fof(t28_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => v2_binop_1(k10_unialg_2(A),k9_unialg_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d15_unialg_2,d16_unialg_2,d16_unialg_2,d8_unialg_2,t8_xboole_1,t8_xboole_1,t8_xboole_1,t8_xboole_1,d14_unialg_2,t24_unialg_2,t23_unialg_2,t4_xboole_1,d14_unialg_2,t23_unialg_2,d3_binop_1]),
    [file(unialg_2,t28_unialg_2),interesting(1.00)]).

fof(t26_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] : 
              ( ( v3_unialg_1(C)
                & m3_unialg_2(C,A) )
             => k8_unialg_2(A,k5_unialg_2(A,B,C),C) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d14_unialg_2,t20_unialg_2,d10_unialg_2,t17_xboole_1,t12_xboole_1,t22_unialg_2]),
    [file(unialg_2,t26_unialg_2),interesting(0.86)]).

fof(t11_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => m3_unialg_2(A,A) ) ),
    inference(mizar_proof,[status(thm)],[d7_unialg_2,t6_unialg_2,d7_unialg_2,t7_unialg_2,t7_unialg_2,t17_finseq_1,d8_unialg_2]),
    [file(unialg_2,t11_unialg_2),interesting(0.85)]).

fof(t15_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] : 
              ( ( v3_unialg_1(C)
                & m3_unialg_2(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_unialg_2,t13_unialg_2]),
    [file(unialg_2,t15_unialg_2),interesting(0.85)]).

fof(t14_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m3_unialg_2(C,A)
             => ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
               => m3_unialg_2(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d8_unialg_2,d8_unialg_2,d8_unialg_2,d7_unialg_2,t10_unialg_2,d5_unialg_2,d4_unialg_2,d4_finseq_1,t1_xboole_1,d4_finseq_1,d11_finseq_1,d11_finseq_1,t1_xboole_1,d4_finseq_1,d11_finseq_1,t11_finseq_2,t6_unialg_2,d4_finseq_2,d5_unialg_2,t9_unialg_2,d7_unialg_2,d6_unialg_2,t72_funct_1,d4_unialg_2,t6_unialg_2,t6_unialg_2,t6_unialg_2,d7_unialg_2,d5_unialg_2,t9_unialg_2,d7_unialg_2,d6_unialg_2,t1_unialg_2,t100_relat_1,d6_unialg_2,d6_unialg_2,d7_unialg_2,t17_finseq_1]),
    [file(unialg_2,t14_unialg_2),interesting(0.84)]).

fof(t30_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => v2_binop_1(k11_unialg_2(A),k9_unialg_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d15_unialg_2,d15_unialg_2,d17_unialg_2,d17_unialg_2,d17_unialg_2,d17_unialg_2,t20_unialg_2,d10_unialg_2,t20_unialg_2,d10_unialg_2,t20_unialg_2,d10_unialg_2,d8_unialg_2,t16_xboole_1,d10_unialg_2,d3_binop_1]),
    [file(unialg_2,t30_unialg_2),interesting(0.82)]).

fof(t22_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => ( C = u1_struct_0(B)
               => k7_unialg_2(A,C) = B ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_unialg_2,d8_unialg_2,d13_unialg_2,d10_xboole_0,t15_unialg_2]),
    [file(unialg_2,t22_unialg_2),interesting(0.74)]).

fof(t29_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => v1_binop_1(k11_unialg_2(A),k9_unialg_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d15_unialg_2,d17_unialg_2,t20_unialg_2,d10_unialg_2,d10_unialg_2,d2_binop_1]),
    [file(unialg_2,t29_unialg_2),interesting(0.71)]).

fof(t20_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m3_unialg_2(C,A)
             => ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_unialg_2,t19_xboole_1,t4_xboole_0]),
    [file(unialg_2,t20_unialg_2),interesting(0.70)]).

fof(t18_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(B))) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t11_finseq_2,d8_unialg_2,d8_unialg_2,t10_unialg_2,t6_unialg_2,d7_unialg_2,d5_funct_1,d5_unialg_2,t2_unialg_2,t112_finseq_2,t112_finseq_2,d3_xboole_0,t68_funct_1,d6_unialg_2,d6_unialg_2,t68_funct_1,d5_funct_1,t12_relset_1]),
    [file(unialg_2,t18_unialg_2),interesting(0.69)]).

