SET007 Axioms: SET007+383.ax
%------------------------------------------------------------------------------
% File : SET007+383 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Defining Functions on 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 : dtconstr [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 103 ( 4 unt; 0 def)
% Number of atoms : 668 ( 133 equ)
% Maximal formula atoms : 25 ( 6 avg)
% Number of connectives : 639 ( 74 ~; 5 |; 294 &)
% ( 33 <=>; 233 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-4 aty)
% Number of functors : 113 ( 113 usr; 36 con; 0-6 aty)
% Number of variables : 276 ( 238 !; 38 ?)
% 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(cc1_dtconstr,axiom,
! [A,B] :
( m1_subset_1(B,k3_finseq_2(A))
=> v1_finseq_1(B) ) ).
fof(cc2_dtconstr,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m4_trees_3(B,A) )
=> ! [C] :
( m1_finseq_1(C,B)
=> v6_trees_3(C) ) ) ).
fof(fc1_dtconstr,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_relset_1(B,A,k3_finseq_2(A)) )
=> ( ~ v3_struct_0(g1_lang1(A,B))
& v1_lang1(g1_lang1(A,B)) ) ) ).
fof(rc1_dtconstr,axiom,
? [A] :
( l1_lang1(A)
& ~ v3_struct_0(A)
& v1_lang1(A)
& v1_dtconstr(A)
& v2_dtconstr(A)
& v3_dtconstr(A) ) ).
fof(fc2_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& l1_lang1(A) )
=> ( ~ v1_xboole_0(k4_dtconstr(A))
& v3_trees_3(k4_dtconstr(A)) ) ) ).
fof(fc3_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_dtconstr(A)
& l1_lang1(A) )
=> ( ~ v1_xboole_0(k4_dtconstr(A))
& v3_trees_3(k4_dtconstr(A)) ) ) ).
fof(fc4_dtconstr,axiom,
( ~ v3_struct_0(k5_dtconstr)
& v1_lang1(k5_dtconstr)
& v1_dtconstr(k5_dtconstr)
& v2_dtconstr(k5_dtconstr)
& v3_dtconstr(k5_dtconstr) ) ).
fof(t1_dtconstr,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,k5_trees_3(A))
=> m2_finseq_1(B,k4_trees_3(A)) ) ) ).
fof(t2_dtconstr,axiom,
! [A,B,C] :
( m2_finseq_1(C,A)
=> ( r2_hidden(B,k5_finsop_1(C))
=> r2_hidden(k1_funct_1(C,B),A) ) ) ).
fof(t3_dtconstr,axiom,
k16_trees_3(k1_xboole_0) = k1_xboole_0 ).
fof(t4_dtconstr,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v3_trees_2(A) )
=> k16_trees_3(k9_finseq_1(A)) = k9_finseq_1(k1_funct_1(A,k1_xboole_0)) ) ).
fof(t5_dtconstr,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_trees_3(A)))
=> ! [C] :
( m1_trees_4(C,k5_trees_3(A),B)
=> ~ ( k3_finseq_1(k1_dtconstr(A,k5_trees_3(A),C)) = np__1
& ! [D] :
( m5_trees_3(D,A,k5_trees_3(A))
=> ~ ( C = k3_lang1(k5_trees_3(A),D)
& r2_hidden(D,B) ) ) ) ) ) ) ).
fof(t6_dtconstr,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) )
=> k16_trees_3(k10_finseq_1(A,B)) = k10_finseq_1(k1_funct_1(A,k1_xboole_0),k1_funct_1(B,k1_xboole_0)) ) ) ).
fof(t7_dtconstr,axiom,
( k15_mcart_1(k1_xboole_0) = k1_xboole_0
& k16_mcart_1(k1_xboole_0) = k1_xboole_0 ) ).
fof(t8_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> r1_xboole_0(k5_lang1(A),k6_lang1(A)) ) ).
fof(d1_dtconstr,axiom,
$true ).
fof(d2_dtconstr,axiom,
$true ).
fof(d3_dtconstr,axiom,
$true ).
fof(d4_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_trees_3(u1_struct_0(A))))
=> ( B = k4_dtconstr(A)
<=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k5_lang1(A))
=> r2_hidden(k2_trees_4(u1_struct_0(A),C),B) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_trees_4(D,k5_trees_3(u1_struct_0(A)),B)
=> ( r1_lang1(A,C,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),D))
=> r2_hidden(k12_trees_4(u1_struct_0(A),C,D),B) ) ) )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_trees_3(u1_struct_0(A))))
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,k5_lang1(A))
=> r2_hidden(k2_trees_4(u1_struct_0(A),D),C) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_trees_4(E,k5_trees_3(u1_struct_0(A)),C)
=> ( r1_lang1(A,D,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),E))
=> r2_hidden(k12_trees_4(u1_struct_0(A),D,E),C) ) ) ) )
=> r1_tarski(B,C) ) ) ) ) ) ) ).
fof(d5_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_lang1(A)
& l1_lang1(A) )
=> ( A = k5_dtconstr
<=> ( u1_struct_0(A) = k7_domain_1(k5_numbers,np__0,np__1)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( r1_lang1(A,B,C)
<=> ( B = np__1
& ( C = k3_lang1(k5_numbers,np__0)
| C = k3_lang1(k5_numbers,np__1) ) ) ) ) ) ) ) ) ).
