SET007 Axioms: SET007+163.ax


%------------------------------------------------------------------------------
% File     : SET007+163 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Sets and Functions of Trees and Joining Operations of 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    : trees_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  195 (   9 unit)
%            Number of atoms       : 1147 (  69 equality)
%            Maximal formula depth :   18 (   7 average)
%            Number of connectives : 1193 ( 241 ~  ;   0  |; 611  &)
%                                         (  59 <=>; 282 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   1 propositional; 0-3 arity)
%            Number of functors    :   62 (   8 constant; 0-4 arity)
%            Number of variables   :  381 (   0 singleton; 362 !;  19 ?)
%            Maximal term depth    :    6 (   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(fc1_trees_3,axiom,(
    ~ v1_xboole_0(k1_trees_3) )).

fof(fc2_trees_3,axiom,(
    ~ v1_xboole_0(k2_trees_3) )).

fof(rc1_trees_3,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_trees_3(A)
      & v2_trees_3(A) ) )).

fof(rc2_trees_3,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v3_trees_3(A) ) )).

fof(cc1_trees_3,axiom,(
    ! [A] :
      ( v2_trees_3(A)
     => v1_trees_3(A) ) )).

fof(cc2_trees_3,axiom,(
    ! [A] :
      ( v1_trees_3(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_trees_3(B) ) ) )).

fof(cc3_trees_3,axiom,(
    ! [A] :
      ( v2_trees_3(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_trees_3(B)
            & v2_trees_3(B) ) ) ) )).

fof(cc4_trees_3,axiom,(
    ! [A] :
      ( v3_trees_3(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v3_trees_3(B) ) ) )).

fof(fc3_trees_3,axiom,
    ( ~ v1_xboole_0(k1_trees_3)
    & v1_trees_3(k1_trees_3) )).

fof(rc3_trees_3,axiom,(
    ? [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_trees_3))
      & ~ v1_xboole_0(A)
      & v1_trees_3(A)
      & v2_trees_3(A) ) )).

fof(fc4_trees_3,axiom,
    ( ~ v1_xboole_0(k2_trees_3)
    & v1_trees_3(k2_trees_3)
    & v2_trees_3(k2_trees_3) )).

fof(cc5_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m4_trees_3(B,A)
         => v3_trees_3(B) ) ) )).

fof(rc4_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] :
          ( m4_trees_3(B,A)
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v3_trees_3(B) ) ) )).

fof(cc6_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B) )
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_funct_2(C,A,B)
              & v3_trees_2(C) ) ) ) ) )).

fof(fc5_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k4_trees_3(A))
        & v3_trees_3(k4_trees_3(A)) ) ) )).

fof(fc6_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k5_trees_3(A))
        & v3_trees_3(k5_trees_3(A)) ) ) )).

fof(rc5_trees_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v4_trees_3(A)
      & v5_trees_3(A) ) )).

fof(rc6_trees_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & v6_trees_3(A) ) )).

fof(rc7_trees_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v4_trees_3(A)
      & v5_trees_3(A) ) )).

fof(rc8_trees_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & v6_trees_3(A) ) )).

fof(cc7_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_trees_3(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v4_trees_3(A) ) ) )).

fof(cc8_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_3(A) )
     => ! [B] :
          ( m1_finseq_1(B,A)
         => v4_trees_3(B) ) ) )).

fof(fc7_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v4_trees_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v4_trees_3(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B))
        & v4_trees_3(k7_finseq_1(A,B)) ) ) )).

fof(cc9_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_trees_3(A) )
     => ! [B] :
          ( m1_finseq_1(B,A)
         => ( v4_trees_3(B)
            & v5_trees_3(B) ) ) ) )).

fof(fc8_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v5_trees_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v5_trees_3(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B))
        & v4_trees_3(k7_finseq_1(A,B))
        & v5_trees_3(k7_finseq_1(A,B)) ) ) )).

fof(cc10_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v3_trees_3(A) )
     => ! [B] :
          ( m1_finseq_1(B,A)
         => v6_trees_3(B) ) ) )).

fof(fc9_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v6_trees_3(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B)
        & v6_trees_3(B) )
     => ( v1_relat_1(k7_finseq_1(A,B))
        & v1_funct_1(k7_finseq_1(A,B))
        & v1_finset_1(k7_finseq_1(A,B))
        & v1_finseq_1(k7_finseq_1(A,B))
        & v6_trees_3(k7_finseq_1(A,B)) ) ) )).

fof(fc10_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( v1_relat_1(k5_finseq_1(A))
        & v1_funct_1(k5_finseq_1(A))
        & ~ v1_xboole_0(k5_finseq_1(A))
        & v1_finset_1(k5_finseq_1(A))
        & v1_finseq_1(k5_finseq_1(A))
        & v4_trees_3(k5_finseq_1(A)) ) ) )).

