SET007 Axioms: SET007+648.ax
%------------------------------------------------------------------------------
% File : SET007+648 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Properties of Instructions of SCM over Ring
% 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 : scmring3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 116 ( 0 unt; 0 def)
% Number of atoms : 1756 ( 87 equ)
% Maximal formula atoms : 28 ( 15 avg)
% Number of connectives : 1843 ( 203 ~; 0 |;1386 &)
% ( 0 <=>; 254 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 14 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 72 ( 71 usr; 0 prp; 1-3 aty)
% Number of functors : 65 ( 65 usr; 14 con; 0-5 aty)
% Number of variables : 309 ( 307 !; 2 ?)
% 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_scmring3,axiom,
( ~ v1_xboole_0(k4_numbers)
& ~ v1_finset_1(k4_numbers)
& ~ v1_realset1(k4_numbers)
& v1_membered(k4_numbers)
& v2_membered(k4_numbers)
& v3_membered(k4_numbers)
& v4_membered(k4_numbers) ) ).
fof(fc2_scmring3,axiom,
( ~ v3_struct_0(k1_int_3)
& v2_group_1(k1_int_3)
& v4_group_1(k1_int_3)
& ~ v6_group_1(k1_int_3)
& v7_group_1(k1_int_3)
& v3_rlvect_1(k1_int_3)
& v4_rlvect_1(k1_int_3)
& v5_rlvect_1(k1_int_3)
& v6_rlvect_1(k1_int_3)
& v3_vectsp_1(k1_int_3)
& v4_vectsp_1(k1_int_3)
& v5_vectsp_1(k1_int_3)
& v6_vectsp_1(k1_int_3)
& v7_vectsp_1(k1_int_3)
& v8_vectsp_1(k1_int_3)
& ~ v10_vectsp_1(k1_int_3)
& v1_scmring1(k1_int_3)
& ~ v3_realset2(k1_int_3)
& v1_int_3(k1_int_3)
& v2_vectsp_2(k1_int_3)
& v3_gcd_1(k1_int_3) ) ).
fof(rc1_scmring3,axiom,
? [A] :
( l1_struct_0(A)
& v1_struct_0(A)
& ~ v3_struct_0(A)
& ~ v6_group_1(A)
& ~ v3_realset2(A) ) ).
fof(rc2_scmring3,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v2_group_1(A)
& v4_group_1(A)
& ~ v6_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v3_vectsp_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A) ) ).
fof(fc3_scmring3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v1_xboole_0(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))
& v1_fraenkel(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B)) ) ) ).
fof(fc4_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))) ) ) ).
fof(fc5_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C))) ) ) ).
fof(fc6_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C))) ) ) ).
fof(fc7_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C))) ) ) ).
fof(fc8_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C))) ) ) ).
fof(fc9_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C))) ) ) ).
fof(fc10_scmring3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)))
& v1_realset1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B))) ) ) ).
fof(fc11_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)))
& v1_realset1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B))) ) ) ).
fof(fc12_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_scmring2(A))
& v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ).
fof(fc13_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc14_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ( ~ v1_xboole_0(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
& v3_ami_1(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v2_amistd_1(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v12_amistd_2(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc15_scmring3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc16_scmring3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v3_ami_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v2_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc17_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc18_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v3_ami_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v2_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc19_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc20_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v2_amistd_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc21_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc22_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v2_amistd_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc23_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc24_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v2_amistd_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc25_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc26_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v2_amistd_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc27_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(fc28_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v3_ami_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v2_amistd_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc29_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v5_amistd_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc30_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v5_amistd_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc31_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v5_amistd_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc32_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A) )
=> ( ~ v3_ami_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v5_amistd_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc33_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v3_ami_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v5_amistd_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc34_scmring3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v3_ami_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v2_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v5_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc35_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v3_ami_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v2_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v5_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc36_scmring3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v3_ami_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v2_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v5_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v9_amistd_2(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc37_scmring3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ~ v3_ami_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& v2_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v5_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ v9_amistd_2(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(fc38_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_scmring2(A))
& v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ).
fof(fc39_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_scmring2(A))
& v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v8_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ).
fof(fc40_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k1_scmring2(A))
& v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v8_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v11_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& v13_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ).
fof(t1_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> k3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = u1_struct_0(A) ) ) ).
fof(t2_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ~ r2_hidden(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) ) ) ).
fof(t3_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> B != k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(t4_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> k2_ami_2 != u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(t5_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_scmring2(A)))
=> ~ ( B != k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))
& ~ r2_hidden(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
& ~ m1_scmring2(B,A) ) ) ) ).
fof(t6_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( B != C
& k11_scmring2(A,B) = k11_scmring2(A,C) ) ) ) ) ).
fof(t7_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( r1_funct_7(C,D,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k3_scmring2(A,C,B) = k3_scmring2(A,D,B) ) ) ) ) ) ).
fof(t8_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = np__0 ) ).
fof(t9_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)) = np__1 ) ) ) ).
fof(t10_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)) = np__2 ) ) ) ).
fof(t11_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)) = np__3 ) ) ) ).
fof(t12_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)) = np__4 ) ) ) ).
fof(t13_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_scmring2(C,A)
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)) = np__5 ) ) ) ).
fof(t14_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)) = np__6 ) ) ).
