SET007 Axioms: SET007+298.ax
%------------------------------------------------------------------------------
% File : SET007+298 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Commutator and Center of a 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_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 118 ( 13 unt; 0 def)
% Number of atoms : 922 ( 95 equ)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 919 ( 115 ~; 0 |; 473 &)
% ( 25 <=>; 306 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 53 ( 53 usr; 9 con; 0-4 aty)
% Number of variables : 349 ( 323 !; 26 ?)
% 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(t1_group_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r1_rlvect_1(k5_group_2(B),A)
<=> A = k2_group_1(B) ) ) ).
fof(t2_group_5,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_rlvect_1(D,B)
& r1_rlvect_1(D,C) )
=> r1_rlvect_1(D,k2_group_3(A,B,C)) ) ) ) ) ) ).
fof(t3_group_5,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_group_1(D)
& v1_group_3(D,A)
& m1_group_2(D,A) )
=> ( r1_rlvect_1(D,B)
=> r1_rlvect_1(D,k2_group_3(A,B,C)) ) ) ) ) ) ).
fof(t4_group_5,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)
=> ! [D] :
( m1_group_2(D,B)
=> ( r2_hidden(A,k7_group_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_group_1(B,E,F)
& r1_rlvect_1(C,E)
& r1_rlvect_1(D,F) ) ) ) ) ) ) ).
fof(t5_group_5,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)
=> ! [D] :
( m1_group_2(D,B)
=> ( k7_group_4(B,C,D) = k7_group_4(B,D,C)
=> ( r1_rlvect_1(k8_group_4(B,C,D),A)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_group_1(B,E,F)
& r1_rlvect_1(C,E)
& r1_rlvect_1(D,F) ) ) ) ) ) ) ) ).
fof(t6_group_5,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)
=> ! [D] :
( m1_group_2(D,B)
=> ( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& l1_group_1(B) )
=> ( r1_rlvect_1(k8_group_4(B,C,D),A)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_group_1(B,E,F)
& r1_rlvect_1(C,E)
& r1_rlvect_1(D,F) ) ) ) ) ) ) ) ).
fof(t7_group_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ! [C] :
( ( v1_group_1(C)
& v1_group_3(C,B)
& m1_group_2(C,B) )
=> ! [D] :
( ( v1_group_1(D)
& v1_group_3(D,B)
& m1_group_2(D,B) )
=> ( r1_rlvect_1(k8_group_4(B,C,D),A)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_group_1(B,E,F)
& r1_rlvect_1(C,E)
& r1_rlvect_1(D,F) ) ) ) ) ) ) ).
fof(t8_group_5,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) )
=> k7_group_4(A,B,C) = k7_group_4(A,C,B) ) ) ) ).
fof(d1_group_5,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( D = k1_group_5(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(B))
=> k1_funct_1(D,E) = k2_group_3(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),C) ) ) ) ) ) ) ) ) ).
fof(t9_group_5,axiom,
$true ).
fof(t10_group_5,axiom,
$true ).
fof(t11_group_5,axiom,
$true ).
fof(t12_group_5,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> k8_finseq_1(u1_struct_0(A),k1_group_5(A,C,B),k1_group_5(A,D,B)) = k1_group_5(A,k8_finseq_1(u1_struct_0(A),C,D),B) ) ) ) ) ).
fof(t13_group_5,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_group_5(A,k6_finseq_1(u1_struct_0(A)),B) = k1_xboole_0 ) ) ).
fof(t14_group_5,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_5(A,k12_finseq_1(u1_struct_0(A),B),C) = k12_finseq_1(u1_struct_0(A),k2_group_3(A,B,C)) ) ) ) ).
fof(t15_group_5,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))
=> k1_group_5(A,k7_rlvect_1(A,B,C),D) = k7_rlvect_1(A,k2_group_3(A,B,D),k2_group_3(A,C,D)) ) ) ) ) ).
fof(t16_group_5,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))
=> k1_group_5(A,k8_rlvect_1(A,B,C,D),E) = k8_rlvect_1(A,k2_group_3(A,B,E),k2_group_3(A,C,E),k2_group_3(A,D,E)) ) ) ) ) ) ).
fof(t17_group_5,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> k3_group_4(A,k1_group_5(A,C,B)) = k2_group_3(A,k3_group_4(A,C),B) ) ) ) ).
fof(t18_group_5,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,k4_numbers)
=> k4_group_4(A,D,k1_group_5(A,C,B)) = k1_group_5(A,k4_group_4(A,D,C),B) ) ) ) ) ).
