SET007 Axioms: SET007+255.ax
%------------------------------------------------------------------------------
% File : SET007+255 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Lattice of Subgroups of a Group. Frattini Subgroup
% 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 131 ( 24 unt; 0 def)
% Number of atoms : 917 ( 98 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 903 ( 117 ~; 2 |; 447 &)
% ( 19 <=>; 318 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-3 aty)
% Number of functors : 74 ( 74 usr; 9 con; 0-6 aty)
% Number of variables : 316 ( 299 !; 17 ?)
% 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_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ~ v3_struct_0(k11_group_4(A))
& v3_lattices(k11_group_4(A))
& v4_lattices(k11_group_4(A))
& v5_lattices(k11_group_4(A))
& v6_lattices(k11_group_4(A))
& v7_lattices(k11_group_4(A))
& v8_lattices(k11_group_4(A))
& v9_lattices(k11_group_4(A))
& v10_lattices(k11_group_4(A))
& v13_lattices(k11_group_4(A))
& v14_lattices(k11_group_4(A))
& v15_lattices(k11_group_4(A)) ) ) ).
fof(d1_group_4,axiom,
$true ).
fof(d2_group_4,axiom,
! [A] :
( v1_int_1(A)
=> k2_group_4(A) = A ) ).
fof(t1_group_4,axiom,
$true ).
fof(t2_group_4,axiom,
$true ).
fof(t3_group_4,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] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_group_2(D,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ( C = E
=> k6_group_1(B,A,C) = k6_group_1(D,A,E) ) ) ) ) ) ) ).
fof(t4_group_4,axiom,
! [A] :
( v1_int_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] :
( m1_group_2(D,B)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ( C = E
=> k6_group_1(B,A,C) = k6_group_1(D,A,E) ) ) ) ) ) ) ).
fof(t5_group_4,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] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_group_2(D,B)
=> ( r1_rlvect_1(D,C)
=> r1_rlvect_1(D,k6_group_1(B,A,C)) ) ) ) ) ) ).
fof(t6_group_4,axiom,
! [A] :
( v1_int_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] :
( m1_group_2(D,B)
=> ( r1_rlvect_1(D,C)
=> r1_rlvect_1(D,k6_group_1(B,A,C)) ) ) ) ) ) ).
fof(d3_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> k3_group_4(A,B) = k2_finsop_1(u1_struct_0(A),B,u1_group_1(A)) ) ) ).
fof(t7_group_4,axiom,
$true ).
fof(t8_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> k3_group_4(A,k8_finseq_1(u1_struct_0(A),B,C)) = k1_group_1(A,k3_group_4(A,B),k3_group_4(A,C)) ) ) ) ).
fof(t9_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_group_4(A,k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),C))) = k1_group_1(A,k3_group_4(A,B),C) ) ) ) ).
fof(t10_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_group_4(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),C),B)) = k1_group_1(A,C,k3_group_4(A,B)) ) ) ) ).
fof(t11_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_group_1(A)
& l1_group_1(A) )
=> k3_group_4(A,k6_finseq_1(u1_struct_0(A))) = k2_group_1(A) ) ).
fof(t12_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_group_4(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) ).
fof(t13_group_4,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))
=> k3_group_4(A,k7_rlvect_1(A,B,C)) = k1_group_1(A,B,C) ) ) ) ).
fof(t14_group_4,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))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( k3_group_4(A,k8_rlvect_1(A,B,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D)
& k3_group_4(A,k8_rlvect_1(A,B,C,D)) = k1_group_1(A,B,k1_group_1(A,C,D)) ) ) ) ) ) ).
fof(t15_group_4,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] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_group_4(B,k1_finsop_1(u1_struct_0(B),A,C)) = k6_group_1(B,A,C) ) ) ) ).
fof(t16_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> k3_group_4(A,k1_group_4(u1_struct_0(A),B,k6_domain_1(u1_struct_0(A),k2_group_1(A)))) = k3_group_4(A,B) ) ) ).
fof(t17_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( ( k3_finseq_1(B) = k3_finseq_1(C)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(B))
=> k1_funct_1(C,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),D),np__1)) = k3_group_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,D)) ) ) )
=> k3_group_4(A,B) = k3_group_1(A,k3_group_4(A,C)) ) ) ) ) ).
