pboole,t12_relset_1,d1_funct_2,t46_relat_1,d14_msafree,d1_funct_2,t12_relset_1,d5_funct_1,t22_funct_1,d7_msualg_1,d1_funct_2,t12_msafree,t1_alg_1,t6_msualg_3,d8_msualg_3,t1_msafree,d4_finseq_1,d3_pboole,t46_relat_1,d18_trees_3,d1_lang1,t106_zfmisc_1,t5_msafree,d3_finseq_1,t18_card_3,t22_funct_1,d4_finseq_4,t72_funct_1,t9_funct_1,d3_pboole,d5_funct_1,t92_zfmisc_1,t91_relat_1,t70_funct_1,d23_msafree,d1_msafree,d1_funct_2,d18_msafree,d1_funct_2,d1_funct_2,t14_msafree,t70_funct_1,t70_funct_1,d21_msafree,t9_funct_1,t3_pboole]),
    [file(msafree,t17_msafree),interesting(0.98)]).

fof(t20_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ? [C] : 
              ( v4_msualg_1(C,A)
              & v5_msualg_1(C,A)
              & v2_msafree(C,A)
              & l3_msualg_1(C,A)
              & ? [D] : 
                  ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
                  & r2_msualg_3(A,C,B,D)
                  & k7_msualg_3(A,C,B,D) = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_msafree,d10_msualg_3,t19_msualg_3]),
    [file(msafree,t20_msafree),interesting(0.89)]).

fof(t14_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_msafree(A,B,C) = a_3_1_msafree(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d17_msafree,t7_msafree,t7_mcart_1,d10_xboole_0,d3_tarski,t7_msafree,t7_mcart_1,d17_msafree]),
    [file(msafree,t14_msafree),interesting(0.71)]).

fof(t12_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k3_tarski(k2_relat_1(k8_msafree(A,B))) = k4_dtconstr(k5_msafree(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d3_tarski,d4_tarski,d5_funct_1,d3_pboole,d13_msafree,d10_xboole_0,d3_tarski,d9_trees_2,t47_trees_1,d5_funct_1,t1_lang1,t6_msafree,t9_dtconstr,d4_card_3,d4_tarski,d5_funct_1,d3_pboole,d3_msafree,d2_msafree,d13_msafree,d5_funct_1,d4_tarski,t9_domain_1,d1_tarski,d13_msafree,d5_funct_1,d4_tarski,d2_xboole_0]),
    [file(msafree,t12_msafree),interesting(0.66)]).

fof(t16_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => k3_tarski(k2_relat_1(k13_msafree(A,B))) = a_2_0_msafree(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_pboole,d3_tarski,d4_tarski,d5_funct_1,d3_pboole,d18_msafree,t14_msafree,d10_xboole_0,d3_tarski,t7_msafree,t7_mcart_1,t14_msafree,d18_msafree,d5_funct_1,d4_tarski]),
    [file(msafree,t16_msafree),interesting(0.63)]).

fof(t4_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => r1_xboole_0(k3_card_3(k3_msafree(u1_struct_0(A),B)),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_xboole_0,d3_xboole_0,d4_card_3,d4_tarski,d5_funct_1,d3_pboole,d3_msafree,d2_msafree,t106_zfmisc_1,d1_tarski]),
    [file(msafree,t4_msafree),interesting(0.61)]).

fof(t7_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( r2_hidden(C,k6_dtconstr(k5_msafree(A,B)))
            <=> ? [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                  & ? [E] : 
                      ( r2_hidden(E,k1_funct_1(B,D))
                      & C = k4_tarski(E,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_msafree,d4_card_3,d4_tarski,d5_funct_1,d3_pboole,d3_msafree,d2_msafree,d2_msafree,d3_msafree,d3_pboole,d5_funct_1,d4_tarski]),
    [file(msafree,t7_msafree),interesting(0.61)]).

fof(t13_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( C != D
                   => r1_subset_1(k1_funct_1(k8_msafree(A,B),C),k1_funct_1(k8_msafree(A,B),D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_xboole_0,d3_xboole_0,d13_msafree,t4_trees_4,t33_zfmisc_1,t3_trees_4,t33_zfmisc_1,t3_trees_4,t33_zfmisc_1,t33_zfmisc_1]),
    [file(msafree,t13_msafree),interesting(0.55)]).

