fof(t11_bintree1,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] : 
              ( ( v2_bintree1(A)
                & v2_bintree1(B) )
            <=> v2_bintree1(k6_trees_4(C,A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_bintree1,t10_bintree1,t14_trees_4,d3_bintree1,d3_bintree1,t14_trees_4,t10_bintree1,d3_bintree1]),
    [file(bintree1,t11_bintree1),interesting(1.00)]).

fof(t10_bintree1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( ( v1_bintree1(A)
              & v1_bintree1(B) )
          <=> v1_bintree1(k15_trees_3(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_bintree1,t8_bintree1,d2_bintree1,d5_trees_2,t45_finseq_1,t72_trees_3,t9_bintree1,d2_tarski,t46_finseq_1,d2_tarski,d2_tarski,t45_finseq_1,d2_tarski,t9_bintree1,t2_tarski,t8_bintree1,d2_bintree1,d5_trees_2,t45_finseq_1,t73_trees_3,t9_bintree1,d2_tarski,t46_finseq_1,d2_tarski,d2_tarski,t45_finseq_1,d2_tarski,t9_bintree1,t2_tarski,t71_trees_3,d2_bintree1,t72_trees_3,t8_bintree1,d2_bintree1,d5_trees_2,d5_trees_2,t72_trees_3,t45_finseq_1,d2_tarski,t46_finseq_1,d2_tarski,d2_tarski,d2_tarski,t45_finseq_1,t9_bintree1,t2_tarski,d2_bintree1,t73_trees_3,t8_bintree1,d2_bintree1,d5_trees_2,d5_trees_2,t73_trees_3,t45_finseq_1,d2_tarski,t46_finseq_1,d2_tarski,d2_tarski,d2_tarski,t45_finseq_1,t9_bintree1,t2_tarski,d2_bintree1]),
    [file(bintree1,t10_bintree1),interesting(0.92)]).

fof(t7_bintree1,theorem,(
    v1_bintree1(k2_trees_1(2)) ),
    inference(mizar_proof,[status(thm)],[d2_bintree1,d5_trees_2,t47_finseq_1,t47_finseq_1,d2_tarski,t47_finseq_1,d2_tarski,d1_enumset1,t10_modal_1,d2_tarski,d2_tarski,t47_finseq_1,d1_enumset1,t10_modal_1,t2_tarski,t35_finseq_1,t56_finseq_1,t56_finseq_1,t35_finseq_1,t56_finseq_1,t56_finseq_1,t35_finseq_1,t56_finseq_1,t56_finseq_1,t56_finseq_1,d1_enumset1,t10_modal_1,t53_modal_1,t35_finseq_1,t56_finseq_1,t56_finseq_1,t35_finseq_1,t56_finseq_1,t56_finseq_1,t35_finseq_1,t56_finseq_1,t56_finseq_1,t56_finseq_1,d1_enumset1,t10_modal_1,t53_modal_1,d1_enumset1,t10_modal_1]),
    [file(bintree1,t7_bintree1),interesting(0.82)]).

fof(t6_bintree1,theorem,(
    v1_bintree1(k2_trees_1(0)) ),
    inference(mizar_proof,[status(thm)],[d2_bintree1,d1_tarski,t56_trees_1,d8_trees_1]),
    [file(bintree1,t6_bintree1),interesting(0.71)]).

fof(t5_bintree1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => ( k1_trees_2(A,B) = k1_xboole_0
          <=> r2_hidden(B,k3_trees_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_trees_2,t53_modal_1,t53_modal_1,d5_trees_2,t18_nat_1,d5_trees_1]),
    [file(bintree1,t5_bintree1),interesting(0.69)]).

fof(s1_bintree1,theorem,(
    ? [A] : 
      ( ~ v3_struct_0(A)
      & v1_lang1(A)
      & v3_bintree1(A)
      & l1_lang1(A)
      & u1_struct_0(A) = f1_s1_bintree1
      & ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_lang1(A,B,k4_lang1(u1_struct_0(A),C,D))
                  <=> p1_s1_bintree1(B,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_dtconstr,t61_finseq_1,d1_lang1,t106_zfmisc_1,d3_finseq_2,d4_finseq_1,d9_finseq_1,t44_finseq_1,t56_finseq_1,t56_finseq_1,t41_enumset1,d2_tarski,d4_bintree1]),
    [file(bintree1,s1_bintree1),interesting(0.60)]).

