SET007 Axioms: SET007+312.ax
%------------------------------------------------------------------------------
% File : SET007+312 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Homomorphisms and Isomorphisms of Groups. Quotient Group
% 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_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 142 ( 10 unt; 0 def)
% Number of atoms : 1561 ( 84 equ)
% Maximal formula atoms : 24 ( 10 avg)
% Number of connectives : 1636 ( 217 ~; 0 |;1027 &)
% ( 25 <=>; 367 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 63 ( 63 usr; 3 con; 0-6 aty)
% Number of variables : 398 ( 385 !; 13 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ~ v3_struct_0(k5_group_2(A))
& v1_group_1(k5_group_2(A))
& v2_group_1(k5_group_2(A))
& v3_group_1(k5_group_2(A))
& v4_group_1(k5_group_2(A))
& v1_group_3(k5_group_2(A),A) ) ) ).
fof(fc2_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ~ v3_struct_0(k6_group_2(A))
& v1_group_1(k6_group_2(A))
& v2_group_1(k6_group_2(A))
& v3_group_1(k6_group_2(A))
& v4_group_1(k6_group_2(A))
& v1_group_3(k6_group_2(A),A) ) ) ).
fof(rc1_group_6,axiom,
? [A] :
( l1_group_1(A)
& ~ v3_struct_0(A)
& v2_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& v3_realset2(A) ) ).
fof(fc3_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> ~ v1_xboole_0(k4_group_6(A,B)) ) ).
fof(fc4_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( ~ v3_struct_0(k6_group_6(A,B))
& v1_group_1(k6_group_6(A,B)) ) ) ).
fof(fc5_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( ~ v3_struct_0(k6_group_6(A,B))
& v1_group_1(k6_group_6(A,B))
& v2_group_1(k6_group_6(A,B))
& v3_group_1(k6_group_6(A,B))
& v4_group_1(k6_group_6(A,B)) ) ) ).
fof(rc2_group_6,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) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B) ) ) ).
fof(fc6_group_6,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)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ~ v3_struct_0(k12_group_6(A,B,C))
& v1_group_1(k12_group_6(A,B,C))
& v2_group_1(k12_group_6(A,B,C))
& v3_group_1(k12_group_6(A,B,C))
& v4_group_1(k12_group_6(A,B,C))
& v1_group_3(k12_group_6(A,B,C),A) ) ) ).
fof(t1_group_6,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_funct_1(C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( k8_funct_2(A,B,C,D) = k8_funct_2(A,B,C,E)
=> D = E ) ) ) ) ) ) ) ).
fof(t2_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_group_6(D,A,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E = C
=> ( k12_group_2(B,D,E) = k12_group_2(A,D,C)
& k13_group_2(B,D,E) = k13_group_2(A,D,C) ) ) ) ) ) ) ) ).
fof(t3_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_group_6(C,A,B)
=> ! [D] :
( m1_group_6(D,A,B)
=> k9_group_2(A,C,D) = k9_group_2(B,C,D) ) ) ) ) ).
fof(t4_group_6,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_group_1(A,k1_group_1(A,B,C),k3_group_1(A,B)) = k2_group_3(A,C,k3_group_1(A,B))
& k1_group_1(A,B,k1_group_1(A,C,k3_group_1(A,B))) = k2_group_3(A,C,k3_group_1(A,B)) ) ) ) ) ).
fof(t5_group_6,axiom,
$true ).
fof(t6_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k10_group_2(A,B,k12_group_2(A,B,C)) = k12_group_2(A,B,C)
& k3_group_2(A,C,k7_group_4(A,B,B)) = k12_group_2(A,B,C)
& k4_group_2(A,C,k7_group_4(A,B,B)) = k13_group_2(A,B,C)
& k11_group_2(A,B,k13_group_2(A,B,C)) = k13_group_2(A,B,C) ) ) ) ) ).
fof(t8_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ( m1_group_6(k9_group_5(A),A,B)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_rlvect_1(B,k2_group_5(A,C,D)) ) ) ) ) ) ).
fof(t9_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( m1_group_6(C,A,B)
=> ( v1_group_3(C,B)
& m1_group_6(C,A,B) ) ) ) ) ) ).
fof(d1_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( m1_group_6(g1_group_1(u1_struct_0(C),u1_group_1(C)),A,B)
=> k1_group_6(A,B,C) = g1_group_1(u1_struct_0(C),u1_group_1(C)) ) ) ) ) ).