fof(t18_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_1(B),k4_finseq_1(B))
& v3_funct_2(D,k4_finseq_1(B),k4_finseq_1(B))
& m2_relset_1(D,k4_finseq_1(B),k4_finseq_1(B)) )
=> ( C = k5_relat_1(D,B)
=> k3_group_4(A,B) = k3_group_4(A,C) ) ) ) ) ) ) ).
fof(t19_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A)
& v2_funct_1(B)
& v2_funct_1(C)
& k2_relat_1(B) = k2_relat_1(C) )
=> k3_group_4(A,B) = k3_group_4(A,C) ) ) ) ) ).
fof(t20_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A)
& k3_finseq_1(B) = k3_finseq_1(C)
& k3_finseq_1(B) = k3_finseq_1(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(B))
=> k1_funct_1(B,E) = k1_group_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E),k4_finseq_4(k5_numbers,u1_struct_0(A),D,E)) ) ) )
=> k3_group_4(A,B) = k1_group_1(A,k3_group_4(A,C),k3_group_4(A,D)) ) ) ) ) ) ).
fof(t21_group_4,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( r1_tarski(k2_relat_1(C),k7_group_2(A,B))
=> r1_rlvect_1(B,k3_group_4(A,C)) ) ) ) ) ).
fof(d4_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( D = k4_group_4(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(C))
=> k1_funct_1(D,E) = k6_group_1(A,k2_group_4(k4_finseq_4(k5_numbers,k4_numbers,B,E)),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E)) ) ) ) ) ) ) ) ) ).
fof(t22_group_4,axiom,
$true ).
fof(t23_group_4,axiom,
$true ).
fof(t24_group_4,axiom,
$true ).
fof(t25_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,k4_numbers)
=> ! [E] :
( m2_finseq_1(E,k4_numbers)
=> ( ( k3_finseq_1(B) = k3_finseq_1(D)
& k3_finseq_1(C) = k3_finseq_1(E) )
=> k4_group_4(A,k8_finseq_1(k4_numbers,D,E),k8_finseq_1(u1_struct_0(A),B,C)) = k8_finseq_1(u1_struct_0(A),k4_group_4(A,D,B),k4_group_4(A,E,C)) ) ) ) ) ) ) ).
fof(t26_group_4,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,k4_numbers)
=> ( r1_tarski(k2_relat_1(C),k7_group_2(A,B))
=> r1_rlvect_1(B,k3_group_4(A,k4_group_4(A,D,C))) ) ) ) ) ) ).
fof(t27_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k4_group_4(A,k6_finseq_1(k4_numbers),k6_finseq_1(u1_struct_0(A))) = k1_xboole_0 ) ).
fof(t28_group_4,axiom,
! [A] :
( v1_int_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))
=> k4_group_4(B,k12_finseq_1(k4_numbers,k2_group_4(A)),k12_finseq_1(u1_struct_0(B),C)) = k12_finseq_1(u1_struct_0(B),k6_group_1(B,A,C)) ) ) ) ).
fof(t29_group_4,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_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(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k4_group_4(C,k2_finseq_4(k4_numbers,k2_group_4(A),k2_group_4(B)),k7_rlvect_1(C,D,E)) = k7_rlvect_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) ) ) ) ) ) ).
fof(t30_group_4,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_group_1(D)
& v4_group_1(D)
& l1_group_1(D) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(D))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> k4_group_4(D,k3_finseq_4(k4_numbers,k2_group_4(A),k2_group_4(B),k2_group_4(C)),k8_rlvect_1(D,E,F,G)) = k8_rlvect_1(D,k6_group_1(D,A,E),k6_group_1(D,B,F),k6_group_1(D,C,G)) ) ) ) ) ) ) ) ).
fof(t31_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> k4_group_4(A,k1_finsop_1(k4_numbers,k3_finseq_1(B),k2_group_4(np__1)),B) = B ) ) ).
fof(t32_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> k4_group_4(A,k1_finsop_1(k4_numbers,k3_finseq_1(B),k2_group_4(np__0)),B) = k1_finsop_1(u1_struct_0(A),k3_finseq_1(B),k2_group_1(A)) ) ) ).
fof(t33_group_4,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] :
( m2_finseq_1(C,k4_numbers)
=> ( k3_finseq_1(C) = A
=> k4_group_4(B,C,k1_finsop_1(u1_struct_0(B),A,k2_group_1(B))) = k1_finsop_1(u1_struct_0(B),A,k2_group_1(B)) ) ) ) ) ).
