SET007 Axioms: SET007+390.ax
%------------------------------------------------------------------------------
% File : SET007+390 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Defining Functions on Binary Trees
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : bintree1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 33 ( 4 unt; 0 def)
% Number of atoms : 365 ( 64 equ)
% Maximal formula atoms : 59 ( 11 avg)
% Number of connectives : 370 ( 38 ~; 0 |; 194 &)
% ( 11 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 11 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 1 prp; 0-4 aty)
% Number of functors : 61 ( 61 usr; 21 con; 0-6 aty)
% Number of variables : 140 ( 128 !; 12 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_bintree1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v1_trees_1(A)
& v1_bintree1(A) ) ).
fof(rc2_bintree1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m3_trees_2(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v3_trees_2(B)
& v2_bintree1(B) ) ) ).
fof(rc3_bintree1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v3_trees_2(A)
& v2_bintree1(A) ) ).
fof(cc1_bintree1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_trees_1(A)
& v1_bintree1(A) )
=> ( ~ v1_xboole_0(A)
& v1_trees_1(A)
& v1_trees_2(A) ) ) ).
fof(rc4_bintree1,axiom,
? [A] :
( l1_lang1(A)
& ~ v3_struct_0(A)
& v1_lang1(A)
& v1_dtconstr(A)
& v2_dtconstr(A)
& v3_dtconstr(A)
& v3_bintree1(A) ) ).
fof(cc2_bintree1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& v2_dtconstr(A)
& v3_bintree1(A)
& l1_lang1(A) )
=> ! [B] :
( m1_subset_1(B,k4_dtconstr(A))
=> v2_bintree1(B) ) ) ).
fof(d1_bintree1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,A) )
=> k1_bintree1(A,B) = k1_funct_1(B,k1_xboole_0) ) ) ).
fof(t1_bintree1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,A) )
=> k16_trees_3(k9_finseq_1(B)) = k3_lang1(A,k1_bintree1(A,B)) ) ) ).
fof(t2_bintree1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v3_trees_2(C)
& m3_trees_2(C,A) )
=> k16_trees_3(k10_finseq_1(B,C)) = k4_lang1(A,k1_bintree1(A,B),k1_bintree1(A,C)) ) ) ) ).
fof(d2_bintree1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_trees_1(A) )
=> ( v1_bintree1(A)
<=> ! [B] :
( m1_trees_1(B,A)
=> ( ~ r2_hidden(B,k3_trees_1(A))
=> k1_trees_2(A,B) = k2_tarski(k7_finseq_1(B,k3_lang1(k1_numbers,np__0)),k7_finseq_1(B,k3_lang1(k1_numbers,np__1))) ) ) ) ) ).
fof(t3_bintree1,axiom,
$true ).
fof(t4_bintree1,axiom,
$true ).
fof(t5_bintree1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_trees_1(A) )
=> ! [B] :
( m1_trees_1(B,A)
=> ( k1_trees_2(A,B) = k1_xboole_0
<=> r2_hidden(B,k3_trees_1(A)) ) ) ) ).
fof(t6_bintree1,axiom,
v1_bintree1(k2_trees_1(np__0)) ).
fof(t7_bintree1,axiom,
v1_bintree1(k2_trees_1(np__2)) ).
fof(d3_bintree1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v3_trees_2(A) )
=> ( v2_bintree1(A)
<=> v1_bintree1(k1_relat_1(A)) ) ) ).
fof(t8_bintree1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_trees_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_trees_1(B) )
=> ! [C] :
( m1_trees_1(C,k15_trees_3(A,B))
=> ( ! [D] :
( m1_trees_1(D,A)
=> ( C = k7_finseq_1(k3_lang1(k1_numbers,np__0),D)
=> ( r2_hidden(C,k3_trees_1(k15_trees_3(A,B)))
<=> r2_hidden(D,k3_trees_1(A)) ) ) )
& ! [D] :
( m1_trees_1(D,B)
=> ( C = k7_finseq_1(k3_lang1(k1_numbers,np__1),D)
=> ( r2_hidden(C,k3_trees_1(k15_trees_3(A,B)))
<=> r2_hidden(D,k3_trees_1(B)) ) ) ) ) ) ) ) ).
