SET007 Axioms: SET007+554.ax
%------------------------------------------------------------------------------
% File : SET007+554 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Product of the Families of the Groups
% 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 : group_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 113 ( 0 unt; 0 def)
% Number of atoms : 986 ( 82 equ)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 1065 ( 192 ~; 0 |; 645 &)
% ( 10 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 30 ( 29 usr; 0 prp; 1-3 aty)
% Number of functors : 48 ( 48 usr; 4 con; 0-6 aty)
% Number of variables : 326 ( 320 !; 6 ?)
% 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_group_7,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_group_7(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_pralg_1(A) ) ) ).
fof(rc1_group_7,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_pralg_1(B)
& v1_group_7(B) ) ).
fof(rc2_group_7,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_pralg_1(A)
& v1_group_7(A) ) ).
fof(fc1_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v1_relat_1(k12_pralg_1(A,B))
& v2_relat_1(k12_pralg_1(A,B))
& v1_funct_1(k12_pralg_1(A,B)) ) ) ).
fof(fc2_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k2_group_7(A,B))
& v1_group_1(k2_group_7(A,B))
& v1_monoid_0(k2_group_7(A,B)) ) ) ).
fof(rc3_group_7,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v2_pralg_1(B)
& v1_group_7(B)
& v2_group_7(B,A)
& v3_group_7(B,A)
& v4_group_7(B,A) ) ).
fof(fc3_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& v2_group_7(B,A)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k2_group_7(A,B))
& v1_group_1(k2_group_7(A,B))
& v2_group_1(k2_group_7(A,B))
& v3_group_1(k2_group_7(A,B))
& v1_monoid_0(k2_group_7(A,B)) ) ) ).
fof(fc4_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& v3_group_7(B,A)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k2_group_7(A,B))
& v1_group_1(k2_group_7(A,B))
& v4_group_1(k2_group_7(A,B))
& v1_monoid_0(k2_group_7(A,B)) ) ) ).
fof(fc5_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& v4_group_7(B,A)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k2_group_7(A,B))
& v1_group_1(k2_group_7(A,B))
& v7_group_1(k2_group_7(A,B))
& v1_monoid_0(k2_group_7(A,B)) ) ) ).
fof(fc6_group_7,axiom,
! [A,B,C,D] :
( ( v1_group_7(B)
& v2_group_7(B,A)
& v3_group_7(B,A)
& m1_pboole(B,A)
& m1_subset_1(C,u1_struct_0(k3_group_7(A,B)))
& m1_subset_1(D,u1_struct_0(k3_group_7(A,B))) )
=> ( v1_relat_1(k1_binop_1(u1_group_1(k3_group_7(A,B)),C,D))
& v1_funct_1(k1_binop_1(u1_group_1(k3_group_7(A,B)),C,D)) ) ) ).
fof(cc2_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(k12_pralg_1(k18_group_2(k1_numbers,np__1),k4_group_7(A))))
=> v1_finseq_1(B) ) ) ).
fof(cc3_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k4_group_7(A))))
=> ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B) ) ) ) ).
fof(cc4_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(k12_pralg_1(k2_tarski(np__1,np__2),k11_group_7(A,B))))
=> v1_finseq_1(C) ) ) ).
fof(cc5_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B))))
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_finseq_1(C) ) ) ) ).
fof(cc6_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& l1_group_1(C) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(k12_pralg_1(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C))))
=> v1_finseq_1(D) ) ) ).
fof(cc7_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& l1_group_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_group_7(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C))))
=> ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finset_1(D)
& v1_finseq_1(D) ) ) ) ).
fof(t1_group_7,axiom,
! [A,B] :
( k9_finseq_1(A) = k9_finseq_1(B)
=> A = B ) ).
fof(t2_group_7,axiom,
! [A,B,C,D] :
( k10_finseq_1(A,B) = k10_finseq_1(C,D)
=> ( A = C
& B = D ) ) ).
