SET007 Axioms: SET007+163.ax
%------------------------------------------------------------------------------
% File : SET007+163 : TPTP v9.0.0. 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 unt; 0 def)
% Number of atoms : 1147 ( 69 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1193 ( 241 ~; 0 |; 611 &)
% ( 59 <=>; 282 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 8 con; 0-4 aty)
% Number of variables : 381 ( 362 !; 19 ?)
% 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) ) ) ) ).
%------------------------------------------------------------------------------