fof(t16_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => r1_unialg_2(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d8_unialg_2,d11_unialg_1,t31_finseq_3,d11_unialg_1,t31_finseq_3,d8_unialg_2,d7_unialg_2,d7_unialg_2,t6_unialg_2,d11_unialg_1,t6_unialg_2,d11_unialg_1,t9_unialg_2,t17_finseq_1,d2_unialg_2]),
    [file(unialg_2,t16_unialg_2),interesting(0.67)]).

fof(t21_unialg_2,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) )
     => k7_unialg_2(A,k2_subset_1(u1_struct_0(A))) = A ) ),
    inference(mizar_proof,[status(thm)],[d4_subset_1,d8_unialg_2,d13_unialg_2,d10_xboole_0,d8_unialg_2,d8_unialg_2,d7_unialg_2,t6_unialg_2,d7_unialg_2,t7_unialg_2,t17_finseq_1]),
    [file(unialg_2,t21_unialg_2),interesting(0.63)]).

fof(t27_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => v1_binop_1(k10_unialg_2(A),k9_unialg_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d15_unialg_2,d16_unialg_2,d8_unialg_2,t8_xboole_1,d14_unialg_2,d2_binop_1]),
    [file(unialg_2,t27_unialg_2),interesting(0.63)]).

fof(t24_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m3_unialg_2(C,A)
             => k8_unialg_2(A,B,C) = k8_unialg_2(A,C,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d14_unialg_2,d14_unialg_2]),
    [file(unialg_2,t24_unialg_2),interesting(0.63)]).

fof(t25_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( v3_unialg_1(B)
            & m3_unialg_2(B,A) )
         => ! [C] : 
              ( ( v3_unialg_1(C)
                & m3_unialg_2(C,A) )
             => k5_unialg_2(A,B,k8_unialg_2(A,B,C)) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_unialg_2,d10_unialg_2,d8_unialg_2,d14_unialg_2,d13_unialg_2,t7_xboole_1,t1_xboole_1,t19_xboole_1,t17_xboole_1,d8_unialg_2,d10_unialg_2,d8_unialg_2,d7_unialg_2,t6_unialg_2,d10_unialg_2,d7_unialg_2,d10_xboole_0,d7_unialg_2,d8_unialg_2,t17_finseq_1,d10_xboole_0]),
    [file(unialg_2,t25_unialg_2),interesting(0.58)]).

fof(t2_unialg_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_funct_1(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,d4_finseq_2,t1_unialg_1,d3_tarski,d11_finseq_1,d10_unialg_1,d2_unialg_1]),
    [file(unialg_2,t2_unialg_2),interesting(0.53)]).

fof(t1_unialg_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(B)) )
             => k3_xboole_0(k4_finseq_2(A,B),k4_finseq_2(A,C)) = k4_finseq_2(A,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t129_finseq_2,t28_xboole_1]),
    [file(unialg_2,t1_unialg_2),interesting(0.49)]).

fof(t19_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & v2_unialg_2(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ( ~ v1_xboole_0(k6_unialg_2(A))
            & m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_unialg_2]),
    [file(unialg_2,t19_unialg_2),interesting(0.48)]).

fof(t6_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( r2_hidden(B,k4_finseq_1(u1_unialg_1(A)))
         => m2_unialg_2(k1_funct_1(u1_unialg_1(A),B),u1_struct_0(A),k1_unialg_2(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1]),
    [file(unialg_2,t6_unialg_2),interesting(0.40)]).

fof(t23_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( D = k2_xboole_0(C,u1_struct_0(B))
                   => ( ( C = k1_xboole_0
                        & k6_unialg_2(A) = k1_xboole_0 )
                      | k8_unialg_2(A,k7_unialg_2(A,C),B) = k7_unialg_2(A,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_unialg_2,d8_unialg_2,d14_unialg_2,d13_unialg_2,t13_xboole_1,t1_xboole_1,d13_unialg_2,d13_unialg_2,t7_xboole_1,t1_xboole_1,t19_xboole_1,t3_xboole_1,t18_unialg_2,t19_xboole_1,t3_xboole_1,d7_xboole_0,d10_unialg_2,d13_unialg_2,d8_unialg_2,t17_xboole_1,d10_xboole_0,t17_xboole_1,t8_xboole_1,d13_unialg_2,t13_unialg_2]),
    [file(unialg_2,t23_unialg_2),interesting(0.40)]).