fof(d2_group_5,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_5(A,B,C) = k1_group_1(A,k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),B),C) ) ) ) ).
fof(t19_group_5,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_5(A,B,C) = k1_group_1(A,k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),B),C)
& k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k3_group_1(A,C),B)),C)
& k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k1_group_1(A,k3_group_1(A,C),B),C))
& k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k1_group_1(A,k3_group_1(A,C),k1_group_1(A,B,C)))
& k2_group_5(A,B,C) = k1_group_1(A,k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)),k1_group_1(A,B,C)) ) ) ) ) ).
fof(t20_group_5,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_5(A,B,C) = k1_group_1(A,k3_group_1(A,k1_group_1(A,C,B)),k1_group_1(A,B,C)) ) ) ) ).
fof(t21_group_5,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_5(A,B,C) = k1_group_1(A,k2_group_3(A,k3_group_1(A,C),B),C)
& k2_group_5(A,B,C) = k1_group_1(A,k3_group_1(A,B),k2_group_3(A,B,C)) ) ) ) ) ).
fof(t22_group_5,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_5(A,k2_group_1(A),B) = k2_group_1(A)
& k2_group_5(A,B,k2_group_1(A)) = k2_group_1(A) ) ) ) ).
fof(t23_group_5,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_5(A,B,B) = k2_group_1(A) ) ) ).
fof(t24_group_5,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_5(A,B,k3_group_1(A,B)) = k2_group_1(A)
& k2_group_5(A,k3_group_1(A,B),B) = k2_group_1(A) ) ) ) ).
fof(t25_group_5,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_1(A,k2_group_5(A,B,C)) = k2_group_5(A,C,B) ) ) ) ).
fof(t26_group_5,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_5(A,B,C),D) = k2_group_5(A,k2_group_3(A,B,D),k2_group_3(A,C,D)) ) ) ) ) ).
fof(t27_group_5,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_5(A,B,C) = k1_group_1(A,k1_group_1(A,k6_group_1(A,np__2,k3_group_1(A,B)),k6_group_1(A,np__2,k1_group_1(A,B,k3_group_1(A,C)))),k6_group_1(A,np__2,C)) ) ) ) ).
fof(t28_group_5,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_5(A,k1_group_1(A,B,C),D) = k1_group_1(A,k2_group_3(A,k2_group_5(A,B,D),C),k2_group_5(A,C,D)) ) ) ) ) ).
fof(t29_group_5,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_5(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k2_group_5(A,B,D),k2_group_3(A,k2_group_5(A,B,C),D)) ) ) ) ) ).
fof(t30_group_5,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_5(A,k3_group_1(A,B),C) = k2_group_3(A,k2_group_5(A,C,B),k3_group_1(A,B)) ) ) ) ).
fof(t31_group_5,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_5(A,B,k3_group_1(A,C)) = k2_group_3(A,k2_group_5(A,C,B),k3_group_1(A,C)) ) ) ) ).
fof(t32_group_5,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_5(A,k3_group_1(A,B),k3_group_1(A,C)) = k2_group_3(A,k2_group_5(A,B,C),k3_group_1(A,k1_group_1(A,B,C)))
& k2_group_5(A,k3_group_1(A,B),k3_group_1(A,C)) = k2_group_3(A,k2_group_5(A,B,C),k3_group_1(A,k1_group_1(A,C,B))) ) ) ) ) ).
fof(t33_group_5,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_5(A,B,k2_group_3(A,C,k3_group_1(A,B))) = k2_group_5(A,C,k3_group_1(A,B)) ) ) ) ).
fof(t34_group_5,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_5(A,k2_group_3(A,B,k3_group_1(A,C)),C) = k2_group_5(A,k3_group_1(A,C),B) ) ) ) ).
fof(t35_group_5,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_subset_1(D,u1_struct_0(B))
=> k2_group_5(B,k6_group_1(B,A,C),D) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),C),k6_group_1(B,A,k2_group_3(B,C,D))) ) ) ) ) ).
fof(t36_group_5,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_subset_1(D,u1_struct_0(B))
=> k2_group_5(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),k2_group_3(B,D,C)),k6_group_1(B,A,D)) ) ) ) ) ).
fof(t37_group_5,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_subset_1(D,u1_struct_0(B))
=> k2_group_5(B,k6_group_1(B,A,C),D) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),C),k6_group_1(B,A,k2_group_3(B,C,D))) ) ) ) ) ).