fof(fc11_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B) )
     => ( v1_relat_1(k10_finseq_1(A,B))
        & v1_funct_1(k10_finseq_1(A,B))
        & ~ v1_xboole_0(k10_finseq_1(A,B))
        & v1_finset_1(k10_finseq_1(A,B))
        & v1_finseq_1(k10_finseq_1(A,B))
        & v4_trees_3(k10_finseq_1(A,B)) ) ) )).

fof(fc12_trees_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B) )
     => ( v1_relat_1(k2_finseq_2(A,B))
        & v1_funct_1(k2_finseq_2(A,B))
        & v1_finset_1(k2_finseq_2(A,B))
        & v1_finseq_1(k2_finseq_2(A,B))
        & v4_trees_3(k2_finseq_2(A,B)) ) ) )).

fof(fc13_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ( v1_relat_1(k5_finseq_1(A))
        & v1_funct_1(k5_finseq_1(A))
        & ~ v1_xboole_0(k5_finseq_1(A))
        & v1_finset_1(k5_finseq_1(A))
        & v1_finseq_1(k5_finseq_1(A))
        & v4_trees_3(k5_finseq_1(A))
        & v5_trees_3(k5_finseq_1(A)) ) ) )).

fof(fc14_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_finset_1(B)
        & v1_trees_1(B) )
     => ( v1_relat_1(k10_finseq_1(A,B))
        & v1_funct_1(k10_finseq_1(A,B))
        & ~ v1_xboole_0(k10_finseq_1(A,B))
        & v1_finset_1(k10_finseq_1(A,B))
        & v1_finseq_1(k10_finseq_1(A,B))
        & v4_trees_3(k10_finseq_1(A,B))
        & v5_trees_3(k10_finseq_1(A,B)) ) ) )).

fof(fc15_trees_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & ~ v1_xboole_0(B)
        & v1_finset_1(B)
        & v1_trees_1(B) )
     => ( v1_relat_1(k2_finseq_2(A,B))
        & v1_funct_1(k2_finseq_2(A,B))
        & v1_finset_1(k2_finseq_2(A,B))
        & v1_finseq_1(k2_finseq_2(A,B))
        & v4_trees_3(k2_finseq_2(A,B))
        & v5_trees_3(k2_finseq_2(A,B)) ) ) )).

fof(fc16_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) )
     => ( v1_relat_1(k5_finseq_1(A))
        & v1_funct_1(k5_finseq_1(A))
        & ~ v1_xboole_0(k5_finseq_1(A))
        & v1_finset_1(k5_finseq_1(A))
        & v1_finseq_1(k5_finseq_1(A))
        & v6_trees_3(k5_finseq_1(A)) ) ) )).

fof(fc17_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) )
     => ( v1_relat_1(k10_finseq_1(A,B))
        & v1_funct_1(k10_finseq_1(A,B))
        & ~ v1_xboole_0(k10_finseq_1(A,B))
        & v1_finset_1(k10_finseq_1(A,B))
        & v1_finseq_1(k10_finseq_1(A,B))
        & v6_trees_3(k10_finseq_1(A,B)) ) ) )).

fof(fc18_trees_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k5_numbers)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) )
     => ( v1_relat_1(k2_finseq_2(A,B))
        & v1_funct_1(k2_finseq_2(A,B))
        & v1_finset_1(k2_finseq_2(A,B))
        & v1_finseq_1(k2_finseq_2(A,B))
        & v6_trees_3(k2_finseq_2(A,B)) ) ) )).

fof(fc19_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v6_trees_3(A) )
     => ( v1_relat_1(k2_funct_6(A))
        & v1_funct_1(k2_funct_6(A))
        & v1_finset_1(k2_funct_6(A))
        & v1_finseq_1(k2_funct_6(A))
        & v4_trees_3(k2_funct_6(A)) ) ) )).

fof(fc20_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) )
     => ( v1_relat_1(k13_funct_3(A,B))
        & v1_funct_1(k13_funct_3(A,B))
        & v3_trees_2(k13_funct_3(A,B)) ) ) )).

fof(fc21_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ( ~ v1_xboole_0(k3_trees_1(A))
        & v1_finset_1(k3_trees_1(A)) ) ) )).

fof(rc9_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ? [B] :
          ( m9_trees_3(B,A)
          & ~ v1_xboole_0(B)
          & v1_finset_1(B)
          & v1_trees_1(B) ) ) )).

fof(fc22_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B) )
     => ( ~ v1_xboole_0(k2_xboole_0(A,B))
        & v1_trees_1(k2_xboole_0(A,B)) ) ) )).

fof(fc23_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v5_trees_3(A) )
     => ( ~ v1_xboole_0(k13_trees_3(A))
        & v1_finset_1(k13_trees_3(A))
        & v1_trees_1(k13_trees_3(A)) ) ) )).