fof(t9_bintree1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_trees_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_trees_1(B) )
=> ! [C] :
( m1_trees_1(C,k15_trees_3(A,B))
=> ( ( C = k1_xboole_0
=> k1_trees_2(k15_trees_3(A,B),C) = k2_tarski(k7_finseq_1(C,k3_lang1(k1_numbers,np__0)),k7_finseq_1(C,k3_lang1(k1_numbers,np__1))) )
& ! [D] :
( m1_trees_1(D,A)
=> ( C = k7_finseq_1(k3_lang1(k1_numbers,np__0),D)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ( r2_hidden(E,k1_trees_2(A,D))
<=> r2_hidden(k7_finseq_1(k3_lang1(k1_numbers,np__0),E),k1_trees_2(k15_trees_3(A,B),C)) ) ) ) )
& ! [D] :
( m1_trees_1(D,B)
=> ( C = k7_finseq_1(k3_lang1(k1_numbers,np__1),D)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ( r2_hidden(E,k1_trees_2(B,D))
<=> r2_hidden(k7_finseq_1(k3_lang1(k1_numbers,np__1),E),k1_trees_2(k15_trees_3(A,B),C)) ) ) ) ) ) ) ) ) ).
fof(t10_bintree1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_trees_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_trees_1(B) )
=> ( ( v1_bintree1(A)
& v1_bintree1(B) )
<=> v1_bintree1(k15_trees_3(A,B)) ) ) ) ).
fof(t11_bintree1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v3_trees_2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v3_trees_2(B) )
=> ! [C] :
( ( v2_bintree1(A)
& v2_bintree1(B) )
<=> v2_bintree1(k6_trees_4(C,A,B)) ) ) ) ).
fof(d4_bintree1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lang1(A) )
=> ( v3_bintree1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ~ ( r1_lang1(A,B,C)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> C != k4_lang1(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ).
fof(t12_bintree1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_dtconstr(A)
& v2_dtconstr(A)
& v3_bintree1(A)
& l1_lang1(A) )
=> ! [B] :
( m1_trees_4(B,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_lang1(A,C,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),B))
=> ( m1_struct_0(C,A,k7_dtconstr(A))
& k4_finseq_1(B) = k2_tarski(np__1,np__2)
& r2_hidden(np__1,k4_finseq_1(B))
& r2_hidden(np__2,k4_finseq_1(B))
& ? [D] :
( m1_dtconstr(D,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
& ? [E] :
( m1_dtconstr(E,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A))
& k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),B) = k4_lang1(u1_struct_0(A),k1_bintree1(u1_struct_0(A),D),k1_bintree1(u1_struct_0(A),E))
& D = k1_funct_1(B,np__1)
& E = k1_funct_1(B,np__2)
& k12_trees_4(u1_struct_0(A),C,B) = k10_trees_4(u1_struct_0(A),C,D,E)
& r2_hidden(D,k2_relat_1(B))
& r2_hidden(E,k2_relat_1(B)) ) ) ) ) ) ) ) ).
fof(s1_bintree1,axiom,
? [A] :
( ~ v3_struct_0(A)
& v1_lang1(A)
& v3_bintree1(A)
& l1_lang1(A)
& u1_struct_0(A) = f1_s1_bintree1
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_lang1(A,B,k4_lang1(u1_struct_0(A),C,D))
<=> p1_s1_bintree1(B,C,D) ) ) ) ) ) ).
fof(s2_bintree1,axiom,
( ( ! [A] :
( m1_struct_0(A,f1_s2_bintree1,k6_dtconstr(f1_s2_bintree1))
=> p1_s2_bintree1(k8_dtconstr(f1_s2_bintree1,A)) )
& ! [A] :
( m1_struct_0(A,f1_s2_bintree1,k7_dtconstr(f1_s2_bintree1))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(f1_s2_bintree1),k5_trees_3(u1_struct_0(f1_s2_bintree1)),k4_dtconstr(f1_s2_bintree1))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(f1_s2_bintree1),k5_trees_3(u1_struct_0(f1_s2_bintree1)),k4_dtconstr(f1_s2_bintree1))
=> ( ( r1_lang1(f1_s2_bintree1,A,k4_lang1(u1_struct_0(f1_s2_bintree1),k1_bintree1(u1_struct_0(f1_s2_bintree1),B),k1_bintree1(u1_struct_0(f1_s2_bintree1),C)))
& p1_s2_bintree1(B)
& p1_s2_bintree1(C) )
=> p1_s2_bintree1(k10_trees_4(u1_struct_0(f1_s2_bintree1),A,B,C)) ) ) ) ) )
=> ! [A] :
( m1_dtconstr(A,u1_struct_0(f1_s2_bintree1),k5_trees_3(u1_struct_0(f1_s2_bintree1)),k4_dtconstr(f1_s2_bintree1))
=> p1_s2_bintree1(A) ) ) ).
