fof(t26_trees_4,theorem,(
    ! [A,B] : k13_funct_3(k1_trees_4(A),k1_trees_4(B)) = k1_trees_4(k4_tarski(A,B)) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_tarski,t25_trees_4,t42_trees_3]),
    [file(trees_4,t26_trees_4),interesting(1.00)]).

fof(l1_trees_4,theorem,(
    ! [A,B,C] : 
      ( m2_finseq_1(C,A)
     => ( ( r2_hidden(B,k4_finseq_1(C))
          | r2_hidden(B,k4_finseq_1(C)) )
       => r2_hidden(k1_funct_1(C,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_finseq_1,d5_funct_1]),
    [file(trees_4,l1_trees_4),interesting(0.93)]).

fof(t2_trees_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( k2_trees_1(A) = k2_trees_1(B)
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_trees_4,t1_xreal_1]),
    [file(trees_4,t2_trees_4),interesting(0.90)]).

fof(t4_trees_4,theorem,(
    ! [A,B] : 
      ( k1_trees_4(A) = k1_trees_4(B)
     => A = B ) ),
    inference(mizar_proof,[status(thm)],[t3_trees_4,t3_trees_4]),
    [file(trees_4,t4_trees_4),interesting(0.90)]).

fof(t1_trees_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_tarski(k2_trees_1(A),k2_trees_1(B))
           => r1_xreal_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_trees_1,t57_trees_1,t57_finseq_1]),
    [file(trees_4,t1_trees_4),interesting(0.86)]).

fof(t16_trees_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( k1_trees_4(A) = k3_trees_4(B,C)
       => ( A = B
          & C = k1_xboole_0 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_trees_4,d3_trees_4,d3_trees_4,t3_trees_4,t2_trees_4,t25_finseq_1]),
    [file(trees_4,t16_trees_4),interesting(0.86)]).

fof(t20_trees_4,theorem,(
    ! [A] : 
      ( k3_trees_4(A,k1_xboole_0) = k1_trees_4(A)
      & k4_trees_4(A,k1_xboole_0) = k1_trees_4(A) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,d3_trees_4,d1_tarski,t56_trees_1,d3_trees_4,t17_funcop_1,t23_trees_3,t10_trees_4,t32_funct_6,t55_trees_3,d1_tarski,t56_trees_1,d4_trees_4,t17_funcop_1]),
    [file(trees_4,t20_trees_4),interesting(0.83)]).

fof(t6_trees_4,theorem,(
    ! [A] : k1_trees_4(A) = k1_tarski(k4_tarski(k1_xboole_0,A)) ),
    inference(mizar_proof,[status(thm)],[d2_funcop_1,t56_trees_1,t35_zfmisc_1]),
    [file(trees_4,t6_trees_4),interesting(0.83)]).

fof(l6_trees_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B,C] : 
          ( m2_finseq_1(C,B)
         => ( ~ r1_xreal_0(k3_finseq_1(C),A)
           => r2_hidden(k1_funct_1(C,k1_nat_1(A,1)),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l5_trees_4,d4_finseq_1]),
    [file(trees_4,l6_trees_4),interesting(0.82)]).

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 ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t56_trees_1,t13_funcop_1,t19_funcop_1]),
    [file(trees_4,t3_trees_4),interesting(0.80)]).

fof(t10_trees_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v6_trees_3(B) )
     => k1_relat_1(k4_trees_4(A,B)) = k13_trees_3(k2_funct_6(B)) ) ),
    inference(mizar_proof,[status(thm)],[d4_trees_4]),
    [file(trees_4,t10_trees_4),interesting(0.78)]).

fof(t21_trees_4,theorem,(
    ! [A,B] : k3_trees_4(A,k9_finseq_1(B)) = k8_trees_2(k2_funcop_1(k2_trees_1(1),A),k12_finseq_1(k5_numbers,0),k1_trees_4(B)) ),
    inference(mizar_proof,[status(thm)],[d3_trees_4,t57_finseq_1,t19_funcop_1,t9_modal_1,d2_tarski,d12_trees_2,t61_trees_3,t70_trees_3,t9_modal_1,d2_tarski,t57_finseq_1,t3_xboole_1,d3_trees_4,t13_funcop_1,t47_trees_3,t48_trees_3,t3_trees_4,t9_funct_1]),
    [file(trees_4,t21_trees_4),interesting(0.78)]).

fof(t7_trees_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D) )
         => ( k3_trees_4(A,C) = k3_trees_4(B,D)
           => ( A = B
              & C = D ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_trees_4,d3_trees_4,d3_trees_4,t2_trees_4,t28_nat_1,t38_nat_1,d3_trees_4,t18_finseq_1]),
    [file(trees_4,t7_trees_4),interesting(0.78)]).

fof(t17_trees_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( ( k1_trees_4(A) = k4_trees_4(B,C)
          & v6_trees_3(C) )
       => ( A = B
          & C = k1_xboole_0 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_trees_4,d4_trees_4,t3_trees_4,t10_trees_4,t26_finseq_1,t23_trees_3,t39_trees_3,t53_trees_3,t55_trees_3,t26_finseq_1]),
    [file(trees_4,t17_trees_4),interesting(0.73)]).

fof(t22_trees_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) )
     => k4_trees_4(A,k9_finseq_1(B)) = k8_trees_2(k2_funcop_1(k2_trees_1(1),A),k12_finseq_1(k5_numbers,0),B) ) ),
    inference(mizar_proof,[status(thm)],[t10_trees_4,t33_funct_6,d16_trees_3,t61_trees_3,t19_funcop_1,t9_modal_1,d2_tarski,d12_trees_2,t47_finseq_1,t25_trees_1,t47_trees_1,d12_trees_1,t47_finseq_1,t9_modal_1,d2_tarski,t3_xboole_1,t48_trees_3,t13_funcop_1,d4_trees_4,t49_trees_3,t57_finseq_1,d4_trees_4,t66_trees_1,d11_trees_2,t9_funct_1]),
    [file(trees_4,t22_trees_4),interesting(0.73)]).