fof(fc24_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ( ~ v1_xboole_0(k14_trees_3(A))
        & v1_finset_1(k14_trees_3(A))
        & v1_trees_1(k14_trees_3(A)) ) ) )).

fof(fc25_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_finset_1(B)
        & v1_trees_1(B) )
     => ( ~ v1_xboole_0(k15_trees_3(A,B))
        & v1_finset_1(k15_trees_3(A,B))
        & v1_trees_1(k15_trees_3(A,B)) ) ) )).

fof(fc26_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_trees_3(A)) )
     => ( ~ v1_xboole_0(k1_relat_1(B))
        & v1_finset_1(k1_relat_1(B))
        & v1_trees_1(k1_relat_1(B)) ) ) )).

fof(d1_trees_3,axiom,(
    ! [A] :
      ( A = k1_trees_3
    <=> ! [B] :
          ( r2_hidden(B,A)
        <=> ( ~ v1_xboole_0(B)
            & v1_trees_1(B) ) ) ) )).

fof(d2_trees_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_zfmisc_1(k1_trees_3))
     => ( A = k2_trees_3
      <=> ! [B] :
            ( r2_hidden(B,A)
          <=> ( ~ v1_xboole_0(B)
              & v1_finset_1(B)
              & v1_trees_1(B) ) ) ) ) )).

fof(d3_trees_3,axiom,(
    ! [A] :
      ( v1_trees_3(A)
    <=> ! [B] :
          ( r2_hidden(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_trees_1(B) ) ) ) )).

fof(d4_trees_3,axiom,(
    ! [A] :
      ( v2_trees_3(A)
    <=> ! [B] :
          ( r2_hidden(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) ) ) ) )).

fof(d5_trees_3,axiom,(
    ! [A] :
      ( v3_trees_3(A)
    <=> ! [B] :
          ( r2_hidden(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) ) ) ) )).

fof(t1_trees_3,axiom,(
    ! [A] :
      ( v1_trees_3(A)
    <=> r1_tarski(A,k1_trees_3) ) )).

fof(t2_trees_3,axiom,(
    ! [A] :
      ( v2_trees_3(A)
    <=> r1_tarski(A,k2_trees_3) ) )).

fof(t3_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_trees_3(A)
        & v1_trees_3(B) )
    <=> v1_trees_3(k2_xboole_0(A,B)) ) )).

fof(t4_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_trees_3(A)
        & v1_trees_3(B) )
     => v1_trees_3(k5_xboole_0(A,B)) ) )).

fof(t5_trees_3,axiom,(
    ! [A,B] :
      ( v1_trees_3(A)
     => ( v1_trees_3(k3_xboole_0(A,B))
        & v1_trees_3(k3_xboole_0(B,A))
        & v1_trees_3(k4_xboole_0(A,B)) ) ) )).

fof(t6_trees_3,axiom,(
    ! [A,B] :
      ( ( v2_trees_3(A)
        & v2_trees_3(B) )
    <=> v2_trees_3(k2_xboole_0(A,B)) ) )).

fof(t7_trees_3,axiom,(
    ! [A,B] :
      ( ( v2_trees_3(A)
        & v2_trees_3(B) )
     => v2_trees_3(k5_xboole_0(A,B)) ) )).

fof(t8_trees_3,axiom,(
    ! [A,B] :
      ( v2_trees_3(A)
     => ( v2_trees_3(k3_xboole_0(A,B))
        & v2_trees_3(k3_xboole_0(B,A))
        & v2_trees_3(k4_xboole_0(A,B)) ) ) )).

fof(t9_trees_3,axiom,(
    ! [A,B] :
      ( ( v3_trees_3(A)
        & v3_trees_3(B) )
    <=> v3_trees_3(k2_xboole_0(A,B)) ) )).

fof(t10_trees_3,axiom,(
    ! [A,B] :
      ( ( v3_trees_3(A)
        & v3_trees_3(B) )
     => v3_trees_3(k5_xboole_0(A,B)) ) )).

fof(t11_trees_3,axiom,(
    ! [A,B] :
      ( v3_trees_3(A)
     => ( v3_trees_3(k3_xboole_0(A,B))
        & v3_trees_3(k3_xboole_0(B,A))
        & v3_trees_3(k4_xboole_0(A,B)) ) ) )).

fof(t12_trees_3,axiom,
    ( v1_trees_3(k1_xboole_0)
    & v2_trees_3(k1_xboole_0)
    & v3_trees_3(k1_xboole_0) )).

fof(t13_trees_3,axiom,(
    ! [A] :
      ( v1_trees_3(k1_tarski(A))
    <=> ( ~ v1_xboole_0(A)
        & v1_trees_1(A) ) ) )).

fof(t14_trees_3,axiom,(
    ! [A] :
      ( v2_trees_3(k1_tarski(A))
    <=> ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) ) ) )).