fof(t8_bintree1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m1_trees_1(C,k15_trees_3(A,B))
             => ( ! [D] : 
                    ( m1_trees_1(D,A)
                   => ( C = k7_finseq_1(k3_lang1(k1_numbers,0),D)
                     => ( r2_hidden(C,k3_trees_1(k15_trees_3(A,B)))
                      <=> r2_hidden(D,k3_trees_1(A)) ) ) )
                & ! [D] : 
                    ( m1_trees_1(D,B)
                   => ( C = k7_finseq_1(k3_lang1(k1_numbers,1),D)
                     => ( r2_hidden(C,k3_trees_1(k15_trees_3(A,B)))
                      <=> r2_hidden(D,k3_trees_1(B)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t54_modal_1,t72_trees_3,t45_finseq_1,t54_modal_1,t54_modal_1,t45_finseq_1,t72_trees_3,t54_modal_1,t54_modal_1,t73_trees_3,t45_finseq_1,t54_modal_1,t54_modal_1,t45_finseq_1,t73_trees_3,t54_modal_1]),
    [file(bintree1,t8_bintree1),interesting(0.59)]).

fof(t1_bintree1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,A) )
         => k16_trees_3(k9_finseq_1(B)) = k3_lang1(A,k1_bintree1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_dtconstr]),
    [file(bintree1,t1_bintree1),interesting(0.55)]).

fof(t2_bintree1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,A) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v3_trees_2(C)
                & m3_trees_2(C,A) )
             => k16_trees_3(k10_finseq_1(B,C)) = k4_lang1(A,k1_bintree1(A,B),k1_bintree1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_dtconstr]),
    [file(bintree1,t2_bintree1),interesting(0.55)]).

fof(t9_bintree1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( m1_trees_1(C,k15_trees_3(A,B))
             => ( ( C = k1_xboole_0
                 => k1_trees_2(k15_trees_3(A,B),C) = k2_tarski(k7_finseq_1(C,k3_lang1(k1_numbers,0)),k7_finseq_1(C,k3_lang1(k1_numbers,1))) )
                & ! [D] : 
                    ( m1_trees_1(D,A)
                   => ( C = k7_finseq_1(k3_lang1(k1_numbers,0),D)
                     => ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ( r2_hidden(E,k1_trees_2(A,D))
                          <=> r2_hidden(k7_finseq_1(k3_lang1(k1_numbers,0),E),k1_trees_2(k15_trees_3(A,B),C)) ) ) ) )
                & ! [D] : 
                    ( m1_trees_1(D,B)
                   => ( C = k7_finseq_1(k3_lang1(k1_numbers,1),D)
                     => ! [E] : 
                          ( ( v1_relat_1(E)
                            & v1_funct_1(E)
                            & v1_finseq_1(E) )
                         => ( r2_hidden(E,k1_trees_2(B,D))
                          <=> r2_hidden(k7_finseq_1(k3_lang1(k1_numbers,1),E),k1_trees_2(k15_trees_3(A,B),C)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_trees_2,t47_finseq_1,t47_trees_1,t71_trees_3,t47_finseq_1,t47_finseq_1,t47_trees_1,t71_trees_3,t47_finseq_1,t47_finseq_1,t71_trees_3,t58_finseq_1,t57_finseq_1,t47_finseq_1,d2_tarski,d2_tarski,t2_tarski,d5_trees_2,t72_trees_3,t45_finseq_1,d5_trees_2,t45_finseq_1,d5_trees_2,t45_finseq_1,t72_trees_3,d5_trees_2,t45_finseq_1,t46_finseq_1,d5_trees_2,t73_trees_3,t45_finseq_1,d5_trees_2,t45_finseq_1,d5_trees_2,t45_finseq_1,t73_trees_3,d5_trees_2,t45_finseq_1,t46_finseq_1]),
    [file(bintree1,t9_bintree1),interesting(0.51)]).

fof(s2_bintree1,theorem,
    ( ( ! [A] : 
          ( m1_struct_0(A,f1_s2_bintree1,k6_dtconstr(f1_s2_bintree1))
         => p1_s2_bintree1(k8_dtconstr(f1_s2_bintree1,A)) )
      & ! [A] : 
          ( m1_struct_0(A,f1_s2_bintree1,k7_dtconstr(f1_s2_bintree1))
         => ! [B] : 
              ( m1_dtconstr(B,u1_struct_0(f1_s2_bintree1),k5_trees_3(u1_struct_0(f1_s2_bintree1)),k4_dtconstr(f1_s2_bintree1))
             => ! [C] : 
                  ( m1_dtconstr(C,u1_struct_0(f1_s2_bintree1),k5_trees_3(u1_struct_0(f1_s2_bintree1)),k4_dtconstr(f1_s2_bintree1))
                 => ( ( r1_lang1(f1_s2_bintree1,A,k4_lang1(u1_struct_0(f1_s2_bintree1),k1_bintree1(u1_struct_0(f1_s2_bintree1),B),k1_bintree1(u1_struct_0(f1_s2_bintree1),C)))
                      & p1_s2_bintree1(B)
                      & p1_s2_bintree1(C) )
                   => p1_s2_bintree1(k10_trees_4(u1_struct_0(f1_s2_bintree1),A,B,C)) ) ) ) ) )
   => ! [A] : 
        ( m1_dtconstr(A,u1_struct_0(f1_s2_bintree1),k5_trees_3(u1_struct_0(f1_s2_bintree1)),k4_dtconstr(f1_s2_bintree1))
       => p1_s2_bintree1(A) ) ),
    inference(mizar_proof,[status(thm)],[t12_bintree1,t12_bintree1,s7_dtconstr]),
    [file(bintree1,s2_bintree1),interesting(0.46)]).