fof(t38_group_5,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_subset_1(D,u1_struct_0(B))
=> k2_group_5(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,k4_xcmplx_0(A),k2_group_3(B,D,C)),k6_group_1(B,A,D)) ) ) ) ) ).
fof(t39_group_5,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_5(A,B,C) = k2_group_1(A)
<=> k1_group_1(A,B,C) = k1_group_1(A,C,B) ) ) ) ) ).
fof(t40_group_5,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,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_group_5(A,B,C) = k2_group_1(A) ) ) ) ) ).
fof(t41_group_5,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_rlvect_1(D,B)
& r1_rlvect_1(D,C) )
=> r1_rlvect_1(D,k2_group_5(A,B,C)) ) ) ) ) ) ).
fof(d3_group_5,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_5(A,B,C,D) = k2_group_5(A,k2_group_5(A,B,C),D) ) ) ) ) ).
fof(t42_group_5,axiom,
$true ).
fof(t43_group_5,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_5(A,B,C,k2_group_1(A)) = k2_group_1(A)
& k3_group_5(A,B,k2_group_1(A),C) = k2_group_1(A)
& k3_group_5(A,k2_group_1(A),B,C) = k2_group_1(A) ) ) ) ) ).
fof(t44_group_5,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_5(A,B,B,C) = k2_group_1(A) ) ) ) ).
fof(t45_group_5,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_5(A,B,C,B) = k2_group_5(A,k2_group_3(A,B,C),B) ) ) ) ).
fof(t46_group_5,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_5(A,B,C,C) = k2_group_3(A,k1_group_1(A,k2_group_5(A,B,k3_group_1(A,C)),k2_group_5(A,B,C)),C) ) ) ) ).
fof(t47_group_5,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_5(A,B,C,k2_group_3(A,C,B)) = k2_group_5(A,C,k2_group_5(A,C,B)) ) ) ) ).
fof(t48_group_5,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_5(A,k1_group_1(A,B,C),D) = k1_group_1(A,k1_group_1(A,k2_group_5(A,B,D),k3_group_5(A,B,D,C)),k2_group_5(A,C,D)) ) ) ) ) ).
fof(t49_group_5,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_5(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,k2_group_5(A,B,D),k2_group_5(A,B,C)),k3_group_5(A,B,C,D)) ) ) ) ) ).
fof(t50_group_5,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))
=> k1_group_1(A,k1_group_1(A,k2_group_3(A,k3_group_5(A,B,k3_group_1(A,C),D),C),k2_group_3(A,k3_group_5(A,C,k3_group_1(A,D),B),D)),k2_group_3(A,k3_group_5(A,D,k3_group_1(A,B),C),B)) = k2_group_1(A) ) ) ) ) ).
fof(t51_group_5,axiom,
$true ).
fof(t52_group_5,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,k4_group_5(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k2_group_5(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ) ) ) ).
fof(t53_group_5,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_5(A,k1_subset_1(u1_struct_0(A)),B) = k1_xboole_0
& k4_group_5(A,B,k1_subset_1(u1_struct_0(A))) = k1_xboole_0 ) ) ) ).
fof(t54_group_5,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))
=> k4_group_5(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_5(A,B,C)) ) ) ) ).
fof(t55_group_5,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(k4_group_5(A,B,D),k4_group_5(A,C,E)) ) ) ) ) ) ) ).
fof(t56_group_5,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)))
=> ~ ( B != k1_xboole_0
& C != k1_xboole_0
& k4_group_5(A,B,C) != k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) ) ) ).
fof(d5_group_5,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)
=> k5_group_5(A,B,C) = k4_group_5(A,k7_group_2(A,B),k7_group_2(A,C)) ) ) ) ).
fof(t57_group_5,axiom,
$true ).
fof(t58_group_5,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)
=> ! [D] :
( m1_group_2(D,B)
=> ( r2_hidden(A,k5_group_5(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k2_group_5(B,E,F)
& r1_rlvect_1(C,E)
& r1_rlvect_1(D,F) ) ) ) ) ) ) ).
fof(t59_group_5,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)
=> r2_hidden(k2_group_1(A),k5_group_5(A,B,C)) ) ) ) ).
fof(t60_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( k5_group_5(A,k5_group_2(A),B) = k6_domain_1(u1_struct_0(A),k2_group_1(A))
& k5_group_5(A,B,k5_group_2(A)) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) ).
fof(t61_group_5,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) )
=> ( r1_tarski(k5_group_5(A,B,C),k7_group_2(A,C))
& r1_tarski(k5_group_5(A,C,B),k7_group_2(A,C)) ) ) ) ) ).