fof(t23_trees_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( ~ ( r2_hidden(C,k2_relat_1(A))
                  & r2_hidden(C,k4_trees_2(A)) )
             => k13_trees_4(A,B,C) = A ) ) ) ),
    inference(mizar_proof,[status(thm)],[t144_relat_1,d1_trees_2,d7_trees_4,d12_funct_1,d1_trees_4,d12_funct_1,d7_trees_4]),
    [file(trees_4,t23_trees_4),interesting(0.71)]).

fof(t13_trees_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) )
     => k1_relat_1(k5_trees_4(A,B)) = k14_trees_3(k1_relat_1(B)) ) ),
    inference(mizar_proof,[status(thm)],[t10_trees_4,t33_funct_6,d16_trees_3]),
    [file(trees_4,t13_trees_4),interesting(0.69)]).

fof(t8_trees_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,A)
           => k4_trees_1(k2_trees_1(B),k12_finseq_1(k5_numbers,A)) = k2_trees_1(0) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t69_finseq_2,t29_nat_1,t38_nat_1,t52_trees_3,t57_trees_3,t70_finseq_2]),
    [file(trees_4,t8_trees_4),interesting(0.69)]).

fof(t15_trees_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C)
        & v6_trees_3(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D)
            & v6_trees_3(D) )
         => ( k4_trees_4(A,C) = k4_trees_4(B,D)
           => ( A = B
              & C = D ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_trees_4,d4_trees_4,t10_trees_4,t39_trees_3,t53_trees_3,t31_finseq_3,t28_nat_1,t38_nat_1,d4_trees_4,t18_finseq_1]),
    [file(trees_4,t15_trees_4),interesting(0.67)]).

fof(t24_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v3_trees_2(C)
                & m3_trees_2(C,k2_zfmisc_1(A,B)) )
             => ( k1_relat_1(k10_trees_3(A,B,C)) = k1_relat_1(C)
                & k1_relat_1(k11_trees_3(A,B,C)) = k1_relat_1(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d9_trees_2,d12_trees_3,d13_trees_3,t46_relat_1]),
    [file(trees_4,t24_trees_4),interesting(0.67)]).

fof(s1_trees_4,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_trees_1(A)
      & ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r2_hidden(B,A)
          <=> ~ ( ~ r2_hidden(B,f1_s1_trees_4)
                & ! [C] : 
                    ( m1_trees_1(C,f1_s1_trees_4)
                   => ! [D] : 
                        ( m1_trees_1(D,f2_s1_trees_4)
                       => ~ ( p1_s1_trees_4(C)
                            & B = k8_finseq_1(k5_numbers,C,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,d11_finseq_1,d3_tarski,d5_trees_1,d3_tarski,d4_trees_1,d8_xboole_0,t8_trees_1,t50_finseq_1,d11_finseq_1,t46_trees_1,t64_finseq_1,d11_finseq_1,t46_trees_1,t64_finseq_1,t50_finseq_1,t45_finseq_1,t46_finseq_1,d11_finseq_1,t46_trees_1,d11_finseq_1,d5_trees_1,t47_finseq_1,t63_finseq_1,t50_finseq_1,t45_finseq_1,t35_finseq_1,t57_finseq_1,t59_finseq_1,t46_finseq_1,t45_finseq_1,d11_finseq_1,d5_trees_1,d11_finseq_1]),
    [file(trees_4,s1_trees_4),interesting(0.66)]).

fof(t5_trees_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( k1_relat_1(A) = k2_trees_1(0)
       => A = k1_trees_4(k1_funct_1(A,k1_xboole_0)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,t56_trees_1,t17_funcop_1]),
    [file(trees_4,t5_trees_4),interesting(0.59)]).

fof(t14_trees_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v3_trees_2(C) )
         => k1_relat_1(k6_trees_4(A,B,C)) = k15_trees_3(k1_relat_1(B),k1_relat_1(C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_trees_4,t34_funct_6,d17_trees_3]),
    [file(trees_4,t14_trees_4),interesting(0.58)]).

fof(t29_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & m4_trees_3(E,k2_zfmisc_1(A,B)) )
                     => ! [F] : 
                          ( m2_finseq_1(F,E)
                         => ? [G] : 
                              ( m2_finseq_1(G,k4_trees_3(A))
                              & k4_finseq_1(G) = k4_finseq_1(F)
                              & ! [H] : 
                                  ( m2_subset_1(H,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(H,k4_finseq_1(F))
                                      & ! [I] : 
                                          ( m5_trees_3(I,k2_zfmisc_1(A,B),E)
                                         => ~ ( I = k1_funct_1(F,H)
                                              & k1_funct_1(G,H) = k10_trees_3(A,B,I) ) ) ) )
                              & k10_trees_3(A,B,k8_trees_4(k2_zfmisc_1(A,B),E,k1_domain_1(A,B,C,D),F)) = k8_trees_4(A,k4_trees_3(A),C,G) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,l1_trees_4,d7_trees_3,s5_finseq_1,d3_finseq_1,t27_trees_4]),
    [file(trees_4,t29_trees_4),interesting(0.57)]).