fof(d6_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ( v1_dtconstr(A)
<=> k5_lang1(A) != k1_xboole_0 ) ) ).
fof(d7_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ( v2_dtconstr(A)
<=> k6_lang1(A) != k1_xboole_0 ) ) ).
fof(d8_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ( v3_dtconstr(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ( r2_hidden(B,k6_lang1(A))
& ! [C] :
( m1_trees_4(C,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ~ r1_lang1(A,B,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),C)) ) ) ) ) ) ).
fof(d9_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& v3_dtconstr(A)
& l1_lang1(A) )
=> ! [B] :
( m1_struct_0(B,A,k7_dtconstr(A))
=> ! [C] :
( m1_trees_4(C,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ( m2_dtconstr(C,A,B)
<=> r1_lang1(A,B,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),C)) ) ) ) ) ).
fof(t9_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& l1_lang1(A) )
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ! [C] :
( m1_struct_0(C,A,k6_dtconstr(A))
=> ( k1_funct_1(B,k1_xboole_0) = C
=> B = k8_dtconstr(A,C) ) ) ) ) ).
fof(t10_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& v2_dtconstr(A)
& l1_lang1(A) )
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ! [C] :
( m1_struct_0(C,A,k7_dtconstr(A))
=> ~ ( k1_funct_1(B,k1_xboole_0) = C
& ! [D] :
( m1_trees_4(D,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ~ ( B = k12_trees_4(u1_struct_0(A),C,D)
& r1_lang1(A,C,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),D)) ) ) ) ) ) ) ).
fof(d10_dtconstr,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ( A != k1_xboole_0
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k11_dtconstr(A)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& B = k1_nat_1(C,np__1)
& k1_funct_1(A,np__1) = C ) ) ) ) ) ).
fof(d11_dtconstr,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_dtconstr(k5_dtconstr),k5_numbers)
& m2_relset_1(A,k4_dtconstr(k5_dtconstr),k5_numbers) )
=> ( A = k12_dtconstr
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(k5_dtconstr))
=> ( r2_hidden(B,k6_dtconstr(k5_dtconstr))
=> k1_funct_1(A,k2_trees_4(u1_struct_0(k5_dtconstr),B)) = np__0 ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k5_dtconstr))
=> ! [C] :
( m1_trees_4(C,k5_trees_3(u1_struct_0(k5_dtconstr)),k4_dtconstr(k5_dtconstr))
=> ( r1_lang1(k5_dtconstr,B,k1_dtconstr(u1_struct_0(k5_dtconstr),k5_trees_3(u1_struct_0(k5_dtconstr)),C))
=> k1_funct_1(A,k12_trees_4(u1_struct_0(k5_dtconstr),B,C)) = k11_dtconstr(k5_finseqop(k4_dtconstr(k5_dtconstr),k5_numbers,C,A)) ) ) ) ) ) ) ).
fof(d12_dtconstr,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k5_dtconstr),k5_trees_3(u1_struct_0(k5_dtconstr)),k4_dtconstr(k5_dtconstr))
=> k13_dtconstr(A) = k4_trees_4(np__1,k3_lang1(k4_dtconstr(k5_dtconstr),A)) ) ).
fof(d13_dtconstr,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k4_dtconstr(k5_dtconstr))
& m2_relset_1(A,k5_numbers,k4_dtconstr(k5_dtconstr)) )
=> ( A = k14_dtconstr
<=> ( k8_funct_2(k5_numbers,k4_dtconstr(k5_dtconstr),A,np__0) = k2_trees_4(k5_numbers,np__0)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k4_dtconstr(k5_dtconstr),A,k1_nat_1(B,np__1)) = k13_dtconstr(k8_funct_2(k5_numbers,k4_dtconstr(k5_dtconstr),A,B)) ) ) ) ) ).
fof(t11_dtconstr,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k5_dtconstr),k5_trees_3(u1_struct_0(k5_dtconstr)),k4_dtconstr(k5_dtconstr))
=> A = k8_funct_2(k5_numbers,k4_dtconstr(k5_dtconstr),k14_dtconstr,k8_funct_2(k4_dtconstr(k5_dtconstr),k5_numbers,k12_dtconstr,A)) ) ).
fof(t12_dtconstr,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> A = k8_funct_2(k4_dtconstr(k5_dtconstr),k5_numbers,k12_dtconstr,k8_funct_2(k5_numbers,k4_dtconstr(k5_dtconstr),k14_dtconstr,A)) ) ).
fof(d14_dtconstr,axiom,
! [A,B] :
( m2_finseq_1(B,k3_finseq_2(A))
=> ! [C] :
( m2_finseq_2(C,A,k3_finseq_2(A))
=> ( C = k15_dtconstr(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k3_finseq_2(A),k3_finseq_2(A)),k3_finseq_2(A))
& m2_relset_1(D,k2_zfmisc_1(k3_finseq_2(A),k3_finseq_2(A)),k3_finseq_2(A))
& ! [E] :
( m2_finseq_2(E,A,k3_finseq_2(A))
=> ! [F] :
( m2_finseq_2(F,A,k3_finseq_2(A))
=> k2_binop_1(k3_finseq_2(A),k3_finseq_2(A),k3_finseq_2(A),D,E,F) = k1_lang1(A,E,F) ) )
& C = k2_finsop_1(k3_finseq_2(A),B,D) ) ) ) ) ).