fof(t15_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => v2_relat_1(k13_msafree(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_pboole,d18_msafree]),
    [file(msafree,t15_msafree),interesting(0.54)]).

fof(t6_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ( k6_lang1(k5_msafree(A,B)) = k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))
            & k5_lang1(k5_msafree(A,B)) = k3_card_3(k3_msafree(u1_struct_0(A),B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_msafree,t8_dtconstr,t1_lang1,d3_tarski,d3_lang1,d1_lang1,t106_zfmisc_1,d1_lang1,d9_msafree,d10_xboole_0,d3_tarski,t9_domain_1,d1_tarski,d2_xboole_0,d3_finseq_1,d4_finseq_1,d5_funct_1,d16_pboole,d1_xboole_0,d2_msafree,s1_zfrefle1,d2_finseq_1,d3_tarski,d5_funct_1,d3_finseq_1,d4_finseq_1,d5_funct_1,d3_pboole,d5_funct_1,d3_msafree,d4_tarski,d4_card_3,d2_xboole_0,d4_finseq_1,d11_finseq_1,d3_finseq_1,d3_finseq_1,d4_finseq_1,d5_funct_1,d3_pboole,d5_funct_1,d3_msafree,d4_tarski,d4_card_3,t3_xboole_0,t5_msafree,d1_lang1,d3_lang1,d3_tarski,d2_xboole_0,t3_xboole_0,d2_xboole_0,d10_xboole_0,d3_tarski,d2_xboole_0,d2_xboole_0,t3_xboole_0]),
    [file(msafree,t6_msafree),interesting(0.53)]).

fof(t1_msafree,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,k3_finseq_2(B))
            & m2_relset_1(C,A,k3_finseq_2(B)) )
         => ! [D] : 
              ( m1_pboole(D,B)
             => ! [E] : 
                  ( m2_finseq_2(E,B,k3_finseq_2(B))
                 => ! [F] : 
                      ( ( r2_hidden(F,A)
                        & E = k1_funct_1(C,F) )
                     => k1_funct_1(k7_pboole(A,k3_finseq_2(B),C,k6_pboole(B,D)),F) = k4_card_3(k5_relat_1(E,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,d3_pboole,t22_funct_1,d19_pboole]),
    [file(msafree,t1_msafree),interesting(0.47)]).

fof(t3_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v4_msualg_1(B,A)
            & v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( m1_msafree(C,A,B)
              <=> k12_msualg_2(A,B,C) = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_msualg_2,d4_msafree,t10_msualg_2,d4_msafree]),
    [file(msafree,t3_msafree),interesting(0.45)]).

fof(t8_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C))
                 => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_msualg_1,t1_msafree,d5_card_3,d4_finseq_1,d3_pboole,t46_relat_1,d3_finseq_1,d2_finseq_1,d3_tarski,d5_funct_1,t22_funct_1,d4_finseq_4,d13_msafree,d4_finseq_1]),
    [file(msafree,t8_msafree),interesting(0.38)]).

fof(t10_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B)))
                 => ( r1_lang1(k5_msafree(A,B),k6_msafree(A,B,C),k1_dtconstr(u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),D))
                  <=> r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_msafree,d1_lang1,t106_zfmisc_1,t5_msafree,d18_trees_3,d3_finseq_1,d18_trees_3,d4_finseq_1,d5_funct_1,d4_finseq_1,d5_funct_1,t9_domain_1,d1_tarski,t5_msafree,d4_finseq_4,t5_msafree,d4_finseq_4,d2_msafree,t6_msafree,t9_dtconstr,d2_xboole_0,t9_msafree,t9_msafree,d18_trees_3,d3_finseq_1,d11_finseq_1,t8_finseq_1,t9_msafree,d18_trees_3,d4_finseq_4,t3_trees_4,d2_msafree,d3_pboole,d5_funct_1,d3_msafree,d4_tarski,d4_card_3,t3_xboole_0,t33_zfmisc_1,d1_tarski,t106_zfmisc_1,t3_xboole_0,t3_trees_4,d2_msafree,t5_msafree,d1_lang1]),
    [file(msafree,t10_msafree),interesting(0.30)]).