fof(t10_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( v1_group_3(k9_group_2(A,B,C),B)
& m1_group_6(k9_group_2(A,B,C),A,B)
& v1_group_3(k9_group_2(A,C,B),B)
& m1_group_6(k9_group_2(A,C,B),A,B) ) ) ) ) ).
fof(d2_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ( v3_realset2(A)
<=> ? [B] : u1_struct_0(A) = k1_tarski(B) ) ) ).
fof(t11_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> v3_realset2(k5_group_2(A)) ) ).
fof(t12_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v3_realset2(A)
<=> ( k9_group_1(A) = np__1
& v6_group_1(A) ) ) ) ).
fof(t13_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v3_realset2(A)
=> k5_group_2(A) = A ) ) ).
fof(d3_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> k4_group_6(A,B) = k14_group_2(A,B) ) ) ).
fof(t14_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( k4_group_6(A,B) = k14_group_2(A,B)
& k4_group_6(A,B) = k15_group_2(A,B) ) ) ) ).
fof(t15_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B,C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ~ ( r2_hidden(B,k4_group_6(A,C))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( B = k12_group_2(A,C,D)
& B = k13_group_2(A,C,D) ) ) ) ) ) ).
fof(t16_group_6,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))
=> ! [C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( r2_hidden(k12_group_2(A,C,B),k4_group_6(A,C))
& r2_hidden(k13_group_2(A,C,B),k4_group_6(A,C)) ) ) ) ) ).
fof(t17_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B,C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( r2_hidden(B,k4_group_6(A,C))
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ).
fof(t18_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( ( v1_group_3(D,A)
& m1_group_2(D,A) )
=> ( ( r2_hidden(B,k4_group_6(A,D))
& r2_hidden(C,k4_group_6(A,D)) )
=> r2_hidden(k2_group_2(A,B,C),k4_group_6(A,D)) ) ) ) ) ) ).
fof(d4_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B))
& m2_relset_1(C,k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) )
=> ( C = k5_group_6(A,B)
<=> ! [D] :
( m1_subset_1(D,k4_group_6(A,B))
=> ! [E] :
( m1_subset_1(E,k4_group_6(A,B))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( D = F
& E = G )
=> k2_binop_1(k4_group_6(A,B),k4_group_6(A,B),k4_group_6(A,B),C,D,E) = k2_group_2(A,F,G) ) ) ) ) ) ) ) ) ) ).
fof(d5_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> k6_group_6(A,B) = g1_group_1(k4_group_6(A,B),k5_group_6(A,B)) ) ) ).
fof(t19_group_6,axiom,
$true ).
fof(t20_group_6,axiom,
$true ).
fof(t21_group_6,axiom,
$true ).
fof(t22_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> u1_struct_0(k6_group_6(A,B)) = k4_group_6(A,B) ) ) ).
fof(t23_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> u1_group_1(k6_group_6(A,B)) = k5_group_6(A,B) ) ) ).
fof(d6_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
=> k7_group_6(A,B,C) = C ) ) ) ).
fof(t24_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_group_6(A,B)))
=> k2_group_2(A,k7_group_6(A,B,C),k7_group_6(A,B,D)) = k1_group_1(k6_group_6(A,B),C,D) ) ) ) ) ).
fof(t25_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_group_6(A,B)))
=> k7_group_6(A,B,k1_group_1(k6_group_6(A,B),C,D)) = k2_group_2(A,k7_group_6(A,B,C),k7_group_6(A,B,D)) ) ) ) ) ).
fof(t26_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_group_6(A,B)))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k12_group_2(A,B,D)
& C = k13_group_2(A,B,D) ) ) ) ) ).
fof(t27_group_6,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))
=> ! [C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( m1_subset_1(k13_group_2(A,C,B),u1_struct_0(k6_group_6(A,C)))
& m1_subset_1(k12_group_2(A,C,B),u1_struct_0(k6_group_6(A,C)))
& m1_subset_1(k7_group_2(A,C),u1_struct_0(k6_group_6(A,C))) ) ) ) ) ).
fof(t28_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B,C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( r1_rlvect_1(k6_group_6(A,C),B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k12_group_2(A,C,D)
& B = k13_group_2(A,C,D) ) ) ) ) ).
fof(t29_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> k2_group_1(k6_group_6(A,B)) = k7_group_2(A,B) ) ) ).