fof(d5_group_4,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] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> ( C = k5_group_4(A,B)
<=> ( r1_tarski(B,u1_struct_0(C))
& ! [D] :
( ( v1_group_1(D)
& m1_group_2(D,A) )
=> ( r1_tarski(B,u1_struct_0(D))
=> m1_group_2(C,D) ) ) ) ) ) ) ) ).
fof(t34_group_4,axiom,
$true ).
fof(t35_group_4,axiom,
$true ).
fof(t36_group_4,axiom,
$true ).
fof(t37_group_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_rlvect_1(k5_group_4(A,C),B)
<=> ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& ? [E] :
( m2_finseq_1(E,k4_numbers)
& k3_finseq_1(D) = k3_finseq_1(E)
& r1_tarski(k2_relat_1(D),C)
& k3_group_4(A,k4_group_4(A,E,D)) = B ) ) ) ) ) ) ).
fof(t38_group_4,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,C)
=> r1_rlvect_1(k5_group_4(A,C),B) ) ) ) ) ).
fof(t39_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> r1_group_2(A,k5_group_4(A,k1_subset_1(u1_struct_0(A))),k5_group_2(A)) ) ).
fof(t40_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> r1_group_2(A,k5_group_4(A,k7_group_2(A,B)),B) ) ) ).
fof(t41_group_4,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)))
=> ( r1_tarski(B,C)
=> m1_group_2(k5_group_4(A,B),k5_group_4(A,C)) ) ) ) ) ).
fof(t42_group_4,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)))
=> m1_group_2(k5_group_4(A,k5_subset_1(u1_struct_0(A),B,C)),k9_group_2(A,k5_group_4(A,B),k5_group_4(A,C))) ) ) ) ).
fof(t44_group_4,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)))
=> r1_group_2(A,k5_group_4(A,B),k5_group_4(A,k6_subset_1(u1_struct_0(A),B,k6_domain_1(u1_struct_0(A),k2_group_1(A))))) ) ) ).
fof(d6_group_4,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))
=> ( v1_group_4(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& k5_group_4(A,C) = g1_group_1(u1_struct_0(A),u1_group_1(A))
& k5_group_4(A,k6_subset_1(u1_struct_0(A),C,k6_domain_1(u1_struct_0(A),B))) != g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ) ).
fof(t45_group_4,axiom,
$true ).
fof(t46_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ~ v1_group_4(k2_group_1(A),A) ) ).
fof(d7_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( v2_group_4(B,A)
<=> ( g1_group_1(u1_struct_0(B),u1_group_1(B)) != g1_group_1(u1_struct_0(A),u1_group_1(A))
& ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> ( m1_group_2(B,C)
=> ( g1_group_1(u1_struct_0(B),u1_group_1(B)) = C
| C = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ) ) ) ) ).
fof(t47_group_4,axiom,
$true ).
fof(t48_group_4,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) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( v2_group_4(B,A)
=> ( r1_rlvect_1(B,C)
| k5_group_4(A,k4_subset_1(u1_struct_0(A),k7_group_2(A,B),k6_domain_1(u1_struct_0(A),C))) = A ) ) ) ) ) ).
fof(t49_group_4,axiom,
$true ).
fof(t50_group_4,axiom,
$true ).
fof(t51_group_4,axiom,
$true ).
fof(t52_group_4,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] :
( ( ~ v3_struct_0(C)
& v3_group_1(C)
& v4_group_1(C)
& l1_group_1(C) )
=> ( ? [D] :
( v1_group_1(D)
& m1_group_2(D,C)
& v2_group_4(D,C) )
=> ( r1_rlvect_1(k6_group_4(C),B)
<=> ! [D] :
( ( v1_group_1(D)
& m1_group_2(D,C) )
=> ( v2_group_4(D,C)
=> r1_rlvect_1(D,B) ) ) ) ) ) ) ) ).
fof(t53_group_4,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_1(C)
& m1_group_2(C,A) )
=> ~ v2_group_4(C,A) )
=> r1_rlvect_1(k6_group_4(A),B) ) ) ) ).
fof(t54_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ( v2_group_4(B,A)
=> m1_group_2(k6_group_4(A),B) ) ) ) ).
fof(t56_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r1_rlvect_1(k6_group_4(A),B)
<=> ~ v1_group_4(B,A) ) ) ) ).
