SET007 Axioms: SET007+252.ax
%------------------------------------------------------------------------------
% File : SET007+252 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Classes of Conjugation. Normal Subgroups
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 207 ( 24 unt; 0 def)
% Number of atoms : 1543 ( 136 equ)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 1545 ( 209 ~; 4 |; 763 &)
% ( 54 <=>; 515 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-3 aty)
% Number of functors : 52 ( 52 usr; 4 con; 0-5 aty)
% Number of variables : 560 ( 536 !; 24 ?)
% 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_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ~ v1_xboole_0(k1_group_3(A)) ) ).
fof(rc1_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ? [B] :
( m1_group_2(B,A)
& ~ v3_struct_0(B)
& v1_group_1(B)
& v2_group_1(B)
& v3_group_1(B)
& v4_group_1(B)
& v1_group_3(B,A) ) ) ).
fof(t1_group_3,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,C)) = B
& k1_group_1(A,k1_group_1(A,B,k3_group_1(A,C)),C) = B
& k1_group_1(A,k1_group_1(A,k3_group_1(A,C),C),B) = B
& k1_group_1(A,k1_group_1(A,C,k3_group_1(A,C)),B) = B
& k1_group_1(A,B,k1_group_1(A,C,k3_group_1(A,C))) = B
& k1_group_1(A,B,k1_group_1(A,k3_group_1(A,C),C)) = B
& k1_group_1(A,k3_group_1(A,C),k1_group_1(A,C,B)) = B
& k1_group_1(A,C,k1_group_1(A,k3_group_1(A,C),B)) = B ) ) ) ) ).
fof(t2_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
<=> v1_binop_1(u1_group_1(A),u1_struct_0(A)) ) ) ).
fof(t3_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> v7_group_1(k5_group_2(A)) ) ).
fof(t4_group_3,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] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,C)
& r1_tarski(D,E) )
=> r1_tarski(k2_group_2(A,B,D),k2_group_2(A,C,E)) ) ) ) ) ) ) ).
fof(t5_group_3,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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,D)
=> ( r1_tarski(k3_group_2(A,B,C),k3_group_2(A,B,D))
& r1_tarski(k4_group_2(A,B,C),k4_group_2(A,B,D)) ) ) ) ) ) ) ).
fof(t6_group_3,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)
=> ( m1_group_2(C,D)
=> ( r1_tarski(k12_group_2(A,C,B),k12_group_2(A,D,B))
& r1_tarski(k13_group_2(A,C,B),k13_group_2(A,D,B)) ) ) ) ) ) ) ).
fof(t7_group_3,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)
=> k12_group_2(A,C,B) = k10_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) ) ) ) ).
fof(t8_group_3,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)
=> k13_group_2(A,C,B) = k11_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) ) ) ) ).
fof(t9_group_3,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)))
=> ! [D] :
( m1_group_2(D,A)
=> k10_group_2(A,D,k3_group_2(A,B,C)) = k3_group_2(A,B,k10_group_2(A,D,C)) ) ) ) ) ).
fof(t10_group_3,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)))
=> ! [D] :
( m1_group_2(D,A)
=> k10_group_2(A,D,k4_group_2(A,B,C)) = k2_group_2(A,C,k12_group_2(A,D,B)) ) ) ) ) ).
fof(t11_group_3,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)))
=> ! [D] :
( m1_group_2(D,A)
=> k2_group_2(A,k12_group_2(A,D,B),C) = k3_group_2(A,B,k11_group_2(A,D,C)) ) ) ) ) ).
fof(t12_group_3,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)))
=> ! [D] :
( m1_group_2(D,A)
=> k4_group_2(A,B,k10_group_2(A,D,C)) = k2_group_2(A,C,k13_group_2(A,D,B)) ) ) ) ) ).
fof(t13_group_3,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)))
=> ! [D] :
( m1_group_2(D,A)
=> k2_group_2(A,k13_group_2(A,D,B),C) = k11_group_2(A,D,k3_group_2(A,B,C)) ) ) ) ) ).
fof(t14_group_3,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)))
=> ! [D] :
( m1_group_2(D,A)
=> k4_group_2(A,B,k11_group_2(A,D,C)) = k11_group_2(A,D,k4_group_2(A,B,C)) ) ) ) ) ).
