SET007 Axioms: SET007+386.ax
%------------------------------------------------------------------------------
% File : SET007+386 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Free Universal Algebra Construction
% 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 : freealg [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 70 ( 1 unt; 0 def)
% Number of atoms : 479 ( 38 equ)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 538 ( 129 ~; 0 |; 274 &)
% ( 14 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 4 con; 0-5 aty)
% Number of variables : 170 ( 158 !; 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_freealg,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_freealg(A) ) ).
fof(rc2_freealg,axiom,
? [A] :
( m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& ~ v2_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A) ) ).
fof(rc3_freealg,axiom,
? [A] :
( m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A) ) ).
fof(rc4_freealg,axiom,
? [A] :
( l1_unialg_1(A)
& ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v3_freealg(A) ) ).
fof(rc5_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v3_freealg(A)
& l1_unialg_1(A) )
=> ? [B] :
( m1_freealg(B,A)
& v2_freealg(B,A) ) ) ).
fof(fc1_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers) )
=> ( ~ v3_struct_0(k3_freealg(A,B))
& v1_lang1(k3_freealg(A,B)) ) ) ).
fof(fc2_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers) )
=> ( ~ v3_struct_0(k3_freealg(A,B))
& v1_lang1(k3_freealg(A,B))
& v2_dtconstr(k3_freealg(A,B)) ) ) ).
fof(fc3_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers) )
=> ( ~ v3_struct_0(k3_freealg(A,B))
& v1_lang1(k3_freealg(A,B))
& v2_dtconstr(k3_freealg(A,B))
& v3_dtconstr(k3_freealg(A,B)) ) ) ).
fof(fc4_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ( ~ v3_struct_0(k3_freealg(A,B))
& v1_lang1(k3_freealg(A,B))
& v1_dtconstr(k3_freealg(A,B))
& v2_dtconstr(k3_freealg(A,B))
& v3_dtconstr(k3_freealg(A,B)) ) ) ).
fof(fc5_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ( ~ v3_struct_0(k7_freealg(A,B))
& v3_unialg_1(k7_freealg(A,B))
& v6_unialg_1(k7_freealg(A,B))
& v7_unialg_1(k7_freealg(A,B))
& v8_unialg_1(k7_freealg(A,B))
& v3_freealg(k7_freealg(A,B)) ) ) ).
fof(fc6_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> ( ~ v3_struct_0(k15_freealg(A,B))
& v3_unialg_1(k15_freealg(A,B))
& v6_unialg_1(k15_freealg(A,B))
& v7_unialg_1(k15_freealg(A,B))
& v8_unialg_1(k15_freealg(A,B))
& v3_freealg(k15_freealg(A,B)) ) ) ).
fof(rc6_freealg,axiom,
? [A] :
( l1_unialg_1(A)
& ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& v3_freealg(A) ) ).
fof(d1_freealg,axiom,
! [A] :
( v1_freealg(A)
<=> r1_xboole_0(A,k5_numbers) ) ).
fof(d2_freealg,axiom,
! [A] :
( v1_relat_1(A)
=> ( v2_relat_1(A)
<=> ~ r2_hidden(np__0,k2_relat_1(A)) ) ) ).
fof(d3_freealg,axiom,
$true ).
fof(d4_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k4_finseq_1(u1_unialg_1(A)))
=> k1_freealg(A,B) = k1_funct_1(u1_unialg_1(A),B) ) ) ) ).
fof(d5_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_freealg(B,A)
<=> u1_struct_0(k7_unialg_2(A,B)) = u1_struct_0(A) ) ) ) ).
fof(d6_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_freealg(B,A)
=> ( v2_freealg(B,A)
<=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_unialg_1(C)
& v7_unialg_1(C)
& v8_unialg_1(C)
& l1_unialg_1(C) )
=> ( r1_unialg_2(A,C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(C))
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C))
& r1_alg_1(A,C,E)
& k2_partfun1(u1_struct_0(A),u1_struct_0(C),E,B) = D ) ) ) ) ) ) ) ).
fof(d7_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v3_freealg(A)
<=> ? [B] :
( m1_freealg(B,A)
& v2_freealg(B,A) ) ) ) ).