fof(t30_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & m4_trees_3(E,k2_zfmisc_1(A,B)) )
                     => ! [F] : 
                          ( m2_finseq_1(F,E)
                         => ? [G] : 
                              ( m2_finseq_1(G,k4_trees_3(B))
                              & k4_finseq_1(G) = k4_finseq_1(F)
                              & ! [H] : 
                                  ( m2_subset_1(H,k1_numbers,k5_numbers)
                                 => ~ ( r2_hidden(H,k4_finseq_1(F))
                                      & ! [I] : 
                                          ( m5_trees_3(I,k2_zfmisc_1(A,B),E)
                                         => ~ ( I = k1_funct_1(F,H)
                                              & k1_funct_1(G,H) = k11_trees_3(A,B,I) ) ) ) )
                              & k11_trees_3(A,B,k8_trees_4(k2_zfmisc_1(A,B),E,k1_domain_1(A,B,C,D),F)) = k8_trees_4(B,k4_trees_3(B),D,G) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_finseq_1,l1_trees_4,d7_trees_3,s5_finseq_1,d3_finseq_1,t28_trees_4]),
    [file(trees_4,t30_trees_4),interesting(0.56)]).

fof(t9_trees_4,theorem,(
    ! [A,B] : 
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v1_finseq_1(C) )
         => ( ~ r1_xreal_0(k3_finseq_1(C),B)
           => k5_trees_2(k3_trees_4(A,C),k12_finseq_1(k5_numbers,B)) = k1_trees_4(k1_funct_1(C,k1_nat_1(B,1))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_trees_1,d3_trees_4,t8_trees_4,t55_trees_1,t47_finseq_1,d11_trees_2,t5_trees_4]),
    [file(trees_4,t9_trees_4),interesting(0.54)]).

fof(l5_trees_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ~ r1_xreal_0(k3_finseq_1(B),A)
           => ( r2_hidden(k1_nat_1(A,1),k4_finseq_1(B))
              & r2_hidden(k1_funct_1(B,k1_nat_1(A,1)),k2_relat_1(B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_nat_1,t38_nat_1,t9_xreal_1,t27_finseq_3,d5_funct_1]),
    [file(trees_4,l5_trees_4),interesting(0.46)]).

fof(t27_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & m4_trees_3(E,k2_zfmisc_1(A,B)) )
                     => ! [F] : 
                          ( ( ~ v1_xboole_0(F)
                            & m4_trees_3(F,A) )
                         => ! [G] : 
                              ( m2_finseq_1(G,E)
                             => ! [H] : 
                                  ( m2_finseq_1(H,F)
                                 => ( ( k4_finseq_1(H) = k4_finseq_1(G)
                                      & ! [I] : 
                                          ( m2_subset_1(I,k1_numbers,k5_numbers)
                                         => ( r2_hidden(I,k4_finseq_1(G))
                                           => ! [J] : 
                                                ( ( v1_funct_1(J)
                                                  & v3_trees_2(J)
                                                  & m3_trees_2(J,k2_zfmisc_1(A,B)) )
                                               => ( J = k1_funct_1(G,I)
                                                 => k1_funct_1(H,I) = k10_trees_3(A,B,J) ) ) ) ) )
                                   => k10_trees_3(A,B,k8_trees_4(k2_zfmisc_1(A,B),E,k1_domain_1(A,B,C,D),G)) = k8_trees_4(A,F,C,H) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_finseq_3,t40_trees_3,t31_finseq_3,l1_trees_4,t31_funct_6,t24_trees_4,t17_finseq_1,t24_trees_4,t10_trees_4,t10_trees_4,d1_trees_4,t24_trees_4,t41_trees_3,d4_trees_4,t7_mcart_1,t11_trees_4,l6_trees_4,t24_trees_4,l5_trees_4,t12_trees_4,t41_trees_3]),
    [file(trees_4,t27_trees_4),interesting(0.42)]).

fof(t31_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(A,B)))
                     => ? [F] : 
                          ( m2_finseq_1(F,k5_trees_3(A))
                          & k4_finseq_1(F) = k4_finseq_1(E)
                          & ! [G] : 
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => ~ ( r2_hidden(G,k4_finseq_1(E))
                                  & ! [H] : 
                                      ( m5_trees_3(H,k2_zfmisc_1(A,B),k5_trees_3(k2_zfmisc_1(A,B)))
                                     => ~ ( H = k1_funct_1(E,G)
                                          & k1_funct_1(F,G) = k10_trees_3(A,B,H) ) ) ) )
                          & k10_trees_3(A,B,k12_trees_4(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),E)) = k12_trees_4(A,C,F) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_trees_4,d3_tarski,d5_funct_1,t24_trees_4,d8_trees_3,d4_finseq_1]),
    [file(trees_4,t31_trees_4),interesting(0.42)]).

fof(t32_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(A,B)))
                     => ? [F] : 
                          ( m2_finseq_1(F,k5_trees_3(B))
                          & k4_finseq_1(F) = k4_finseq_1(E)
                          & ! [G] : 
                              ( m2_subset_1(G,k1_numbers,k5_numbers)
                             => ~ ( r2_hidden(G,k4_finseq_1(E))
                                  & ! [H] : 
                                      ( m5_trees_3(H,k2_zfmisc_1(A,B),k5_trees_3(k2_zfmisc_1(A,B)))
                                     => ~ ( H = k1_funct_1(E,G)
                                          & k1_funct_1(F,G) = k11_trees_3(A,B,H) ) ) ) )
                          & k11_trees_3(A,B,k12_trees_4(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),E)) = k12_trees_4(B,D,F) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_trees_4,d3_tarski,d5_funct_1,t24_trees_4,d8_trees_3,d4_finseq_1]),
    [file(trees_4,t32_trees_4),interesting(0.42)]).