fof(t30_group_6,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))
=> ! [C] :
( ( v1_group_3(C,A)
& m1_group_2(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_group_6(A,C)))
=> ( D = k12_group_2(A,C,B)
=> k3_group_1(k6_group_6(A,C),D) = k12_group_2(A,C,k3_group_1(A,B)) ) ) ) ) ) ).
fof(t31_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( v1_finset_1(k14_group_2(A,B))
=> v6_group_1(k6_group_6(A,B)) ) ) ) ).
fof(t32_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> k8_group_1(k6_group_6(A,B)) = k16_group_2(A,B) ) ) ).
fof(t33_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( v1_finset_1(k14_group_2(A,B))
=> k9_group_1(k6_group_6(A,B)) = k17_group_2(A,B) ) ) ) ).
fof(t34_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( ( v1_group_1(C)
& v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( m1_group_6(C,A,B)
=> m1_group_2(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C)) ) ) ) ) ).
fof(t35_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( m1_group_6(C,A,B)
=> ( v1_group_3(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C))
& m1_group_2(k6_group_6(B,k1_group_6(A,B,C)),k6_group_6(A,C)) ) ) ) ) ) ).
fof(t36_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( ( ~ v3_struct_0(k6_group_6(A,B))
& v3_group_1(k6_group_6(A,B))
& v4_group_1(k6_group_6(A,B))
& v7_group_1(k6_group_6(A,B))
& l1_group_1(k6_group_6(A,B)) )
<=> m1_group_6(k9_group_5(A),A,B) ) ) ) ).
fof(d7_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_group_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_group_6(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_group_1(A,D,E)) = k1_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ).
fof(t37_group_6,axiom,
$true ).
fof(t38_group_6,axiom,
$true ).
fof(t39_group_6,axiom,
$true ).
fof(t40_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_group_1(A)) = k2_group_1(B) ) ) ) ).
fof(t41_group_6,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,k3_group_1(A,C)) = k3_group_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C)) ) ) ) ) ).
fof(t42_group_6,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(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(E,A,B)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,k2_group_3(A,C,D)) = k2_group_3(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) ) ) ) ) ) ).
fof(t43_group_6,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(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(E,A,B)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,k2_group_5(A,C,D)) = k2_group_5(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) ) ) ) ) ) ).
fof(t44_group_6,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(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(F,A,B)
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,k3_group_5(A,C,D,E)) = k3_group_5(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),F,E)) ) ) ) ) ) ) ).
fof(t45_group_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_group_6(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,k6_group_1(B,A,D)) = k6_group_1(C,A,k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,D)) ) ) ) ) ) ).
fof(t46_group_6,axiom,
! [A] :
( v1_int_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(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_group_6(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,k6_group_1(B,A,D)) = k6_group_1(C,A,k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,D)) ) ) ) ) ) ).
fof(t47_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_funct_1(k6_partfun1(u1_struct_0(A)))
& v1_funct_2(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A))
& v1_group_6(k6_partfun1(u1_struct_0(A)),A,A)
& m2_relset_1(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(t48_group_6,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& v1_group_6(E,A,C)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( v1_funct_1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E))
& v1_funct_2(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),u1_struct_0(B),u1_struct_0(C))
& v1_group_6(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),B,C)
& m2_relset_1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(C),D,E),u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(d8_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( C = k10_group_6(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k2_group_1(B) ) ) ) ) ) ).
fof(t49_group_6,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_group_6(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( k8_group_6(A,B,C,k10_group_6(A,B),E) = k10_group_6(A,C)
& k8_group_6(A,B,C,D,k10_group_6(B,C)) = k10_group_6(A,C) ) ) ) ) ) ) ).
fof(d9_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k6_group_6(A,B)))
& v1_group_6(C,A,k6_group_6(A,B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) )
=> ( C = k11_group_6(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k6_group_6(A,B)),C,D) = k12_group_2(A,B,D) ) ) ) ) ) ).
fof(t50_group_6,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( r1_rlvect_1(k12_group_6(A,B,D),C)
<=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C) = k2_group_1(B) ) ) ) ) ) ).
fof(t51_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> k12_group_6(A,B,k10_group_6(A,B)) = A ) ) ).
fof(t52_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> r1_group_2(A,k12_group_6(A,k6_group_6(A,B),k11_group_6(A,B)),B) ) ) ).
fof(d11_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_group_1(D)
& m1_group_2(D,B) )
=> ( D = k13_group_6(A,B,C)
<=> u1_struct_0(D) = k2_funct_2(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(A)) ) ) ) ) ) ).