fof(t15_group_3,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,k13_group_2(A,C,B)) = k11_group_2(A,C,k12_group_2(A,D,B)) ) ) ) ) ).
fof(d1_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( B = k1_group_3(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v1_group_1(C)
& m1_group_2(C,A) ) ) ) ) ).
fof(t16_group_3,axiom,
$true ).
fof(t17_group_3,axiom,
$true ).
fof(t18_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> r2_hidden(A,k1_group_3(A)) ) ).
fof(t19_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v6_group_1(A)
=> v1_finset_1(k1_group_3(A)) ) ) ).
fof(d2_group_3,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))
=> k2_group_3(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C) ) ) ) ).
fof(t20_group_3,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))
=> ( k2_group_3(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C)
& k2_group_3(A,B,C) = k1_group_1(A,k3_group_1(A,C),k1_group_1(A,B,C)) ) ) ) ) ).
fof(t21_group_3,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))
=> ( k2_group_3(A,B,C) = k2_group_3(A,D,C)
=> B = D ) ) ) ) ) ).
fof(t22_group_3,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))
=> k2_group_3(A,k2_group_1(A),B) = k2_group_1(A) ) ) ).
fof(t23_group_3,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))
=> ( k2_group_3(A,B,C) = k2_group_1(A)
=> B = k2_group_1(A) ) ) ) ) ).
fof(t24_group_3,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))
=> k2_group_3(A,B,k2_group_1(A)) = B ) ) ).
fof(t25_group_3,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))
=> k2_group_3(A,B,B) = B ) ) ).
fof(t26_group_3,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))
=> ( k2_group_3(A,B,k3_group_1(A,B)) = B
& k2_group_3(A,k3_group_1(A,B),B) = k3_group_1(A,B) ) ) ) ).
fof(t27_group_3,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))
=> ( k2_group_3(A,B,C) = B
<=> k1_group_1(A,B,C) = k1_group_1(A,C,B) ) ) ) ) ).
fof(t28_group_3,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))
=> k2_group_3(A,k1_group_1(A,B,C),D) = k1_group_1(A,k2_group_3(A,B,D),k2_group_3(A,C,D)) ) ) ) ) ).
fof(t29_group_3,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))
=> k2_group_3(A,k2_group_3(A,B,C),D) = k2_group_3(A,B,k1_group_1(A,C,D)) ) ) ) ) ).
fof(t30_group_3,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))
=> ( k2_group_3(A,k2_group_3(A,B,C),k3_group_1(A,C)) = B
& k2_group_3(A,k2_group_3(A,B,k3_group_1(A,C)),C) = B ) ) ) ) ).
fof(t31_group_3,axiom,
$true ).
fof(t32_group_3,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))
=> k2_group_3(A,k3_group_1(A,B),C) = k3_group_1(A,k2_group_3(A,B,C)) ) ) ) ).
fof(t33_group_3,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_group_3(A,k6_group_1(A,D,B),C) = k6_group_1(A,D,k2_group_3(A,B,C)) ) ) ) ) ).
fof(t34_group_3,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] :
( v1_int_1(D)
=> k2_group_3(A,k6_group_1(A,D,B),C) = k6_group_1(A,D,k2_group_3(A,B,C)) ) ) ) ) ).
fof(t35_group_3,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))
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> k2_group_3(A,B,C) = B ) ) ) ) ).
fof(t36_group_3,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))
=> k2_group_3(A,B,C) = B ) )
=> v7_group_1(A) ) ) ).
fof(t37_group_3,axiom,
$true ).
fof(t38_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(A,k3_group_3(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k2_group_3(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ) ) ) ).
fof(t39_group_3,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)))
=> ( k3_group_3(A,B,C) != k1_xboole_0
<=> ( B != k1_xboole_0
& C != k1_xboole_0 ) ) ) ) ) ).
fof(t40_group_3,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(k3_group_3(A,B,C),k2_group_2(A,k2_group_2(A,k1_group_2(A,C),B),C)) ) ) ) ).