fof(t28_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ! [E] : 
                      ( ( ~ v1_xboole_0(E)
                        & m4_trees_3(E,k2_zfmisc_1(A,B)) )
                     => ! [F] : 
                          ( ( ~ v1_xboole_0(F)
                            & m4_trees_3(F,B) )
                         => ! [G] : 
                              ( m2_finseq_1(G,E)
                             => ! [H] : 
                                  ( m2_finseq_1(H,F)
                                 => ( ( k4_finseq_1(H) = k4_finseq_1(G)
                                      & ! [I] : 
                                          ( m2_subset_1(I,k1_numbers,k5_numbers)
                                         => ( r2_hidden(I,k4_finseq_1(G))
                                           => ! [J] : 
                                                ( ( v1_funct_1(J)
                                                  & v3_trees_2(J)
                                                  & m3_trees_2(J,k2_zfmisc_1(A,B)) )
                                               => ( J = k1_funct_1(G,I)
                                                 => k1_funct_1(H,I) = k11_trees_3(A,B,J) ) ) ) ) )
                                   => k11_trees_3(A,B,k8_trees_4(k2_zfmisc_1(A,B),E,k1_domain_1(A,B,C,D),G)) = k8_trees_4(B,F,D,H) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_finseq_3,t40_trees_3,t31_finseq_3,l1_trees_4,t31_funct_6,t24_trees_4,t17_finseq_1,t24_trees_4,t10_trees_4,t10_trees_4,d1_trees_4,t24_trees_4,t41_trees_3,d4_trees_4,t7_mcart_1,t11_trees_4,l6_trees_4,t24_trees_4,l5_trees_4,t12_trees_4,t41_trees_3]),
    [file(trees_4,t28_trees_4),interesting(0.41)]).

fof(t12_trees_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v6_trees_3(B) )
     => ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D)
                & v3_trees_2(D) )
             => ! [E] : 
                  ( m1_trees_1(E,k1_relat_1(D))
                 => ( D = k1_funct_1(B,k1_nat_1(C,1))
                   => ( r1_xreal_0(k3_finseq_1(B),C)
                      | k1_funct_1(k4_trees_4(A,B),k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,C),E)) = k1_funct_1(D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_trees_4,t10_trees_4,t46_trees_1,d9_trees_1,d4_trees_4,d11_trees_2]),
    [file(trees_4,t12_trees_4),interesting(0.29)]).

fof(t18_trees_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D)
            & v1_finseq_1(D) )
         => ( ( k3_trees_4(A,C) = k4_trees_4(B,D)
              & v6_trees_3(D) )
           => ( A = B
              & k3_finseq_1(C) = k3_finseq_1(D)
              & ! [E] : 
                  ( m2_subset_1(E,k1_numbers,k5_numbers)
                 => ( r2_hidden(E,k4_finseq_1(C))
                   => k1_funct_1(D,E) = k1_trees_4(k1_funct_1(C,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_trees_4,d4_trees_4,t57_trees_3,d3_trees_4,t10_trees_4,t40_trees_3,t53_trees_3,t69_finseq_2,t27_finseq_3,t28_nat_1,t38_nat_1,d4_trees_4,t9_trees_4]),
    [file(trees_4,t18_trees_4),interesting(0.23)]).

fof(t11_trees_4,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C)
        & v6_trees_3(C) )
     => ( r2_hidden(A,k1_relat_1(k4_trees_4(B,C)))
      <=> ~ ( A != k1_xboole_0
            & ! [D] : 
                ( m2_subset_1(D,k1_numbers,k5_numbers)
               => ! [E] : 
                    ( ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & v3_trees_2(E) )
                   => ! [F] : 
                        ( m1_trees_1(F,k1_relat_1(E))
                       => ~ ( ~ r1_xreal_0(k3_finseq_1(C),D)
                            & E = k1_funct_1(C,k1_nat_1(D,1))
                            & A = k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,D),F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t10_trees_4,t40_trees_3,l5_trees_4,t26_trees_3,t31_funct_6,t40_trees_3,l5_trees_4,t31_funct_6,t40_trees_3,d15_trees_3]),
    [file(trees_4,t11_trees_4),interesting(0.03)]).

fof(s1_xboole_0,theorem,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,f1_s1_xboole_0)
        & p1_s1_xboole_0(B) ) ) ),
    file(xboole_0,s1_xboole_0),
    [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(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(d5_trees_1,definition,(
    ! [A] : 
      ( v1_trees_1(A)
    <=> ( r1_tarski(A,k13_finseq_1(k5_numbers))
        & ! [B] : 
            ( m2_finseq_1(B,k5_numbers)
           => ( r2_hidden(B,A)
             => r1_tarski(k1_trees_1(B),A) ) )
        & ! [B] : 
            ( m2_finseq_1(B,k5_numbers)
           => ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A)
                        & r1_xreal_0(D,C) )
                     => r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,D)),A) ) ) ) ) ) ) ),
    file(trees_1,d5_trees_1),
    [interesting(0.00)]).

fof(d4_trees_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( B = k1_trees_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( v1_relat_1(D)
                  & v1_funct_1(D)
                  & v1_finseq_1(D)
                  & C = D
                  & r2_xboole_0(D,A) ) ) ) ) ),
    file(trees_1,d4_trees_1),
    [interesting(0.00)]).

fof(d8_xboole_0,definition,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    [interesting(0.00)]).

fof(t8_trees_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) )
         => ( r1_tarski(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C)
                & B = k7_finseq_1(A,C) ) ) ) ) ),
    file(trees_1,t8_trees_1),
    [interesting(0.00)]).

fof(t50_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) )
         => ! [C] : 
              ( m2_finseq_1(k7_finseq_1(A,B),C)
             => ( m2_finseq_1(A,C)
                & m2_finseq_1(B,C) ) ) ) ) ),
    file(finseq_1,t50_finseq_1),
    [interesting(0.00)]).