fof(t3_group_7,axiom,
! [A,B,C,D,E,F] :
( k11_finseq_1(A,B,C) = k11_finseq_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ).
fof(d1_group_7,axiom,
! [A] :
( v1_relat_1(A)
=> ( v1_group_7(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> ( ~ v3_struct_0(B)
& l1_group_1(B) ) ) ) ) ).
fof(d2_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& l1_group_1(C) )
=> ( C = k2_group_7(A,B)
<=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
& ! [D] :
( m1_pralg_2(D,k4_card_3(k12_pralg_1(A,B)))
=> ! [E] :
( m1_pralg_2(E,k4_card_3(k12_pralg_1(A,B)))
=> ! [F] :
~ ( r2_hidden(F,A)
& ! [G] :
( ( ~ v3_struct_0(G)
& l1_group_1(G) )
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ~ ( G = k1_funct_1(B,F)
& H = k1_binop_1(u1_group_1(C),D,E)
& k1_funct_1(H,F) = k1_binop_1(u1_group_1(G),k1_funct_1(D,F),k1_funct_1(E,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_group_7,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ! [F] :
( ( v1_group_7(F)
& m1_pboole(F,A) )
=> ! [G] :
( ( ~ v3_struct_0(G)
& l1_group_1(G) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_group_7(A,F)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_group_7(A,F)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(G))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(G))
=> ( ( r2_hidden(B,A)
& G = k1_funct_1(F,B)
& C = H
& D = I
& E = k1_group_1(k2_group_7(A,F),H,I)
& k1_funct_1(C,B) = J
& k1_funct_1(D,B) = K )
=> k1_group_1(G,J,K) = k1_funct_1(E,B) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v2_group_7(B,A)
<=> ! [C] :
~ ( r2_hidden(C,A)
& ! [D] :
( ( ~ v3_struct_0(D)
& v3_group_1(D)
& l1_group_1(D) )
=> D != k1_funct_1(B,C) ) ) ) ) ).
fof(d4_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v3_group_7(B,A)
<=> ! [C] :
~ ( r2_hidden(C,A)
& ! [D] :
( ( ~ v3_struct_0(D)
& v4_group_1(D)
& l1_group_1(D) )
=> D != k1_funct_1(B,C) ) ) ) ) ).
fof(d5_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v4_group_7(B,A)
<=> ! [C] :
~ ( r2_hidden(C,A)
& ! [D] :
( ( ~ v3_struct_0(D)
& v7_group_1(D)
& l1_group_1(D) )
=> D != k1_funct_1(B,C) ) ) ) ) ).
fof(d6_group_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v2_group_7(B,A)
<=> ! [C] :
( m1_subset_1(C,A)
=> v3_group_1(k1_group_7(A,B,C)) ) ) ) ) ).
fof(d7_group_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v3_group_7(B,A)
<=> ! [C] :
( m1_subset_1(C,A)
=> v4_group_1(k1_group_7(A,B,C)) ) ) ) ) ).
fof(d8_group_7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v4_group_7(B,A)
<=> ! [C] :
( m1_subset_1(C,A)
=> v7_group_1(k1_group_7(A,B,C)) ) ) ) ) ).
fof(t5_group_7,axiom,
! [A,B,C] :
( ( v1_group_7(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_group_1(D) )
=> ( ( r2_hidden(B,A)
& D = k1_funct_1(C,B)
& v3_group_1(k2_group_7(A,C)) )
=> v3_group_1(D) ) ) ) ).
fof(t6_group_7,axiom,
! [A,B,C] :
( ( v1_group_7(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_group_1(D) )
=> ( ( r2_hidden(B,A)
& D = k1_funct_1(C,B)
& v4_group_1(k2_group_7(A,C)) )
=> v4_group_1(D) ) ) ) ).
fof(t7_group_7,axiom,
! [A,B,C] :
( ( v1_group_7(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_group_1(D) )
=> ( ( r2_hidden(B,A)
& D = k1_funct_1(C,B)
& v7_group_1(k2_group_7(A,C)) )
=> v7_group_1(D) ) ) ) ).