fof(t41_group_3,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] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k3_group_3(A,k2_group_2(A,B,C),D),k2_group_2(A,k3_group_3(A,B,D),k3_group_3(A,C,D))) ) ) ) ) ).
fof(t42_group_3,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] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k3_group_3(A,k3_group_3(A,B,C),D) = k3_group_3(A,B,k2_group_2(A,C,D)) ) ) ) ) ).
fof(t43_group_3,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)))
=> k3_group_3(A,k1_group_2(A,B),C) = k1_group_2(A,k3_group_3(A,B,C)) ) ) ) ).
fof(t44_group_3,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))
=> k3_group_3(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)) = k6_domain_1(u1_struct_0(A),k2_group_3(A,B,C)) ) ) ) ).
fof(t45_group_3,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_3(A,k6_domain_1(u1_struct_0(A),B),k7_domain_1(u1_struct_0(A),C,D)) = k7_domain_1(u1_struct_0(A),k2_group_3(A,B,C),k2_group_3(A,B,D)) ) ) ) ) ).
fof(t46_group_3,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_3(A,k7_domain_1(u1_struct_0(A),B,C),k6_domain_1(u1_struct_0(A),D)) = k7_domain_1(u1_struct_0(A),k2_group_3(A,B,D),k2_group_3(A,C,D)) ) ) ) ) ).
fof(t47_group_3,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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_group_3(A,k7_domain_1(u1_struct_0(A),B,C),k7_domain_1(u1_struct_0(A),D,E)) = k9_domain_1(u1_struct_0(A),k2_group_3(A,B,D),k2_group_3(A,B,E),k2_group_3(A,C,D),k2_group_3(A,C,E)) ) ) ) ) ) ).
fof(d4_group_3,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,u1_struct_0(A))
=> k4_group_3(A,B,C) = k3_group_3(A,B,k6_domain_1(u1_struct_0(A),C)) ) ) ) ).
fof(d5_group_3,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,u1_struct_0(A))
=> k5_group_3(A,B,C) = k3_group_3(A,k6_domain_1(u1_struct_0(A),C),B) ) ) ) ).
fof(t48_group_3,axiom,
$true ).
fof(t49_group_3,axiom,
$true ).
fof(t50_group_3,axiom,
! [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_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(A,k4_group_3(B,D,C))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k2_group_3(B,E,C)
& r2_hidden(E,D) ) ) ) ) ) ).
fof(t51_group_3,axiom,
! [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_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(A,k5_group_3(B,D,C))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k2_group_3(B,C,E)
& r2_hidden(E,D) ) ) ) ) ) ).
fof(t52_group_3,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_tarski(k5_group_3(A,C,B),k2_group_2(A,k4_group_2(A,B,k1_group_2(A,C)),C)) ) ) ) ).
fof(t53_group_3,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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k4_group_3(A,k3_group_3(A,C,D),B) = k3_group_3(A,C,k4_group_2(A,B,D)) ) ) ) ) ).
fof(t54_group_3,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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k3_group_3(A,k4_group_3(A,C,B),D) = k3_group_3(A,C,k3_group_2(A,B,D)) ) ) ) ) ).
fof(t55_group_3,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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k3_group_3(A,k5_group_3(A,C,B),D) = k5_group_3(A,k2_group_2(A,C,D),B) ) ) ) ) ).
fof(t56_group_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> k4_group_3(A,k4_group_3(A,D,B),C) = k4_group_3(A,D,k1_group_1(A,B,C)) ) ) ) ) ).
fof(t57_group_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> k4_group_3(A,k5_group_3(A,D,B),C) = k5_group_3(A,k4_group_2(A,C,D),B) ) ) ) ) ).
fof(t58_group_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> k5_group_3(A,D,k2_group_3(A,B,C)) = k5_group_3(A,k3_group_2(A,C,D),B) ) ) ) ) ).
fof(t59_group_3,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)))
=> k4_group_3(A,C,B) = k4_group_2(A,B,k3_group_2(A,k3_group_1(A,B),C)) ) ) ) ).
fof(t60_group_3,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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k4_group_3(A,k2_group_2(A,C,D),B),k2_group_2(A,k4_group_3(A,C,B),k4_group_3(A,D,B))) ) ) ) ) ).