fof(t9_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B)))
                 => ( r2_hidden(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C))
                  <=> ( k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C))
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(E,k4_finseq_1(D))
                           => r2_hidden(k1_funct_1(D,E),k7_msafree(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_msualg_1,t1_msafree,t18_card_3,d4_finseq_1,d3_pboole,t46_relat_1,t46_relat_1,t22_funct_1,d4_finseq_4,d13_msafree,d6_msualg_1,t1_msafree,d4_finseq_1,d3_pboole,t46_relat_1,d13_msafree,d4_finseq_4,t22_funct_1,t18_card_3]),
    [file(msafree,t9_msafree),interesting(0.03)]).

fof(t11_msafree,theorem,(
    $true ),
    file(msafree,t11_msafree),
    [interesting(0.00)]).

fof(d16_pboole,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v2_relat_1(B)
      <=> ! [C] : ~ ( r2_hidden(C,A)
            & v1_xboole_0(k1_funct_1(B,C)) ) ) ) ),
    file(pboole,d16_pboole),
    [interesting(0.00)]).

fof(d18_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_msafree(C,A,k11_msafree(A,B))
             => ( C = k13_msafree(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k12_msafree(A,B,D) ) ) ) ) ) ),
    file(msafree,d18_msafree),
    [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(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_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [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(d17_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(k8_msafree(A,B),C)))
                 => ( D = k12_msafree(A,B,C)
                  <=> ! [E] : 
                        ( r2_hidden(E,D)
                      <=> ? [F] : 
                            ( r2_hidden(F,k1_funct_1(B,C))
                            & E = k1_trees_4(k4_tarski(F,C)) ) ) ) ) ) ) ) ),
    file(msafree,d17_msafree),
    [interesting(0.00)]).

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(d4_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    [interesting(0.00)]).

fof(d3_msafree,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( C = k3_msafree(A,B)
          <=> ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(C,D) = k2_msafree(A,B,D) ) ) ) ) ),
    file(msafree,d3_msafree),
    [interesting(0.00)]).

fof(d2_msafree,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( r2_hidden(C,A)
         => ! [D] : 
              ( D = k2_msafree(A,B,C)
            <=> ! [E] : 
                  ( r2_hidden(E,D)
                <=> ? [F] : 
                      ( r2_hidden(F,k1_funct_1(B,C))
                      & E = k4_tarski(F,C) ) ) ) ) ) ),
    file(msafree,d2_msafree),
    [interesting(0.00)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [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(t8_dtconstr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => r1_xboole_0(k5_lang1(A),k6_lang1(A)) ) ),
    file(dtconstr,t8_dtconstr),
    [interesting(0.00)]).

fof(t1_lang1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => k2_xboole_0(k5_lang1(A),k6_lang1(A)) = u1_struct_0(A) ) ),
    file(lang1,t1_lang1),
    [interesting(0.00)]).

fof(d3_lang1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => k6_lang1(A) = a_1_1_lang1(A) ) ),
    file(lang1,d3_lang1),
    [interesting(0.00)]).

fof(d1_lang1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r1_lang1(A,B,C)
              <=> r2_hidden(k4_tarski(B,C),u1_lang1(A)) ) ) ) ) ),
    file(lang1,d1_lang1),
    [interesting(0.00)]).