fof(t8_group_7,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v1_group_7(C)
& v2_group_7(C,A)
& m1_pboole(C,A) )
=> ( ! [D] :
~ ( r2_hidden(D,A)
& ! [E] :
( ( ~ v3_struct_0(E)
& v3_group_1(E)
& l1_group_1(E) )
=> ~ ( E = k1_funct_1(C,D)
& k1_funct_1(B,D) = k2_group_1(E) ) ) )
=> B = k2_group_1(k2_group_7(A,C)) ) ) ) ).
fof(t9_group_7,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_group_7(D)
& v2_group_7(D,A)
& m1_pboole(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_group_1(E)
& l1_group_1(E) )
=> ( ( r2_hidden(B,A)
& E = k1_funct_1(D,B)
& C = k2_group_1(k2_group_7(A,D)) )
=> k1_funct_1(C,B) = k2_group_1(E) ) ) ) ) ).
fof(t10_group_7,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( ( v1_group_7(D)
& v2_group_7(D,A)
& v3_group_7(D,A)
& m1_pboole(D,A) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_group_7(A,D)))
=> ( ( E = B
& ! [F] :
~ ( r2_hidden(F,A)
& ! [G] :
( ( ~ v3_struct_0(G)
& v3_group_1(G)
& v4_group_1(G)
& l1_group_1(G) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(G))
=> ~ ( G = k1_funct_1(D,F)
& k1_funct_1(C,F) = k3_group_1(G,H)
& H = k1_funct_1(B,F) ) ) ) ) )
=> C = k3_group_1(k2_group_7(A,D),E) ) ) ) ) ) ).
fof(t11_group_7,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_group_7(E)
& v2_group_7(E,A)
& v3_group_7(E,A)
& m1_pboole(E,A) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_group_7(A,E)))
=> ! [G] :
( ( ~ v3_struct_0(G)
& v3_group_1(G)
& v4_group_1(G)
& l1_group_1(G) )
=> ! [H] :
( m1_subset_1(H,u1_struct_0(G))
=> ( ( r2_hidden(B,A)
& G = k1_funct_1(E,B)
& C = F
& D = k3_group_1(k2_group_7(A,E),F)
& k1_funct_1(C,B) = H )
=> k1_funct_1(D,B) = k3_group_1(G,H) ) ) ) ) ) ) ) ).
fof(d9_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& v2_group_7(B,A)
& v3_group_7(B,A)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,k2_group_7(A,B)) )
=> ( C = k3_group_7(A,B)
<=> ! [D] :
( r2_hidden(D,u1_struct_0(C))
<=> ? [E] :
( m1_pralg_2(E,k4_card_3(k12_pralg_1(A,B)))
& ? [F] :
( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(A))
& ? [G] :
( m1_pboole(G,F)
& E = k2_group_1(k2_group_7(A,B))
& D = k1_funct_4(E,G)
& ! [H] :
~ ( r2_hidden(H,F)
& ! [I] :
( ( ~ v3_struct_0(I)
& v3_group_1(I)
& l1_group_1(I) )
=> ~ ( I = k1_funct_1(B,H)
& r2_hidden(k1_funct_1(G,H),u1_struct_0(I))
& k1_funct_1(G,H) != k2_group_1(I) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_group_7,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( ( v1_group_7(B)
& v2_group_7(B,A)
& v3_group_7(B,A)
& m1_pboole(B,A) )
=> k2_group_7(A,B) = k3_group_7(A,B) ) ) ).