fof(t61_group_3,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)))
=> k4_group_3(A,B,k2_group_1(A)) = B ) ) ).
fof(t62_group_3,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 != k1_xboole_0
=> k5_group_3(A,B,k2_group_1(A)) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) ).
fof(t63_group_3,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)))
=> ( k4_group_3(A,k4_group_3(A,C,B),k3_group_1(A,B)) = C
& k4_group_3(A,k4_group_3(A,C,k3_group_1(A,B)),B) = C ) ) ) ) ).
fof(t64_group_3,axiom,
$true ).
fof(t65_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_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)))
=> ( C != k1_xboole_0
=> k3_group_3(A,B,C) = B ) ) ) ) ) ).
fof(t66_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_group_3(A,B,C) = B ) ) ) ) ).
fof(t67_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( B != k1_xboole_0
=> k5_group_3(A,B,C) = k6_domain_1(u1_struct_0(A),C) ) ) ) ) ) ).
fof(d6_group_3,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] :
( ( v1_group_1(D)
& m1_group_2(D,A) )
=> ( D = k6_group_3(A,B,C)
<=> u1_struct_0(D) = k4_group_3(A,k7_group_2(A,B),C) ) ) ) ) ) ).
fof(t68_group_3,axiom,
$true ).
fof(t69_group_3,axiom,
$true ).
fof(t70_group_3,axiom,
! [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(k6_group_3(B,D,C),A)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k2_group_3(B,E,C)
& r1_rlvect_1(D,E) ) ) ) ) ) ).
fof(t71_group_3,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)
=> u1_struct_0(k6_group_3(A,C,B)) = k4_group_2(A,B,k12_group_2(A,C,k3_group_1(A,B))) ) ) ) ).
fof(t72_group_3,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_group_2(D,A)
=> r1_group_2(A,k6_group_3(A,k6_group_3(A,D,B),C),k6_group_3(A,D,k1_group_1(A,B,C))) ) ) ) ) ).
fof(t73_group_3,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,k6_group_3(A,B,k2_group_1(A)),B) ) ) ).
fof(t74_group_3,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) )
=> ( r1_group_2(A,k6_group_3(A,k6_group_3(A,C,B),k3_group_1(A,B)),C)
& r1_group_2(A,k6_group_3(A,k6_group_3(A,C,k3_group_1(A,B)),B),C) ) ) ) ) ).
fof(t75_group_3,axiom,
$true ).
fof(t76_group_3,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_group_2(A,k6_group_3(A,k9_group_2(A,C,D),B),k9_group_2(A,k6_group_3(A,C,B),k6_group_3(A,D,B))) ) ) ) ) ).
fof(t77_group_3,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)
=> k8_group_1(C) = k8_group_1(k6_group_3(A,C,B)) ) ) ) ).
fof(t78_group_3,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)
=> ( v6_group_1(C)
<=> v6_group_1(k6_group_3(A,C,B)) ) ) ) ) ).
fof(t79_group_3,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)
=> ( v6_group_1(C)
=> k9_group_1(C) = k9_group_1(k6_group_3(A,C,B)) ) ) ) ) ).
fof(t80_group_3,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))
=> r1_group_2(A,k6_group_3(A,k5_group_2(A),B),k5_group_2(A)) ) ) ).
fof(t81_group_3,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) )
=> ( r1_group_2(A,k6_group_3(A,C,B),k5_group_2(A))
=> r1_group_2(A,C,k5_group_2(A)) ) ) ) ) ).
fof(t82_group_3,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))
=> r1_group_2(A,k6_group_3(A,k6_group_2(A),B),k6_group_2(A)) ) ) ).
fof(t83_group_3,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) )
=> ( k6_group_3(A,C,B) = A
=> C = A ) ) ) ) ).
fof(t84_group_3,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)
=> k16_group_2(A,C) = k16_group_2(A,k6_group_3(A,C,B)) ) ) ) ).
fof(t85_group_3,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)
=> ( v1_finset_1(k14_group_2(A,C))
=> k17_group_2(A,C) = k17_group_2(A,k6_group_3(A,C,B)) ) ) ) ) ).
fof(t86_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_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))
=> r1_group_2(A,k6_group_3(A,B,C),B) ) ) ) ) ).