fof(s3_bintree1,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1)
& m2_relset_1(A,k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1)
& ! [B] :
( m1_struct_0(B,f1_s3_bintree1,k6_dtconstr(f1_s3_bintree1))
=> k8_funct_2(k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1,A,k8_dtconstr(f1_s3_bintree1,B)) = f3_s3_bintree1(B) )
& ! [B] :
( m1_struct_0(B,f1_s3_bintree1,k7_dtconstr(f1_s3_bintree1))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(f1_s3_bintree1),k5_trees_3(u1_struct_0(f1_s3_bintree1)),k4_dtconstr(f1_s3_bintree1))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(f1_s3_bintree1),k5_trees_3(u1_struct_0(f1_s3_bintree1)),k4_dtconstr(f1_s3_bintree1))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f1_s3_bintree1))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(f1_s3_bintree1))
=> ( ( E = k1_bintree1(u1_struct_0(f1_s3_bintree1),C)
& F = k1_bintree1(u1_struct_0(f1_s3_bintree1),D)
& r1_lang1(f1_s3_bintree1,B,k4_lang1(u1_struct_0(f1_s3_bintree1),E,F)) )
=> ! [G] :
( m1_subset_1(G,f2_s3_bintree1)
=> ! [H] :
( m1_subset_1(H,f2_s3_bintree1)
=> ( ( G = k8_funct_2(k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1,A,C)
& H = k8_funct_2(k4_dtconstr(f1_s3_bintree1),f2_s3_bintree1,A,D) )
=> k1_funct_1(A,k10_trees_4(u1_struct_0(f1_s3_bintree1),B,C,D)) = f4_s3_bintree1(B,E,F,G,H) ) ) ) ) ) ) ) ) ) ) ).
fof(s4_bintree1,axiom,
( ( ! [A] :
( m1_struct_0(A,f1_s4_bintree1,k6_dtconstr(f1_s4_bintree1))
=> k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f3_s4_bintree1,k8_dtconstr(f1_s4_bintree1,A)) = f5_s4_bintree1(A) )
& ! [A] :
( m1_struct_0(A,f1_s4_bintree1,k7_dtconstr(f1_s4_bintree1))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f1_s4_bintree1))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f1_s4_bintree1))
=> ( ( D = k1_bintree1(u1_struct_0(f1_s4_bintree1),B)
& E = k1_bintree1(u1_struct_0(f1_s4_bintree1),C)
& r1_lang1(f1_s4_bintree1,A,k4_lang1(u1_struct_0(f1_s4_bintree1),D,E)) )
=> ! [F] :
( m1_subset_1(F,f2_s4_bintree1)
=> ! [G] :
( m1_subset_1(G,f2_s4_bintree1)
=> ( ( F = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f3_s4_bintree1,B)
& G = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f3_s4_bintree1,C) )
=> k1_funct_1(f3_s4_bintree1,k10_trees_4(u1_struct_0(f1_s4_bintree1),A,B,C)) = f6_s4_bintree1(A,D,E,F,G) ) ) ) ) ) ) ) ) )
& ! [A] :
( m1_struct_0(A,f1_s4_bintree1,k6_dtconstr(f1_s4_bintree1))
=> k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f4_s4_bintree1,k8_dtconstr(f1_s4_bintree1,A)) = f5_s4_bintree1(A) )
& ! [A] :
( m1_struct_0(A,f1_s4_bintree1,k7_dtconstr(f1_s4_bintree1))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(f1_s4_bintree1),k5_trees_3(u1_struct_0(f1_s4_bintree1)),k4_dtconstr(f1_s4_bintree1))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f1_s4_bintree1))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f1_s4_bintree1))
=> ( ( D = k1_bintree1(u1_struct_0(f1_s4_bintree1),B)
& E = k1_bintree1(u1_struct_0(f1_s4_bintree1),C)
& r1_lang1(f1_s4_bintree1,A,k4_lang1(u1_struct_0(f1_s4_bintree1),D,E)) )
=> ! [F] :
( m1_subset_1(F,f2_s4_bintree1)
=> ! [G] :
( m1_subset_1(G,f2_s4_bintree1)
=> ( ( F = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f4_s4_bintree1,B)
& G = k8_funct_2(k4_dtconstr(f1_s4_bintree1),f2_s4_bintree1,f4_s4_bintree1,C) )
=> k1_funct_1(f4_s4_bintree1,k10_trees_4(u1_struct_0(f1_s4_bintree1),A,B,C)) = f6_s4_bintree1(A,D,E,F,G) ) ) ) ) ) ) ) ) ) )
=> f3_s4_bintree1 = f4_s4_bintree1 ) ).