fof(t13_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ( v1_group_7(k9_finseq_1(A))
& m1_pboole(k9_finseq_1(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(t14_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k4_group_7(A))
& v2_group_7(k4_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(t15_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k4_group_7(A))
& v3_group_7(k4_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(t16_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k4_group_7(A))
& v4_group_7(k4_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(t17_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k6_group_7(A))
& v2_group_7(k6_group_7(A),k18_group_2(k1_numbers,np__1))
& v3_group_7(k6_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k6_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(t18_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k8_group_7(A))
& v2_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
& v3_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
& v4_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k8_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(t19_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ( v1_group_7(k10_finseq_1(A,B))
& m1_pboole(k10_finseq_1(A,B),k2_tarski(np__1,np__2)) ) ) ) ).
fof(t20_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k11_group_7(A,B))
& v2_group_7(k11_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) ).
fof(t21_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k11_group_7(A,B))
& v3_group_7(k11_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) ).
fof(t22_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v7_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k11_group_7(A,B))
& v4_group_7(k11_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) ).
fof(t23_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k13_group_7(A,B))
& v2_group_7(k13_group_7(A,B),k2_tarski(np__1,np__2))
& v3_group_7(k13_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k13_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) ).
fof(t24_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k15_group_7(A,B))
& v2_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
& v3_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
& v4_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k15_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ) ).
fof(t25_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_group_1(C) )
=> ( v1_group_7(k11_finseq_1(A,B,C))
& m1_pboole(k11_finseq_1(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) ).
fof(t26_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k18_group_7(A,B,C))
& v2_group_7(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) ).
fof(t27_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k18_group_7(A,B,C))
& v3_group_7(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) ).
fof(t28_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v7_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v7_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k18_group_7(A,B,C))
& v4_group_7(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) ).
fof(t29_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k20_group_7(A,B,C))
& v2_group_7(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& v3_group_7(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) ).
fof(t30_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k22_group_7(A,B,C))
& v2_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& v3_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& v4_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ) ) ).
fof(t31_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_group_1(k2_group_7(k18_group_2(k1_numbers,np__1),k4_group_7(A)),k10_group_7(A,B),k10_group_7(A,C)) = k10_group_7(A,k1_group_1(A,B,C)) ) ) ) ).
fof(t32_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k1_group_1(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B)),k17_group_7(A,B,C,E),k17_group_7(A,B,D,F)) = k17_group_7(A,B,k1_group_1(A,C,D),k1_group_1(B,E,F)) ) ) ) ) ) ) ).
fof(t33_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_group_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(C))
=> k1_group_1(k2_group_7(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C)),k24_group_7(A,B,C,D,F,H),k24_group_7(A,B,C,E,G,I)) = k24_group_7(A,B,C,k1_group_1(A,D,E),k1_group_1(B,F,G),k1_group_1(C,H,I)) ) ) ) ) ) ) ) ) ) ).
fof(t34_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> k2_group_1(k2_group_7(k18_group_2(k1_numbers,np__1),k5_group_7(A))) = k10_group_7(A,k2_group_1(A)) ) ).
fof(t35_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) )
=> k2_group_1(k2_group_7(k2_tarski(np__1,np__2),k12_group_7(A,B))) = k17_group_7(A,B,k2_group_1(A),k2_group_1(B)) ) ) ).
fof(t36_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& l1_group_1(C) )
=> k2_group_1(k2_group_7(k1_enumset1(np__1,np__2,np__3),k19_group_7(A,B,C))) = k24_group_7(A,B,C,k2_group_1(A),k2_group_1(B),k2_group_1(C)) ) ) ) ).
fof(t37_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_group_1(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)),k10_group_7(A,B)) = k10_group_7(A,k3_group_1(A,B)) ) ) ).
fof(t38_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k3_group_1(k2_group_7(k2_tarski(np__1,np__2),k15_group_7(A,B)),k17_group_7(A,B,C,D)) = k17_group_7(A,B,k3_group_1(A,C),k3_group_1(B,D)) ) ) ) ) ).
fof(t39_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k3_group_1(k2_group_7(k1_enumset1(np__1,np__2,np__3),k22_group_7(A,B,C)),k24_group_7(A,B,C,D,E,F)) = k24_group_7(A,B,C,k3_group_1(A,D),k3_group_1(B,E),k3_group_1(C,F)) ) ) ) ) ) ) ).