fof(d7_group_3,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))
=> ( r1_group_3(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k2_group_3(A,C,D) ) ) ) ) ) ).
fof(t87_group_3,axiom,
$true ).
fof(t88_group_3,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))
=> ( r1_group_3(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k2_group_3(A,B,D) ) ) ) ) ) ).
fof(t89_group_3,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))
=> r1_group_3(A,B,B) ) ) ).
fof(t90_group_3,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))
=> ( r1_group_3(A,B,C)
=> r1_group_3(A,C,B) ) ) ) ) ).
fof(t91_group_3,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))
=> ( ( r2_group_3(A,B,C)
& r2_group_3(A,C,D) )
=> r2_group_3(A,B,D) ) ) ) ) ) ).
fof(t92_group_3,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))
=> ( ( r2_group_3(A,B,k2_group_1(A))
| r2_group_3(A,k2_group_1(A),B) )
=> B = k2_group_1(A) ) ) ) ).
fof(d8_group_3,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))
=> k7_group_3(A,B) = k5_group_3(A,k7_group_2(A,k6_group_2(A)),B) ) ) ).
fof(t94_group_3,axiom,
$true ).
fof(t95_group_3,axiom,
! [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))
=> ( r2_hidden(A,k7_group_3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& D = A
& r2_group_3(B,C,D) ) ) ) ) ).
fof(t96_group_3,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))
=> ( r2_hidden(B,k7_group_3(A,C))
<=> r2_group_3(A,B,C) ) ) ) ) ).
fof(t97_group_3,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))
=> r2_hidden(k2_group_3(A,B,C),k7_group_3(A,B)) ) ) ) ).
fof(t98_group_3,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))
=> r2_hidden(B,k7_group_3(A,B)) ) ) ).
fof(t99_group_3,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))
=> ( r2_hidden(B,k7_group_3(A,C))
=> r2_hidden(C,k7_group_3(A,B)) ) ) ) ) ).
fof(t100_group_3,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))
=> ( k7_group_3(A,B) = k7_group_3(A,C)
<=> ~ r1_xboole_0(k7_group_3(A,B),k7_group_3(A,C)) ) ) ) ) ).
fof(t101_group_3,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))
=> ( k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),k2_group_1(A))
<=> B = k2_group_1(A) ) ) ) ).
fof(t102_group_3,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)))
=> k2_group_2(A,k7_group_3(A,B),C) = k2_group_2(A,C,k7_group_3(A,B)) ) ) ) ).
fof(d9_group_3,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)))
=> ( r3_group_3(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& B = k4_group_3(A,C,D) ) ) ) ) ) ).
fof(t103_group_3,axiom,
$true ).
fof(t104_group_3,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)))
=> ( r3_group_3(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k4_group_3(A,B,D) ) ) ) ) ) ).
fof(t105_group_3,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)))
=> r3_group_3(A,B,B) ) ) ).
fof(t106_group_3,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)))
=> ( r3_group_3(A,B,C)
=> r3_group_3(A,C,B) ) ) ) ) ).
fof(t107_group_3,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] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r4_group_3(A,B,C)
& r4_group_3(A,C,D) )
=> r4_group_3(A,B,D) ) ) ) ) ) ).
fof(t108_group_3,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))
=> ( r4_group_3(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C))
<=> r2_group_3(A,B,C) ) ) ) ) ).
fof(t109_group_3,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)
=> ~ ( r4_group_3(A,B,k7_group_2(A,C))
& ! [D] :
( ( v1_group_1(D)
& m1_group_2(D,A) )
=> u1_struct_0(D) != B ) ) ) ) ) ).
fof(t110_group_3,axiom,
$true ).
fof(t111_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(A,k8_group_3(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& r4_group_3(B,C,D) ) ) ) ) ).
fof(t112_group_3,axiom,
$true ).
fof(t113_group_3,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)))
=> ( r2_hidden(B,k8_group_3(A,C))
<=> r4_group_3(A,B,C) ) ) ) ) ).
fof(t114_group_3,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(k4_group_3(A,C,B),k8_group_3(A,C)) ) ) ) ).