fof(t53_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k9_group_6(A,B,C) = u1_struct_0(k13_group_6(A,B,C)) ) ) ) ).
fof(t54_group_6,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,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( r1_rlvect_1(k13_group_6(B,A,D),C)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& C = k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) ) ) ) ) ) ).
fof(t55_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> r1_group_2(B,k13_group_6(A,B,C),k5_group_4(B,k9_group_6(A,B,C))) ) ) ) ).
fof(t56_group_6,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) )
=> r1_group_2(B,k13_group_6(A,B,k10_group_6(A,B)),k5_group_2(B)) ) ) ).
fof(t57_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> k13_group_6(A,k6_group_6(A,B),k11_group_6(A,B)) = k6_group_6(A,B) ) ) ).
fof(t58_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(k13_group_6(B,A,C)))
& v1_group_6(C,B,k13_group_6(B,A,C))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(k13_group_6(B,A,C))) ) ) ) ) ).
fof(t59_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v6_group_1(B)
=> v6_group_1(k13_group_6(B,A,C)) ) ) ) ) ).
fof(t60_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B) )
=> v7_group_1(k13_group_6(B,A,C)) ) ) ) ) ).
fof(t61_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> r1_tarski(k8_group_1(k13_group_6(B,A,C)),k8_group_1(B)) ) ) ) ).
fof(t62_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v6_group_1(B)
=> r1_xreal_0(k9_group_1(k13_group_6(B,A,C)),k9_group_1(B)) ) ) ) ) ).
fof(d12_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v2_group_6(C,A,B)
<=> v2_funct_1(C) ) ) ) ) ).
fof(d13_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_group_6(C,A,B)
<=> k9_group_6(A,B,C) = u1_struct_0(B) ) ) ) ) ).
fof(t63_group_6,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(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v2_group_6(D,A,B)
& r1_rlvect_1(k13_group_6(A,B,D),C) )
=> k1_funct_1(D,k1_funct_1(k2_funct_1(D),C)) = C ) ) ) ) ) ).
fof(t64_group_6,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v2_group_6(D,A,B)
=> k1_funct_1(k2_funct_1(D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,C)) = C ) ) ) ) ) ).
fof(t65_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v2_group_6(C,B,A)
=> ( v1_funct_1(k2_funct_1(C))
& v1_funct_2(k2_funct_1(C),u1_struct_0(k13_group_6(B,A,C)),u1_struct_0(B))
& v1_group_6(k2_funct_1(C),k13_group_6(B,A,C),B)
& m2_relset_1(k2_funct_1(C),u1_struct_0(k13_group_6(B,A,C)),u1_struct_0(B)) ) ) ) ) ) ).
fof(t66_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v2_group_6(C,B,A)
<=> r1_group_2(B,k12_group_6(B,A,C),k5_group_2(B)) ) ) ) ) ).
fof(t67_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_group_6(C,A,B)
<=> k13_group_6(A,B,C) = B ) ) ) ) ).
fof(t68_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_group_6(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) = D ) ) ) ) ) ) ).
fof(t69_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> v3_group_6(k11_group_6(A,B),A,k6_group_6(A,B)) ) ) ).
fof(d14_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v4_group_6(C,A,B)
<=> ( v3_group_6(C,A,B)
& v2_group_6(C,A,B) ) ) ) ) ) ).
fof(t70_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v4_group_6(C,A,B)
<=> ( k9_group_6(A,B,C) = u1_struct_0(B)
& v2_funct_1(C) ) ) ) ) ) ).
fof(t71_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v4_group_6(C,A,B)
=> ( k1_relat_1(C) = u1_struct_0(A)
& k9_group_6(A,B,C) = u1_struct_0(B) ) ) ) ) ) ).
fof(t72_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v4_group_6(C,A,B)
=> ( v1_funct_1(k2_funct_1(C))
& v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))
& v1_group_6(k2_funct_1(C),B,A)
& m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ).
fof(t73_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v4_group_6(C,B,A)
& D = k2_funct_1(C) )
=> v4_group_6(D,A,B) ) ) ) ) ) ).
fof(t74_group_6,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_group_6(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v4_group_6(D,A,B)
& v4_group_6(E,B,C) )
=> v4_group_6(k8_group_6(A,B,C,D,E),A,C) ) ) ) ) ) ) ).