fof(t40_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))),B,C) = k10_group_7(A,C) )
=> ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))))
& v1_group_6(B,A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))) ) ) ) ) ).
fof(t41_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))))
& v1_group_6(B,A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A)))) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))),B,C) = k10_group_7(A,C) )
=> v4_group_6(B,A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))) ) ) ) ).
fof(t42_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> r1_group_6(A,k2_group_7(k18_group_2(k1_numbers,np__1),k8_group_7(A))) ) ).
fof(dt_k1_group_7,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_group_7(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ( ~ v3_struct_0(k1_group_7(A,B,C))
& l1_group_1(k1_group_7(A,B,C)) ) ) ).
fof(redefinition_k1_group_7,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_group_7(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> k1_group_7(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k2_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& m1_pboole(B,A) )
=> ( v1_group_1(k2_group_7(A,B))
& l1_group_1(k2_group_7(A,B)) ) ) ).
fof(dt_k3_group_7,axiom,
! [A,B] :
( ( v1_group_7(B)
& v2_group_7(B,A)
& v3_group_7(B,A)
& m1_pboole(B,A) )
=> ( v1_group_1(k3_group_7(A,B))
& m1_group_2(k3_group_7(A,B),k2_group_7(A,B)) ) ) ).
fof(dt_k4_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ( v1_group_7(k4_group_7(A))
& m1_pboole(k4_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(redefinition_k4_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> k4_group_7(A) = k5_finseq_1(A) ) ).
fof(dt_k5_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k5_group_7(A))
& v2_group_7(k5_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k5_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(redefinition_k5_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> k5_group_7(A) = k5_finseq_1(A) ) ).
fof(dt_k6_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k6_group_7(A))
& v3_group_7(k6_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k6_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(redefinition_k6_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k6_group_7(A) = k5_finseq_1(A) ) ).
fof(dt_k7_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k7_group_7(A))
& v4_group_7(k7_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k7_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(redefinition_k7_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A) )
=> k7_group_7(A) = k5_finseq_1(A) ) ).
fof(dt_k8_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k8_group_7(A))
& v2_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
& v3_group_7(k8_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k8_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(redefinition_k8_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k8_group_7(A) = k5_finseq_1(A) ) ).
fof(dt_k9_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ( v1_group_7(k9_group_7(A))
& v2_group_7(k9_group_7(A),k18_group_2(k1_numbers,np__1))
& v3_group_7(k9_group_7(A),k18_group_2(k1_numbers,np__1))
& v4_group_7(k9_group_7(A),k18_group_2(k1_numbers,np__1))
& m1_pboole(k9_group_7(A),k18_group_2(k1_numbers,np__1)) ) ) ).
fof(redefinition_k9_group_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> k9_group_7(A) = k5_finseq_1(A) ) ).
fof(dt_k10_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k10_group_7(A,B),u1_struct_0(k2_group_7(k18_group_2(k1_numbers,np__1),k4_group_7(A)))) ) ).
fof(redefinition_k10_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k10_group_7(A,B) = k5_finseq_1(B) ) ).
fof(dt_k11_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B) )
=> ( v1_group_7(k11_group_7(A,B))
& m1_pboole(k11_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ).
fof(redefinition_k11_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B) )
=> k11_group_7(A,B) = k10_finseq_1(A,B) ) ).
fof(dt_k12_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k12_group_7(A,B))
& v2_group_7(k12_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k12_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ).
fof(redefinition_k12_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) )
=> k12_group_7(A,B) = k10_finseq_1(A,B) ) ).
fof(dt_k13_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k13_group_7(A,B))
& v3_group_7(k13_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k13_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ).
fof(redefinition_k13_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v4_group_1(B)
& l1_group_1(B) )
=> k13_group_7(A,B) = k10_finseq_1(A,B) ) ).