fof(t46_trees_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(k7_finseq_1(A,C),B)
               => r2_hidden(A,B) ) ) ) ) ),
    file(trees_1,t46_trees_1),
    [interesting(0.00)]).

fof(t64_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) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ! [D] : 
                  ( ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D) )
                 => ~ ( k7_finseq_1(A,B) = k7_finseq_1(C,D)
                      & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C))
                      & ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => k7_finseq_1(A,E) != C ) ) ) ) ) ) ),
    file(finseq_1,t64_finseq_1),
    [interesting(0.00)]).

fof(t45_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) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ),
    file(finseq_1,t45_finseq_1),
    [interesting(0.00)]).

fof(t46_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) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( k7_finseq_1(A,B) = k7_finseq_1(C,B)
                  | k7_finseq_1(B,A) = k7_finseq_1(B,C) )
               => A = C ) ) ) ) ),
    file(finseq_1,t46_finseq_1),
    [interesting(0.00)]).

fof(t47_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k7_finseq_1(A,k1_xboole_0) = A
        & k7_finseq_1(k1_xboole_0,A) = A ) ) ),
    file(finseq_1,t47_finseq_1),
    [interesting(0.00)]).

fof(t63_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ~ ( A != k1_xboole_0
          & ! [B] : 
              ( ( v1_relat_1(B)
                & v1_funct_1(B)
                & v1_finseq_1(B) )
             => ! [C] : A != k7_finseq_1(B,k9_finseq_1(C)) ) ) ) ),
    file(finseq_1,t63_finseq_1),
    [interesting(0.00)]).

fof(t35_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) )
         => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    file(finseq_1,t35_finseq_1),
    [interesting(0.00)]).

fof(t57_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,t57_finseq_1),
    [interesting(0.00)]).

fof(t59_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),1)) = A ) ),
    file(finseq_1,t59_finseq_1),
    [interesting(0.00)]).

fof(d4_trees_4,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( v6_trees_3(B)
       => ! [C] : 
            ( ( v1_relat_1(C)
              & v1_funct_1(C)
              & v3_trees_2(C) )
           => ( C = k4_trees_4(A,B)
            <=> ( ? [D] : 
                    ( v1_relat_1(D)
                    & v1_funct_1(D)
                    & v1_finseq_1(D)
                    & v6_trees_3(D)
                    & B = D
                    & k1_relat_1(C) = k13_trees_3(k2_funct_6(D)) )
                & k1_funct_1(C,k1_xboole_0) = A
                & ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(k3_finseq_1(B),D)
                     => k5_trees_2(C,k12_finseq_1(k5_numbers,D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) ) ),
    file(trees_4,d4_trees_4),
    [interesting(0.00)]).

fof(t33_funct_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( k2_funct_6(k9_finseq_1(A)) = k9_finseq_1(k1_relat_1(A))
        & k3_funct_6(k9_finseq_1(A)) = k9_finseq_1(k2_relat_1(A)) ) ) ),
    file(funct_6,t33_funct_6),
    [interesting(0.00)]).

fof(d16_trees_3,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => k14_trees_3(A) = k13_trees_3(k9_finseq_1(A)) ) ),
    file(trees_3,d16_trees_3),
    [interesting(0.00)]).

fof(t34_funct_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k2_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k1_relat_1(A),k1_relat_1(B))
            & k3_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k2_relat_1(A),k2_relat_1(B)) ) ) ) ),
    file(funct_6,t34_funct_6),
    [interesting(0.00)]).

fof(d17_trees_3,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => k15_trees_3(A,B) = k13_trees_3(k10_finseq_1(A,B)) ) ) ),
    file(trees_3,d17_trees_3),
    [interesting(0.00)]).

fof(t39_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v6_trees_3(A) )
     => ( k1_relat_1(k2_funct_6(A)) = k1_relat_1(A)
        & v4_trees_3(k2_funct_6(A)) ) ) ),
    file(trees_3,t39_trees_3),
    [interesting(0.00)]).

fof(t53_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v4_trees_3(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B)
            & v4_trees_3(B) )
         => ( k13_trees_3(A) = k13_trees_3(B)
           => A = B ) ) ) ),
    file(trees_3,t53_trees_3),
    [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(t28_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => B != k2_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,t28_nat_1),
    [interesting(0.00)]).

fof(t38_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    [interesting(0.00)]).

fof(t18_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) )
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,C)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t18_finseq_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(t56_trees_1,theorem,(
    k2_trees_1(0) = k1_tarski(k1_xboole_0) ),
    file(trees_1,t56_trees_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.00)]).

fof(d3_trees_4,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C)
            & v3_trees_2(C) )
         => ( C = k3_trees_4(A,B)
          <=> ( k1_relat_1(C) = k2_trees_1(k3_finseq_1(B))
              & k1_funct_1(C,k1_xboole_0) = A
              & ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ~ r1_xreal_0(k3_finseq_1(B),D)
                   => k1_funct_1(C,k12_finseq_1(k5_numbers,D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) ),
    file(trees_4,d3_trees_4),
    [interesting(0.00)]).

fof(t55_trees_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ~ r1_xreal_0(B,A)
           => r2_hidden(k12_finseq_1(k5_numbers,A),k2_trees_1(B)) ) ) ) ),
    file(trees_1,t55_trees_1),
    [interesting(0.00)]).

fof(t57_trees_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ~ ( r2_hidden(B,k2_trees_1(A))
              & B != k1_xboole_0
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(A,C)
                      & B = k12_finseq_1(k5_numbers,C) ) ) ) ) ) ),
    file(trees_1,t57_trees_1),
    [interesting(0.00)]).

fof(t1_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,A) )
           => A = B ) ) ) ),
    file(xreal_1,t1_xreal_1),
    [interesting(0.00)]).