fof(d9_group_4,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_2(C,A)
=> k7_group_4(A,B,C) = k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) ) ) ) ).
fof(t57_group_4,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_2(C,A)
=> ( k7_group_4(A,B,C) = k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C))
& k7_group_4(A,B,C) = k11_group_2(A,B,k7_group_2(A,C))
& k7_group_4(A,B,C) = k10_group_2(A,C,k7_group_2(A,B)) ) ) ) ) ).
fof(t58_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> k7_group_4(A,B,B) = k7_group_2(A,B) ) ) ).
fof(t59_group_4,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_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> k10_group_2(A,D,k7_group_4(A,B,C)) = k11_group_2(A,B,k7_group_4(A,C,D)) ) ) ) ) ).
fof(t60_group_4,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_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> k10_group_2(A,D,k12_group_2(A,C,B)) = k3_group_2(A,B,k7_group_4(A,C,D)) ) ) ) ) ).
fof(t61_group_4,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_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> k4_group_2(A,B,k7_group_4(A,C,D)) = k11_group_2(A,C,k13_group_2(A,D,B)) ) ) ) ) ).
fof(t62_group_4,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_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> k10_group_2(A,D,k10_group_2(A,C,B)) = k2_group_2(A,B,k7_group_4(A,C,D)) ) ) ) ) ).
fof(t63_group_4,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_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> k2_group_2(A,k7_group_4(A,C,D),B) = k11_group_2(A,C,k11_group_2(A,D,B)) ) ) ) ) ).
fof(t64_group_4,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) )
=> k7_group_4(A,B,C) = k7_group_4(A,C,B) ) ) ) ).
fof(t65_group_4,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_2(C,A)
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> k7_group_4(A,B,C) = k7_group_4(A,C,B) ) ) ) ) ).
fof(d10_group_4,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_2(C,A)
=> k8_group_4(A,B,C) = k5_group_4(A,k4_subset_1(u1_struct_0(A),k7_group_2(A,B),k7_group_2(A,C))) ) ) ) ).
fof(t66_group_4,axiom,
$true ).
fof(t67_group_4,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_group_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> ( r1_rlvect_1(k8_group_4(A,C,D),B)
<=> ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ? [F] :
( m2_finseq_1(F,k4_numbers)
& k3_finseq_1(E) = k3_finseq_1(F)
& r1_tarski(k2_relat_1(E),k4_subset_1(u1_struct_0(A),k7_group_2(A,C),k7_group_2(A,D)))
& B = k3_group_4(A,k4_group_4(A,F,E)) ) ) ) ) ) ) ) ).
fof(t68_group_4,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_2(C,A)
=> r1_group_2(A,k8_group_4(A,B,C),k5_group_4(A,k7_group_4(A,B,C))) ) ) ) ).
fof(t69_group_4,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_2(C,A)
=> ( k7_group_4(A,B,C) = k7_group_4(A,C,B)
=> u1_struct_0(k8_group_4(A,B,C)) = k7_group_4(A,B,C) ) ) ) ) ).
fof(t70_group_4,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_2(C,A)
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> u1_struct_0(k8_group_4(A,B,C)) = k7_group_4(A,B,C) ) ) ) ) ).
fof(t71_group_4,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) )
=> u1_struct_0(k8_group_4(A,B,C)) = k7_group_4(A,B,C) ) ) ) ).
fof(t72_group_4,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) )
=> ( v1_group_3(k8_group_4(A,B,C),A)
& m1_group_2(k8_group_4(A,B,C),A) ) ) ) ) ).
fof(t73_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> r1_group_2(A,k8_group_4(A,B,B),B) ) ) ).
fof(t74_group_4,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_2(C,A)
=> r1_group_2(A,k8_group_4(A,B,C),k8_group_4(A,C,B)) ) ) ) ).
fof(t75_group_4,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_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> r1_group_2(A,k8_group_4(A,k8_group_4(A,B,C),D),k8_group_4(A,B,k8_group_4(A,C,D))) ) ) ) ) ).
fof(t76_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ( r1_group_2(A,k8_group_4(A,k5_group_2(A),B),B)
& r1_group_2(A,k8_group_4(A,B,k5_group_2(A)),B) ) ) ) ).
fof(t77_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( r1_group_2(A,k8_group_4(A,k6_group_2(A),B),k6_group_2(A))
& r1_group_2(A,k8_group_4(A,B,k6_group_2(A)),k6_group_2(A)) ) ) ) ).