fof(t7_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( B = u1_struct_0(A)
           => ( v1_unialg_2(B,A)
              & ! [C] : 
                  ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
                 => k2_unialg_2(A,B,C) = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_unialg_2,t12_relset_1,t2_unialg_2,t110_finseq_2,d5_funct_1,t2_unialg_2,d6_unialg_2,t97_relat_1,d5_unialg_2]),
    [file(unialg_2,t7_unialg_2),interesting(0.37)]).

fof(t3_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
           => k3_finseq_1(u1_unialg_1(A)) = k3_finseq_1(u1_unialg_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_unialg_1,d2_unialg_2]),
    [file(unialg_2,t3_unialg_2),interesting(0.37)]).

fof(t5_unialg_2,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(k2_relat_1(u1_unialg_1(A)))
        & m1_subset_1(k2_relat_1(u1_unialg_1(A)),k1_zfmisc_1(k4_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)))) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_finseq_1,d4_finseq_1]),
    [file(unialg_2,t5_unialg_2),interesting(0.21)]).

fof(t8_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
               => k2_unialg_1(B,k2_unialg_2(A,B,C)) = k2_unialg_1(u1_struct_0(A),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_unialg_2,t90_relat_1,t2_unialg_2,t1_unialg_2,t2_unialg_2,t130_finseq_2]),
    [file(unialg_2,t8_unialg_2),interesting(0.20)]).

fof(t17_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ~ v3_struct_0(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v3_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v6_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v7_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & v8_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
            & l1_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_unialg_2,t6_unialg_2,d7_unialg_2,d4_unialg_1,t6_unialg_2,d7_unialg_2,d5_unialg_1,t26_finseq_1,t26_finseq_1,t6_unialg_2,d7_unialg_2,d15_funct_1,d7_unialg_1,d8_unialg_1,d9_unialg_1]),
    [file(unialg_2,t17_unialg_2),interesting(0.18)]).

fof(d7_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m2_finseq_1(C,k4_partfun1(k13_finseq_1(B),B))
             => ( C = k3_unialg_2(A,B)
              <=> ( k4_finseq_1(C) = k4_finseq_1(u1_unialg_1(A))
                  & ! [D,E] : 
                      ( m2_unialg_2(E,u1_struct_0(A),k1_unialg_2(A))
                     => ( ( r2_hidden(D,k4_finseq_1(C))
                          & E = k1_funct_1(u1_unialg_1(A),D) )
                       => k1_funct_1(C,D) = k2_unialg_2(A,B,E) ) ) ) ) ) ) ) ),
    file(unialg_2,d7_unialg_2),
    [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(d4_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
              <=> ! [D] : 
                    ( m2_finseq_1(D,B)
                   => ( k3_finseq_1(D) = k2_unialg_1(u1_struct_0(A),C)
                     => r2_hidden(k1_funct_1(C,D),B) ) ) ) ) ) ) ),
    file(unialg_2,d4_unialg_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(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(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(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(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(t1_unialg_1,theorem,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & m2_relset_1(B,k13_finseq_1(A),A) )
     => ( ~ ( ~ v1_xboole_0(B)
            & k1_relat_1(B) = k1_xboole_0 )
        & ~ ( k1_relat_1(B) != k1_xboole_0
            & v1_xboole_0(B) ) ) ) ),
    file(unialg_1,t1_unialg_1),
    [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)]).

fof(d6_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ( r2_unialg_2(A,B,C)
               => k2_unialg_2(A,B,C) = k2_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),C,k4_finseq_2(k2_unialg_1(u1_struct_0(A),C),B)) ) ) ) ) ),
    file(unialg_2,d6_unialg_2),
    [interesting(0.00)]).

fof(t97_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k1_relat_1(B),A)
       => k7_relat_1(B,A) = B ) ) ),
    file(relat_1,t97_relat_1),
    [interesting(0.00)]).

fof(d5_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_unialg_2(B,A)
          <=> ! [C] : 
                ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
               => r2_unialg_2(A,B,C) ) ) ) ) ),
    file(unialg_2,d5_unialg_2),
    [interesting(0.00)]).

fof(t17_finseq_1,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) )
         => ( ( k4_finseq_1(A) = k4_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(A))
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t17_finseq_1),
    [interesting(0.00)]).