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

fof(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(t23_trees_3,theorem,
    ( v4_trees_3(k1_xboole_0)
    & v5_trees_3(k1_xboole_0)
    & v6_trees_3(k1_xboole_0) ),
    file(trees_3,t23_trees_3),
    [interesting(0.00)]).

fof(t55_trees_3,theorem,(
    k13_trees_3(k1_xboole_0) = k2_trees_1(0) ),
    file(trees_3,t55_trees_3),
    [interesting(0.00)]).

fof(t57_trees_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_trees_1(A) = k13_trees_3(k2_finseq_2(A,k2_trees_1(0))) ) ),
    file(trees_3,t57_trees_3),
    [interesting(0.00)]).

fof(t40_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v6_trees_3(A) )
     => k3_finseq_1(k2_funct_6(A)) = k3_finseq_1(A) ) ),
    file(trees_3,t40_trees_3),
    [interesting(0.00)]).

fof(t69_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k3_finseq_1(k2_finseq_2(A,B)) = A ) ),
    file(finseq_2,t69_finseq_2),
    [interesting(0.00)]).

fof(t27_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(B,k4_finseq_1(A))
          <=> ( r1_xreal_0(1,B)
              & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ),
    file(finseq_3,t27_finseq_3),
    [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(t29_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    [interesting(0.00)]).

fof(t52_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v4_trees_3(A)
       => ( k2_trees_2(k13_trees_3(A),1) = a_1_0_trees_3(A)
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ~ r1_xreal_0(k3_finseq_1(A),B)
               => k4_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,B)) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) ) ) ),
    file(trees_3,t52_trees_3),
    [interesting(0.00)]).

fof(t70_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( r2_hidden(B,k2_finseq_1(A))
         => k1_funct_1(k2_finseq_2(A,C),B) = C ) ) ),
    file(finseq_2,t70_finseq_2),
    [interesting(0.00)]).

fof(d11_trees_2,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( C = k5_trees_2(A,B)
              <=> ( k1_relat_1(C) = k4_trees_1(k1_relat_1(A),B)
                  & ! [D] : 
                      ( m2_finseq_1(D,k5_numbers)
                     => ( r2_hidden(D,k4_trees_1(k1_relat_1(A),B))
                       => k1_funct_1(C,D) = k1_funct_1(A,k8_finseq_1(k5_numbers,B,D)) ) ) ) ) ) ) ) ),
    file(trees_2,d11_trees_2),
    [interesting(0.00)]).

fof(t17_funcop_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ! [C] : 
              ( r2_hidden(C,k1_relat_1(A))
             => k1_funct_1(A,C) = B )
         => A = k2_funcop_1(k1_relat_1(A),B) ) ) ),
    file(funcop_1,t17_funcop_1),
    [interesting(0.00)]).

fof(d9_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ( r2_hidden(B,A)
           => ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_trees_1(C) )
               => ( C = k4_trees_1(A,B)
                <=> ! [D] : 
                      ( m2_finseq_1(D,k5_numbers)
                     => ( r2_hidden(D,C)
                      <=> r2_hidden(k8_finseq_1(k5_numbers,B,D),A) ) ) ) ) ) ) ) ),
    file(trees_1,d9_trees_1),
    [interesting(0.00)]).

fof(t51_trees_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( v4_trees_3(B)
               => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,A),C),k13_trees_3(B))
                <=> ( ~ r1_xreal_0(k3_finseq_1(B),A)
                    & r2_hidden(C,k1_funct_1(B,k1_nat_1(A,1))) ) ) ) ) ) ) ),
    file(trees_3,t51_trees_3),
    [interesting(0.00)]).

fof(t18_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r1_xreal_0(0,A) ) ),
    file(nat_1,t18_nat_1),
    [interesting(0.00)]).

fof(t9_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ),
    file(xreal_1,t9_xreal_1),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(t44_funct_6,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( ( v1_relat_1(D)
            & v1_funct_1(D) )
         => ( ( r2_hidden(A,k1_relat_1(C))
              & D = k1_funct_1(C,A)
              & r2_hidden(B,k1_relat_1(D)) )
           => k5_funct_6(C,A,B) = k1_funct_1(D,B) ) ) ) ),
    file(funct_6,t44_funct_6),
    [interesting(0.00)]).

fof(t19_trees_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v6_trees_3(B) )
     => ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ! [D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D)
                & v1_finseq_1(D) )
             => ( r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,C),D),k1_relat_1(k4_trees_4(A,B)))
               => k1_funct_1(k4_trees_4(A,B),k7_finseq_1(k12_finseq_1(k5_numbers,C),D)) = k5_funct_6(B,k1_nat_1(C,1),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_finseq_1,t10_trees_4,t46_trees_1,t40_trees_3,d9_trees_1,t51_trees_3,d4_trees_4,l5_trees_4,d11_trees_2,t44_funct_6]),
    [file(trees_4,t19_trees_4),interesting(0.00)]).

fof(t32_funct_6,theorem,
    ( k2_funct_6(k1_xboole_0) = k1_xboole_0
    & k3_funct_6(k1_xboole_0) = k1_xboole_0 ),
    file(funct_6,t32_funct_6),
    [interesting(0.00)]).

fof(t9_modal_1,theorem,(
    k2_trees_1(1) = k2_tarski(k1_xboole_0,k12_finseq_1(k5_numbers,0)) ),
    file(modal_1,t9_modal_1),
    [interesting(0.00)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.00)]).