fof(t75_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> v4_group_6(k11_group_6(A,k5_group_2(A)),A,k6_group_6(A,k5_group_2(A))) ) ).
fof(d15_group_6,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) )
=> ( r1_group_6(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v4_group_6(C,A,B) ) ) ) ) ).
fof(t76_group_6,axiom,
$true ).
fof(t77_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r1_group_6(A,B)
=> r1_group_6(B,A) ) ) ) ).
fof(t78_group_6,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) )
=> ( ( r1_group_6(A,B)
& r1_group_6(B,C) )
=> r1_group_6(A,C) ) ) ) ) ).
fof(t79_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v2_group_6(C,B,A)
=> r1_group_6(B,k13_group_6(B,A,C)) ) ) ) ) ).
fof(t80_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( ( v3_realset2(A)
& v3_realset2(B) )
=> r2_group_6(A,B) ) ) ) ).
fof(t81_group_6,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) )
=> r2_group_6(k5_group_2(A),k5_group_2(B)) ) ) ).
fof(t82_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> r2_group_6(A,k6_group_6(A,k5_group_2(A))) ) ).
fof(t83_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> v3_realset2(k6_group_6(A,k6_group_2(A))) ) ).
fof(t84_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r2_group_6(A,B)
=> k8_group_1(A) = k8_group_1(B) ) ) ) ).
fof(t85_group_6,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) )
=> ( ( r1_group_6(A,B)
& v6_group_1(A) )
=> v6_group_1(B) ) ) ) ).
fof(t86_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( ( r2_group_6(A,B)
& v6_group_1(A) )
=> k9_group_1(A) = k9_group_1(B) ) ) ) ).
fof(t87_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( ( r2_group_6(A,B)
& v3_realset2(A) )
=> v3_realset2(B) ) ) ) ).
fof(t88_group_6,axiom,
$true ).
fof(t89_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( ( r1_group_6(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) ) ) ) ) ).
fof(t90_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> r2_group_6(k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C)) ) ) ) ).
fof(t91_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_group_6(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k6_group_6(B,k12_group_6(B,A,C))),u1_struct_0(k13_group_6(B,A,C)))
& v1_group_6(D,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C))
& m2_relset_1(D,u1_struct_0(k6_group_6(B,k12_group_6(B,A,C))),u1_struct_0(k13_group_6(B,A,C)))
& v4_group_6(D,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C))
& C = k8_group_6(B,k6_group_6(B,k12_group_6(B,A,C)),k13_group_6(B,A,C),k11_group_6(B,k12_group_6(B,A,C)),D) ) ) ) ) ).
fof(t92_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_3(B,A)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& v1_group_3(C,A)
& m1_group_2(C,A) )
=> ! [D] :
( ( v1_group_1(D)
& v1_group_3(D,k6_group_6(A,C))
& m1_group_2(D,k6_group_6(A,C)) )
=> ( ( D = k6_group_6(B,k1_group_6(A,B,C))
& m1_group_6(C,A,B) )
=> r2_group_6(k6_group_6(k6_group_6(A,C),D),k6_group_6(A,B)) ) ) ) ) ) ).
fof(t93_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ! [C] :
( ( v1_group_1(C)
& v1_group_3(C,A)
& m1_group_2(C,A) )
=> r2_group_6(k6_group_6(k8_group_4(A,B,C),k1_group_6(A,k8_group_4(A,B,C),C)),k6_group_6(B,k2_group_6(A,B,C))) ) ) ) ).
fof(dt_m1_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A) )
=> ! [C] :
( m1_group_6(C,A,B)
=> m1_group_2(C,A) ) ) ).
fof(existence_m1_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A) )
=> ? [C] : m1_group_6(C,A,B) ) ).
fof(redefinition_m1_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A) )
=> ! [C] :
( m1_group_6(C,A,B)
<=> m1_group_2(C,B) ) ) ).
fof(reflexivity_r1_group_6,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) )
=> r1_group_6(A,A) ) ).
fof(symmetry_r2_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r2_group_6(A,B)
=> r2_group_6(B,A) ) ) ).
fof(reflexivity_r2_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> r2_group_6(A,A) ) ).
fof(redefinition_r2_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r2_group_6(A,B)
<=> r1_group_6(A,B) ) ) ).
fof(dt_k1_group_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A)
& v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( v1_group_1(k1_group_6(A,B,C))
& v1_group_3(k1_group_6(A,B,C),B)
& m1_group_6(k1_group_6(A,B,C),A,B) ) ) ).