fof(s3_bintree1,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1)
      & m2_relset_1(A,k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1)
      & ! [B] : 
          ( m1_struct_0(B,f1_s3_bintree1,k6_dtconstr(f1_s3_bintree1))
         => k8_funct_2(k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1,A,k8_dtconstr(f1_s3_bintree1,B)) = f3_s3_bintree1(B) )
      & ! [B] : 
          ( m1_struct_0(B,f1_s3_bintree1,k7_dtconstr(f1_s3_bintree1))
         => ! [C] : 
              ( m1_dtconstr(C,u1_struct_0(f1_s3_bintree1),k5_trees_3(u1_struct_0(f1_s3_bintree1)),k4_dtconstr(f1_s3_bintree1))
             => ! [D] : 
                  ( m1_dtconstr(D,u1_struct_0(f1_s3_bintree1),k5_trees_3(u1_struct_0(f1_s3_bintree1)),k4_dtconstr(f1_s3_bintree1))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(f1_s3_bintree1))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(f1_s3_bintree1))
                         => ( ( E = k1_bintree1(u1_struct_0(f1_s3_bintree1),C)
                              & F = k1_bintree1(u1_struct_0(f1_s3_bintree1),D)
                              & r1_lang1(f1_s3_bintree1,B,k4_lang1(u1_struct_0(f1_s3_bintree1),E,F)) )
                           => ! [G] : 
                                ( m1_subset_1(G,f2_s3_bintree1)
                               => ! [H] : 
                                    ( m1_subset_1(H,f2_s3_bintree1)
                                   => ( ( G = k8_funct_2(k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1,A,C)
                                        & H = k8_funct_2(k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1,A,D) )
                                     => k1_funct_1(A,k10_trees_4(u1_struct_0(f1_s3_bintree1),B,C,D)) = f4_s3_bintree1(B,E,F,G,H) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s8_dtconstr,d1_funct_2,t61_finseq_1,t4_finseq_1,t29_finseq_3,t4_finseq_1,t29_finseq_3,d3_finseq_1,t61_finseq_1,t4_finseq_1,d2_tarski,d18_trees_3,t4_finseq_1,t29_finseq_3,d2_tarski,d2_tarski,d2_tarski,d2_tarski,d2_tarski,d2_tarski,d2_tarski,t61_finseq_1,t20_funct_1,t61_finseq_1,d6_trees_4]),
    [file(bintree1,s3_bintree1),interesting(0.37)]).

fof(s4_bintree1,theorem,
    ( ( ! [A] : 
          ( m1_struct_0(A,f1_s4_bintree1,k6_dtconstr(f1_s4_bintree1))
         => k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f3_s4_bintree1,k8_dtconstr(f1_s4_bintree1,A)) = f5_s4_bintree1(A) )
      & ! [A] : 
          ( m1_struct_0(A,f1_s4_bintree1,k7_dtconstr(f1_s4_bintree1))
         => ! [B] : 
              ( m1_dtconstr(B,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
             => ! [C] : 
                  ( m1_dtconstr(C,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(f1_s4_bintree1))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(f1_s4_bintree1))
                         => ( ( D = k1_bintree1(u1_struct_0(f1_s4_bintree1),B)
                              & E = k1_bintree1(u1_struct_0(f1_s4_bintree1),C)
                              & r1_lang1(f1_s4_bintree1,A,k4_lang1(u1_struct_0(f1_s4_bintree1),D,E)) )
                           => ! [F] : 
                                ( m1_subset_1(F,f2_s4_bintree1)
                               => ! [G] : 
                                    ( m1_subset_1(G,f2_s4_bintree1)
                                   => ( ( F = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f3_s4_bintree1,B)
                                        & G = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f3_s4_bintree1,C) )
                                     => k1_funct_1(f3_s4_bintree1,k10_trees_4(u1_struct_0(f1_s4_bintree1),A,B,C)) = f6_s4_bintree1(A,D,E,F,G) ) ) ) ) ) ) ) ) )
      & ! [A] : 
          ( m1_struct_0(A,f1_s4_bintree1,k6_dtconstr(f1_s4_bintree1))
         => k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f4_s4_bintree1,k8_dtconstr(f1_s4_bintree1,A)) = f5_s4_bintree1(A) )
      & ! [A] : 
          ( m1_struct_0(A,f1_s4_bintree1,k7_dtconstr(f1_s4_bintree1))
         => ! [B] : 
              ( m1_dtconstr(B,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
             => ! [C] : 
                  ( m1_dtconstr(C,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(f1_s4_bintree1))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(f1_s4_bintree1))
                         => ( ( D = k1_bintree1(u1_struct_0(f1_s4_bintree1),B)
                              & E = k1_bintree1(u1_struct_0(f1_s4_bintree1),C)
                              & r1_lang1(f1_s4_bintree1,A,k4_lang1(u1_struct_0(f1_s4_bintree1),D,E)) )
                           => ! [F] : 
                                ( m1_subset_1(F,f2_s4_bintree1)
                               => ! [G] : 
                                    ( m1_subset_1(G,f2_s4_bintree1)
                                   => ( ( F = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f4_s4_bintree1,B)
                                        & G = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f4_s4_bintree1,C) )
                                     => k1_funct_1(f4_s4_bintree1,k10_trees_4(u1_struct_0(f1_s4_bintree1),A,B,C)) = f6_s4_bintree1(A,D,E,F,G) ) ) ) ) ) ) ) ) ) )
   => f3_s4_bintree1 = f4_s4_bintree1 ),
    inference(mizar_proof,[status(thm)],[t12_bintree1,t61_finseq_1,t12_bintree1,t23_funct_1,t12_bintree1,t61_finseq_1,t12_bintree1,t23_funct_1,s9_dtconstr]),
    [file(bintree1,s4_bintree1),interesting(0.35)]).