fof(d12_trees_2,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v3_trees_2(C) )
             => ( r2_hidden(B,k1_relat_1(A))
               => ! [D] : 
                    ( ( v1_relat_1(D)
                      & v1_funct_1(D)
                      & v3_trees_2(D) )
                   => ( D = k8_trees_2(A,B,C)
                    <=> ( k1_relat_1(D) = k5_trees_1(k1_relat_1(A),B,k1_relat_1(C))
                        & ! [E] : 
                            ( m2_finseq_1(E,k5_numbers)
                           => ~ ( r2_hidden(E,k5_trees_1(k1_relat_1(A),B,k1_relat_1(C)))
                                & ~ ( ~ r1_tarski(B,E)
                                    & k1_funct_1(D,E) = k1_funct_1(A,E) )
                                & ! [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                   => ~ ( r2_hidden(F,k1_relat_1(C))
                                        & E = k8_finseq_1(k5_numbers,B,F)
                                        & k1_funct_1(D,E) = k1_funct_1(C,F) ) ) ) ) ) ) ) ) ) ) ) ),
    file(trees_2,d12_trees_2),
    [interesting(0.00)]).

fof(t61_trees_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => k14_trees_3(A) = k5_trees_1(k2_trees_1(1),k12_finseq_1(k5_numbers,0),A) ) ),
    file(trees_3,t61_trees_3),
    [interesting(0.00)]).

fof(t70_trees_3,theorem,(
    k14_trees_3(k2_trees_1(0)) = k2_trees_1(1) ),
    file(trees_3,t70_trees_3),
    [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(t47_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(A))
             => k1_funct_1(k8_trees_2(A,C,B),C) = k1_funct_1(B,k1_xboole_0) ) ) ) ),
    file(trees_3,t47_trees_3),
    [interesting(0.00)]).

fof(t48_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(A))
             => ! [D] : 
                  ( m1_trees_1(D,k1_relat_1(A))
                 => ( ~ r1_tarski(C,D)
                   => k1_funct_1(k8_trees_2(A,C,B),D) = k1_funct_1(A,D) ) ) ) ) ) ),
    file(trees_3,t48_trees_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(t25_trees_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ~ r2_xboole_0(B,k1_xboole_0)
            & ~ r2_xboole_0(B,k6_finseq_1(A)) ) ) ) ),
    file(trees_1,t25_trees_1),
    [interesting(0.00)]).

fof(d12_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m2_finseq_1(B,k5_numbers)
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ( r2_hidden(B,A)
               => ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_trees_1(D) )
                   => ( D = k5_trees_1(A,B,C)
                    <=> ! [E] : 
                          ( m2_finseq_1(E,k5_numbers)
                         => ( r2_hidden(E,D)
                          <=> ~ ( ~ ( r2_hidden(E,A)
                                    & ~ r2_xboole_0(B,E) )
                                & ! [F] : 
                                    ( m2_finseq_1(F,k5_numbers)
                                   => ~ ( r2_hidden(F,C)
                                        & E = k8_finseq_1(k5_numbers,B,F) ) ) ) ) ) ) ) ) ) ) ) ),
    file(trees_1,d12_trees_1),
    [interesting(0.00)]).

fof(t49_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C] : 
              ( m1_trees_1(C,k1_relat_1(A))
             => ! [D] : 
                  ( m1_trees_1(D,k1_relat_1(B))
                 => k1_funct_1(k8_trees_2(A,C,B),k8_finseq_1(k5_numbers,C,D)) = k1_funct_1(B,D) ) ) ) ) ),
    file(trees_3,t49_trees_3),
    [interesting(0.00)]).

fof(t66_trees_1,theorem,(
    ! [A] : 
      ( m2_finseq_1(A,k5_numbers)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ( r2_hidden(A,B)
               => C = k4_trees_1(k5_trees_1(B,A,C),A) ) ) ) ) ),
    file(trees_1,t66_trees_1),
    [interesting(0.00)]).

fof(t144_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ),
    file(relat_1,t144_relat_1),
    [interesting(0.00)]).

fof(d1_trees_2,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( A = B
          <=> ! [C] : 
                ( m2_finseq_1(C,k5_numbers)
               => ( r2_hidden(C,A)
                <=> r2_hidden(C,B) ) ) ) ) ) ),
    file(trees_2,d1_trees_2),
    [interesting(0.00)]).

fof(d7_trees_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ! [C,D] : 
              ( ( v1_relat_1(D)
                & v1_funct_1(D)
                & v3_trees_2(D) )
             => ( D = k13_trees_4(A,B,C)
              <=> ( ! [E] : 
                      ( ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & v1_finseq_1(E) )
                     => ( r2_hidden(E,k1_relat_1(D))
                      <=> ~ ( ~ r2_hidden(E,k1_relat_1(A))
                            & ! [F] : 
                                ( m1_trees_1(F,k1_relat_1(A))
                               => ! [G] : 
                                    ( m1_trees_1(G,k1_relat_1(B))
                                   => ~ ( r2_hidden(F,k3_trees_1(k1_relat_1(A)))
                                        & k1_funct_1(A,F) = C
                                        & E = k8_finseq_1(k5_numbers,F,G) ) ) ) ) ) )
                  & ! [E] : 
                      ( m1_trees_1(E,k1_relat_1(A))
                     => ( ~ ( r2_hidden(E,k3_trees_1(k1_relat_1(A)))
                            & k1_funct_1(A,E) = C )
                       => k1_funct_1(D,E) = k1_funct_1(A,E) ) )
                  & ! [E] : 
                      ( m1_trees_1(E,k1_relat_1(A))
                     => ! [F] : 
                          ( m1_trees_1(F,k1_relat_1(B))
                         => ( ( r2_hidden(E,k3_trees_1(k1_relat_1(A)))
                              & k1_funct_1(A,E) = C )
                           => k1_funct_1(D,k8_finseq_1(k5_numbers,E,F)) = k1_funct_1(B,F) ) ) ) ) ) ) ) ) ),
    file(trees_4,d7_trees_4),
    [interesting(0.00)]).