fof(d9_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_relset_1(C,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
             => ( C = k4_msafree(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))
                   => ! [E] : 
                        ( m2_finseq_2(E,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
                       => ( r2_hidden(k4_tarski(D,E),C)
                        <=> ( r2_hidden(D,k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
                            & ! [F] : 
                                ( m1_subset_1(F,u1_msualg_1(A))
                               => ( k4_tarski(F,u1_struct_0(A)) = D
                                 => ( k3_finseq_1(E) = k3_finseq_1(k1_msualg_1(A,F))
                                    & ! [G] : 
                                        ( r2_hidden(G,k4_finseq_1(E))
                                       => ( ( r2_hidden(k1_funct_1(E,G),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
                                           => ! [H] : 
                                                ( m1_subset_1(H,u1_msualg_1(A))
                                               => ( k4_tarski(H,u1_struct_0(A)) = k1_funct_1(E,G)
                                                 => k2_msualg_1(A,H) = k1_funct_1(k1_msualg_1(A,F),G) ) ) )
                                          & ( r2_hidden(k1_funct_1(E,G),k3_card_3(k3_msafree(u1_struct_0(A),B)))
                                           => r2_hidden(k1_funct_1(E,G),k2_msafree(u1_struct_0(A),B,k1_funct_1(k1_msualg_1(A,F),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(msafree,d9_msafree),
    [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(t9_domain_1,theorem,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( ~ v1_xboole_0(C)
         => ~ ( r2_hidden(A,k2_zfmisc_1(B,C))
              & ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( m1_subset_1(E,C)
                     => A != k4_tarski(D,E) ) ) ) ) ) ),
    file(domain_1,t9_domain_1),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [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(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(s1_zfrefle1,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s1_zfrefle1)
        & ! [B] : ~ p1_s1_zfrefle1(A,B) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s1_zfrefle1
        & ! [B] : 
            ( r2_hidden(B,f1_s1_zfrefle1)
           => p1_s1_zfrefle1(B,k1_funct_1(A,B)) ) ) ),
    file(zfrefle1,s1_zfrefle1),
    [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(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(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.00)]).

fof(t33_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    [interesting(0.00)]).

fof(t5_msafree,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_pboole(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( m2_finseq_2(D,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))))
                 => ( r2_hidden(k4_tarski(k4_tarski(C,u1_struct_0(A)),D),k4_msafree(A,B))
                  <=> ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C))
                      & ! [E] : 
                          ( r2_hidden(E,k4_finseq_1(D))
                         => ( ( r2_hidden(k1_funct_1(D,E),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))))
                             => ! [F] : 
                                  ( m1_subset_1(F,u1_msualg_1(A))
                                 => ( k4_tarski(F,u1_struct_0(A)) = k1_funct_1(D,E)
                                   => k2_msualg_1(A,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) )
                            & ( r2_hidden(k1_funct_1(D,E),k3_card_3(k3_msafree(u1_struct_0(A),B)))
                             => r2_hidden(k1_funct_1(D,E),k2_msafree(u1_struct_0(A),B,k1_funct_1(k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t106_zfmisc_1,d2_xboole_0,d9_msafree,t33_zfmisc_1,d9_msafree]),
    [file(msafree,t5_msafree),interesting(0.00)]).

fof(t7_mcart_1,theorem,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    [interesting(0.00)]).

fof(d5_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m1_msafree(C,A,B)
             => ( v1_msafree(C,A,B)
              <=> ! [D] : 
                    ( ( v5_msualg_1(D,A)
                      & l3_msualg_1(D,A) )
                   => ! [E] : 
                        ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,D))
                       => ? [F] : 
                            ( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D))
                            & r1_msualg_3(A,B,D,F)
                            & r6_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,D),C,F),E) ) ) ) ) ) ) ) ),
    file(msafree,d5_msafree),
    [interesting(0.00)]).

fof(s8_dtconstr,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k4_dtconstr(f1_s8_dtconstr),f2_s8_dtconstr)
      & m2_relset_1(A,k4_dtconstr(f1_s8_dtconstr),f2_s8_dtconstr)
      & ! [B] : 
          ( m1_subset_1(B,u1_struct_0(f1_s8_dtconstr))
         => ( r2_hidden(B,k5_lang1(f1_s8_dtconstr))
           => k1_funct_1(A,k2_trees_4(u1_struct_0(f1_s8_dtconstr),B)) = f3_s8_dtconstr(B) ) )
      & ! [B] : 
          ( m1_subset_1(B,u1_struct_0(f1_s8_dtconstr))
         => ! [C] : 
              ( m1_trees_4(C,k5_trees_3(u1_struct_0(f1_s8_dtconstr)),k4_dtconstr(f1_s8_dtconstr))
             => ( r1_lang1(f1_s8_dtconstr,B,k1_dtconstr(u1_struct_0(f1_s8_dtconstr),k5_trees_3(u1_struct_0(f1_s8_dtconstr)),C))
               => k1_funct_1(A,k12_trees_4(u1_struct_0(f1_s8_dtconstr),B,C)) = f4_s8_dtconstr(B,k1_dtconstr(u1_struct_0(f1_s8_dtconstr),k5_trees_3(u1_struct_0(f1_s8_dtconstr)),C),k5_finseqop(k4_dtconstr(f1_s8_dtconstr),f2_s8_dtconstr,C,A)) ) ) ) ) ),
    file(dtconstr,s8_dtconstr),
    [interesting(0.00)]).