fof(t13_dtconstr,axiom,
! [A,B] :
( m2_finseq_2(B,A,k3_finseq_2(A))
=> k15_dtconstr(A,k3_lang1(k3_finseq_2(A),B)) = B ) ).
fof(d15_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A)) )
=> ( r2_hidden(B,k4_dtconstr(A))
=> ! [C] :
( m2_finseq_1(C,k5_lang1(A))
=> ( C = k16_dtconstr(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_dtconstr(A),k3_finseq_2(k5_lang1(A)))
& m2_relset_1(D,k4_dtconstr(A),k3_finseq_2(k5_lang1(A)))
& C = k1_funct_1(D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,k5_lang1(A))
=> k1_funct_1(D,k2_trees_4(u1_struct_0(A),E)) = k3_lang1(u1_struct_0(A),E) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_trees_4(F,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ( r1_lang1(A,E,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),F))
=> k1_funct_1(D,k12_trees_4(u1_struct_0(A),E,F)) = k15_dtconstr(k5_lang1(A),k5_finseqop(k4_dtconstr(A),k3_finseq_2(k5_lang1(A)),F,D)) ) ) ) ) ) ) ) ) ) ).
fof(d16_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A)) )
=> ( r2_hidden(B,k4_dtconstr(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( C = k17_dtconstr(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_dtconstr(A),k3_finseq_2(u1_struct_0(A)))
& m2_relset_1(D,k4_dtconstr(A),k3_finseq_2(u1_struct_0(A)))
& C = k1_funct_1(D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,k5_lang1(A))
=> k1_funct_1(D,k2_trees_4(u1_struct_0(A),E)) = k3_lang1(u1_struct_0(A),E) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_trees_4(F,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ( ( G = k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),F)
& r1_lang1(A,E,G) )
=> ! [H] :
( m2_finseq_1(H,k3_finseq_2(u1_struct_0(A)))
=> ( H = k5_finseqop(k4_dtconstr(A),k3_finseq_2(u1_struct_0(A)),F,D)
=> k1_funct_1(D,k12_trees_4(u1_struct_0(A),E,F)) = k1_lang1(u1_struct_0(A),k3_lang1(u1_struct_0(A),E),k15_dtconstr(u1_struct_0(A),H)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d17_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A)) )
=> ( r2_hidden(B,k4_dtconstr(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( C = k18_dtconstr(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_dtconstr(A),k3_finseq_2(u1_struct_0(A)))
& m2_relset_1(D,k4_dtconstr(A),k3_finseq_2(u1_struct_0(A)))
& C = k1_funct_1(D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,k5_lang1(A))
=> k1_funct_1(D,k2_trees_4(u1_struct_0(A),E)) = k3_lang1(u1_struct_0(A),E) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_trees_4(F,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ( ( G = k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),F)
& r1_lang1(A,E,G) )
=> ! [H] :
( m2_finseq_1(H,k3_finseq_2(u1_struct_0(A)))
=> ( H = k5_finseqop(k4_dtconstr(A),k3_finseq_2(u1_struct_0(A)),F,D)
=> k1_funct_1(D,k12_trees_4(u1_struct_0(A),E,F)) = k1_lang1(u1_struct_0(A),k15_dtconstr(u1_struct_0(A),H),k3_lang1(u1_struct_0(A),E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_dtconstr,axiom,
! [A] :
( ( v1_funct_1(A)
& v3_trees_2(A)
& m3_trees_2(A,u1_struct_0(k5_dtconstr)) )
=> ( r2_hidden(A,k4_dtconstr(k5_dtconstr))
=> k16_dtconstr(k5_dtconstr,A) = k3_lang1(k5_numbers,np__0) ) ) ).
fof(t15_dtconstr,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_dtconstr))
=> k19_dtconstr(k5_dtconstr,A) = k6_domain_1(k3_finseq_2(k5_numbers),k3_lang1(k5_numbers,np__0)) ) ).
fof(t16_dtconstr,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k5_dtconstr),k5_trees_3(u1_struct_0(k5_dtconstr)),k4_dtconstr(k5_dtconstr))
=> k17_dtconstr(k5_dtconstr,A) = k8_finseq_1(k5_numbers,k4_finseqop(k5_numbers,k6_trees_1(k1_relat_1(A)),np__1),k3_lang1(k5_numbers,np__0)) ) ).
fof(t18_dtconstr,axiom,
! [A] :
( m1_dtconstr(A,u1_struct_0(k5_dtconstr),k5_trees_3(u1_struct_0(k5_dtconstr)),k4_dtconstr(k5_dtconstr))
=> k18_dtconstr(k5_dtconstr,A) = k8_finseq_1(k5_numbers,k3_lang1(k5_numbers,np__0),k4_finseqop(k5_numbers,k6_trees_1(k1_relat_1(A)),np__1)) ) ).
fof(s1_dtconstr,axiom,
? [A] :
( ~ v3_struct_0(A)
& v1_lang1(A)
& l1_lang1(A)
& u1_struct_0(A) = f1_s1_dtconstr
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( r1_lang1(A,B,C)
<=> p1_s1_dtconstr(B,C) ) ) ) ) ).
fof(s2_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_lang1(A)
& l1_lang1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_lang1(B)
& l1_lang1(B) )
=> ( ( u1_struct_0(A) = f1_s2_dtconstr
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( r1_lang1(A,C,D)
<=> p1_s2_dtconstr(C,D) ) ) )
& u1_struct_0(B) = f1_s2_dtconstr
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> ( r1_lang1(B,C,D)
<=> p1_s2_dtconstr(C,D) ) ) ) )
=> A = B ) ) ) ).