fof(t78_group_4,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_2(C,A)
=> ( m1_group_2(B,k8_group_4(A,B,C))
& m1_group_2(C,k8_group_4(A,B,C)) ) ) ) ) ).
fof(t79_group_4,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)
& m1_group_2(C,A) )
=> ( m1_group_2(B,C)
<=> r1_group_2(A,k8_group_4(A,B,C),C) ) ) ) ) ).
fof(t80_group_4,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_2(C,A)
=> ! [D] :
( m1_group_2(D,A)
=> ( m1_group_2(B,C)
=> m1_group_2(B,k8_group_4(A,C,D)) ) ) ) ) ) ).
fof(t81_group_4,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_2(C,A)
=> ! [D] :
( ( v1_group_1(D)
& m1_group_2(D,A) )
=> ( ( m1_group_2(B,D)
& m1_group_2(C,D) )
=> m1_group_2(k8_group_4(A,B,C),D) ) ) ) ) ) ).
fof(t82_group_4,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)
& m1_group_2(C,A) )
=> ! [D] :
( ( v1_group_1(D)
& m1_group_2(D,A) )
=> ( m1_group_2(B,D)
=> m1_group_2(k8_group_4(A,B,C),k8_group_4(A,D,C)) ) ) ) ) ) ).
fof(t83_group_4,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_2(C,A)
=> m1_group_2(k9_group_2(A,B,C),k8_group_4(A,B,C)) ) ) ) ).
fof(t84_group_4,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)
& m1_group_2(C,A) )
=> r1_group_2(A,k8_group_4(A,k9_group_2(A,B,C),C),C) ) ) ) ).
fof(t85_group_4,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)
& m1_group_2(C,A) )
=> r1_group_2(A,k9_group_2(A,C,k8_group_4(A,C,B)),C) ) ) ) ).
fof(t86_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> ( r1_group_2(A,k8_group_4(A,B,C),C)
<=> r1_group_2(A,k9_group_2(A,B,C),B) ) ) ) ) ).
fof(d11_group_4,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,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A))
& m2_relset_1(B,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) )
=> ( B = k9_group_4(A)
<=> ! [C] :
( m1_subset_1(C,k1_group_3(A))
=> ! [D] :
( m1_subset_1(D,k1_group_3(A))
=> ! [E] :
( m1_group_2(E,A)
=> ! [F] :
( m1_group_2(F,A)
=> ( ( C = E
& D = F )
=> k2_binop_1(k1_group_3(A),k1_group_3(A),k1_group_3(A),B,C,D) = k8_group_4(A,E,F) ) ) ) ) ) ) ) ) ).
fof(d12_group_4,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,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A))
& m2_relset_1(B,k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) )
=> ( B = k10_group_4(A)
<=> ! [C] :
( m1_subset_1(C,k1_group_3(A))
=> ! [D] :
( m1_subset_1(D,k1_group_3(A))
=> ! [E] :
( m1_group_2(E,A)
=> ! [F] :
( m1_group_2(F,A)
=> ( ( C = E
& D = F )
=> k2_binop_1(k1_group_3(A),k1_group_3(A),k1_group_3(A),B,C,D) = k9_group_2(A,E,F) ) ) ) ) ) ) ) ) ).
fof(d13_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k11_group_4(A) = g3_lattices(k1_group_3(A),k9_group_4(A),k10_group_4(A)) ) ).
fof(t87_group_4,axiom,
$true ).
fof(t88_group_4,axiom,
$true ).
fof(t89_group_4,axiom,
$true ).
fof(t90_group_4,axiom,
$true ).
fof(t91_group_4,axiom,
$true ).
fof(t92_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> u1_struct_0(k11_group_4(A)) = k1_group_3(A) ) ).
fof(t93_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> u2_lattices(k11_group_4(A)) = k9_group_4(A) ) ).
fof(t94_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> u1_lattices(k11_group_4(A)) = k10_group_4(A) ) ).
fof(t95_group_4,axiom,
$true ).
fof(t96_group_4,axiom,
$true ).
fof(t97_group_4,axiom,
$true ).
fof(t98_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k5_lattices(k11_group_4(A)) = k5_group_2(A) ) ).
fof(t99_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k6_lattices(k11_group_4(A)) = k6_group_2(A) ) ).