fof(dt_k14_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v7_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k14_group_7(A,B))
& v4_group_7(k14_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k14_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ).
fof(redefinition_k14_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v7_group_1(B)
& l1_group_1(B) )
=> k14_group_7(A,B) = k10_finseq_1(A,B) ) ).
fof(dt_k15_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k15_group_7(A,B))
& v2_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
& v3_group_7(k15_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k15_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ).
fof(redefinition_k15_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> k15_group_7(A,B) = k10_finseq_1(A,B) ) ).
fof(dt_k16_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B) )
=> ( v1_group_7(k16_group_7(A,B))
& v2_group_7(k16_group_7(A,B),k2_tarski(np__1,np__2))
& v3_group_7(k16_group_7(A,B),k2_tarski(np__1,np__2))
& v4_group_7(k16_group_7(A,B),k2_tarski(np__1,np__2))
& m1_pboole(k16_group_7(A,B),k2_tarski(np__1,np__2)) ) ) ).
fof(redefinition_k16_group_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B) )
=> k16_group_7(A,B) = k10_finseq_1(A,B) ) ).
fof(dt_k17_group_7,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> m1_subset_1(k17_group_7(A,B,C,D),u1_struct_0(k2_group_7(k2_tarski(np__1,np__2),k11_group_7(A,B)))) ) ).
fof(redefinition_k17_group_7,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(B)) )
=> k17_group_7(A,B,C,D) = k10_finseq_1(C,D) ) ).
fof(dt_k18_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& l1_group_1(C) )
=> ( v1_group_7(k18_group_7(A,B,C))
& m1_pboole(k18_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ).
fof(redefinition_k18_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& l1_group_1(C) )
=> k18_group_7(A,B,C) = k11_finseq_1(A,B,C) ) ).
fof(dt_k19_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k19_group_7(A,B,C))
& v2_group_7(k19_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k19_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ).
fof(redefinition_k19_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& l1_group_1(C) )
=> k19_group_7(A,B,C) = k11_finseq_1(A,B,C) ) ).
fof(dt_k20_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v4_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k20_group_7(A,B,C))
& v3_group_7(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k20_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ).
fof(redefinition_k20_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v4_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v4_group_1(C)
& l1_group_1(C) )
=> k20_group_7(A,B,C) = k11_finseq_1(A,B,C) ) ).
fof(dt_k21_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v7_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v7_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k21_group_7(A,B,C))
& v4_group_7(k21_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k21_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ).
fof(redefinition_k21_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v7_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v7_group_1(C)
& l1_group_1(C) )
=> k21_group_7(A,B,C) = k11_finseq_1(A,B,C) ) ).
fof(dt_k22_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k22_group_7(A,B,C))
& v2_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& v3_group_7(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k22_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ).
fof(redefinition_k22_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C) )
=> k22_group_7(A,B,C) = k11_finseq_1(A,B,C) ) ).
fof(dt_k23_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& l1_group_1(C) )
=> ( v1_group_7(k23_group_7(A,B,C))
& v2_group_7(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& v3_group_7(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& v4_group_7(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3))
& m1_pboole(k23_group_7(A,B,C),k1_enumset1(np__1,np__2,np__3)) ) ) ).
fof(redefinition_k23_group_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& l1_group_1(C) )
=> k23_group_7(A,B,C) = k11_finseq_1(A,B,C) ) ).
fof(dt_k24_group_7,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& l1_group_1(C)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(C)) )
=> m1_subset_1(k24_group_7(A,B,C,D,E,F),u1_struct_0(k2_group_7(k1_enumset1(np__1,np__2,np__3),k18_group_7(A,B,C)))) ) ).
fof(redefinition_k24_group_7,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l1_group_1(B)
& ~ v3_struct_0(C)
& l1_group_1(C)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(C)) )
=> k24_group_7(A,B,C,D,E,F) = k11_finseq_1(D,E,F) ) ).
%------------------------------------------------------------------------------