fof(s7_dtconstr,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s7_dtconstr))
=> ( r2_hidden(A,k5_lang1(f1_s7_dtconstr))
=> p1_s7_dtconstr(k2_trees_4(u1_struct_0(f1_s7_dtconstr),A)) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s7_dtconstr))
=> ! [B] :
( m1_trees_4(B,k5_trees_3(u1_struct_0(f1_s7_dtconstr)),k4_dtconstr(f1_s7_dtconstr))
=> ( ( r1_lang1(f1_s7_dtconstr,A,k1_dtconstr(u1_struct_0(f1_s7_dtconstr),k5_trees_3(u1_struct_0(f1_s7_dtconstr)),B))
& ! [C] :
( ( v1_funct_1(C)
& v3_trees_2(C)
& m3_trees_2(C,u1_struct_0(f1_s7_dtconstr)) )
=> ( r2_hidden(C,k2_relat_1(B))
=> p1_s7_dtconstr(C) ) ) )
=> p1_s7_dtconstr(k12_trees_4(u1_struct_0(f1_s7_dtconstr),A,B)) ) ) ) )
=> ! [A] :
( ( v1_funct_1(A)
& v3_trees_2(A)
& m3_trees_2(A,u1_struct_0(f1_s7_dtconstr)) )
=> ( r2_hidden(A,k4_dtconstr(f1_s7_dtconstr))
=> p1_s7_dtconstr(A) ) ) ) ).
fof(s8_dtconstr,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_dtconstr(f1_s8_dtconstr),f2_s8_dtconstr)
& m2_relset_1(A,k4_dtconstr(f1_s8_dtconstr),f2_s8_dtconstr)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_dtconstr))
=> ( r2_hidden(B,k5_lang1(f1_s8_dtconstr))
=> k1_funct_1(A,k2_trees_4(u1_struct_0(f1_s8_dtconstr),B)) = f3_s8_dtconstr(B) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s8_dtconstr))
=> ! [C] :
( m1_trees_4(C,k5_trees_3(u1_struct_0(f1_s8_dtconstr)),k4_dtconstr(f1_s8_dtconstr))
=> ( r1_lang1(f1_s8_dtconstr,B,k1_dtconstr(u1_struct_0(f1_s8_dtconstr),k5_trees_3(u1_struct_0(f1_s8_dtconstr)),C))
=> k1_funct_1(A,k12_trees_4(u1_struct_0(f1_s8_dtconstr),B,C)) = f4_s8_dtconstr(B,k1_dtconstr(u1_struct_0(f1_s8_dtconstr),k5_trees_3(u1_struct_0(f1_s8_dtconstr)),C),k5_finseqop(k4_dtconstr(f1_s8_dtconstr),f2_s8_dtconstr,C,A)) ) ) ) ) ).
fof(s9_dtconstr,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
=> ( r2_hidden(A,k5_lang1(f1_s9_dtconstr))
=> k1_funct_1(f5_s9_dtconstr,k2_trees_4(u1_struct_0(f1_s9_dtconstr),A)) = f3_s9_dtconstr(A) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
=> ! [B] :
( m1_trees_4(B,k5_trees_3(u1_struct_0(f1_s9_dtconstr)),k4_dtconstr(f1_s9_dtconstr))
=> ( r1_lang1(f1_s9_dtconstr,A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B))
=> k1_funct_1(f5_s9_dtconstr,k12_trees_4(u1_struct_0(f1_s9_dtconstr),A,B)) = f4_s9_dtconstr(A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B),k5_finseqop(k4_dtconstr(f1_s9_dtconstr),f2_s9_dtconstr,B,f5_s9_dtconstr)) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
=> ( r2_hidden(A,k5_lang1(f1_s9_dtconstr))
=> k1_funct_1(f6_s9_dtconstr,k2_trees_4(u1_struct_0(f1_s9_dtconstr),A)) = f3_s9_dtconstr(A) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s9_dtconstr))
=> ! [B] :
( m1_trees_4(B,k5_trees_3(u1_struct_0(f1_s9_dtconstr)),k4_dtconstr(f1_s9_dtconstr))
=> ( r1_lang1(f1_s9_dtconstr,A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B))
=> k1_funct_1(f6_s9_dtconstr,k12_trees_4(u1_struct_0(f1_s9_dtconstr),A,B)) = f4_s9_dtconstr(A,k1_dtconstr(u1_struct_0(f1_s9_dtconstr),k5_trees_3(u1_struct_0(f1_s9_dtconstr)),B),k5_finseqop(k4_dtconstr(f1_s9_dtconstr),f2_s9_dtconstr,B,f6_s9_dtconstr)) ) ) ) )
=> f5_s9_dtconstr = f6_s9_dtconstr ) ).
fof(dt_m1_dtconstr,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m4_trees_3(B,A)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ! [D] :
( m1_dtconstr(D,A,B,C)
=> m5_trees_3(D,A,B) ) ) ).
fof(existence_m1_dtconstr,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m4_trees_3(B,A)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ? [D] : m1_dtconstr(D,A,B,C) ) ).
fof(redefinition_m1_dtconstr,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m4_trees_3(B,A)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> ! [D] :
( m1_dtconstr(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_m2_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& v3_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,k7_dtconstr(A)) )
=> ! [C] :
( m2_dtconstr(C,A,B)
=> m1_trees_4(C,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ) ).