fof(s2_group_4,axiom,
? [A] :
( r1_tarski(A,k1_group_3(f1_s2_group_4))
& ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,f1_s2_group_4) )
=> ( r2_hidden(B,A)
<=> p1_s2_group_4(B) ) ) ) ).
fof(dt_k1_group_4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> m2_finseq_1(k1_group_4(A,B,C),A) ) ).
fof(redefinition_k1_group_4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> k1_group_4(A,B,C) = k1_finseq_3(B,C) ) ).
fof(dt_k2_group_4,axiom,
! [A] :
( v1_int_1(A)
=> m1_subset_1(k2_group_4(A),k4_numbers) ) ).
fof(dt_k3_group_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& m1_finseq_1(B,u1_struct_0(A)) )
=> m1_subset_1(k3_group_4(A,B),u1_struct_0(A)) ) ).
fof(dt_k4_group_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_finseq_1(B,k4_numbers)
& m1_finseq_1(C,u1_struct_0(A)) )
=> m2_finseq_1(k4_group_4(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k5_group_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_group_1(k5_group_4(A,B))
& m1_group_2(k5_group_4(A,B),A) ) ) ).
fof(dt_k6_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_1(k6_group_4(A))
& m1_group_2(k6_group_4(A),A) ) ) ).
fof(dt_k7_group_4,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)
& m1_group_2(C,A) )
=> m1_subset_1(k7_group_4(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k8_group_4,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)
& m1_group_2(C,A) )
=> ( v1_group_1(k8_group_4(A,B,C))
& m1_group_2(k8_group_4(A,B,C),A) ) ) ).
fof(dt_k9_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_funct_1(k9_group_4(A))
& v1_funct_2(k9_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A))
& m2_relset_1(k9_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) ) ) ).
fof(dt_k10_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_funct_1(k10_group_4(A))
& v1_funct_2(k10_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A))
& m2_relset_1(k10_group_4(A),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A)) ) ) ).
fof(dt_k11_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ~ v3_struct_0(k11_group_4(A))
& v3_lattices(k11_group_4(A))
& v10_lattices(k11_group_4(A))
& l3_lattices(k11_group_4(A)) ) ) ).
fof(t43_group_4,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)))
=> u1_struct_0(k5_group_4(A,B)) = k1_setfam_1(a_2_0_group_4(A,B)) ) ) ).
fof(d8_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> ( ( ? [C] :
( v1_group_1(C)
& m1_group_2(C,A)
& v2_group_4(C,A) )
=> ( B = k6_group_4(A)
<=> u1_struct_0(B) = k1_setfam_1(a_1_0_group_4(A)) ) )
& ( ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> ~ v2_group_4(C,A) )
=> ( B = k6_group_4(A)
<=> B = g1_group_1(u1_struct_0(A),u1_group_1(A)) ) ) ) ) ) ).
fof(t55_group_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> u1_struct_0(k6_group_4(A)) = a_1_1_group_4(A) ) ).
fof(s1_group_4,axiom,
( ? [A] :
( v1_group_1(A)
& m1_group_2(A,f1_s1_group_4)
& p1_s1_group_4(A) )
=> ? [A] :
( v1_group_1(A)
& m1_group_2(A,f1_s1_group_4)
& u1_struct_0(A) = k1_setfam_1(a_0_0_group_4) ) ) ).
fof(fraenkel_a_2_0_group_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_group_4(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( v1_group_1(E)
& m1_group_2(E,B)
& D = u1_struct_0(E)
& r1_tarski(C,k7_group_2(B,E)) ) ) ) ) ).
fof(fraenkel_a_1_0_group_4,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_4(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& ? [D] :
( v1_group_1(D)
& m1_group_2(D,B)
& C = u1_struct_0(D)
& v2_group_4(D,B) ) ) ) ) ).
fof(fraenkel_a_1_1_group_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v1_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r2_hidden(A,a_1_1_group_4(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = C
& ~ v1_group_4(C,B) ) ) ) ).
fof(fraenkel_a_0_0_group_4,axiom,
! [A] :
( r2_hidden(A,a_0_0_group_4)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_group_4)))
& A = B
& ? [C] :
( v1_group_1(C)
& m1_group_2(C,f1_s1_group_4)
& B = u1_struct_0(C)
& p1_s1_group_4(C) ) ) ) ).
%------------------------------------------------------------------------------