fof(dt_k2_group_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A)
& v1_group_3(C,A)
& m1_group_2(C,A) )
=> ( v1_group_1(k2_group_6(A,B,C))
& v1_group_3(k2_group_6(A,B,C),B)
& m1_group_6(k2_group_6(A,B,C),A,B) ) ) ).
fof(redefinition_k2_group_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A)
& v1_group_3(C,A)
& m1_group_2(C,A) )
=> k2_group_6(A,B,C) = k8_group_2(A,B,C) ) ).
fof(dt_k3_group_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A)
& m1_group_2(C,A) )
=> ( v1_group_1(k3_group_6(A,B,C))
& v1_group_3(k3_group_6(A,B,C),C)
& m1_group_6(k3_group_6(A,B,C),A,C) ) ) ).
fof(redefinition_k3_group_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A)
& m1_group_2(C,A) )
=> k3_group_6(A,B,C) = k8_group_2(A,B,C) ) ).
fof(dt_k4_group_6,axiom,
$true ).
fof(dt_k5_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( v1_funct_1(k5_group_6(A,B))
& v1_funct_2(k5_group_6(A,B),k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B))
& m2_relset_1(k5_group_6(A,B),k2_zfmisc_1(k4_group_6(A,B),k4_group_6(A,B)),k4_group_6(A,B)) ) ) ).
fof(dt_k6_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> l1_group_1(k6_group_6(A,B)) ) ).
fof(dt_k7_group_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A)
& m1_subset_1(C,u1_struct_0(k6_group_6(A,B))) )
=> m1_subset_1(k7_group_6(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k8_group_6,axiom,
! [A,B,C,D,E] :
( ( ~ 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_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_group_6(E,B,C)
& m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k8_group_6(A,B,C,D,E))
& v1_funct_2(k8_group_6(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
& v1_group_6(k8_group_6(A,B,C,D,E),A,C)
& m2_relset_1(k8_group_6(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ).
fof(redefinition_k8_group_6,axiom,
! [A,B,C,D,E] :
( ( ~ 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_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(D,A,B)
& m1_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_group_6(E,B,C)
& m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> k8_group_6(A,B,C,D,E) = k5_relat_1(D,E) ) ).
fof(dt_k9_group_6,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)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m1_subset_1(k9_group_6(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(redefinition_k9_group_6,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)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k9_group_6(A,B,C) = k2_relat_1(C) ) ).
fof(dt_k10_group_6,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_funct_1(k10_group_6(A,B))
& v1_funct_2(k10_group_6(A,B),u1_struct_0(A),u1_struct_0(B))
& v1_group_6(k10_group_6(A,B),A,B)
& m2_relset_1(k10_group_6(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(dt_k11_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_3(B,A)
& m1_group_2(B,A) )
=> ( v1_funct_1(k11_group_6(A,B))
& v1_funct_2(k11_group_6(A,B),u1_struct_0(A),u1_struct_0(k6_group_6(A,B)))
& v1_group_6(k11_group_6(A,B),A,k6_group_6(A,B))
& m2_relset_1(k11_group_6(A,B),u1_struct_0(A),u1_struct_0(k6_group_6(A,B))) ) ) ).
fof(dt_k12_group_6,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)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_group_1(k12_group_6(A,B,C))
& m1_group_2(k12_group_6(A,B,C),A) ) ) ).
fof(dt_k13_group_6,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)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_group_1(k13_group_6(A,B,C))
& m1_group_2(k13_group_6(A,B,C),B) ) ) ).
fof(t7_group_6,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = a_1_0_group_6(A)
=> r1_group_2(A,k9_group_5(A),k5_group_4(A,B)) ) ) ) ).
fof(d10_group_6,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_group_6(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_group_1(D)
& m1_group_2(D,A) )
=> ( D = k12_group_6(A,B,C)
<=> u1_struct_0(D) = a_3_0_group_6(A,B,C) ) ) ) ) ) ).
fof(fraenkel_a_1_0_group_6,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r2_hidden(A,a_1_0_group_6(B))
<=> ? [C,D] :
( m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B))
& A = k2_group_5(B,C,D) ) ) ) ).
fof(fraenkel_a_3_0_group_6,axiom,
! [A,B,C,D] :
( ( ~ 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_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& v1_group_6(D,B,C)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_group_6(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) = k2_group_1(C) ) ) ) ).
%------------------------------------------------------------------------------