fof(t12_bintree1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & v2_dtconstr(A)
        & v3_bintree1(A)
        & l1_lang1(A) )
     => ! [B] : 
          ( m1_trees_4(B,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_lang1(A,C,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),B))
               => ( m1_struct_0(C,A,k7_dtconstr(A))
                  & k4_finseq_1(B) = k2_tarski(1,2)
                  & r2_hidden(1,k4_finseq_1(B))
                  & r2_hidden(2,k4_finseq_1(B))
                  & ? [D] : 
                      ( m1_dtconstr(D,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
                      & ? [E] : 
                          ( m1_dtconstr(E,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
                          & k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),B) = k4_lang1(u1_struct_0(A),k1_bintree1(u1_struct_0(A),D),k1_bintree1(u1_struct_0(A),E))
                          & D = k1_funct_1(B,1)
                          & E = k1_funct_1(B,2)
                          & k12_trees_4(u1_struct_0(A),C,B) = k10_trees_4(u1_struct_0(A),C,D,E)
                          & r2_hidden(D,k2_relat_1(B))
                          & r2_hidden(E,k2_relat_1(B)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_lang1,d4_bintree1,d18_trees_3,t61_finseq_1,t4_finseq_1,d3_finseq_1,d2_tarski,d18_trees_3,d18_trees_3,d4_finseq_1,d5_funct_1,t61_finseq_1,d3_finseq_1,d3_finseq_1,t8_finseq_1,t61_finseq_1,d6_trees_4,d5_funct_1]),
    [file(bintree1,t12_bintree1),interesting(0.29)]).