fof(existence_m2_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& v3_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,k7_dtconstr(A)) )
=> ? [C] : m2_dtconstr(C,A,B) ) ).
fof(dt_k1_dtconstr,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m4_trees_3(B,A)
& m1_finseq_1(C,B) )
=> m2_finseq_1(k1_dtconstr(A,B,C),A) ) ).
fof(redefinition_k1_dtconstr,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m4_trees_3(B,A)
& m1_finseq_1(C,B) )
=> k1_dtconstr(A,B,C) = k16_trees_3(C) ) ).
fof(dt_k2_dtconstr,axiom,
! [A,B,C] :
( m1_finseq_1(C,k2_zfmisc_1(A,B))
=> m2_finseq_1(k2_dtconstr(A,B,C),A) ) ).
fof(redefinition_k2_dtconstr,axiom,
! [A,B,C] :
( m1_finseq_1(C,k2_zfmisc_1(A,B))
=> k2_dtconstr(A,B,C) = k15_mcart_1(C) ) ).
fof(dt_k3_dtconstr,axiom,
! [A,B,C] :
( m1_finseq_1(C,k2_zfmisc_1(A,B))
=> m2_finseq_1(k3_dtconstr(A,B,C),B) ) ).
fof(redefinition_k3_dtconstr,axiom,
! [A,B,C] :
( m1_finseq_1(C,k2_zfmisc_1(A,B))
=> k3_dtconstr(A,B,C) = k16_mcart_1(C) ) ).
fof(dt_k4_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> m1_subset_1(k4_dtconstr(A),k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) ) ).
fof(dt_k5_dtconstr,axiom,
( ~ v3_struct_0(k5_dtconstr)
& v1_lang1(k5_dtconstr)
& l1_lang1(k5_dtconstr) ) ).
fof(dt_k6_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& l1_lang1(A) )
=> ( ~ v1_xboole_0(k6_dtconstr(A))
& m1_subset_1(k6_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(redefinition_k6_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& l1_lang1(A) )
=> k6_dtconstr(A) = k5_lang1(A) ) ).
fof(dt_k7_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A) )
=> ( ~ v1_xboole_0(k7_dtconstr(A))
& m1_subset_1(k7_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(redefinition_k7_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A) )
=> k7_dtconstr(A) = k6_lang1(A) ) ).
fof(dt_k8_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,k6_dtconstr(A)) )
=> m1_dtconstr(k8_dtconstr(A,B),u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ).
fof(redefinition_k8_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,k6_dtconstr(A)) )
=> k8_dtconstr(A,B) = k1_trees_4(B) ) ).
fof(dt_k9_dtconstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& v3_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,k7_dtconstr(A))
& m2_dtconstr(C,A,B) )
=> m1_dtconstr(k9_dtconstr(A,B,C),u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ).
fof(redefinition_k9_dtconstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& v3_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,k7_dtconstr(A))
& m2_dtconstr(C,A,B) )
=> k9_dtconstr(A,B,C) = k4_trees_4(B,C) ) ).
fof(dt_k10_dtconstr,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_dtconstr(k5_dtconstr))
& m1_subset_1(B,k4_dtconstr(k5_dtconstr)) )
=> m1_dtconstr(k10_dtconstr(A,B),u1_struct_0(k5_dtconstr),k5_trees_3(u1_struct_0(k5_dtconstr)),k4_dtconstr(k5_dtconstr)) ) ).
fof(redefinition_k10_dtconstr,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_dtconstr(k5_dtconstr))
& m1_subset_1(B,k4_dtconstr(k5_dtconstr)) )
=> k10_dtconstr(A,B) = k5_trees_4(A,B) ) ).
fof(dt_k11_dtconstr,axiom,
! [A] :
( m1_finseq_1(A,k5_numbers)
=> m2_subset_1(k11_dtconstr(A),k1_numbers,k5_numbers) ) ).
fof(dt_k12_dtconstr,axiom,
( v1_funct_1(k12_dtconstr)
& v1_funct_2(k12_dtconstr,k4_dtconstr(k5_dtconstr),k5_numbers)
& m2_relset_1(k12_dtconstr,k4_dtconstr(k5_dtconstr),k5_numbers) ) ).
fof(dt_k13_dtconstr,axiom,
! [A] :
( m1_subset_1(A,k4_dtconstr(k5_dtconstr))
=> m1_dtconstr(k13_dtconstr(A),u1_struct_0(k5_dtconstr),k5_trees_3(u1_struct_0(k5_dtconstr)),k4_dtconstr(k5_dtconstr)) ) ).
fof(dt_k14_dtconstr,axiom,
( v1_funct_1(k14_dtconstr)
& v1_funct_2(k14_dtconstr,k5_numbers,k4_dtconstr(k5_dtconstr))
& m2_relset_1(k14_dtconstr,k5_numbers,k4_dtconstr(k5_dtconstr)) ) ).
fof(dt_k15_dtconstr,axiom,
! [A,B] :
( m1_finseq_1(B,k3_finseq_2(A))
=> m2_finseq_2(k15_dtconstr(A,B),A,k3_finseq_2(A)) ) ).
fof(dt_k16_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_lang1(A)
& v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A)) )
=> m2_finseq_1(k16_dtconstr(A,B),k5_lang1(A)) ) ).