fof(t1_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_freealg(B,A)
<=> k7_unialg_2(A,B) = A ) ) ) ).
fof(d8_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B,C] :
( m2_relset_1(C,k2_xboole_0(k4_finseq_1(A),B),k3_finseq_2(k2_xboole_0(k4_finseq_1(A),B)))
=> ( C = k2_freealg(A,B)
<=> ! [D] :
( m1_subset_1(D,k2_xboole_0(k4_finseq_1(A),B))
=> ! [E] :
( m2_finseq_2(E,k2_xboole_0(k4_finseq_1(A),B),k3_finseq_2(k2_xboole_0(k4_finseq_1(A),B)))
=> ( r2_hidden(k4_tarski(D,E),C)
<=> ( r2_hidden(D,k4_finseq_1(A))
& k1_funct_1(A,D) = k3_finseq_1(E) ) ) ) ) ) ) ) ).
fof(d9_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] : k3_freealg(A,B) = g1_lang1(k2_xboole_0(k4_finseq_1(A),B),k2_freealg(A,B)) ) ).
fof(t2_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( r1_tarski(k5_lang1(k3_freealg(A,B)),B)
& k6_lang1(k3_freealg(A,B)) = k4_finseq_1(A) ) ) ).
fof(t3_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> k5_lang1(k3_freealg(A,B)) = B ) ) ).
fof(d10_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B,C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(A))
=> k4_freealg(A,B,C) = C ) ) ) ).
fof(d11_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(A))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_funct_1(D)
& v1_unialg_1(D,k4_dtconstr(k3_freealg(A,B)))
& v2_unialg_1(D,k4_dtconstr(k3_freealg(A,B)))
& m2_relset_1(D,k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))) )
=> ( D = k5_freealg(A,B,C)
<=> ( k4_relset_1(k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)),D) = k4_finseq_2(k4_finseq_4(k5_numbers,k5_numbers,A,C),k4_dtconstr(k3_freealg(A,B)))
& ! [E] :
( m1_trees_4(E,k5_trees_3(u1_struct_0(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)))
=> ( r2_hidden(E,k4_relset_1(k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)),D))
=> k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k3_freealg(A,B)),k4_freealg(A,B,C),E) ) ) ) ) ) ) ) ) ) ).
fof(d12_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ! [C] :
( m2_finseq_1(C,k4_partfun1(k13_finseq_1(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))))
=> ( C = k6_freealg(A,B)
<=> ( k3_finseq_1(C) = k3_finseq_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(C))
=> k1_funct_1(C,D) = k5_freealg(A,B,D) ) ) ) ) ) ) ) ).
fof(d13_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> k7_freealg(A,B) = g1_unialg_1(k4_dtconstr(k3_freealg(A,B)),k6_freealg(A,B)) ) ) ).
fof(t4_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> k3_unialg_1(k7_freealg(A,B)) = A ) ) ).
fof(t5_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ~ v1_xboole_0(k8_freealg(A,B)) ) ) ).
fof(d15_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_freealg(A,B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k9_freealg(A,B),C)
& m2_relset_1(E,k9_freealg(A,B),C) )
=> ( r2_hidden(D,k6_dtconstr(k3_freealg(A,B)))
=> k10_freealg(A,B,C,D,E) = k1_funct_1(E,k2_trees_4(u1_struct_0(k3_freealg(A,B)),D)) ) ) ) ) ) ) ).
fof(d16_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B,C] :
( m1_subset_1(C,u1_struct_0(k3_freealg(A,B)))
=> ( ? [D] :
( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D)
& r1_lang1(k3_freealg(A,B),C,D) )
=> k11_freealg(A,B,C) = C ) ) ) ).
fof(t6_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> v2_freealg(k9_freealg(A,B),k7_freealg(A,B)) ) ) ).
fof(d17_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(A))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_funct_1(D)
& v1_unialg_1(D,k4_dtconstr(k3_freealg(A,B)))
& v2_unialg_1(D,k4_dtconstr(k3_freealg(A,B)))
& m2_relset_1(D,k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))) )
=> ( D = k13_freealg(A,B,C)
<=> ( k4_relset_1(k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)),D) = k4_finseq_2(k4_finseq_4(k5_numbers,k5_numbers,A,C),k4_dtconstr(k3_freealg(A,B)))
& ! [E] :
( m1_trees_4(E,k5_trees_3(u1_struct_0(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)))
=> ( r2_hidden(E,k4_relset_1(k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)),D))
=> k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k3_freealg(A,B)),k4_freealg(A,B,C),E) ) ) ) ) ) ) ) ) ) ).