fof(s5_bintree1,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1))
      & m2_relset_1(A,k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1))
      & ! [B] : 
          ( m1_struct_0(B,f1_s5_bintree1,k6_dtconstr(f1_s5_bintree1))
         => ? [C] : 
              ( v1_funct_1(C)
              & v1_funct_2(C,f2_s5_bintree1,f3_s5_bintree1)
              & m2_relset_1(C,f2_s5_bintree1,f3_s5_bintree1)
              & C = k8_funct_2(k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1),A,k8_dtconstr(f1_s5_bintree1,B))
              & ! [D] : 
                  ( m1_subset_1(D,f2_s5_bintree1)
                 => k8_funct_2(f2_s5_bintree1,f3_s5_bintree1,C,D) = f4_s5_bintree1(B,D) ) ) )
      & ! [B] : 
          ( m1_struct_0(B,f1_s5_bintree1,k7_dtconstr(f1_s5_bintree1))
         => ! [C] : 
              ( m1_dtconstr(C,u1_struct_0(f1_s5_bintree1),k5_trees_3(u1_struct_0(f1_s5_bintree1)),k4_dtconstr(f1_s5_bintree1))
             => ! [D] : 
                  ( m1_dtconstr(D,u1_struct_0(f1_s5_bintree1),k5_trees_3(u1_struct_0(f1_s5_bintree1)),k4_dtconstr(f1_s5_bintree1))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(f1_s5_bintree1))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(f1_s5_bintree1))
                         => ~ ( E = k1_bintree1(u1_struct_0(f1_s5_bintree1),C)
                              & F = k1_bintree1(u1_struct_0(f1_s5_bintree1),D)
                              & r1_lang1(f1_s5_bintree1,B,k4_lang1(u1_struct_0(f1_s5_bintree1),E,F))
                              & ! [G] : 
                                  ( ( v1_funct_1(G)
                                    & v1_funct_2(G,f2_s5_bintree1,f3_s5_bintree1)
                                    & m2_relset_1(G,f2_s5_bintree1,f3_s5_bintree1) )
                                 => ! [H] : 
                                      ( ( v1_funct_1(H)
                                        & v1_funct_2(H,f2_s5_bintree1,f3_s5_bintree1)
                                        & m2_relset_1(H,f2_s5_bintree1,f3_s5_bintree1) )
                                     => ! [I] : 
                                          ( ( v1_funct_1(I)
                                            & v1_funct_2(I,f2_s5_bintree1,f3_s5_bintree1)
                                            & m2_relset_1(I,f2_s5_bintree1,f3_s5_bintree1) )
                                         => ~ ( G = k1_funct_1(A,k10_trees_4(u1_struct_0(f1_s5_bintree1),B,C,D))
                                              & H = k8_funct_2(k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1),A,C)
                                              & I = k8_funct_2(k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1),A,D)
                                              & ! [J] : 
                                                  ( m1_subset_1(J,f2_s5_bintree1)
                                                 => k8_funct_2(f2_s5_bintree1,f3_s5_bintree1,G,J) = f5_s5_bintree1(B,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_funct_2,s4_funct_2,d1_funct_2,t12_relset_1,d2_funct_2,s3_funct_2,s4_funct_2,d1_funct_2,t12_relset_1,d2_funct_2,s1_multop_1,s3_bintree1,d2_funct_2,d1_funct_2,t11_relset_1,d2_funct_2,d1_funct_2,t11_relset_1,d2_funct_2,d1_funct_2,t11_relset_1,d2_funct_2,d1_funct_2,t11_relset_1]),
    [file(bintree1,s5_bintree1),interesting(0.14)]).

fof(s1_dtconstr,theorem,(
    ? [A] : 
      ( ~ v3_struct_0(A)
      & v1_lang1(A)
      & l1_lang1(A)
      & u1_struct_0(A) = f1_s1_dtconstr
      & ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_struct_0(A))
             => ( r1_lang1(A,B,C)
              <=> p1_s1_dtconstr(B,C) ) ) ) ) ),
    file(dtconstr,s1_dtconstr),
    [interesting(0.00)]).

fof(t61_finseq_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( C = k10_finseq_1(A,B)
      <=> ( k3_finseq_1(C) = 2
          & k1_funct_1(C,1) = A
          & k1_funct_1(C,2) = B ) ) ) ),
    file(finseq_1,t61_finseq_1),
    [interesting(0.00)]).

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

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(d3_finseq_2,definition,(
    ! [A,B] : 
      ( m1_finseq_2(B,A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,d3_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(d9_finseq_1,definition,(
    ! [A,B] : k10_finseq_1(A,B) = k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)) ),
    file(finseq_1,d9_finseq_1),
    [interesting(0.00)]).

fof(t44_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) )
         => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    file(finseq_1,t44_finseq_1),
    [interesting(0.00)]).

fof(t56_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
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t56_finseq_1),
    [interesting(0.00)]).

fof(t41_enumset1,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    file(enumset1,t41_enumset1),
    [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(d4_bintree1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_lang1(A) )
     => ( v3_bintree1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( ( v1_relat_1(C)
                  & v1_funct_1(C)
                  & v1_finseq_1(C) )
               => ~ ( r1_lang1(A,B,C)
                    & ! [D] : 
                        ( m1_subset_1(D,u1_struct_0(A))
                       => ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => C != k4_lang1(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ),
    file(bintree1,d4_bintree1),
    [interesting(0.00)]).

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

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

fof(t4_finseq_1,theorem,
    ( k2_finseq_1(0) = k1_xboole_0
    & k2_finseq_1(1) = k1_tarski(1)
    & k2_finseq_1(2) = k2_tarski(1,2) ),
    file(finseq_1,t4_finseq_1),
    [interesting(0.00)]).

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

fof(d5_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(t8_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_finseq_1(A) = k2_finseq_1(B)
           => A = B ) ) ) ),
    file(finseq_1,t8_finseq_1),
    [interesting(0.00)]).

fof(d6_trees_4,definition,(
    ! [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) )
         => k6_trees_4(A,B,C) = k4_trees_4(A,k10_finseq_1(B,C)) ) ) ),
    file(trees_4,d6_trees_4),
    [interesting(0.00)]).