fof(dt_k17_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_lang1(A)
& v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A)) )
=> m2_finseq_1(k17_dtconstr(A,B),u1_struct_0(A)) ) ).
fof(dt_k18_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_lang1(A)
& v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,u1_struct_0(A)) )
=> m2_finseq_1(k18_dtconstr(A,B),u1_struct_0(A)) ) ).
fof(dt_k19_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k19_dtconstr(A,B),k1_zfmisc_1(k3_finseq_2(k5_lang1(A)))) ) ).
fof(dt_k20_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k20_dtconstr(A,B),k1_zfmisc_1(k3_finseq_2(u1_struct_0(A)))) ) ).
fof(dt_k21_dtconstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k21_dtconstr(A,B),k1_zfmisc_1(k3_finseq_2(u1_struct_0(A)))) ) ).
fof(d18_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k19_dtconstr(A,B) = a_2_0_dtconstr(A,B) ) ) ).
fof(d19_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k20_dtconstr(A,B) = a_2_1_dtconstr(A,B) ) ) ).
fof(d20_dtconstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_dtconstr(A)
& l1_lang1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k21_dtconstr(A,B) = a_2_2_dtconstr(A,B) ) ) ).
fof(t17_dtconstr,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_dtconstr))
=> ( ( A = np__0
=> k20_dtconstr(k5_dtconstr,A) = k6_domain_1(k3_finseq_2(k5_numbers),k3_lang1(k5_numbers,np__0)) )
& ( A = np__1
=> k20_dtconstr(k5_dtconstr,A) = a_0_0_dtconstr ) ) ) ).
fof(t19_dtconstr,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k5_dtconstr))
=> ( ( A = np__0
=> k21_dtconstr(k5_dtconstr,A) = k6_domain_1(k3_finseq_2(k5_numbers),k3_lang1(k5_numbers,np__0)) )
& ( A = np__1
=> k21_dtconstr(k5_dtconstr,A) = a_0_1_dtconstr ) ) ) ).
fof(s3_dtconstr,axiom,
( ( k1_relat_1(f1_s3_dtconstr) = k5_numbers
& k1_funct_1(f1_s3_dtconstr,np__0) = a_0_2_dtconstr
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_funct_1(f1_s3_dtconstr,k1_nat_1(A,np__1)) = k2_xboole_0(k1_funct_1(f1_s3_dtconstr,A),a_1_0_dtconstr(A)) ) )
=> ? [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr))))
& A = k3_card_3(f1_s3_dtconstr)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s3_dtconstr))
=> ( r2_hidden(B,k5_lang1(f2_s3_dtconstr))
=> r2_hidden(k2_trees_4(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k1_domain_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,B,f4_s3_dtconstr(B))),A) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s3_dtconstr))
=> ! [C] :
( m1_trees_4(C,k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),A)
=> ( r1_lang1(f2_s3_dtconstr,B,k2_dtconstr(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),C)))
=> r2_hidden(k12_trees_4(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k1_domain_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,B,f5_s3_dtconstr(B,k2_dtconstr(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),C)),k3_dtconstr(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),C)))),C),A) ) ) )
& ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr))))
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s3_dtconstr))
=> ( r2_hidden(C,k5_lang1(f2_s3_dtconstr))
=> r2_hidden(k2_trees_4(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k1_domain_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,C,f4_s3_dtconstr(C))),B) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s3_dtconstr))
=> ! [D] :
( m1_trees_4(D,k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),B)
=> ( r1_lang1(f2_s3_dtconstr,C,k2_dtconstr(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),D)))
=> r2_hidden(k12_trees_4(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k1_domain_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,C,f5_s3_dtconstr(C,k2_dtconstr(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),D)),k3_dtconstr(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),D)))),D),B) ) ) ) )
=> r1_tarski(A,B) ) ) ) ) ).
fof(s4_dtconstr,axiom,
( ( k1_relat_1(f1_s4_dtconstr) = k5_numbers
& k1_funct_1(f1_s4_dtconstr,np__0) = a_0_3_dtconstr
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_funct_1(f1_s4_dtconstr,k1_nat_1(A,np__1)) = k2_xboole_0(k1_funct_1(f1_s4_dtconstr,A),a_1_1_dtconstr(A)) ) )
=> ? [A] :
( m1_subset_1(A,k1_zfmisc_1(k5_trees_3(u1_struct_0(f2_s4_dtconstr))))
& A = a_0_4_dtconstr
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s4_dtconstr))
=> ( r2_hidden(B,k5_lang1(f2_s4_dtconstr))
=> r2_hidden(k2_trees_4(u1_struct_0(f2_s4_dtconstr),B),A) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s4_dtconstr))
=> ! [C] :
( m1_trees_4(C,k5_trees_3(u1_struct_0(f2_s4_dtconstr)),A)
=> ( r1_lang1(f2_s4_dtconstr,B,k1_dtconstr(u1_struct_0(f2_s4_dtconstr),k5_trees_3(u1_struct_0(f2_s4_dtconstr)),C))
=> r2_hidden(k12_trees_4(u1_struct_0(f2_s4_dtconstr),B,C),A) ) ) )
& ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k5_trees_3(u1_struct_0(f2_s4_dtconstr))))
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s4_dtconstr))
=> ( r2_hidden(C,k5_lang1(f2_s4_dtconstr))
=> r2_hidden(k2_trees_4(u1_struct_0(f2_s4_dtconstr),C),B) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(f2_s4_dtconstr))
=> ! [D] :
( m1_trees_4(D,k5_trees_3(u1_struct_0(f2_s4_dtconstr)),B)
=> ( r1_lang1(f2_s4_dtconstr,C,k1_dtconstr(u1_struct_0(f2_s4_dtconstr),k5_trees_3(u1_struct_0(f2_s4_dtconstr)),D))
=> r2_hidden(k12_trees_4(u1_struct_0(f2_s4_dtconstr),C,D),B) ) ) ) )
=> r1_tarski(A,B) ) ) ) ) ).