fof(t15_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)) = np__7 ) ) ) ).
fof(t16_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__0
=> B = k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ) ).
fof(t17_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__1
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k4_scmring2(A,C,D) ) ) ) ) ) ).
fof(t18_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__2
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k5_scmring2(A,C,D) ) ) ) ) ) ).
fof(t19_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__3
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k6_scmring2(A,C,D) ) ) ) ) ) ).
fof(t20_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__4
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k7_scmring2(A,C,D) ) ) ) ) ) ).
fof(t21_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__5
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> B != k8_scmring2(A,C,D) ) ) ) ) ) ).
fof(t22_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__6
& ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> B != k9_scmring2(A,C) ) ) ) ) ).
fof(t23_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__7
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> B != k10_scmring2(A,D,C) ) ) ) ) ) ).
fof(t24_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k1_xboole_0 ) ).
fof(t25_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) ).
fof(t26_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) ).
fof(t27_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) ).
fof(t28_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) ).
fof(t29_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_scmring2(C,A)
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)) = k10_finseq_1(C,B) ) ) ) ).
fof(t30_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)) = k12_finseq_1(u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B) ) ) ).
fof(t31_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)) = k10_finseq_1(C,B) ) ) ) ).
fof(t32_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__0
=> k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = k5_realset1(k5_numbers,np__0) ) ) ) ).
fof(t33_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__1
=> k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) ).
fof(t34_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__2
=> k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) ).
fof(t35_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__3
=> k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) ).
fof(t36_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__4
=> k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) ).
fof(t37_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__5
=> k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) ).
fof(t38_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__6
=> k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k5_realset1(k5_numbers,np__1) ) ) ) ).
fof(t39_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( B = np__7
=> k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) ).
fof(t40_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) ).
fof(t41_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) ).
fof(t42_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) ).
fof(t43_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) ).
fof(t44_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) ).
fof(t45_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) ).
fof(t46_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) ).
fof(t47_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) ).
fof(t48_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)))),np__1) = k2_ami_2 ) ) ) ).
fof(t49_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_scmring2(C,A)
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)))),np__2) = u1_struct_0(A) ) ) ) ).
fof(t50_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)))),np__1) = u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ).
fof(t51_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)))),np__1) = u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ) ).
fof(t52_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)))),np__2) = k2_ami_2 ) ) ) ).
fof(t53_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B,k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k1_struct_0(k1_scmring2(A),B) ) ) ).
fof(t54_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k4_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) ).
fof(t55_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k5_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) ).
fof(t56_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k6_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) ).
fof(t57_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k7_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) ).
fof(t58_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k8_scmring2(A,C,B)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) ).
fof(t59_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C,k9_scmring2(A,B)) = k1_struct_0(k1_scmring2(A),B) ) ) ) ).
fof(t60_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)) = k1_struct_0(k1_scmring2(A),B) ) ) ).
fof(t61_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ( r2_hidden(C,k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k10_scmring2(A,C,B)))
& r1_tarski(k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k10_scmring2(A,C,B)),k2_struct_0(k1_scmring2(A),C,k11_scmring2(A,D))) ) ) ) ) ) ).
fof(t62_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ! [D] :
( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C,k10_scmring2(A,D,B)) = k2_struct_0(k1_scmring2(A),D,k11_scmring2(A,C)) ) ) ) ) ).
fof(t63_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)) = k1_struct_0(k1_scmring2(A),C) ) ) ) ).
fof(t64_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k3_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = k2_struct_0(k1_scmring2(A),B,k11_scmring2(A,B)) ) ) ).
fof(t65_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
& m2_relset_1(B,k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,C) = k16_ami_3(C) )
=> ( v3_funct_2(B,k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,k1_nat_1(C,np__1)),k3_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,C)))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,D),k3_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,C)))
=> r1_xreal_0(C,D) ) ) ) ) ) ) ) ) ).
fof(t66_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( v4_ordinal2(B)
=> k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = k16_ami_3(B) ) ) ).
fof(t67_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( v4_ordinal2(B)
=> k11_scmring2(A,k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B)) = k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k2_xcmplx_0(B,np__1)) ) ) ).
fof(t68_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> k11_scmring2(A,B) = k9_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) ) ) ).
fof(d1_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_scmring3(A,B) = k15_ami_3(B) ) ) ).
fof(t69_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ! [C] :
( v4_ordinal2(C)
=> k8_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B),C) = k9_scmring2(A,k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k2_xcmplx_0(k7_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B),C))) ) ) ) ).
fof(t70_scmring3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_scmring2(B,A)
=> ! [C] :
( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
=> ! [D] :
( v4_ordinal2(D)
=> k8_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B),D) = k10_scmring2(A,k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k2_xcmplx_0(k7_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C),D)),B) ) ) ) ) ).
fof(dt_k1_scmring3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> m1_ami_1(k1_scmring3(A,B,C,D,E),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ).
fof(redefinition_k1_scmring3,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_scmring2(B,A)
& m1_scmring2(C,A)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> k1_scmring3(A,B,C,D,E) = k4_funct_4(B,C,D,E) ) ).
fof(dt_k2_scmring3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,k5_numbers) )
=> m1_scmring2(k2_scmring3(A,B),A) ) ).
%------------------------------------------------------------------------------