fof(t115_group_3,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)))
=> r2_hidden(B,k8_group_3(A,B)) ) ) ).
fof(t116_group_3,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)))
=> ( r2_hidden(B,k8_group_3(A,C))
=> r2_hidden(C,k8_group_3(A,B)) ) ) ) ) ).
fof(t117_group_3,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)))
=> ( k8_group_3(A,B) = k8_group_3(A,C)
<=> ~ r1_xboole_0(k8_group_3(A,B),k8_group_3(A,C)) ) ) ) ) ).
fof(t119_group_3,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)))
=> ( v6_group_1(A)
=> v1_finset_1(k8_group_3(A,B)) ) ) ) ).
fof(d11_group_3,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)
=> ( r5_group_3(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& g1_group_1(u1_struct_0(B),u1_group_1(B)) = k6_group_3(A,C,D) ) ) ) ) ) ).
fof(t120_group_3,axiom,
$true ).
fof(t121_group_3,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) )
=> ( r5_group_3(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r1_group_2(A,C,k6_group_3(A,B,D)) ) ) ) ) ) ).
fof(t122_group_3,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) )
=> r5_group_3(A,B,B) ) ) ).
fof(t123_group_3,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) )
=> ( r5_group_3(A,B,C)
=> r5_group_3(A,C,B) ) ) ) ) ).
fof(t124_group_3,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) )
=> ( ( r6_group_3(A,C,D)
& r5_group_3(A,D,B) )
=> r5_group_3(A,C,B) ) ) ) ) ) ).
fof(d12_group_3,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,k1_zfmisc_1(k1_group_3(A)))
=> ( C = k9_group_3(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v1_group_1(E)
& m1_group_2(E,A)
& D = E
& r5_group_3(A,B,E) ) ) ) ) ) ) ).
fof(t125_group_3,axiom,
$true ).
fof(t126_group_3,axiom,
$true ).
fof(t127_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( m1_group_2(C,B)
=> ( r2_hidden(A,k9_group_3(B,C))
=> ( v1_group_1(A)
& m1_group_2(A,B) ) ) ) ) ).
fof(t128_group_3,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) )
=> ( r2_hidden(B,k9_group_3(A,C))
<=> r6_group_3(A,B,C) ) ) ) ) ).
fof(t129_group_3,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) )
=> r2_hidden(k6_group_3(A,C,B),k9_group_3(A,C)) ) ) ) ).
fof(t130_group_3,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) )
=> r2_hidden(B,k9_group_3(A,B)) ) ) ).
fof(t131_group_3,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) )
=> ( r2_hidden(B,k9_group_3(A,C))
=> r2_hidden(C,k9_group_3(A,B)) ) ) ) ) ).
fof(t132_group_3,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) )
=> ( k9_group_3(A,B) = k9_group_3(A,C)
<=> ~ r1_xboole_0(k9_group_3(A,B),k9_group_3(A,C)) ) ) ) ) ).
fof(t133_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( v6_group_1(A)
=> v1_finset_1(k9_group_3(A,B)) ) ) ) ).
fof(t134_group_3,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) )
=> ( r5_group_3(A,C,B)
<=> r4_group_3(A,k7_group_2(A,C),k7_group_2(A,B)) ) ) ) ) ).
fof(d13_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( v1_group_3(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_group_3(A,B,C) = g1_group_1(u1_struct_0(B),u1_group_1(B)) ) ) ) ) ).
fof(t135_group_3,axiom,
$true ).
fof(t136_group_3,axiom,
$true ).
fof(t137_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_3(k5_group_2(A),A)
& v1_group_3(k6_group_2(A),A) ) ) ).
fof(t138_group_3,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(k9_group_2(A,B,C),A) ) ) ) ).
fof(t139_group_3,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) )
=> ( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& l1_group_1(A) )
=> v1_group_3(B,A) ) ) ) ).
fof(t140_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_group_2(A,B,C) = k13_group_2(A,B,C) ) ) ) ) ).
fof(t141_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_tarski(k12_group_2(A,B,C),k13_group_2(A,B,C)) ) ) ) ) ).
fof(t142_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_tarski(k13_group_2(A,B,C),k12_group_2(A,B,C)) ) ) ) ) ).