fof(d8_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(B,A)
          <=> ( m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A)))
              & ! [C] : 
                  ( ( ~ v1_xboole_0(C)
                    & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
                 => ( C = u1_struct_0(B)
                   => ( u1_unialg_1(B) = k3_unialg_2(A,C)
                      & v1_unialg_2(C,A) ) ) ) ) ) ) ) ),
    file(unialg_2,d8_unialg_2),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(t11_finseq_2,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ~ ( r2_hidden(A,k2_relat_1(B))
          & ! [C] : 
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_hidden(C,k4_finseq_1(B))
                  & k1_funct_1(B,C) = A ) ) ) ) ),
    file(finseq_2,t11_finseq_2),
    [interesting(0.00)]).

fof(t68_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( B = k7_relat_1(C,A)
          <=> ( k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)
              & ! [D] : 
                  ( r2_hidden(D,k1_relat_1(B))
                 => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ),
    file(funct_1,t68_funct_1),
    [interesting(0.00)]).

fof(t129_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(B)) )
             => ! [D] : 
                  ( m2_finseq_2(D,C,k4_finseq_2(A,C))
                 => m2_finseq_2(D,B,k4_finseq_2(A,B)) ) ) ) ) ),
    file(finseq_2,t129_finseq_2),
    [interesting(0.00)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.00)]).

fof(t130_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] : 
              ( ~ v1_xboole_0(C)
             => ( k4_finseq_2(A,C) = k4_finseq_2(B,C)
               => A = B ) ) ) ) ),
    file(finseq_2,t130_finseq_2),
    [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(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(t100_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)) ) ),
    file(relat_1,t100_relat_1),
    [interesting(0.00)]).

fof(t90_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ),
    file(relat_1,t90_relat_1),
    [interesting(0.00)]).

fof(t9_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
             => ! [D] : 
                  ( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
                 => ! [E] : 
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( ( m3_unialg_2(A,B)
                          & r2_hidden(E,k4_finseq_1(u1_unialg_1(A)))
                          & C = k1_funct_1(u1_unialg_1(A),E)
                          & D = k1_funct_1(u1_unialg_1(B),E) )
                       => k2_unialg_1(u1_struct_0(A),C) = k2_unialg_1(u1_struct_0(B),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d8_unialg_2,d5_unialg_2,d8_unialg_2,d8_unialg_2,d7_unialg_2,d6_unialg_2,t90_relat_1,t2_unialg_2,t1_unialg_2,t2_unialg_2,t130_finseq_2]),
    [file(unialg_2,t9_unialg_2),interesting(0.00)]).

fof(t12_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ( ( m3_unialg_2(A,B)
                  & m3_unialg_2(B,C) )
               => m3_unialg_2(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d8_unialg_2,t1_xboole_1,d8_unialg_2,d8_unialg_2,d8_unialg_2,d8_unialg_2,d8_unialg_2,d5_unialg_2,t11_finseq_2,d7_unialg_2,d5_funct_1,d5_unialg_2,d7_unialg_2,d7_unialg_2,d5_funct_1,d7_unialg_2,t2_unialg_2,d6_unialg_2,t68_funct_1,t1_unialg_2,t130_finseq_2,t68_funct_1,t1_unialg_2,t130_finseq_2,d11_finseq_1,d11_finseq_1,d4_finseq_1,t1_xboole_1,d4_finseq_1,d11_finseq_1,d4_finseq_2,d4_finseq_2,d6_unialg_2,t72_funct_1,d6_unialg_2,t72_funct_1,d4_finseq_2,d5_funct_1,t12_relset_1,d4_unialg_2,d8_unialg_2,d7_unialg_2,d8_unialg_2,d7_unialg_2,d7_unialg_2,t6_unialg_2,t6_unialg_2,d5_unialg_2,d5_unialg_2,d7_unialg_2,d6_unialg_2,t1_unialg_2,t100_relat_1,d6_unialg_2,d7_unialg_2,t9_unialg_2,d6_unialg_2,d7_unialg_2,t17_finseq_1,d5_unialg_2]),
    [file(unialg_2,t12_unialg_2),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(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(d2_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( r1_unialg_2(A,B)
          <=> k3_unialg_1(A) = k3_unialg_1(B) ) ) ) ),
    file(unialg_2,d2_unialg_2),
    [interesting(0.00)]).

fof(d4_unialg_1,definition,(
    ! [A,B] : 
      ( m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ( v4_unialg_1(B,A)
      <=> ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ! [D] : 
                ( ( v1_funct_1(D)
                  & m2_relset_1(D,k13_finseq_1(A),A) )
               => ( ( r2_hidden(C,k4_finseq_1(B))
                    & D = k1_funct_1(B,C) )
                 => v1_unialg_1(D,A) ) ) ) ) ) ),
    file(unialg_1,d4_unialg_1),
    [interesting(0.00)]).