fof(t62_group_5,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)
=> ! [E] :
( m1_group_2(E,A)
=> ( ( m1_group_2(B,C)
& m1_group_2(D,E) )
=> r1_tarski(k5_group_5(A,B,D),k5_group_5(A,C,E)) ) ) ) ) ) ) ).
fof(t63_group_5,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_group_2(B,A)
=> ! [C] :
( m1_group_2(C,A)
=> k5_group_5(A,B,C) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ) ) ).
fof(d6_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k6_group_5(A) = k5_group_5(A,k6_group_2(A),k6_group_2(A)) ) ).
fof(t64_group_5,axiom,
$true ).
fof(t65_group_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r2_hidden(A,k6_group_5(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = k2_group_5(B,C,D) ) ) ) ) ).
fof(t66_group_5,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) )
<=> k6_group_5(A) = k6_domain_1(u1_struct_0(A),k2_group_1(A)) ) ) ).
fof(d7_group_5,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)))
=> k7_group_5(A,B,C) = k5_group_4(A,k4_group_5(A,B,C)) ) ) ) ).
fof(t67_group_5,axiom,
$true ).
fof(t68_group_5,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)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_hidden(B,D)
& r2_hidden(C,E) )
=> r1_rlvect_1(k7_group_5(A,D,E),k2_group_5(A,B,C)) ) ) ) ) ) ) ).
fof(t69_group_5,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)))
=> ( r1_rlvect_1(k7_group_5(B,C,D),A)
<=> ? [E] :
( m2_finseq_1(E,u1_struct_0(B))
& ? [F] :
( m2_finseq_1(F,k4_numbers)
& k3_finseq_1(E) = k3_finseq_1(F)
& r1_tarski(k2_relat_1(E),k4_group_5(B,C,D))
& A = k3_group_4(B,k4_group_4(B,F,E)) ) ) ) ) ) ) ).
fof(t70_group_5,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) )
=> m1_group_2(k7_group_5(A,B,D),k7_group_5(A,C,E)) ) ) ) ) ) ) ).
fof(d8_group_5,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_5(A,B,C) = k7_group_5(A,k7_group_2(A,B),k7_group_2(A,C)) ) ) ) ).
fof(t71_group_5,axiom,
$true ).
fof(t72_group_5,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_5(A,B,C),k5_group_4(A,k5_group_5(A,B,C))) ) ) ) ).
fof(t73_group_5,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)
=> ! [D] :
( m1_group_2(D,B)
=> ( r1_rlvect_1(k8_group_5(B,C,D),A)
<=> ? [E] :
( m2_finseq_1(E,u1_struct_0(B))
& ? [F] :
( m2_finseq_1(F,k4_numbers)
& k3_finseq_1(E) = k3_finseq_1(F)
& r1_tarski(k2_relat_1(E),k5_group_5(B,C,D))
& A = k3_group_4(B,k4_group_4(B,F,E)) ) ) ) ) ) ) ).
fof(t74_group_5,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)
=> ! [E] :
( m1_group_2(E,A)
=> ( ( r1_rlvect_1(D,B)
& r1_rlvect_1(E,C) )
=> r1_rlvect_1(k8_group_5(A,D,E),k2_group_5(A,B,C)) ) ) ) ) ) ) ).
fof(t75_group_5,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)
=> ! [E] :
( m1_group_2(E,A)
=> ( ( m1_group_2(B,C)
& m1_group_2(D,E) )
=> m1_group_2(k8_group_5(A,B,D),k8_group_5(A,C,E)) ) ) ) ) ) ) ).
fof(t76_group_5,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_2(k8_group_5(A,C,B),C)
& m1_group_2(k8_group_5(A,B,C),C) ) ) ) ) ).
fof(t77_group_5,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_5(A,B,C),A)
& m1_group_2(k8_group_5(A,B,C),A) ) ) ) ) ).
fof(t78_group_5,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_3(C,A)
& m1_group_2(C,A) )
=> r1_group_2(A,k8_group_5(A,B,C),k8_group_5(A,C,B)) ) ) ) ).
fof(t79_group_5,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) )
=> r1_group_2(A,k8_group_5(A,k8_group_4(A,B,C),D),k8_group_4(A,k8_group_5(A,B,D),k8_group_5(A,C,D))) ) ) ) ) ).
fof(t80_group_5,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) )
=> r1_group_2(A,k8_group_5(A,B,k8_group_4(A,C,D)),k8_group_4(A,k8_group_5(A,B,C),k8_group_5(A,B,D))) ) ) ) ) ).