fof(t15_trees_3,axiom,(
    ! [A] :
      ( v3_trees_3(k1_tarski(A))
    <=> ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) ) ) )).

fof(t16_trees_3,axiom,(
    ! [A,B] :
      ( v1_trees_3(k2_tarski(A,B))
    <=> ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B) ) ) )).

fof(t17_trees_3,axiom,(
    ! [A,B] :
      ( v2_trees_3(k2_tarski(A,B))
    <=> ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_finset_1(B)
        & v1_trees_1(B) ) ) )).

fof(t18_trees_3,axiom,(
    ! [A,B] :
      ( v3_trees_3(k2_tarski(A,B))
    <=> ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) ) ) )).

fof(t19_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_trees_3(A)
        & r1_tarski(B,A) )
     => v1_trees_3(B) ) )).

fof(t20_trees_3,axiom,(
    ! [A,B] :
      ( ( v2_trees_3(A)
        & r1_tarski(B,A) )
     => v2_trees_3(B) ) )).

fof(t21_trees_3,axiom,(
    ! [A,B] :
      ( ( v3_trees_3(A)
        & r1_tarski(B,A) )
     => v3_trees_3(B) ) )).

fof(d6_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m4_trees_3(B,A)
        <=> ! [C] :
              ( r2_hidden(C,B)
             => ( v1_funct_1(C)
                & v3_trees_2(C)
                & m3_trees_2(C,A) ) ) ) ) )).

fof(d7_trees_3,axiom,(
    ! [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) ) ) ) ) )).

fof(d8_trees_3,axiom,(
    ! [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) ) ) ) ) ) )).

fof(t22_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => r1_tarski(k5_trees_3(A),k4_trees_3(A)) ) )).

fof(d9_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v4_trees_3(A)
      <=> v1_trees_3(k2_relat_1(A)) ) ) )).

fof(d10_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v5_trees_3(A)
      <=> v2_trees_3(k2_relat_1(A)) ) ) )).

fof(d11_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v6_trees_3(A)
      <=> v3_trees_3(k2_relat_1(A)) ) ) )).

fof(t23_trees_3,axiom,
    ( v4_trees_3(k1_xboole_0)
    & v5_trees_3(k1_xboole_0)
    & v6_trees_3(k1_xboole_0) )).

fof(t24_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v4_trees_3(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => ( ~ v1_xboole_0(k1_funct_1(A,B))
              & v1_trees_1(k1_funct_1(A,B)) ) ) ) ) )).

fof(t25_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v5_trees_3(A)
      <=> ! [B] :
            ( r2_hidden(B,k1_relat_1(A))
           => ( ~ v1_xboole_0(k1_funct_1(A,B))
              & v1_finset_1(k1_funct_1(A,B))
              & v1_trees_1(k1_funct_1(A,B)) ) ) ) ) )).

fof(t26_trees_3,axiom,(
    ! [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)) ) ) ) ) )).

fof(t27_trees_3,axiom,(
    ! [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) )
         => ( ( v4_trees_3(A)
              & v4_trees_3(B) )
          <=> v4_trees_3(k7_finseq_1(A,B)) ) ) ) )).

fof(t28_trees_3,axiom,(
    ! [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) )
         => ( ( v5_trees_3(A)
              & v5_trees_3(B) )
          <=> v5_trees_3(k7_finseq_1(A,B)) ) ) ) )).

fof(t29_trees_3,axiom,(
    ! [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) )
         => ( ( v6_trees_3(A)
              & v6_trees_3(B) )
          <=> v6_trees_3(k7_finseq_1(A,B)) ) ) ) )).

fof(t30_trees_3,axiom,(
    ! [A] :
      ( v4_trees_3(k9_finseq_1(A))
    <=> ( ~ v1_xboole_0(A)
        & v1_trees_1(A) ) ) )).

fof(t31_trees_3,axiom,(
    ! [A] :
      ( v5_trees_3(k9_finseq_1(A))
    <=> ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) ) ) )).

fof(t32_trees_3,axiom,(
    ! [A] :
      ( v6_trees_3(k9_finseq_1(A))
    <=> ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A) ) ) )).

fof(t33_trees_3,axiom,(
    ! [A,B] :
      ( v4_trees_3(k10_finseq_1(A,B))
    <=> ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B) ) ) )).

fof(t34_trees_3,axiom,(
    ! [A,B] :
      ( v5_trees_3(k10_finseq_1(A,B))
    <=> ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_finset_1(B)
        & v1_trees_1(B) ) ) )).

fof(t35_trees_3,axiom,(
    ! [A,B] :
      ( v6_trees_3(k10_finseq_1(A,B))
    <=> ( v1_relat_1(A)
        & v1_funct_1(A)
        & v3_trees_2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v3_trees_2(B) ) ) )).