fof(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

fof(d6_funcop_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funcop_1(A)
      <=> ! [B] : 
            ( r2_hidden(B,k1_relat_1(A))
           => ( v1_relat_1(k1_funct_1(A,B))
              & v1_funct_1(k1_funct_1(A,B)) ) ) ) ) ),
    file(funcop_1,d6_funcop_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(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(t72_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,A)
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t72_funct_1),
    [interesting(0.00)]).

fof(d21_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( ( v2_relat_1(C)
                & m1_pboole(C,u1_struct_0(A)) )
             => ! [D] : 
                  ( m3_pboole(D,u1_struct_0(A),k13_msafree(A,B),C)
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k5_msafree(A,B)))
                     => ( r2_hidden(E,k6_dtconstr(k5_msafree(A,B)))
                       => ! [F] : 
                            ( m1_subset_1(F,k3_card_3(C))
                           => ( F = k16_msafree(A,B,C,D,E)
                            <=> ! [G] : 
                                  ( ( v1_relat_1(G)
                                    & v1_funct_1(G) )
                                 => ( G = k1_funct_1(D,k2_mcart_1(E))
                                   => F = k1_funct_1(G,k2_trees_4(u1_struct_0(k5_msafree(A,B)),E)) ) ) ) ) ) ) ) ) ) ) ),
    file(msafree,d21_msafree),
    [interesting(0.00)]).

fof(t4_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B)) )
      & ~ ( ? [C] : r2_hidden(C,k3_xboole_0(A,B))
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t4_xboole_0),
    [interesting(0.00)]).

fof(d13_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_pboole(C,u1_struct_0(A))
             => ( C = k8_msafree(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(C,D) = k7_msafree(A,B,D) ) ) ) ) ) ),
    file(msafree,d13_msafree),
    [interesting(0.00)]).

fof(t4_trees_4,theorem,(
    ! [A,B] : 
      ( k1_trees_4(A) = k1_trees_4(B)
     => A = B ) ),
    file(trees_4,t4_trees_4),
    [interesting(0.00)]).

fof(t3_trees_4,theorem,(
    ! [A] : 
      ( k1_relat_1(k1_trees_4(A)) = k2_trees_1(0)
      & k1_funct_1(k1_trees_4(A),k1_xboole_0) = A ) ),
    file(trees_4,t3_trees_4),
    [interesting(0.00)]).

fof(d6_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => k1_msualg_1(A,B) = k1_funct_1(u2_msualg_1(A),B) ) ) ),
    file(msualg_1,d6_msualg_1),
    [interesting(0.00)]).

fof(d9_msualg_1,definition,(
    ! [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)
             => k3_msualg_1(A,B,C) = k1_funct_1(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,C))),B) ) ) ) ),
    file(msualg_1,d9_msualg_1),
    [interesting(0.00)]).

fof(t22_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(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),
    [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(t1_alg_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,A)
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,B)
                    & m2_relset_1(D,A,B) )
                 => ( k4_finseq_1(k5_finseqop(A,B,C,D)) = k4_finseq_1(C)
                    & k3_finseq_1(k5_finseqop(A,B,C,D)) = k3_finseq_1(C)
                    & ! [E] : 
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r2_hidden(E,k4_finseq_1(k5_finseqop(A,B,C,D)))
                         => k1_funct_1(k5_finseqop(A,B,C,D),E) = k1_funct_1(D,k1_funct_1(C,E)) ) ) ) ) ) ) ) ),
    file(alg_1,t1_alg_1),
    [interesting(0.00)]).