fof(d5_unialg_1,definition,(
    ! [A,B] : 
      ( m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
     => ( v5_unialg_1(B,A)
      <=> ! [C] : 
            ( m2_subset_1(C,k1_numbers,k5_numbers)
           => ! [D] : 
                ( ( v1_funct_1(D)
                  & m2_relset_1(D,k13_finseq_1(A),A) )
               => ( ( r2_hidden(C,k4_finseq_1(B))
                    & D = k1_funct_1(B,C) )
                 => v2_unialg_1(D,A) ) ) ) ) ) ),
    file(unialg_1,d5_unialg_1),
    [interesting(0.00)]).

fof(t26_finseq_1,theorem,(
    ! [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),
    [interesting(0.00)]).

fof(d15_funct_1,definition,(
    ! [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),
    [interesting(0.00)]).

fof(d7_unialg_1,definition,(
    ! [A] : 
      ( l1_unialg_1(A)
     => ( v6_unialg_1(A)
      <=> v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,d7_unialg_1),
    [interesting(0.00)]).

fof(d8_unialg_1,definition,(
    ! [A] : 
      ( l1_unialg_1(A)
     => ( v7_unialg_1(A)
      <=> v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) ) ) ),
    file(unialg_1,d8_unialg_1),
    [interesting(0.00)]).

fof(d9_unialg_1,definition,(
    ! [A] : 
      ( l1_unialg_1(A)
     => ( v8_unialg_1(A)
      <=> ( u1_unialg_1(A) != k1_xboole_0
          & v2_relat_1(u1_unialg_1(A)) ) ) ) ),
    file(unialg_1,d9_unialg_1),
    [interesting(0.00)]).

fof(t10_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( m3_unialg_2(A,B)
           => k4_finseq_1(u1_unialg_1(A)) = k4_finseq_1(u1_unialg_1(B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d8_unialg_2,d7_unialg_2]),
    [file(unialg_2,t10_unialg_2),interesting(0.00)]).

fof(t112_finseq_2,theorem,(
    ! [A] : k4_finseq_2(0,A) = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A)) ),
    file(finseq_2,t112_finseq_2),
    [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_subset_1,definition,(
    ! [A] : k2_subset_1(A) = A ),
    file(subset_1,d4_subset_1),
    [interesting(0.00)]).

fof(d13_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ~ ( k6_unialg_2(A) = k1_xboole_0
                & B = k1_xboole_0 )
           => ! [C] : 
                ( ( v3_unialg_1(C)
                  & m3_unialg_2(C,A) )
               => ( C = k7_unialg_2(A,B)
                <=> ( r1_tarski(B,u1_struct_0(C))
                    & ! [D] : 
                        ( m3_unialg_2(D,A)
                       => ( r1_tarski(B,u1_struct_0(D))
                         => m3_unialg_2(C,D) ) ) ) ) ) ) ) ) ),
    file(unialg_2,d13_unialg_2),
    [interesting(0.00)]).

fof(t19_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(A,k3_xboole_0(B,C)) ) ),
    file(xboole_1,t19_xboole_1),
    [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(d10_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m3_unialg_2(C,A)
             => ( ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C))
               => ! [D] : 
                    ( ( v3_unialg_1(D)
                      & m3_unialg_2(D,A) )
                   => ( D = k5_unialg_2(A,B,C)
                    <=> ( u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C))
                        & ! [E] : 
                            ( ( ~ v1_xboole_0(E)
                              & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
                           => ( E = u1_struct_0(D)
                             => ( u1_unialg_1(D) = k3_unialg_2(A,E)
                                & v1_unialg_2(E,A) ) ) ) ) ) ) ) ) ) ) ),
    file(unialg_2,d10_unialg_2),
    [interesting(0.00)]).

fof(d14_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( m3_unialg_2(B,A)
         => ! [C] : 
              ( m3_unialg_2(C,A)
             => ! [D] : 
                  ( ( v3_unialg_1(D)
                    & m3_unialg_2(D,A) )
                 => ( D = k8_unialg_2(A,B,C)
                  <=> ! [E] : 
                        ( ( ~ v1_xboole_0(E)
                          & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
                       => ( E = k2_xboole_0(u1_struct_0(B),u1_struct_0(C))
                         => D = k7_unialg_2(A,E) ) ) ) ) ) ) ) ),
    file(unialg_2,d14_unialg_2),
    [interesting(0.00)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).