fof(t36_trees_3,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( B != np__0
       => ( v4_trees_3(k2_finseq_2(B,A))
        <=> ( ~ v1_xboole_0(A)
            & v1_trees_1(A) ) ) ) ) )).

fof(t37_trees_3,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( B != np__0
       => ( v5_trees_3(k2_finseq_2(B,A))
        <=> ( ~ v1_xboole_0(A)
            & v1_finset_1(A)
            & v1_trees_1(A) ) ) ) ) )).

fof(t38_trees_3,axiom,(
    ! [A,B] :
      ( m2_subset_1(B,k1_numbers,k5_numbers)
     => ( B != np__0
       => ( v6_trees_3(k2_finseq_2(B,A))
        <=> ( v1_relat_1(A)
            & v1_funct_1(A)
            & v3_trees_2(A) ) ) ) ) )).

fof(t39_trees_3,axiom,(
    ! [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)) ) ) )).

fof(t40_trees_3,axiom,(
    ! [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) ) )).

fof(d12_trees_3,axiom,(
    ! [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)) ) ) ) )).

fof(d13_trees_3,axiom,(
    ! [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)) ) ) ) )).

fof(t41_trees_3,axiom,(
    ! [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)) ) ) ) ) ) )).

fof(t42_trees_3,axiom,(
    ! [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 ) ) ) )).

fof(d14_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( m9_trees_3(B,A)
          <=> ! [C] :
                ( m1_trees_1(C,B)
               => ~ ( ~ r2_hidden(C,A)
                    & ! [D] :
                        ( m8_trees_3(D,A)
                       => ~ r2_xboole_0(D,C) ) ) ) ) ) ) )).

fof(t43_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => m9_trees_3(A,k2_trees_1(np__0)) ) )).

fof(t44_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( ( r1_tarski(k2_trees_2(A,np__1),k2_trees_2(B,np__1))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(k12_finseq_1(k5_numbers,C),A)
                   => k4_trees_1(A,k12_finseq_1(k5_numbers,C)) = k4_trees_1(B,k12_finseq_1(k5_numbers,C)) ) ) )
           => r1_tarski(A,B) ) ) ) )).

fof(t45_trees_3,axiom,(
    $true )).

fof(t46_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] :
              ( m2_finseq_1(C,k5_numbers)
             => ( r2_hidden(C,k3_trees_1(A))
               => r1_tarski(A,k5_trees_1(A,C,B)) ) ) ) ) )).

fof(t47_trees_3,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] :
              ( 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) ) ) ) )).

fof(t48_trees_3,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] :
              ( 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) ) ) ) ) ) )).

fof(t49_trees_3,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] :
              ( 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) ) ) ) ) )).

fof(t50_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] :
              ( m1_trees_1(C,k2_xboole_0(A,B))
             => ( ( ( r2_hidden(C,A)
                    & r2_hidden(C,B) )
                 => k4_trees_1(k2_xboole_0(A,B),C) = k2_xboole_0(k4_trees_1(A,C),k4_trees_1(B,C)) )
                & ( ~ r2_hidden(C,A)
                 => k4_trees_1(k2_xboole_0(A,B),C) = k4_trees_1(B,C) )
                & ( ~ r2_hidden(C,B)
                 => k4_trees_1(k2_xboole_0(A,B),C) = k4_trees_1(A,C) ) ) ) ) ) )).

fof(d15_trees_3,axiom,(
    ! [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,np__1)))
                                  & C = k7_finseq_1(k12_finseq_1(k5_numbers,D),E) ) ) ) ) ) ) ) ) ) )).

fof(d16_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => k14_trees_3(A) = k13_trees_3(k9_finseq_1(A)) ) )).

fof(d17_trees_3,axiom,(
    ! [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)) ) ) )).

fof(t51_trees_3,axiom,(
    ! [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,np__1))) ) ) ) ) ) ) )).

fof(t53_trees_3,axiom,(
    ! [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 ) ) ) )).

fof(t54_trees_3,axiom,(
    ! [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)
            & v4_trees_3(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C)
                & v4_trees_3(C) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_trees_1(D) )
                 => ( r2_hidden(A,D)
                  <=> r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,k3_finseq_1(B)),A),k13_trees_3(k7_finseq_1(k7_finseq_1(B,k9_finseq_1(D)),C))) ) ) ) ) ) )).

fof(t55_trees_3,axiom,(
    k13_trees_3(k1_xboole_0) = k2_trees_1(np__0) )).

fof(t56_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v4_trees_3(A)
       => r1_tarski(k2_trees_1(k3_finseq_1(A)),k13_trees_3(A)) ) ) )).

fof(t57_trees_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_trees_1(A) = k13_trees_3(k2_finseq_2(A,k2_trees_1(np__0))) ) )).