fof(d18_trees_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v6_trees_3(A)
       => ! [B] : 
            ( ( v1_relat_1(B)
              & v1_funct_1(B)
              & v1_finseq_1(B) )
           => ( B = k16_trees_3(A)
            <=> ( k4_finseq_1(B) = k4_finseq_1(A)
                & ! [C] : 
                    ( m2_subset_1(C,k1_numbers,k5_numbers)
                   => ~ ( r2_hidden(C,k4_finseq_1(A))
                        & ! [D] : 
                            ( ( v1_relat_1(D)
                              & v1_funct_1(D)
                              & v3_trees_2(D) )
                           => ~ ( D = k1_funct_1(A,C)
                                & k1_funct_1(B,C) = k1_funct_1(D,k1_xboole_0) ) ) ) ) ) ) ) ) ) ),
    file(trees_3,d18_trees_3),
    [interesting(0.00)]).

fof(d22_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_msafree(A,B)))
             => ( ? [D] : 
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D)
                    & r1_lang1(k5_msafree(A,B),C,D) )
               => ! [D] : 
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => ( D = k17_msafree(A,B,C)
                    <=> k4_tarski(D,u1_struct_0(A)) = C ) ) ) ) ) ) ),
    file(msafree,d22_msafree),
    [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(d4_finseq_4,definition,(
    ! [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),
    [interesting(0.00)]).

fof(t9_dtconstr,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & l1_lang1(A) )
     => ! [B] : 
          ( m1_dtconstr(B,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
         => ! [C] : 
              ( m1_struct_0(C,A,k6_dtconstr(A))
             => ( k1_funct_1(B,k1_xboole_0) = C
               => B = k8_dtconstr(A,C) ) ) ) ) ),
    file(dtconstr,t9_dtconstr),
    [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(t8_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_finseq_1(A) = k2_finseq_1(B)
           => A = B ) ) ) ),
    file(finseq_1,t8_finseq_1),
    [interesting(0.00)]).

fof(d9_trees_2,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( m3_trees_2(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(trees_2,d9_trees_2),
    [interesting(0.00)]).

fof(t47_trees_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( r2_hidden(k1_xboole_0,A)
        & r2_hidden(k6_finseq_1(k5_numbers),A) ) ) ),
    file(trees_1,t47_trees_1),
    [interesting(0.00)]).

fof(t92_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    [interesting(0.00)]).

fof(t91_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(A,k1_relat_1(B))
       => k1_relat_1(k7_relat_1(B,A)) = A ) ) ),
    file(relat_1,t91_relat_1),
    [interesting(0.00)]).

fof(t70_funct_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( r2_hidden(B,k1_relat_1(k7_relat_1(C,A)))
       => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ),
    file(funct_1,t70_funct_1),
    [interesting(0.00)]).

fof(d23_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ( r2_hidden(D,k3_msualg_1(A,C,B))
                   => k18_msafree(A,B,C,D) = k1_funct_1(k5_msualg_1(A,C,B),D) ) ) ) ) ) ),
    file(msafree,d23_msafree),
    [interesting(0.00)]).

fof(d10_msualg_1,definition,(
    ! [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)
             => k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B) ) ) ) ),
    file(msualg_1,d10_msualg_1),
    [interesting(0.00)]).

fof(d7_msualg_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_msualg_1(A))
         => k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B) ) ) ),
    file(msualg_1,d7_msualg_1),
    [interesting(0.00)]).

fof(d14_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_msualg_1(A))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C))
                    & m2_relset_1(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C)) )
                 => ( D = k9_msafree(A,B,C)
                  <=> ! [E] : 
                        ( m1_trees_4(E,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B)))
                       => ( r1_lang1(k5_msafree(A,B),k6_msafree(A,B,C),k1_dtconstr(u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),E))
                         => k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k5_msafree(A,B)),k6_msafree(A,B,C),E) ) ) ) ) ) ) ) ),
    file(msafree,d14_msafree),
    [interesting(0.00)]).