fof(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.00)]).

fof(d1_trees_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) )
         => ( A = B
          <=> ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( m1_trees_1(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ),
    file(trees_4,d1_trees_4),
    [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(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(d12_trees_3,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v3_trees_2(C)
                & m3_trees_2(C,k2_zfmisc_1(A,B)) )
             => k10_trees_3(A,B,C) = k7_trees_3(k2_zfmisc_1(A,B),A,C,k8_trees_3(A,B)) ) ) ) ),
    file(trees_3,d12_trees_3),
    [interesting(0.00)]).

fof(d13_trees_3,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v3_trees_2(C)
                & m3_trees_2(C,k2_zfmisc_1(A,B)) )
             => k11_trees_3(A,B,C) = k7_trees_3(k2_zfmisc_1(A,B),B,C,k9_trees_3(A,B)) ) ) ) ),
    file(trees_3,d13_trees_3),
    [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(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(t41_trees_3,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v3_trees_2(C)
                & m3_trees_2(C,k2_zfmisc_1(A,B)) )
             => ! [D] : 
                  ( m1_trees_1(D,k1_relat_1(C))
                 => ( k2_domain_1(A,B,k3_trees_2(k2_zfmisc_1(A,B),C,D)) = k1_funct_1(k10_trees_3(A,B,C),D)
                    & k1_funct_1(k11_trees_3(A,B,C),D) = k3_domain_1(A,B,k3_trees_2(k2_zfmisc_1(A,B),C,D)) ) ) ) ) ) ),
    file(trees_3,t41_trees_3),
    [interesting(0.00)]).

fof(t25_trees_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,B)
                 => ( k10_trees_3(A,B,k2_trees_4(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D))) = k2_trees_4(A,C)
                    & k11_trees_3(A,B,k2_trees_4(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D))) = k2_trees_4(B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_trees_1,t3_trees_4,t24_trees_4,t7_mcart_1,t5_trees_4,t41_trees_3,t5_trees_4,t41_trees_3]),
    [file(trees_4,t25_trees_4),interesting(0.00)]).

fof(t42_trees_3,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v3_trees_2(C)
                & m3_trees_2(C,k2_zfmisc_1(A,B)) )
             => k6_trees_3(A,B,k10_trees_3(A,B,C),k11_trees_3(A,B,C)) = C ) ) ) ),
    file(trees_3,t42_trees_3),
    [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(d7_trees_3,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m4_trees_3(B,A)
         => ( B = k4_trees_3(A)
          <=> ! [C] : 
                ( ( v1_funct_1(C)
                  & v3_trees_2(C)
                  & m3_trees_2(C,A) )
               => r2_hidden(C,B) ) ) ) ) ),
    file(trees_3,d7_trees_3),
    [interesting(0.00)]).

fof(s5_finseq_1,theorem,
    ( ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ~ ( r2_hidden(A,k2_finseq_1(f2_s5_finseq_1))
            & ! [B] : 
                ( m1_subset_1(B,f1_s5_finseq_1)
               => ~ p1_s5_finseq_1(A,B) ) ) )
   => ? [A] : 
        ( m2_finseq_1(A,f1_s5_finseq_1)
        & k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( r2_hidden(B,k2_finseq_1(f2_s5_finseq_1))
             => p1_s5_finseq_1(B,k1_funct_1(A,B)) ) ) ) ),
    file(finseq_1,s5_finseq_1),
    [interesting(0.00)]).

fof(t31_funct_6,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ( r2_hidden(A,k1_relat_1(B))
              & C = k1_funct_1(B,A) )
           => ( r2_hidden(A,k1_relat_1(k2_funct_6(B)))
              & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C)
              & r2_hidden(A,k1_relat_1(k3_funct_6(B)))
              & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) ) ) ) ) ),
    file(funct_6,t31_funct_6),
    [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(t26_trees_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v6_trees_3(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))
              & v3_trees_2(k1_funct_1(A,B)) ) ) ) ) ),
    file(trees_3,t26_trees_3),
    [interesting(0.00)]).

fof(d15_trees_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v4_trees_3(A)
       => ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_trees_1(B) )
           => ( B = k13_trees_3(A)
            <=> ! [C] : 
                  ( r2_hidden(C,B)
                <=> ~ ( C != k1_xboole_0
                      & ! [D] : 
                          ( m2_subset_1(D,k1_numbers,k5_numbers)
                         => ! [E] : 
                              ( ( v1_relat_1(E)
                                & v1_funct_1(E)
                                & v1_finseq_1(E) )
                             => ~ ( ~ r1_xreal_0(k3_finseq_1(A),D)
                                  & r2_hidden(E,k1_funct_1(A,k1_nat_1(D,1)))
                                  & C = k7_finseq_1(k12_finseq_1(k5_numbers,D),E) ) ) ) ) ) ) ) ) ) ),
    file(trees_3,d15_trees_3),
    [interesting(0.00)]).

fof(d8_trees_3,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m4_trees_3(B,A)
         => ( B = k5_trees_3(A)
          <=> ! [C] : 
                ( ( v1_funct_1(C)
                  & v3_trees_2(C)
                  & m3_trees_2(C,A) )
               => ( v1_finset_1(k1_relat_1(C))
                <=> r2_hidden(C,B) ) ) ) ) ) ),
    file(trees_3,d8_trees_3),
    [interesting(0.00)]).

fof(d2_funcop_1,definition,(
    ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ),
    file(funcop_1,d2_funcop_1),
    [interesting(0.00)]).

fof(t35_zfmisc_1,theorem,(
    ! [A,B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) ),
    file(zfmisc_1,t35_zfmisc_1),
    [interesting(0.00)]).