fof(t58_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B)
            & v4_trees_3(B) )
         => k13_trees_3(k7_finseq_1(B,k9_finseq_1(A))) = k5_trees_1(k2_xboole_0(k13_trees_3(B),k2_trees_1(k1_nat_1(k3_finseq_1(B),np__1))),k12_finseq_1(k5_numbers,k3_finseq_1(B)),A) ) ) )).

fof(t59_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v4_trees_3(A) )
     => k13_trees_3(k7_finseq_1(A,k9_finseq_1(k2_trees_1(np__0)))) = k2_xboole_0(k13_trees_3(A),k2_trees_1(k1_nat_1(k3_finseq_1(A),np__1))) ) )).

fof(t60_trees_3,axiom,(
    ! [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) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_trees_1(D) )
                 => k13_trees_3(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(C)),B)) = k5_trees_1(k13_trees_3(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(D)),B)),k12_finseq_1(k5_numbers,k3_finseq_1(A)),C) ) ) ) ) )).

fof(t61_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => k14_trees_3(A) = k5_trees_1(k2_trees_1(np__1),k12_finseq_1(k5_numbers,np__0),A) ) )).

fof(t62_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => k15_trees_3(A,B) = k5_trees_1(k5_trees_1(k2_trees_1(np__2),k12_finseq_1(k5_numbers,np__0),A),k12_finseq_1(k5_numbers,np__1),B) ) ) )).

fof(t63_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( r2_hidden(B,k14_trees_3(A))
        <=> ~ ( B != k1_xboole_0
              & ! [C] :
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v1_finseq_1(C) )
                 => ~ ( r2_hidden(C,A)
                      & B = k7_finseq_1(k12_finseq_1(k5_numbers,np__0),C) ) ) ) ) ) )).

fof(t64_trees_3,axiom,(
    ! [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(k7_finseq_1(k12_finseq_1(k5_numbers,np__0),B),k14_trees_3(A)) ) ) ) )).

fof(t65_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => r1_tarski(k2_trees_1(np__1),k14_trees_3(A)) ) )).

fof(t66_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( r1_tarski(A,B)
           => r1_tarski(k14_trees_3(A),k14_trees_3(B)) ) ) ) )).

fof(t67_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( k14_trees_3(A) = k14_trees_3(B)
           => A = B ) ) ) )).

fof(t68_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => k4_trees_1(k14_trees_3(A),k12_finseq_1(k5_numbers,np__0)) = A ) )).

fof(t69_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => k5_trees_1(k14_trees_3(A),k12_finseq_1(k5_numbers,np__0),B) = k14_trees_3(B) ) ) )).

fof(t70_trees_3,axiom,(
    k14_trees_3(k2_trees_1(np__0)) = k2_trees_1(np__1) )).

fof(t71_trees_3,axiom,(
    ! [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,np__0),D) )
                        & ~ ( r2_hidden(D,B)
                            & C = k7_finseq_1(k12_finseq_1(k5_numbers,np__1),D) ) ) ) ) ) ) ) )).

fof(t72_trees_3,axiom,(
    ! [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,np__0),C),k15_trees_3(A,B)) ) ) ) ) )).

fof(t73_trees_3,axiom,(
    ! [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,np__1),C),k15_trees_3(A,B)) ) ) ) ) )).

fof(t74_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => r1_tarski(k2_trees_1(np__2),k15_trees_3(A,B)) ) ) )).

fof(t75_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_trees_1(D) )
                 => ( ( r1_tarski(A,C)
                      & r1_tarski(B,D) )
                   => r1_tarski(k15_trees_3(A,B),k15_trees_3(C,D)) ) ) ) ) ) )).

fof(t76_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_trees_1(D) )
                 => ( k15_trees_3(A,B) = k15_trees_3(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t77_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( k4_trees_1(k15_trees_3(A,B),k12_finseq_1(k5_numbers,np__0)) = A
            & k4_trees_1(k15_trees_3(A,B),k12_finseq_1(k5_numbers,np__1)) = B ) ) ) )).

fof(t78_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_trees_1(C) )
             => ( k5_trees_1(k15_trees_3(B,C),k12_finseq_1(k5_numbers,np__0),A) = k15_trees_3(A,C)
                & k5_trees_1(k15_trees_3(B,C),k12_finseq_1(k5_numbers,np__1),A) = k15_trees_3(B,A) ) ) ) ) )).

fof(t79_trees_3,axiom,(
    k15_trees_3(k2_trees_1(np__0),k2_trees_1(np__0)) = k2_trees_1(np__2) )).

fof(t80_trees_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B)
            & v5_trees_3(B) )
         => ( ! [C] :
                ( ( ~ v1_xboole_0(C)
                  & v1_finset_1(C)
                  & v1_trees_1(C) )
               => ( r2_hidden(C,k2_relat_1(B))
                 => r1_xreal_0(k6_trees_1(C),A) ) )
           => r1_xreal_0(k6_trees_1(k13_trees_3(B)),k1_nat_1(A,np__1)) ) ) ) )).