fof(s7_dtconstr,theorem,
    ( ( ! [A] : 
          ( m1_subset_1(A,u1_struct_0(f1_s7_dtconstr))
         => ( r2_hidden(A,k5_lang1(f1_s7_dtconstr))
           => p1_s7_dtconstr(k2_trees_4(u1_struct_0(f1_s7_dtconstr),A)) ) )
      & ! [A] : 
          ( m1_subset_1(A,u1_struct_0(f1_s7_dtconstr))
         => ! [B] : 
              ( m1_trees_4(B,k5_trees_3(u1_struct_0(f1_s7_dtconstr)),k4_dtconstr(f1_s7_dtconstr))
             => ( ( r1_lang1(f1_s7_dtconstr,A,k1_dtconstr(u1_struct_0(f1_s7_dtconstr),k5_trees_3(u1_struct_0(f1_s7_dtconstr)),B))
                  & ! [C] : 
                      ( ( v1_funct_1(C)
                        & v3_trees_2(C)
                        & m3_trees_2(C,u1_struct_0(f1_s7_dtconstr)) )
                     => ( r2_hidden(C,k2_relat_1(B))
                       => p1_s7_dtconstr(C) ) ) )
               => p1_s7_dtconstr(k12_trees_4(u1_struct_0(f1_s7_dtconstr),A,B)) ) ) ) )
   => ! [A] : 
        ( ( v1_funct_1(A)
          & v3_trees_2(A)
          & m3_trees_2(A,u1_struct_0(f1_s7_dtconstr)) )
       => ( r2_hidden(A,k4_dtconstr(f1_s7_dtconstr))
         => p1_s7_dtconstr(A) ) ) ),
    file(dtconstr,s7_dtconstr),
    [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(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(d9_msualg_3,definition,(
    ! [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),
    [interesting(0.00)]).

fof(d11_msualg_1,definition,(
    ! [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),
    [interesting(0.00)]).

fof(d15_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m3_pboole(C,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)))
             => ( C = k10_msafree(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_msualg_1(A))
                   => k1_msualg_3(u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B)),C,D) = k9_msafree(A,B,D) ) ) ) ) ) ),
    file(msafree,d15_msafree),
    [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(t6_msualg_3,theorem,(
    ! [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)
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D) )
                 => ( r2_hidden(D,k3_msualg_1(A,B,C))
                   => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,B))
                      & ! [E] : 
                          ( r2_hidden(E,k1_relat_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C))))
                         => r2_hidden(k1_funct_1(D,E),k1_funct_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)),E)) ) ) ) ) ) ) ) ),
    file(msualg_3,t6_msualg_3),
    [interesting(0.00)]).

fof(d8_msualg_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v5_msualg_1(C,A)
                & 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))
                         => ! [G] : 
                              ( m1_subset_1(G,k3_msualg_1(A,D,C))
                             => ( G = k6_msualg_3(A,B,C,D,E,F)
                              <=> ! [H] : 
                                    ( m2_subset_1(H,k1_numbers,k5_numbers)
                                   => ( r2_hidden(H,k1_relat_1(F))
                                     => k1_funct_1(G,H) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),H)),k1_funct_1(F,H)) ) ) ) ) ) ) ) ) ) ) ),
    file(msualg_3,d8_msualg_3),
    [interesting(0.00)]).

fof(t9_funct_1,theorem,(
    ! [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),
    [interesting(0.00)]).

fof(d1_msafree,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,B)
             => ! [E] : 
                  ( m3_pboole(E,A,B,C)
                 => ! [F] : 
                      ( m3_pboole(F,A,D,C)
                     => ( F = k1_msafree(A,B,C,D,E)
                      <=> ! [G] : 
                            ( r2_hidden(G,A)
                           => ! [H] : 
                                ( ( v1_funct_1(H)
                                  & v1_funct_2(H,k1_funct_1(B,G),k1_funct_1(C,G))
                                  & m2_relset_1(H,k1_funct_1(B,G),k1_funct_1(C,G)) )
                               => ( H = k1_funct_1(E,G)
                                 => k1_funct_1(F,G) = k8_relset_1(k1_funct_1(B,G),k1_funct_1(C,G),H,k1_funct_1(D,G)) ) ) ) ) ) ) ) ) ) ),
    file(msafree,d1_msafree),
    [interesting(0.00)]).

fof(t3_pboole,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    [interesting(0.00)]).