fof(d9_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> k9_group_5(A) = k8_group_5(A,k6_group_2(A),k6_group_2(A)) ) ).
fof(t81_group_5,axiom,
$true ).
fof(t82_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> r1_group_2(A,k9_group_5(A),k5_group_4(A,k6_group_5(A))) ) ).
fof(t83_group_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_group_1(B)
& v4_group_1(B)
& l1_group_1(B) )
=> ( r1_rlvect_1(k9_group_5(B),A)
<=> ? [C] :
( m2_finseq_1(C,u1_struct_0(B))
& ? [D] :
( m2_finseq_1(D,k4_numbers)
& k3_finseq_1(C) = k3_finseq_1(D)
& r1_tarski(k2_relat_1(C),k6_group_5(B))
& A = k3_group_4(B,k4_group_4(B,D,C)) ) ) ) ) ).
fof(t84_group_5,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_rlvect_1(k9_group_5(A),k2_group_5(A,B,C)) ) ) ) ).
fof(t85_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(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) )
<=> r1_group_2(A,k9_group_5(A),k5_group_2(A)) ) ) ).
fof(t86_group_5,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(k14_group_2(A,B))
& k17_group_2(A,B) = np__2 )
=> m1_group_2(k9_group_5(A),B) ) ) ) ).
fof(t87_group_5,axiom,
$true ).
fof(t88_group_5,axiom,
$true ).
fof(t89_group_5,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_rlvect_1(k10_group_5(A),B)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_group_1(A,B,C) = k1_group_1(A,C,B) ) ) ) ) ).
fof(t90_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_3(k10_group_5(A),A)
& m1_group_2(k10_group_5(A),A) ) ) ).
fof(t91_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( m1_group_2(B,k10_group_5(A))
=> ( v1_group_3(B,A)
& m1_group_2(B,A) ) ) ) ) ).
fof(t92_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> v7_group_1(k10_group_5(A)) ) ).
fof(t93_group_5,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_rlvect_1(k10_group_5(A),B)
<=> k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),B) ) ) ) ).
fof(t94_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(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) )
<=> k10_group_5(A) = A ) ) ).
fof(dt_k1_group_5,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_finseq_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m2_finseq_1(k1_group_5(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_group_5,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_5(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_group_5,axiom,
! [A,B,C,D] :
( ( ~ 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(D,u1_struct_0(A)) )
=> m1_subset_1(k3_group_5(A,B,C,D),u1_struct_0(A)) ) ).
fof(dt_k4_group_5,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(k4_group_5(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_group_5,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(k5_group_5(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> m1_subset_1(k6_group_5(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k7_group_5,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))) )
=> ( v1_group_1(k7_group_5(A,B,C))
& m1_group_2(k7_group_5(A,B,C),A) ) ) ).
fof(dt_k8_group_5,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_5(A,B,C))
& m1_group_2(k8_group_5(A,B,C),A) ) ) ).
fof(dt_k9_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_1(k9_group_5(A))
& v1_group_3(k9_group_5(A),A)
& m1_group_2(k9_group_5(A),A) ) ) ).
fof(dt_k10_group_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_1(k10_group_5(A))
& m1_group_2(k10_group_5(A),A) ) ) ).
fof(d4_group_5,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)))
=> k4_group_5(A,B,C) = a_3_0_group_5(A,B,C) ) ) ) ).
fof(d10_group_5,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) )
=> ( B = k10_group_5(A)
<=> u1_struct_0(B) = a_1_0_group_5(A) ) ) ) ).
fof(s1_group_5,axiom,
m1_subset_1(a_0_0_group_5,k1_zfmisc_1(f2_s1_group_5)) ).
fof(fraenkel_a_3_0_group_5,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_5(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k2_group_5(B,E,F)
& r2_hidden(E,C)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_1_0_group_5,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_5(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = C
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k1_group_1(B,C,D) = k1_group_1(B,D,C) ) ) ) ) ).
fof(fraenkel_a_0_0_group_5,axiom,
! [A] :
( r2_hidden(A,a_0_0_group_5)
<=> ? [B,C,D] :
( m1_subset_1(B,f1_s1_group_5)
& m1_subset_1(C,f2_s1_group_5)
& m1_subset_1(D,f3_s1_group_5)
& A = f4_s1_group_5(B,C,D)
& p1_s1_group_5(B,C,D) ) ) ).
%------------------------------------------------------------------------------