fof(s5_dtconstr,axiom,
( ( k1_relat_1(f1_s5_dtconstr) = k5_numbers
& k1_funct_1(f1_s5_dtconstr,np__0) = a_0_5_dtconstr
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_funct_1(f1_s5_dtconstr,k1_nat_1(A,np__1)) = k2_xboole_0(k1_funct_1(f1_s5_dtconstr,A),a_1_2_dtconstr(A)) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m5_trees_3(B,k2_zfmisc_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr)))
=> ( r2_hidden(B,k3_card_3(f1_s5_dtconstr))
=> ( r2_hidden(B,k1_funct_1(f1_s5_dtconstr,A))
<=> r1_xreal_0(k6_trees_1(k1_relat_1(B)),A) ) ) ) ) ) ).
fof(s6_dtconstr,axiom,
( ( k1_relat_1(f1_s6_dtconstr) = k5_numbers
& k1_funct_1(f1_s6_dtconstr,np__0) = a_0_6_dtconstr
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_funct_1(f1_s6_dtconstr,k1_nat_1(A,np__1)) = k2_xboole_0(k1_funct_1(f1_s6_dtconstr,A),a_1_3_dtconstr(A)) ) )
=> ! [A] :
( ( v1_funct_1(A)
& v3_trees_2(A)
& m3_trees_2(A,k2_zfmisc_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr)) )
=> ! [B] :
( ( v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,k2_zfmisc_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr)) )
=> ( ( r2_hidden(A,k3_card_3(f1_s6_dtconstr))
& r2_hidden(B,k3_card_3(f1_s6_dtconstr))
& k10_trees_3(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr,A) = k10_trees_3(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr,B) )
=> A = B ) ) ) ) ).
fof(fraenkel_a_2_0_dtconstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_dtconstr(B)
& l1_lang1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_dtconstr(B,C))
<=> ? [D] :
( m5_trees_3(D,u1_struct_0(B),k5_trees_3(u1_struct_0(B)))
& A = k16_dtconstr(B,D)
& r2_hidden(D,k4_dtconstr(B))
& k1_funct_1(D,k1_xboole_0) = C ) ) ) ).
fof(fraenkel_a_2_1_dtconstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_dtconstr(B)
& l1_lang1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_1_dtconstr(B,C))
<=> ? [D] :
( m5_trees_3(D,u1_struct_0(B),k5_trees_3(u1_struct_0(B)))
& A = k17_dtconstr(B,D)
& r2_hidden(D,k4_dtconstr(B))
& k1_funct_1(D,k1_xboole_0) = C ) ) ) ).
fof(fraenkel_a_2_2_dtconstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_dtconstr(B)
& l1_lang1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_2_dtconstr(B,C))
<=> ? [D] :
( m5_trees_3(D,u1_struct_0(B),k5_trees_3(u1_struct_0(B)))
& A = k18_dtconstr(B,D)
& r2_hidden(D,k4_dtconstr(B))
& k1_funct_1(D,k1_xboole_0) = C ) ) ) ).
fof(fraenkel_a_0_0_dtconstr,axiom,
! [A] :
( r2_hidden(A,a_0_0_dtconstr)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k8_finseq_1(k5_numbers,k4_finseqop(k5_numbers,B,np__1),k3_lang1(k5_numbers,np__0))
& B != np__0 ) ) ).
fof(fraenkel_a_0_1_dtconstr,axiom,
! [A] :
( r2_hidden(A,a_0_1_dtconstr)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k8_finseq_1(k5_numbers,k3_lang1(k5_numbers,np__0),k4_finseqop(k5_numbers,B,np__1))
& B != np__0 ) ) ).
fof(fraenkel_a_0_2_dtconstr,axiom,
! [A] :
( r2_hidden(A,a_0_2_dtconstr)
<=> ? [B,C] :
( m1_subset_1(B,u1_struct_0(f2_s3_dtconstr))
& m1_subset_1(C,f3_s3_dtconstr)
& A = k2_trees_4(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k1_domain_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,B,C))
& ( ( r2_hidden(B,k5_lang1(f2_s3_dtconstr))
& C = f4_s3_dtconstr(B) )
| ( r1_lang1(f2_s3_dtconstr,B,k1_xboole_0)
& C = f5_s3_dtconstr(B,k1_xboole_0,k1_xboole_0) ) ) ) ) ).
fof(fraenkel_a_1_0_dtconstr,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,a_1_0_dtconstr(B))
<=> ? [C,D] :
( m1_subset_1(C,u1_struct_0(f2_s3_dtconstr))
& m2_finseq_2(D,k1_funct_1(f1_s3_dtconstr,B),k3_finseq_2(k1_funct_1(f1_s3_dtconstr,B)))
& A = k4_trees_4(k1_domain_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,C,f5_s3_dtconstr(C,k15_mcart_1(k16_trees_3(D)),k16_mcart_1(k16_trees_3(D)))),D)
& ? [E] :
( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)))
& D = E
& r1_lang1(f2_s3_dtconstr,C,k2_dtconstr(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s3_dtconstr),f3_s3_dtconstr)),E))) ) ) ) ) ).
