SET007 Axioms: SET007+390.ax


%------------------------------------------------------------------------------
% File     : SET007+390 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On Defining Functions on Binary Trees
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : bintree1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   33 (   4 unit)
%            Number of atoms       :  365 (  64 equality)
%            Maximal formula depth :   32 (  11 average)
%            Number of connectives :  370 (  38 ~  ;   0  |; 194  &)
%                                         (  11 <=>; 127 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   31 (   1 propositional; 0-4 arity)
%            Number of functors    :   61 (  21 constant; 0-6 arity)
%            Number of variables   :  140 (   0 singleton; 128 !;  12 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_bintree1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_trees_1(A)
      & v1_bintree1(A) ) )).

fof(rc2_bintree1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m3_trees_2(B,A)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_finset_1(B)
          & v3_trees_2(B)
          & v2_bintree1(B) ) ) )).

fof(rc3_bintree1,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v3_trees_2(A)
      & v2_bintree1(A) ) )).

fof(cc1_bintree1,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_bintree1(A) )
     => ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & v1_trees_2(A) ) ) )).

fof(rc4_bintree1,axiom,(
    ? [A] :
      ( l1_lang1(A)
      & ~ v3_struct_0(A)
      & v1_lang1(A)
      & v1_dtconstr(A)
      & v2_dtconstr(A)
      & v3_dtconstr(A)
      & v3_bintree1(A) ) )).

fof(cc2_bintree1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_dtconstr(A)
        & v2_dtconstr(A)
        & v3_bintree1(A)
        & l1_lang1(A) )
     => ! [B] :
          ( m1_subset_1(B,k4_dtconstr(A))
         => v2_bintree1(B) ) ) )).

fof(d1_bintree1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v3_trees_2(B)
            & m3_trees_2(B,A) )
         => k1_bintree1(A,B) = k1_funct_1(B,k1_xboole_0) ) ) )).

fof(t1_bintree1,axiom,(
    ! [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)) ) ) )).

fof(t2_bintree1,axiom,(
    ! [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)) ) ) ) )).

fof(d2_bintree1,axiom,(
    ! [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,np__0)),k7_finseq_1(B,k3_lang1(k1_numbers,np__1))) ) ) ) ) )).

fof(t3_bintree1,axiom,(
    $true )).

fof(t4_bintree1,axiom,(
    $true )).

fof(t5_bintree1,axiom,(
    ! [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)) ) ) ) )).

fof(t6_bintree1,axiom,(
    v1_bintree1(k2_trees_1(np__0)) )).

fof(t7_bintree1,axiom,(
    v1_bintree1(k2_trees_1(np__2)) )).

fof(d3_bintree1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( v2_bintree1(A)
      <=> v1_bintree1(k1_relat_1(A)) ) ) )).

fof(t8_bintree1,axiom,(
    ! [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,np__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,np__1),D)
                     => ( r2_hidden(C,k3_trees_1(k15_trees_3(A,B)))
                      <=> r2_hidden(D,k3_trees_1(B)) ) ) ) ) ) ) ) )).

fof(t9_bintree1,axiom,(
    ! [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,np__0)),k7_finseq_1(C,k3_lang1(k1_numbers,np__1))) )
                & ! [D] :
                    ( m1_trees_1(D,A)
                   => ( C = k7_finseq_1(k3_lang1(k1_numbers,np__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,np__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,np__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,np__1),E),k1_trees_2(k15_trees_3(A,B),C)) ) ) ) ) ) ) ) ) )).

fof(t10_bintree1,axiom,(
    ! [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)) ) ) ) )).

fof(t11_bintree1,axiom,(
    ! [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)) ) ) ) )).

fof(d4_bintree1,axiom,(
    ! [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) ) ) ) ) ) ) ) )).

fof(t12_bintree1,axiom,(
    ! [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(np__1,np__2)
                  & r2_hidden(np__1,k4_finseq_1(B))
                  & r2_hidden(np__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,np__1)
                          & E = k1_funct_1(B,np__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)) ) ) ) ) ) ) ) )).

fof(s1_bintree1,axiom,(
    ? [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) ) ) ) ) ) )).

fof(s2_bintree1,axiom,
    ( ( ! [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) ) )).

fof(s3_bintree1,axiom,(
    ? [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) ) ) ) ) ) ) ) ) ) ) )).

fof(s4_bintree1,axiom,
    ( ( ! [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 )).

fof(s5_bintree1,axiom,(
    ? [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) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(s6_bintree1,axiom,
    ( ( ! [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 )).

fof(dt_k1_bintree1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v3_trees_2(B)
        & m3_trees_2(B,A) )
     => m1_subset_1(k1_bintree1(A,B),A) ) )).

fof(dt_k2_bintree1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_finset_1(C)
        & v3_trees_2(C)
        & v2_bintree1(C)
        & m3_trees_2(C,A)
        & v1_funct_1(D)
        & v1_finset_1(D)
        & v3_trees_2(D)
        & v2_bintree1(D)
        & m3_trees_2(D,A) )
     => ( v1_funct_1(k2_bintree1(A,B,C,D))
        & v1_finset_1(k2_bintree1(A,B,C,D))
        & v3_trees_2(k2_bintree1(A,B,C,D))
        & v2_bintree1(k2_bintree1(A,B,C,D))
        & m3_trees_2(k2_bintree1(A,B,C,D),A) ) ) )).

fof(redefinition_k2_bintree1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,A)
        & v1_funct_1(C)
        & v1_finset_1(C)
        & v3_trees_2(C)
        & v2_bintree1(C)
        & m3_trees_2(C,A)
        & v1_funct_1(D)
        & v1_finset_1(D)
        & v3_trees_2(D)
        & v2_bintree1(D)
        & m3_trees_2(D,A) )
     => k2_bintree1(A,B,C,D) = k6_trees_4(B,C,D) ) )).

fof(dt_k3_bintree1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,A)
        & m1_subset_1(E,B)
        & m1_subset_1(F,C) )
     => m1_subset_1(k3_bintree1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)) ) )).

fof(redefinition_k3_bintree1,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_subset_1(D,A)
        & m1_subset_1(E,B)
        & m1_subset_1(F,C) )
     => k3_bintree1(A,B,C,D,E,F) = k3_mcart_1(D,E,F) ) )).
%------------------------------------------------------------------------------