fof(t143_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k10_group_2(A,B,C) = k11_group_2(A,B,C) ) ) ) ) ).
fof(t144_group_3,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) )
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> m1_group_2(B,k6_group_3(A,B,C)) ) ) ) ) ).
fof(t145_group_3,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) )
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> m1_group_2(k6_group_3(A,B,C),B) ) ) ) ) ).
fof(t146_group_3,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) )
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> k9_group_3(A,B) = k1_tarski(B) ) ) ) ).
fof(t147_group_3,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) )
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
=> r1_tarski(k7_group_3(A,C),k7_group_2(A,B)) ) ) ) ) ) ).
fof(t148_group_3,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) )
=> k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) = k2_group_2(A,k7_group_2(A,C),k7_group_2(A,B)) ) ) ) ).
fof(t149_group_3,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) )
=> ? [D] :
( v1_group_1(D)
& v1_group_3(D,A)
& m1_group_2(D,A)
& u1_struct_0(D) = k2_group_2(A,k7_group_2(A,B),k7_group_2(A,C)) ) ) ) ) ).
fof(t150_group_3,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) )
=> k14_group_2(A,B) = k15_group_2(A,B) ) ) ).
fof(t151_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ( v1_finset_1(k14_group_2(A,B))
& k17_group_2(A,B) = np__2 )
=> ( v1_group_3(B,A)
& m1_group_2(B,A) ) ) ) ) ).
fof(t152_group_3,axiom,
$true ).
fof(t153_group_3,axiom,
$true ).
fof(t154_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_rlvect_1(k10_group_3(B,C),A)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& k4_group_3(B,C,D) = C ) ) ) ) ).
fof(t155_group_3,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)))
=> k1_card_1(k8_group_3(A,B)) = k16_group_2(A,k10_group_3(A,B)) ) ) ).
fof(t156_group_3,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)))
=> ~ ( ( v1_finset_1(k8_group_3(A,B))
| v1_finset_1(k14_group_2(A,k10_group_3(A,B))) )
& ! [C] :
( v1_finset_1(C)
=> ~ ( C = k8_group_3(A,B)
& k4_card_1(C) = k17_group_2(A,k10_group_3(A,B)) ) ) ) ) ) ).
fof(t157_group_3,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))
=> k1_card_1(k7_group_3(A,B)) = k16_group_2(A,k10_group_3(A,k6_domain_1(u1_struct_0(A),B))) ) ) ).
fof(t158_group_3,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_finset_1(k7_group_3(A,B))
| v1_finset_1(k14_group_2(A,k10_group_3(A,k6_domain_1(u1_struct_0(A),B)))) )
& ! [C] :
( v1_finset_1(C)
=> ~ ( C = k7_group_3(A,B)
& k4_card_1(C) = k17_group_2(A,k10_group_3(A,k6_domain_1(u1_struct_0(A),B))) ) ) ) ) ) ).
fof(d15_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> k11_group_3(A,B) = k10_group_3(A,k7_group_2(A,B)) ) ) ).
fof(t159_group_3,axiom,
$true ).
fof(t160_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,B) )
=> ( r1_rlvect_1(k11_group_3(B,C),A)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r1_group_2(B,k6_group_3(B,C,D),C) ) ) ) ) ).
fof(t161_group_3,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) )
=> k1_card_1(k9_group_3(A,B)) = k16_group_2(A,k11_group_3(A,B)) ) ) ).
fof(t162_group_3,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) )
=> ~ ( ( v1_finset_1(k9_group_3(A,B))
| v1_finset_1(k14_group_2(A,k11_group_3(A,B))) )
& ! [C] :
( v1_finset_1(C)
=> ~ ( C = k9_group_3(A,B)
& k4_card_1(C) = k17_group_2(A,k11_group_3(A,B)) ) ) ) ) ) ).
fof(t163_group_3,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) )
=> ( ( v1_group_3(B,A)
& m1_group_2(B,A) )
<=> k11_group_3(A,B) = A ) ) ) ).
fof(t164_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k11_group_3(A,k5_group_2(A)) = A ) ).
fof(t165_group_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k11_group_3(A,k6_group_2(A)) = A ) ).