fof(t81_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v5_trees_3(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) )
         => ~ ( r2_hidden(B,k2_relat_1(A))
              & r1_xreal_0(k6_trees_1(k13_trees_3(A)),k6_trees_1(B)) ) ) ) )).

fof(t82_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v5_trees_3(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) )
         => ( ( r2_hidden(B,k2_relat_1(A))
              & ! [C] :
                  ( ( ~ v1_xboole_0(C)
                    & v1_finset_1(C)
                    & v1_trees_1(C) )
                 => ( r2_hidden(C,k2_relat_1(A))
                   => r1_xreal_0(k6_trees_1(C),k6_trees_1(B)) ) ) )
           => k6_trees_1(k13_trees_3(A)) = k1_nat_1(k6_trees_1(B),np__1) ) ) ) )).

fof(t83_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => k6_trees_1(k14_trees_3(A)) = k1_nat_1(k6_trees_1(A),np__1) ) )).

fof(t84_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) )
         => k6_trees_1(k15_trees_3(A,B)) = k2_xcmplx_0(k4_square_1(k6_trees_1(A),k6_trees_1(B)),np__1) ) ) )).

fof(d18_trees_3,axiom,(
    ! [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) ) ) ) ) ) ) ) ) ) )).

fof(dt_m1_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_3(A) )
     => ! [B] :
          ( m1_trees_3(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_trees_1(B) ) ) ) )).

fof(existence_m1_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_3(A) )
     => ? [B] : m1_trees_3(B,A) ) )).

fof(redefinition_m1_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_3(A) )
     => ! [B] :
          ( m1_trees_3(B,A)
        <=> m1_subset_1(B,A) ) ) )).

fof(dt_m2_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_trees_3(A) )
     => ! [B] :
          ( m2_trees_3(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_finset_1(B)
            & v1_trees_1(B) ) ) ) )).

fof(existence_m2_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_trees_3(A) )
     => ? [B] : m2_trees_3(B,A) ) )).

fof(redefinition_m2_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v2_trees_3(A) )
     => ! [B] :
          ( m2_trees_3(B,A)
        <=> m1_subset_1(B,A) ) ) )).

fof(dt_m3_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v3_trees_3(A) )
     => ! [B] :
          ( m3_trees_3(B,A)
         => ( v1_relat_1(B)
            & v1_funct_1(B)
            & v3_trees_2(B) ) ) ) )).

fof(existence_m3_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v3_trees_3(A) )
     => ? [B] : m3_trees_3(B,A) ) )).

fof(redefinition_m3_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v3_trees_3(A) )
     => ! [B] :
          ( m3_trees_3(B,A)
        <=> m1_subset_1(B,A) ) ) )).

fof(dt_m4_trees_3,axiom,(
    $true )).

fof(existence_m4_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ? [B] : m4_trees_3(B,A) ) )).

fof(dt_m5_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] :
          ( m5_trees_3(C,A,B)
         => ( v1_funct_1(C)
            & v3_trees_2(C)
            & m3_trees_2(C,A) ) ) ) )).

fof(existence_m5_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ? [C] : m5_trees_3(C,A,B) ) )).

fof(redefinition_m5_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m4_trees_3(B,A) )
     => ! [C] :
          ( m5_trees_3(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_m6_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B) )
     => ! [C] :
          ( m6_trees_3(C,A,B)
         => m3_trees_2(C,B) ) ) )).

fof(existence_m6_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B) )
     => ? [C] : m6_trees_3(C,A,B) ) )).

fof(redefinition_m6_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B) )
     => ! [C] :
          ( m6_trees_3(C,A,B)
        <=> m1_relset_1(C,A,B) ) ) )).

fof(dt_m7_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m7_trees_3(C,A,B)
         => m1_trees_1(C,A) ) ) )).

fof(existence_m7_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m7_trees_3(C,A,B) ) )).

fof(redefinition_m7_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] :
          ( m7_trees_3(C,A,B)
        <=> m1_subset_1(C,B) ) ) )).

fof(dt_m8_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( m8_trees_3(B,A)
         => m7_trees_3(B,A,k3_trees_1(A)) ) ) )).

fof(existence_m8_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ? [B] : m8_trees_3(B,A) ) )).

fof(redefinition_m8_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( m8_trees_3(B,A)
        <=> m2_trees_1(B,A) ) ) )).

fof(dt_m9_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( m9_trees_3(B,A)
         => ( ~ v1_xboole_0(B)
            & v1_trees_1(B) ) ) ) )).

fof(existence_m9_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A) )
     => ? [B] : m9_trees_3(B,A) ) )).

fof(dt_k1_trees_3,axiom,(
    $true )).