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

fof(t11_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => r2_hidden(C,k1_funct_2(A,B)) ) ) ),
    file(funct_2,t11_funct_2),
    [interesting(0.00)]).

fof(s4_funct_2,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2)
      & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2)
      & ! [B] : 
          ( m1_subset_1(B,f1_s4_funct_2)
         => k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B) ) ) ),
    file(funct_2,s4_funct_2),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

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

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.00)]).

fof(s3_funct_2,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s3_funct_2)
       => ? [B] : 
            ( m1_subset_1(B,f2_s3_funct_2)
            & p1_s3_funct_2(A,B) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2)
        & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2)
        & ! [B] : 
            ( m1_subset_1(B,f1_s3_funct_2)
           => p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)) ) ) ),
    file(funct_2,s3_funct_2),
    [interesting(0.00)]).

fof(s1_multop_1,theorem,
    ( ! [A] : 
        ( m1_subset_1(A,f1_s1_multop_1)
       => ! [B] : 
            ( m1_subset_1(B,f2_s1_multop_1)
           => ! [C] : 
                ( m1_subset_1(C,f3_s1_multop_1)
               => ? [D] : 
                    ( m1_subset_1(D,f4_s1_multop_1)
                    & p1_s1_multop_1(A,B,C,D) ) ) ) )
   => ? [A] : 
        ( v1_funct_1(A)
        & v1_funct_2(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1)
        & m2_relset_1(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1)
        & ! [B] : 
            ( m1_subset_1(B,f1_s1_multop_1)
           => ! [C] : 
                ( m1_subset_1(C,f2_s1_multop_1)
               => ! [D] : 
                    ( m1_subset_1(D,f3_s1_multop_1)
                   => p1_s1_multop_1(B,C,D,k8_funct_2(k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1,A,k4_domain_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1,B,C,D))) ) ) ) ) ),
    file(multop_1,s1_multop_1),
    [interesting(0.00)]).

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

fof(t29_finseq_3,theorem,(
    ! [A,B] : k4_finseq_1(k10_finseq_1(A,B)) = k2_finseq_1(2) ),
    file(finseq_3,t29_finseq_3),
    [interesting(0.00)]).

fof(t20_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( ( ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                    <=> ( r2_hidden(D,k1_relat_1(A))
                        & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) ) )
                  & ! [D] : 
                      ( r2_hidden(D,k1_relat_1(C))
                     => k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)) ) )
               => C = k5_relat_1(A,B) ) ) ) ) ),
    file(funct_1,t20_funct_1),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

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

fof(s9_dtconstr,theorem,
    ( ( ! [A] : 
          ( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
         => ( r2_hidden(A,k5_lang1(f1_s9_dtconstr))
           => k1_funct_1(f5_s9_dtconstr,k2_trees_4(u1_struct_0(f1_s9_dtconstr),A)) = f3_s9_dtconstr(A) ) )
      & ! [A] : 
          ( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
         => ! [B] : 
              ( m1_trees_4(B,k5_trees_3(u1_struct_0(f1_s9_dtconstr)),k4_dtconstr(f1_s9_dtconstr))
             => ( r1_lang1(f1_s9_dtconstr,A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B))
               => k1_funct_1(f5_s9_dtconstr,k12_trees_4(u1_struct_0(f1_s9_dtconstr),A,B)) = f4_s9_dtconstr(A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B),k5_finseqop(k4_dtconstr(f1_s9_dtconstr),f2_s9_dtconstr,B,f5_s9_dtconstr)) ) ) )
      & ! [A] : 
          ( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
         => ( r2_hidden(A,k5_lang1(f1_s9_dtconstr))
           => k1_funct_1(f6_s9_dtconstr,k2_trees_4(u1_struct_0(f1_s9_dtconstr),A)) = f3_s9_dtconstr(A) ) )
      & ! [A] : 
          ( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
         => ! [B] : 
              ( m1_trees_4(B,k5_trees_3(u1_struct_0(f1_s9_dtconstr)),k4_dtconstr(f1_s9_dtconstr))
             => ( r1_lang1(f1_s9_dtconstr,A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B))
               => k1_funct_1(f6_s9_dtconstr,k12_trees_4(u1_struct_0(f1_s9_dtconstr),A,B)) = f4_s9_dtconstr(A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B),k5_finseqop(k4_dtconstr(f1_s9_dtconstr),f2_s9_dtconstr,B,f6_s9_dtconstr)) ) ) ) )
   => f5_s9_dtconstr = f6_s9_dtconstr ),
    file(dtconstr,s9_dtconstr),
    [interesting(0.00)]).