fof(s5_bintree1,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1))
& m2_relset_1(A,k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1))
& ! [B] :
( m1_struct_0(B,f1_s5_bintree1,k6_dtconstr(f1_s5_bintree1))
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,f2_s5_bintree1,f3_s5_bintree1)
& m2_relset_1(C,f2_s5_bintree1,f3_s5_bintree1)
& C = k8_funct_2(k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1),A,k8_dtconstr(f1_s5_bintree1,B))
& ! [D] :
( m1_subset_1(D,f2_s5_bintree1)
=> k8_funct_2(f2_s5_bintree1,f3_s5_bintree1,C,D) = f4_s5_bintree1(B,D) ) ) )
& ! [B] :
( m1_struct_0(B,f1_s5_bintree1,k7_dtconstr(f1_s5_bintree1))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(f1_s5_bintree1),k5_trees_3(u1_struct_0(f1_s5_bintree1)),k4_dtconstr(f1_s5_bintree1))
=> ! [D] :
( m1_dtconstr(D,u1_struct_0(f1_s5_bintree1),k5_trees_3(u1_struct_0(f1_s5_bintree1)),k4_dtconstr(f1_s5_bintree1))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f1_s5_bintree1))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(f1_s5_bintree1))
=> ~ ( E = k1_bintree1(u1_struct_0(f1_s5_bintree1),C)
& F = k1_bintree1(u1_struct_0(f1_s5_bintree1),D)
& r1_lang1(f1_s5_bintree1,B,k4_lang1(u1_struct_0(f1_s5_bintree1),E,F))
& ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,f2_s5_bintree1,f3_s5_bintree1)
& m2_relset_1(G,f2_s5_bintree1,f3_s5_bintree1) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,f2_s5_bintree1,f3_s5_bintree1)
& m2_relset_1(H,f2_s5_bintree1,f3_s5_bintree1) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,f2_s5_bintree1,f3_s5_bintree1)
& m2_relset_1(I,f2_s5_bintree1,f3_s5_bintree1) )
=> ~ ( G = k1_funct_1(A,k10_trees_4(u1_struct_0(f1_s5_bintree1),B,C,D))
& H = k8_funct_2(k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1),A,C)
& I = k8_funct_2(k4_dtconstr(f1_s5_bintree1),k1_funct_2(f2_s5_bintree1,f3_s5_bintree1),A,D)
& ! [J] :
( m1_subset_1(J,f2_s5_bintree1)
=> k8_funct_2(f2_s5_bintree1,f3_s5_bintree1,G,J) = f5_s5_bintree1(B,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s6_bintree1,axiom,
( ( ! [A] :
( m1_struct_0(A,f1_s6_bintree1,k6_dtconstr(f1_s6_bintree1))
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(B,f2_s6_bintree1,f3_s6_bintree1)
& B = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f4_s6_bintree1,k8_dtconstr(f1_s6_bintree1,A))
& ! [C] :
( m1_subset_1(C,f2_s6_bintree1)
=> k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,B,C) = f6_s6_bintree1(A,C) ) ) )
& ! [A] :
( m1_struct_0(A,f1_s6_bintree1,k7_dtconstr(f1_s6_bintree1))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f1_s6_bintree1))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f1_s6_bintree1))
=> ~ ( D = k1_bintree1(u1_struct_0(f1_s6_bintree1),B)
& E = k1_bintree1(u1_struct_0(f1_s6_bintree1),C)
& r1_lang1(f1_s6_bintree1,A,k4_lang1(u1_struct_0(f1_s6_bintree1),D,E))
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(F,f2_s6_bintree1,f3_s6_bintree1) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(G,f2_s6_bintree1,f3_s6_bintree1) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(H,f2_s6_bintree1,f3_s6_bintree1) )
=> ~ ( F = k1_funct_1(f4_s6_bintree1,k10_trees_4(u1_struct_0(f1_s6_bintree1),A,B,C))
& G = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f4_s6_bintree1,B)
& H = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f4_s6_bintree1,C)