fof(dt_k2_trees_3,axiom,(
    m1_subset_1(k2_trees_3,k1_zfmisc_1(k1_trees_3)) )).

fof(dt_k3_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B) )
     => ( ~ v1_xboole_0(k3_trees_3(A,B))
        & m4_trees_3(k3_trees_3(A,B),B) ) ) )).

fof(redefinition_k3_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B) )
     => k3_trees_3(A,B) = k1_funct_2(A,B) ) )).

fof(dt_k4_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => m4_trees_3(k4_trees_3(A),A) ) )).

fof(dt_k5_trees_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => m4_trees_3(k5_trees_3(A),A) ) )).

fof(dt_k6_trees_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m3_trees_2(C,A)
        & v1_funct_1(D)
        & v3_trees_2(D)
        & m3_trees_2(D,B) )
     => ( v1_funct_1(k6_trees_3(A,B,C,D))
        & v3_trees_2(k6_trees_3(A,B,C,D))
        & m3_trees_2(k6_trees_3(A,B,C,D),k2_zfmisc_1(A,B)) ) ) )).

fof(redefinition_k6_trees_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m3_trees_2(C,A)
        & v1_funct_1(D)
        & v3_trees_2(D)
        & m3_trees_2(D,B) )
     => k6_trees_3(A,B,C,D) = k13_funct_3(C,D) ) )).

fof(dt_k7_trees_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m3_trees_2(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => ( v1_funct_1(k7_trees_3(A,B,C,D))
        & v3_trees_2(k7_trees_3(A,B,C,D))
        & m3_trees_2(k7_trees_3(A,B,C,D),B) ) ) )).

fof(redefinition_k7_trees_3,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m3_trees_2(C,A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m1_relset_1(D,A,B) )
     => k7_trees_3(A,B,C,D) = k5_relat_1(C,D) ) )).

fof(dt_k8_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( v1_funct_1(k8_trees_3(A,B))
        & v1_funct_2(k8_trees_3(A,B),k2_zfmisc_1(A,B),A)
        & m2_relset_1(k8_trees_3(A,B),k2_zfmisc_1(A,B),A) ) ) )).

fof(redefinition_k8_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => k8_trees_3(A,B) = k7_funct_3(A,B) ) )).

fof(dt_k9_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ( v1_funct_1(k9_trees_3(A,B))
        & v1_funct_2(k9_trees_3(A,B),k2_zfmisc_1(A,B),B)
        & m2_relset_1(k9_trees_3(A,B),k2_zfmisc_1(A,B),B) ) ) )).

fof(redefinition_k9_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => k9_trees_3(A,B) = k8_funct_3(A,B) ) )).

fof(dt_k10_trees_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m3_trees_2(C,k2_zfmisc_1(A,B)) )
     => ( v1_funct_1(k10_trees_3(A,B,C))
        & v3_trees_2(k10_trees_3(A,B,C))
        & m3_trees_2(k10_trees_3(A,B,C),A) ) ) )).

fof(dt_k11_trees_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v3_trees_2(C)
        & m3_trees_2(C,k2_zfmisc_1(A,B)) )
     => ( v1_funct_1(k11_trees_3(A,B,C))
        & v3_trees_2(k11_trees_3(A,B,C))
        & m3_trees_2(k11_trees_3(A,B,C),B) ) ) )).

fof(dt_k12_trees_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & m2_trees_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_trees_1(C) )
     => m9_trees_3(k12_trees_3(A,B,C),A) ) )).

fof(redefinition_k12_trees_3,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v1_trees_1(A)
        & m2_trees_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_trees_1(C) )
     => k12_trees_3(A,B,C) = k5_trees_1(A,B,C) ) )).

fof(dt_k13_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( ~ v1_xboole_0(k13_trees_3(A))
        & v1_trees_1(k13_trees_3(A)) ) ) )).

fof(dt_k14_trees_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ( ~ v1_xboole_0(k14_trees_3(A))
        & v1_trees_1(k14_trees_3(A)) ) ) )).

fof(dt_k15_trees_3,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A)
        & ~ v1_xboole_0(B)
        & v1_trees_1(B) )
     => ( ~ v1_xboole_0(k15_trees_3(A,B))
        & v1_trees_1(k15_trees_3(A,B)) ) ) )).

fof(dt_k16_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(k16_trees_3(A))
        & v1_funct_1(k16_trees_3(A))
        & v1_finseq_1(k16_trees_3(A)) ) ) )).

fof(t52_trees_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v4_trees_3(A)
       => ( k2_trees_2(k13_trees_3(A),np__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,np__1)) ) ) ) ) ) )).

fof(fraenkel_a_1_0_trees_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( r2_hidden(A,a_1_0_trees_3(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = k12_finseq_1(k5_numbers,C)
            & ~ r1_xreal_0(k3_finseq_1(B),C) ) ) ) )).
%------------------------------------------------------------------------------