fof(s6_bintree1,theorem,
    ( ( ! [A] : 
          ( m1_struct_0(A,f1_s6_bintree1,k6_dtconstr(f1_s6_bintree1))
         => ? [B] : 
              ( v1_funct_1(B)
              & v1_funct_2(B,f2_s6_bintree1,f3_s6_bintree1)
              & m2_relset_1(B,f2_s6_bintree1,f3_s6_bintree1)
              & B = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f4_s6_bintree1,k8_dtconstr(f1_s6_bintree1,A))
              & ! [C] : 
                  ( m1_subset_1(C,f2_s6_bintree1)
                 => k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,B,C) = f6_s6_bintree1(A,C) ) ) )
      & ! [A] : 
          ( m1_struct_0(A,f1_s6_bintree1,k7_dtconstr(f1_s6_bintree1))
         => ! [B] : 
              ( m1_dtconstr(B,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
             => ! [C] : 
                  ( m1_dtconstr(C,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(f1_s6_bintree1))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(f1_s6_bintree1))
                         => ~ ( D = k1_bintree1(u1_struct_0(f1_s6_bintree1),B)
                              & E = k1_bintree1(u1_struct_0(f1_s6_bintree1),C)
                              & r1_lang1(f1_s6_bintree1,A,k4_lang1(u1_struct_0(f1_s6_bintree1),D,E))
                              & ! [F] : 
                                  ( ( v1_funct_1(F)
                                    & v1_funct_2(F,f2_s6_bintree1,f3_s6_bintree1)
                                    & m2_relset_1(F,f2_s6_bintree1,f3_s6_bintree1) )
                                 => ! [G] : 
                                      ( ( v1_funct_1(G)
                                        & v1_funct_2(G,f2_s6_bintree1,f3_s6_bintree1)
                                        & m2_relset_1(G,f2_s6_bintree1,f3_s6_bintree1) )
                                     => ! [H] : 
                                          ( ( v1_funct_1(H)
                                            & v1_funct_2(H,f2_s6_bintree1,f3_s6_bintree1)
                                            & m2_relset_1(H,f2_s6_bintree1,f3_s6_bintree1) )
                                         => ~ ( F = k1_funct_1(f4_s6_bintree1,k10_trees_4(u1_struct_0(f1_s6_bintree1),A,B,C))
                                              & G = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f4_s6_bintree1,B)
                                              & H = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f4_s6_bintree1,C)
                                              & ! [I] : 
                                                  ( m1_subset_1(I,f2_s6_bintree1)
                                                 => k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,F,I) = f7_s6_bintree1(A,G,H,I) ) ) ) ) ) ) ) ) ) ) )
      & ! [A] : 
          ( m1_struct_0(A,f1_s6_bintree1,k6_dtconstr(f1_s6_bintree1))
         => ? [B] : 
              ( v1_funct_1(B)
              & v1_funct_2(B,f2_s6_bintree1,f3_s6_bintree1)
              & m2_relset_1(B,f2_s6_bintree1,f3_s6_bintree1)
              & B = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f5_s6_bintree1,k8_dtconstr(f1_s6_bintree1,A))
              & ! [C] : 
                  ( m1_subset_1(C,f2_s6_bintree1)
                 => k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,B,C) = f6_s6_bintree1(A,C) ) ) )
      & ! [A] : 
          ( m1_struct_0(A,f1_s6_bintree1,k7_dtconstr(f1_s6_bintree1))
         => ! [B] : 
              ( m1_dtconstr(B,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
             => ! [C] : 
                  ( m1_dtconstr(C,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(f1_s6_bintree1))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(f1_s6_bintree1))
                         => ~ ( D = k1_bintree1(u1_struct_0(f1_s6_bintree1),B)
                              & E = k1_bintree1(u1_struct_0(f1_s6_bintree1),C)
                              & r1_lang1(f1_s6_bintree1,A,k4_lang1(u1_struct_0(f1_s6_bintree1),D,E))
                              & ! [F] : 
                                  ( ( v1_funct_1(F)
                                    & v1_funct_2(F,f2_s6_bintree1,f3_s6_bintree1)
                                    & m2_relset_1(F,f2_s6_bintree1,f3_s6_bintree1) )
                                 => ! [G] : 
                                      ( ( v1_funct_1(G)
                                        & v1_funct_2(G,f2_s6_bintree1,f3_s6_bintree1)
                                        & m2_relset_1(G,f2_s6_bintree1,f3_s6_bintree1) )
                                     => ! [H] : 
                                          ( ( v1_funct_1(H)
                                            & v1_funct_2(H,f2_s6_bintree1,f3_s6_bintree1)
                                            & m2_relset_1(H,f2_s6_bintree1,f3_s6_bintree1) )
                                         => ~ ( F = k1_funct_1(f5_s6_bintree1,k10_trees_4(u1_struct_0(f1_s6_bintree1),A,B,C))
                                              & G = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f5_s6_bintree1,B)
                                              & H = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f5_s6_bintree1,C)
                                              & ! [I] : 
                                                  ( m1_subset_1(I,f2_s6_bintree1)
                                                 => k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,F,I) = f7_s6_bintree1(A,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )
   => f4_s6_bintree1 = f5_s6_bintree1 ),
    inference(mizar_proof,[status(thm)],[t11_funct_2,s4_funct_2,d1_funct_2,t12_relset_1,d2_funct_2,s3_funct_2,s4_funct_2,d1_funct_2,t12_relset_1,d2_funct_2,s1_multop_1,d2_funct_2,d1_funct_2,t11_relset_1,d1_funct_2,t9_funct_1,d2_funct_2,d1_funct_2,t11_relset_1,d1_funct_2,d1_funct_2,t9_funct_1,d2_funct_2,d1_funct_2,t11_relset_1,d1_funct_2,t9_funct_1,d2_funct_2,d1_funct_2,t11_relset_1,d1_funct_2,d1_funct_2,t9_funct_1,s4_bintree1]),
    [file(bintree1,s6_bintree1),interesting(0.00)]).