fof(d6_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ( v2_msafree(B,A)
          <=> ? [C] : 
                ( m1_msafree(C,A,B)
                & v1_msafree(C,A,B) ) ) ) ) ),
    file(msafree,d6_msafree),
    [interesting(0.00)]).

fof(d10_msualg_3,definition,(
    ! [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))
                 => ( r2_msualg_3(A,B,C,D)
                  <=> ( r1_msualg_3(A,B,C,D)
                      & v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) ) ) ) ) ) ),
    file(msualg_3,d10_msualg_3),
    [interesting(0.00)]).

fof(d3_msualg_3,definition,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( v2_msualg_3(D,A,B,C)
              <=> ! [E] : 
                    ( r2_hidden(E,A)
                   => k2_relat_1(k1_funct_1(D,E)) = k1_funct_1(C,E) ) ) ) ) ) ),
    file(msualg_3,d3_msualg_3),
    [interesting(0.00)]).

fof(t76_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B))
        & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) ) ) ),
    file(funct_1,t76_funct_1),
    [interesting(0.00)]).

fof(d20_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m3_pboole(C,u1_struct_0(A),k13_msafree(A,B),B)
             => ( C = k15_msafree(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_msualg_3(u1_struct_0(A),k13_msafree(A,B),B,C,D) = k14_msafree(A,B,D) ) ) ) ) ) ),
    file(msafree,d20_msafree),
    [interesting(0.00)]).

fof(d19_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v2_relat_1(B)
            & m1_pboole(B,u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k12_msafree(A,B,C),k1_funct_1(B,C))
                    & m2_relset_1(D,k12_msafree(A,B,C),k1_funct_1(B,C)) )
                 => ( D = k14_msafree(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(k5_msafree(A,B)))
                       => ( r2_hidden(k2_trees_4(u1_struct_0(k5_msafree(A,B)),E),k12_msafree(A,B,C))
                         => k1_funct_1(D,k2_trees_4(u1_struct_0(k5_msafree(A,B)),E)) = k1_mcart_1(E) ) ) ) ) ) ) ) ),
    file(msafree,d19_msafree),
    [interesting(0.00)]).

fof(t19_msualg_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( ( v5_msualg_1(B,A)
            & l3_msualg_1(B,A) )
         => ! [C] : 
              ( ( v4_msualg_1(C,A)
                & v5_msualg_1(C,A)
                & 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)
                   => ( r2_msualg_3(A,B,C,D)
                    <=> k7_msualg_3(A,B,C,D) = C ) ) ) ) ) ) ),
    file(msualg_3,t19_msualg_3),
    [interesting(0.00)]).

fof(t2_msafree,theorem,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( r2_hidden(C,A)
         => ( ~ ( k1_funct_1(B,C) != k1_xboole_0
                & k1_funct_1(k3_msafree(A,B),C) = k1_xboole_0 )
            & ~ ( k1_funct_1(k3_msafree(A,B),C) != k1_xboole_0
                & k1_funct_1(B,C) = k1_xboole_0 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_msafree,d1_xboole_0,d2_msafree,d1_xboole_0,d2_msafree]),
    [file(msafree,t2_msafree),interesting(0.00)]).

fof(t6_msualg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => m1_msualg_2(B,A,B) ) ) ),
    file(msualg_2,t6_msualg_2),
    [interesting(0.00)]).

fof(d4_msafree,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
             => ( m1_msafree(C,A,B)
              <=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,k12_msualg_2(A,B,C)),u4_msualg_1(A,B)) ) ) ) ) ),
    file(msafree,d4_msafree),
    [interesting(0.00)]).

fof(t10_msualg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v2_msualg_1(A)
        & l1_msualg_1(A) )
     => ! [B] : 
          ( l3_msualg_1(B,A)
         => ! [C] : 
              ( ( v4_msualg_1(C,A)
                & m1_msualg_2(C,A,B) )
             => ! [D] : 
                  ( ( v4_msualg_1(D,A)
                    & m1_msualg_2(D,A,B) )
                 => ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
                   => C = D ) ) ) ) ) ),
    file(msualg_2,t10_msualg_2),
    [interesting(0.00)]).