fof(d18_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> ! [C] :
( m2_finseq_1(C,k4_partfun1(k13_finseq_1(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))))
=> ( C = k14_freealg(A,B)
<=> ( k3_finseq_1(C) = k3_finseq_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(C))
=> k1_funct_1(C,D) = k13_freealg(A,B,D) ) ) ) ) ) ) ) ).
fof(d19_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> k15_freealg(A,B) = g1_unialg_1(k4_dtconstr(k3_freealg(A,B)),k14_freealg(A,B)) ) ) ).
fof(t7_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> k3_unialg_1(k15_freealg(A,B)) = A ) ) ).
fof(t8_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> v2_unialg_2(k15_freealg(A,B)) ) ) ).
fof(t9_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> k6_unialg_2(k15_freealg(A,B)) != k1_xboole_0 ) ) ).
fof(d21_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_freealg(A,B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k17_freealg(A,B),C)
& m2_relset_1(E,k17_freealg(A,B),C) )
=> ( r2_hidden(D,k5_lang1(k3_freealg(A,B)))
=> k18_freealg(A,B,C,D,E) = k1_funct_1(E,k2_trees_4(u1_struct_0(k3_freealg(A,B)),D)) ) ) ) ) ) ) ).
fof(t10_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> v2_freealg(k17_freealg(A,B),k15_freealg(A,B)) ) ) ).
fof(dt_m1_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_freealg(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_freealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ? [B] : m1_freealg(B,A) ) ).
fof(dt_k1_freealg,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m1_subset_1(B,k5_numbers) )
=> m2_unialg_2(k1_freealg(A,B),u1_struct_0(A),k1_unialg_2(A)) ) ).
fof(dt_k2_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers) )
=> m2_relset_1(k2_freealg(A,B),k2_xboole_0(k4_finseq_1(A),B),k3_finseq_2(k2_xboole_0(k4_finseq_1(A),B))) ) ).
fof(dt_k3_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers) )
=> ( v1_lang1(k3_freealg(A,B))
& l1_lang1(k3_freealg(A,B)) ) ) ).
fof(dt_k4_freealg,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k4_freealg(A,B,C),u1_struct_0(k3_freealg(A,B))) ) ).
fof(dt_k5_freealg,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_xboole_0(k5_freealg(A,B,C))
& v1_funct_1(k5_freealg(A,B,C))
& v1_unialg_1(k5_freealg(A,B,C),k4_dtconstr(k3_freealg(A,B)))
& v2_unialg_1(k5_freealg(A,B,C),k4_dtconstr(k3_freealg(A,B)))
& m2_relset_1(k5_freealg(A,B,C),k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))) ) ) ).
fof(dt_k6_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> m2_finseq_1(k6_freealg(A,B),k4_partfun1(k13_finseq_1(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)))) ) ).
fof(dt_k7_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ( ~ v3_struct_0(k7_freealg(A,B))
& v3_unialg_1(k7_freealg(A,B))
& v6_unialg_1(k7_freealg(A,B))
& v7_unialg_1(k7_freealg(A,B))
& v8_unialg_1(k7_freealg(A,B))
& l1_unialg_1(k7_freealg(A,B)) ) ) ).
fof(dt_k8_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> m1_subset_1(k8_freealg(A,B),k1_zfmisc_1(u1_struct_0(k7_freealg(A,B)))) ) ).
fof(dt_k9_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> m1_freealg(k9_freealg(A,B),k7_freealg(A,B)) ) ).
fof(redefinition_k9_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> k9_freealg(A,B) = k8_freealg(A,B) ) ).
fof(dt_k10_freealg,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,u1_struct_0(k3_freealg(A,B)))
& v1_funct_1(E)
& v1_funct_2(E,k9_freealg(A,B),C)
& m1_relset_1(E,k9_freealg(A,B),C) )
=> m1_subset_1(k10_freealg(A,B,C,D,E),C) ) ).