fof(t13_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ( ( v3_unialg_1(A)
              & m3_unialg_2(A,B)
              & v3_unialg_1(B)
              & m3_unialg_2(B,A) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_unialg_2,d8_unialg_2,d10_xboole_0,d8_unialg_2,d7_unialg_2,t6_unialg_2,d7_unialg_2,t7_unialg_2,t17_finseq_1]),
    [file(unialg_2,t13_unialg_2),interesting(0.00)]).

fof(d15_unialg_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( B = k9_unialg_2(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ( v3_unialg_1(C)
                & m3_unialg_2(C,A) ) ) ) ) ),
    file(unialg_2,d15_unialg_2),
    [interesting(0.00)]).

fof(d16_unialg_2,definition,(
    ! [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,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) )
         => ( B = k10_unialg_2(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k9_unialg_2(A))
               => ! [D] : 
                    ( m1_subset_1(D,k9_unialg_2(A))
                   => ! [E] : 
                        ( ( v3_unialg_1(E)
                          & m3_unialg_2(E,A) )
                       => ! [F] : 
                            ( ( v3_unialg_1(F)
                              & m3_unialg_2(F,A) )
                           => ( ( C = E
                                & D = F )
                             => k2_binop_1(k9_unialg_2(A),k9_unialg_2(A),k9_unialg_2(A),B,C,D) = k8_unialg_2(A,E,F) ) ) ) ) ) ) ) ) ),
    file(unialg_2,d16_unialg_2),
    [interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.00)]).

fof(d2_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v1_binop_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => ! [D] : 
                ( m1_subset_1(D,A)
               => k1_binop_1(B,C,D) = k1_binop_1(B,D,C) ) ) ) ) ),
    file(binop_1,d2_binop_1),
    [interesting(0.00)]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.00)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [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(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    [interesting(0.00)]).

fof(d3_binop_1,definition,(
    ! [A,B] : 
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m2_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v2_binop_1(B,A)
      <=> ! [C] : 
            ( m1_subset_1(C,A)
           => ! [D] : 
                ( m1_subset_1(D,A)
               => ! [E] : 
                    ( m1_subset_1(E,A)
                   => k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E) ) ) ) ) ) ),
    file(binop_1,d3_binop_1),
    [interesting(0.00)]).

fof(d17_unialg_2,definition,(
    ! [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,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
            & m2_relset_1(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) )
         => ( B = k11_unialg_2(A)
          <=> ! [C] : 
                ( m1_subset_1(C,k9_unialg_2(A))
               => ! [D] : 
                    ( m1_subset_1(D,k9_unialg_2(A))
                   => ! [E] : 
                        ( ( v3_unialg_1(E)
                          & m3_unialg_2(E,A) )
                       => ! [F] : 
                            ( ( v3_unialg_1(F)
                              & m3_unialg_2(F,A) )
                           => ( ( C = E
                                & D = F )
                             => k2_binop_1(k9_unialg_2(A),k9_unialg_2(A),k9_unialg_2(A),B,C,D) = k5_unialg_2(A,E,F) ) ) ) ) ) ) ) ) ),
    file(unialg_2,d17_unialg_2),
    [interesting(0.00)]).

fof(t16_xboole_1,theorem,(
    ! [A,B,C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) ),
    file(xboole_1,t16_xboole_1),
    [interesting(0.00)]).

fof(t4_unialg_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v6_unialg_1(A)
        & v7_unialg_1(A)
        & v8_unialg_1(A)
        & l1_unialg_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v6_unialg_1(B)
            & v7_unialg_1(B)
            & v8_unialg_1(B)
            & l1_unialg_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v6_unialg_1(C)
                & v7_unialg_1(C)
                & v8_unialg_1(C)
                & l1_unialg_1(C) )
             => ( ( r1_unialg_2(A,B)
                  & r1_unialg_2(B,C) )
               => r1_unialg_2(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_unialg_2,d2_unialg_2]),
    [file(unialg_2,t4_unialg_2),interesting(0.00)]).

fof(t27_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( A = k1_xboole_0
      <=> k2_relat_1(A) = k1_xboole_0 ) ) ),
    file(finseq_1,t27_finseq_1),
    [interesting(0.00)]).