& ! [I] :
( m1_subset_1(I,f2_s6_bintree1)
=> k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,F,I) = f7_s6_bintree1(A,G,H,I) ) ) ) ) ) ) ) ) ) ) )
& ! [A] :
( m1_struct_0(A,f1_s6_bintree1,k6_dtconstr(f1_s6_bintree1))
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(B,f2_s6_bintree1,f3_s6_bintree1)
& B = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f5_s6_bintree1,k8_dtconstr(f1_s6_bintree1,A))
& ! [C] :
( m1_subset_1(C,f2_s6_bintree1)
=> k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,B,C) = f6_s6_bintree1(A,C) ) ) )
& ! [A] :
( m1_struct_0(A,f1_s6_bintree1,k7_dtconstr(f1_s6_bintree1))
=> ! [B] :
( m1_dtconstr(B,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
=> ! [C] :
( m1_dtconstr(C,u1_struct_0(f1_s6_bintree1),k5_trees_3(u1_struct_0(f1_s6_bintree1)),k4_dtconstr(f1_s6_bintree1))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(f1_s6_bintree1))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(f1_s6_bintree1))
=> ~ ( D = k1_bintree1(u1_struct_0(f1_s6_bintree1),B)
& E = k1_bintree1(u1_struct_0(f1_s6_bintree1),C)
& r1_lang1(f1_s6_bintree1,A,k4_lang1(u1_struct_0(f1_s6_bintree1),D,E))
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(F,f2_s6_bintree1,f3_s6_bintree1) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(G,f2_s6_bintree1,f3_s6_bintree1) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,f2_s6_bintree1,f3_s6_bintree1)
& m2_relset_1(H,f2_s6_bintree1,f3_s6_bintree1) )
=> ~ ( F = k1_funct_1(f5_s6_bintree1,k10_trees_4(u1_struct_0(f1_s6_bintree1),A,B,C))
& G = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f5_s6_bintree1,B)
& H = k8_funct_2(k4_dtconstr(f1_s6_bintree1),k1_funct_2(f2_s6_bintree1,f3_s6_bintree1),f5_s6_bintree1,C)
& ! [I] :
( m1_subset_1(I,f2_s6_bintree1)
=> k8_funct_2(f2_s6_bintree1,f3_s6_bintree1,F,I) = f7_s6_bintree1(A,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )
=> f4_s6_bintree1 = f5_s6_bintree1 ) ).
fof(dt_k1_bintree1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v3_trees_2(B)
& m3_trees_2(B,A) )
=> m1_subset_1(k1_bintree1(A,B),A) ) ).
fof(dt_k2_bintree1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& v1_funct_1(C)
& v1_finset_1(C)
& v3_trees_2(C)
& v2_bintree1(C)
& m3_trees_2(C,A)
& v1_funct_1(D)
& v1_finset_1(D)
& v3_trees_2(D)
& v2_bintree1(D)
& m3_trees_2(D,A) )
=> ( v1_funct_1(k2_bintree1(A,B,C,D))
& v1_finset_1(k2_bintree1(A,B,C,D))
& v3_trees_2(k2_bintree1(A,B,C,D))
& v2_bintree1(k2_bintree1(A,B,C,D))
& m3_trees_2(k2_bintree1(A,B,C,D),A) ) ) ).
fof(redefinition_k2_bintree1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& v1_funct_1(C)
& v1_finset_1(C)
& v3_trees_2(C)
& v2_bintree1(C)
& m3_trees_2(C,A)
& v1_funct_1(D)
& v1_finset_1(D)
& v3_trees_2(D)
& v2_bintree1(D)
& m3_trees_2(D,A) )
=> k2_bintree1(A,B,C,D) = k6_trees_4(B,C,D) ) ).
fof(dt_k3_bintree1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,A)
& m1_subset_1(E,B)
& m1_subset_1(F,C) )
=> m1_subset_1(k3_bintree1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)) ) ).
fof(redefinition_k3_bintree1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,A)
& m1_subset_1(E,B)
& m1_subset_1(F,C) )
=> k3_bintree1(A,B,C,D,E,F) = k3_mcart_1(D,E,F) ) ).
%------------------------------------------------------------------------------