fof(fraenkel_a_0_3_dtconstr,axiom,
! [A] :
( r2_hidden(A,a_0_3_dtconstr)
<=> ? [B,C] :
( m1_subset_1(B,u1_struct_0(f2_s4_dtconstr))
& m1_subset_1(C,f3_s4_dtconstr)
& A = k2_trees_4(k2_zfmisc_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr),k1_domain_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr,B,C))
& ( ( r2_hidden(B,k5_lang1(f2_s4_dtconstr))
& C = f4_s4_dtconstr(B) )
| ( r1_lang1(f2_s4_dtconstr,B,k1_xboole_0)
& C = f5_s4_dtconstr(B,k1_xboole_0,k1_xboole_0) ) ) ) ) ).
fof(fraenkel_a_1_1_dtconstr,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,a_1_1_dtconstr(B))
<=> ? [C,D] :
( m1_subset_1(C,u1_struct_0(f2_s4_dtconstr))
& m2_finseq_2(D,k1_funct_1(f1_s4_dtconstr,B),k3_finseq_2(k1_funct_1(f1_s4_dtconstr,B)))
& A = k4_trees_4(k1_domain_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr,C,f5_s4_dtconstr(C,k15_mcart_1(k16_trees_3(D)),k16_mcart_1(k16_trees_3(D)))),D)
& ? [E] :
( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr)))
& D = E
& r1_lang1(f2_s4_dtconstr,C,k2_dtconstr(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr)),E))) ) ) ) ) ).
fof(fraenkel_a_0_4_dtconstr,axiom,
! [A] :
( r2_hidden(A,a_0_4_dtconstr)
<=> ? [B] :
( m5_trees_3(B,k2_zfmisc_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr)))
& A = k10_trees_3(u1_struct_0(f2_s4_dtconstr),f3_s4_dtconstr,B)
& r2_hidden(B,k3_card_3(f1_s4_dtconstr)) ) ) ).
fof(fraenkel_a_0_5_dtconstr,axiom,
! [A] :
( r2_hidden(A,a_0_5_dtconstr)
<=> ? [B,C] :
( m1_subset_1(B,u1_struct_0(f2_s5_dtconstr))
& m1_subset_1(C,f3_s5_dtconstr)
& A = k2_trees_4(k2_zfmisc_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr),k1_domain_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr,B,C))
& ( ( r2_hidden(B,k5_lang1(f2_s5_dtconstr))
& C = f4_s5_dtconstr(B) )
| ( r1_lang1(f2_s5_dtconstr,B,k1_xboole_0)
& C = f5_s5_dtconstr(B,k1_xboole_0,k1_xboole_0) ) ) ) ) ).
fof(fraenkel_a_1_2_dtconstr,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,a_1_2_dtconstr(B))
<=> ? [C,D] :
( m1_subset_1(C,u1_struct_0(f2_s5_dtconstr))
& m2_finseq_2(D,k1_funct_1(f1_s5_dtconstr,B),k3_finseq_2(k1_funct_1(f1_s5_dtconstr,B)))
& A = k4_trees_4(k1_domain_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr,C,f5_s5_dtconstr(C,k15_mcart_1(k16_trees_3(D)),k16_mcart_1(k16_trees_3(D)))),D)
& ? [E] :
( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr)))
& D = E
& r1_lang1(f2_s5_dtconstr,C,k2_dtconstr(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s5_dtconstr),f3_s5_dtconstr)),E))) ) ) ) ) ).
fof(fraenkel_a_0_6_dtconstr,axiom,
! [A] :
( r2_hidden(A,a_0_6_dtconstr)
<=> ? [B,C] :
( m1_subset_1(B,u1_struct_0(f2_s6_dtconstr))
& m1_subset_1(C,f3_s6_dtconstr)
& A = k2_trees_4(k2_zfmisc_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr),k1_domain_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr,B,C))
& ( ( r2_hidden(B,k5_lang1(f2_s6_dtconstr))
& C = f4_s6_dtconstr(B) )
| ( r1_lang1(f2_s6_dtconstr,B,k1_xboole_0)
& C = f5_s6_dtconstr(B,k1_xboole_0,k1_xboole_0) ) ) ) ) ).
fof(fraenkel_a_1_3_dtconstr,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(A,a_1_3_dtconstr(B))
<=> ? [C,D] :
( m1_subset_1(C,u1_struct_0(f2_s6_dtconstr))
& m2_finseq_2(D,k1_funct_1(f1_s6_dtconstr,B),k3_finseq_2(k1_funct_1(f1_s6_dtconstr,B)))
& A = k4_trees_4(k1_domain_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr,C,f5_s6_dtconstr(C,k15_mcart_1(k16_trees_3(D)),k16_mcart_1(k16_trees_3(D)))),D)
& ? [E] :
( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr)))
& D = E
& r1_lang1(f2_s6_dtconstr,C,k2_dtconstr(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr,k1_dtconstr(k2_zfmisc_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr),k5_trees_3(k2_zfmisc_1(u1_struct_0(f2_s6_dtconstr),f3_s6_dtconstr)),E))) ) ) ) ) ).
%------------------------------------------------------------------------------