fof(dt_k11_freealg,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& m1_subset_1(C,u1_struct_0(k3_freealg(A,B))) )
=> m2_subset_1(k11_freealg(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k12_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> ( v2_freealg(k12_freealg(A,B),k7_freealg(A,B))
& m1_freealg(k12_freealg(A,B),k7_freealg(A,B)) ) ) ).
fof(redefinition_k12_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& v1_freealg(B) )
=> k12_freealg(A,B) = k8_freealg(A,B) ) ).
fof(dt_k13_freealg,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_xboole_0(k13_freealg(A,B,C))
& v1_funct_1(k13_freealg(A,B,C))
& v1_unialg_1(k13_freealg(A,B,C),k4_dtconstr(k3_freealg(A,B)))
& v2_unialg_1(k13_freealg(A,B,C),k4_dtconstr(k3_freealg(A,B)))
& m2_relset_1(k13_freealg(A,B,C),k3_finseq_2(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B))) ) ) ).
fof(dt_k14_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> m2_finseq_1(k14_freealg(A,B),k4_partfun1(k13_finseq_1(k4_dtconstr(k3_freealg(A,B))),k4_dtconstr(k3_freealg(A,B)))) ) ).
fof(dt_k15_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> ( ~ v3_struct_0(k15_freealg(A,B))
& v3_unialg_1(k15_freealg(A,B))
& v6_unialg_1(k15_freealg(A,B))
& v7_unialg_1(k15_freealg(A,B))
& v8_unialg_1(k15_freealg(A,B))
& l1_unialg_1(k15_freealg(A,B)) ) ) ).
fof(dt_k16_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> m1_subset_1(k16_freealg(A,B),k1_zfmisc_1(u1_struct_0(k15_freealg(A,B)))) ) ).
fof(dt_k17_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> m1_freealg(k17_freealg(A,B),k15_freealg(A,B)) ) ).
fof(redefinition_k17_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> k17_freealg(A,B) = k16_freealg(A,B) ) ).
fof(dt_k18_freealg,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B)
& ~ v1_xboole_0(C)
& m1_subset_1(D,u1_struct_0(k3_freealg(A,B)))
& v1_funct_1(E)
& v1_funct_2(E,k17_freealg(A,B),C)
& m1_relset_1(E,k17_freealg(A,B),C) )
=> m1_subset_1(k18_freealg(A,B,C,D,E),C) ) ).
fof(dt_k19_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> ( v2_freealg(k19_freealg(A,B),k15_freealg(A,B))
& m1_freealg(k19_freealg(A,B),k15_freealg(A,B)) ) ) ).
fof(redefinition_k19_freealg,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_finseq_1(A,k5_numbers)
& v1_freealg(B) )
=> k19_freealg(A,B) = k16_freealg(A,B) ) ).
fof(d14_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_freealg(B) )
=> k8_freealg(A,B) = a_2_0_freealg(A,B) ) ) ).
fof(d20_freealg,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_relat_1(A)
& m1_trees_4(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_freealg(B)
=> k16_freealg(A,B) = a_2_1_freealg(A,B) ) ) ).
fof(fraenkel_a_2_0_freealg,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& m1_trees_4(B,k1_numbers,k5_numbers)
& ~ v1_xboole_0(C)
& v1_freealg(C) )
=> ( r2_hidden(A,a_2_0_freealg(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k3_freealg(B,C)))
& A = k2_trees_4(u1_struct_0(k3_freealg(B,C)),D)
& r2_hidden(D,k6_dtconstr(k3_freealg(B,C))) ) ) ) ).
fof(fraenkel_a_2_1_freealg,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& ~ v2_relat_1(B)
& m1_trees_4(B,k1_numbers,k5_numbers)
& v1_freealg(C) )
=> ( r2_hidden(A,a_2_1_freealg(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k3_freealg(B,C)))
& A = k2_trees_4(u1_struct_0(k3_freealg(B,C)),D)
& r2_hidden(D,k5_lang1(k3_freealg(B,C))) ) ) ) ).
%------------------------------------------------------------------------------