fof(d3_bintree1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( v2_bintree1(A)
      <=> v1_bintree1(k1_relat_1(A)) ) ) ),
    file(bintree1,d3_bintree1),
    [interesting(0.00)]).

fof(d5_trees_2,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => k1_trees_2(A,B) = a_2_1_trees_2(A,B) ) ) ),
    file(trees_2,d5_trees_2),
    [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(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(t71_trees_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( r2_hidden(C,k15_trees_3(A,B))
            <=> ~ ( C != k1_xboole_0
                  & ! [D] : 
                      ( ( v1_relat_1(D)
                        & v1_funct_1(D)
                        & v1_finseq_1(D) )
                     => ( ~ ( r2_hidden(D,A)
                            & C = k7_finseq_1(k12_finseq_1(k5_numbers,0),D) )
                        & ~ ( r2_hidden(D,B)
                            & C = k7_finseq_1(k12_finseq_1(k5_numbers,1),D) ) ) ) ) ) ) ) ),
    file(trees_3,t71_trees_3),
    [interesting(0.00)]).

fof(t58_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),1) = A ) ),
    file(finseq_1,t58_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(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(t72_trees_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(C,A)
              <=> r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,0),C),k15_trees_3(A,B)) ) ) ) ) ),
    file(trees_3,t72_trees_3),
    [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(t73_trees_3,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(C,B)
              <=> r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,1),C),k15_trees_3(A,B)) ) ) ) ) ),
    file(trees_3,t73_trees_3),
    [interesting(0.00)]).

fof(t54_modal_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => ( r2_hidden(B,k3_trees_1(A))
          <=> ! [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ~ r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A) ) ) ) ) ),
    file(modal_1,t54_modal_1),
    [interesting(0.00)]).

fof(d2_bintree1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( v1_bintree1(A)
      <=> ! [B] : 
            ( m1_trees_1(B,A)
           => ( ~ r2_hidden(B,k3_trees_1(A))
             => k1_trees_2(A,B) = k2_tarski(k7_finseq_1(B,k3_lang1(k1_numbers,0)),k7_finseq_1(B,k3_lang1(k1_numbers,1))) ) ) ) ) ),
    file(bintree1,d2_bintree1),
    [interesting(0.00)]).

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)) ) ) ),
    file(trees_4,t14_trees_4),
    [interesting(0.00)]).

fof(t4_dtconstr,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => k16_trees_3(k9_finseq_1(A)) = k9_finseq_1(k1_funct_1(A,k1_xboole_0)) ) ),
    file(dtconstr,t4_dtconstr),
    [interesting(0.00)]).

fof(t6_dtconstr,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) )
         => k16_trees_3(k10_finseq_1(A,B)) = k10_finseq_1(k1_funct_1(A,k1_xboole_0),k1_funct_1(B,k1_xboole_0)) ) ) ),
    file(dtconstr,t6_dtconstr),
    [interesting(0.00)]).

fof(t3_bintree1,theorem,(
    $true ),
    file(bintree1,t3_bintree1),
    [interesting(0.00)]).

fof(t4_bintree1,theorem,(
    $true ),
    file(bintree1,t4_bintree1),
    [interesting(0.00)]).

fof(t53_modal_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_trees_1(B,A)
         => ( r2_hidden(B,k3_trees_1(A))
          <=> ~ r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,0)),A) ) ) ) ),
    file(modal_1,t53_modal_1),
    [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(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(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(d8_trees_1,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( B = k3_trees_1(A)
          <=> ! [C] : 
                ( m2_finseq_1(C,k5_numbers)
               => ( r2_hidden(C,B)
                <=> ( r2_hidden(C,A)
                    & ! [D] : 
                        ( m2_finseq_1(D,k5_numbers)
                       => ~ ( r2_hidden(D,A)
                            & r2_xboole_0(C,D) ) ) ) ) ) ) ) ) ),
    file(trees_1,d8_trees_1),
    [interesting(0.00)]).

fof(d1_enumset1,definition,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    [interesting(0.00)]).

fof(t10_modal_1,theorem,(
    k2_trees_1(2) = k1_enumset1(k1_xboole_0,k12_finseq_1(k5_numbers,0),k12_finseq_1(k5_numbers,1)) ),
    file(modal_1,t10_modal_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)]).