fof(symmetry_r2_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r2_group_3(A,B,C)
=> r2_group_3(A,C,B) ) ) ).
fof(reflexivity_r2_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r2_group_3(A,B,B) ) ).
fof(redefinition_r2_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r2_group_3(A,B,C)
<=> r1_group_3(A,B,C) ) ) ).
fof(symmetry_r4_group_3,axiom,
! [A,B,C] :
( ( ~ 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)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r4_group_3(A,B,C)
=> r4_group_3(A,C,B) ) ) ).
fof(reflexivity_r4_group_3,axiom,
! [A,B,C] :
( ( ~ 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)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r4_group_3(A,B,B) ) ).
fof(redefinition_r4_group_3,axiom,
! [A,B,C] :
( ( ~ 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)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r4_group_3(A,B,C)
<=> r3_group_3(A,B,C) ) ) ).
fof(symmetry_r6_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_1(B)
& m1_group_2(B,A)
& v1_group_1(C)
& m1_group_2(C,A) )
=> ( r6_group_3(A,B,C)
=> r6_group_3(A,C,B) ) ) ).
fof(reflexivity_r6_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_1(B)
& m1_group_2(B,A)
& v1_group_1(C)
& m1_group_2(C,A) )
=> r6_group_3(A,B,B) ) ).
fof(redefinition_r6_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& v1_group_1(B)
& m1_group_2(B,A)
& v1_group_1(C)
& m1_group_2(C,A) )
=> ( r6_group_3(A,B,C)
<=> r5_group_3(A,B,C) ) ) ).
fof(dt_k1_group_3,axiom,
$true ).
fof(dt_k2_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_group_3(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_group_3,axiom,
! [A,B,C] :
( ( ~ 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)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k3_group_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k4_group_3,axiom,
! [A,B,C] :
( ( ~ 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)))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_group_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_group_3,axiom,
! [A,B,C] :
( ( ~ 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)))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k5_group_3(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_group_3,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_subset_1(C,u1_struct_0(A)) )
=> ( v1_group_1(k6_group_3(A,B,C))
& m1_group_2(k6_group_3(A,B,C),A) ) ) ).
fof(dt_k7_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k7_group_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k8_group_3,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))) )
=> m1_subset_1(k8_group_3(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k9_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A) )
=> m1_subset_1(k9_group_3(A,B),k1_zfmisc_1(k1_group_3(A))) ) ).
fof(dt_k10_group_3,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(k10_group_3(A,B))
& m1_group_2(k10_group_3(A,B),A) ) ) ).
fof(dt_k11_group_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_group_2(B,A) )
=> ( v1_group_1(k11_group_3(A,B))
& m1_group_2(k11_group_3(A,B),A) ) ) ).
fof(d3_group_3,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)))
=> k3_group_3(A,B,C) = a_3_0_group_3(A,B,C) ) ) ) ).
fof(t93_group_3,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))
=> k5_group_3(A,k7_group_2(A,k6_group_2(A)),B) = a_2_0_group_3(A,B) ) ) ).
fof(d10_group_3,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)))
=> k8_group_3(A,B) = a_2_1_group_3(A,B) ) ) ).
fof(t118_group_3,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))
=> k8_group_3(A,k6_domain_1(u1_struct_0(A),B)) = a_2_2_group_3(A,B) ) ) ).
fof(d14_group_3,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 = k10_group_3(A,B)
<=> u1_struct_0(C) = a_2_3_group_3(A,B) ) ) ) ) ).
fof(fraenkel_a_3_0_group_3,axiom,
! [A,B,C,D] :
( ( ~ 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)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_group_3(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k2_group_3(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_2_0_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_group_3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r2_group_3(B,C,D) ) ) ) ).
fof(fraenkel_a_2_1_group_3,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_1_group_3(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& r4_group_3(B,C,D) ) ) ) ).
fof(fraenkel_a_2_2_group_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_2_group_3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k6_domain_1(u1_struct_0(B),D)
& r2_hidden(D,k7_group_3(B,C)) ) ) ) ).
fof(fraenkel_a_2_3_group_3,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_3_group_3(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& k4_group_3(B,C,D) = C ) ) ) ).
%------------------------------------------------------------------------------