SET007 Axioms: SET007+575.ax
%------------------------------------------------------------------------------
% File : SET007+575 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Basic Properties 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 : scmring2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 65 ( 7 unt; 0 def)
% Number of atoms : 877 ( 67 equ)
% Maximal formula atoms : 33 ( 13 avg)
% Number of connectives : 903 ( 91 ~; 0 |; 655 &)
% ( 5 <=>; 152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 13 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-3 aty)
% Number of functors : 58 ( 58 usr; 13 con; 0-4 aty)
% Number of variables : 179 ( 176 !; 3 ?)
% 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_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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))) ) ) ).
fof(fc2_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
& v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ).
fof(fc3_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) ) ).
fof(fc4_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) ) ).
fof(fc5_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) ) ).
fof(fc6_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) ) ).
fof(fc7_scmring2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) ) ).
fof(fc8_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) ) ).
fof(fc9_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) ) ).
fof(fc10_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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))) ) ) ).
fof(d1_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( v1_ami_1(B,k1_tarski(u1_struct_0(A)))
& l1_ami_1(B,k1_tarski(u1_struct_0(A))) )
=> ( B = k1_scmring2(A)
<=> ( u1_struct_0(B) = k5_numbers
& u1_ami_1(k1_tarski(u1_struct_0(A)),B) = np__0
& u2_ami_1(k1_tarski(u1_struct_0(A)),B) = k3_ami_2
& u3_ami_1(k1_tarski(u1_struct_0(A)),B) = k1_gr_cy_1(np__8)
& u4_ami_1(k1_tarski(u1_struct_0(A)),B) = k1_scmring1(A)
& u5_ami_1(k1_tarski(u1_struct_0(A)),B) = k2_scmring1(A)
& u6_ami_1(k1_tarski(u1_struct_0(A)),B) = k16_scmring1(A) ) ) ) ) ).
fof(d2_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
=> ( m1_scmring2(B,A)
<=> r2_hidden(B,k4_xboole_0(u1_struct_0(k1_scmring2(A)),k2_xboole_0(k3_ami_2,k1_tarski(np__0)))) ) ) ) ).
fof(t1_scmring2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& v1_scmring1(B)
& l3_vectsp_1(B) )
=> ( m1_scmring2(A,B)
<=> r2_hidden(A,k2_ami_2) ) ) ).
fof(t2_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> r2_hidden(k4_tarski(np__0,k1_xboole_0),k1_scmring1(A)) ) ).
fof(t3_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> m2_subset_1(k4_tarski(np__0,k1_xboole_0),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))) ) ).
fof(t4_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B,C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v1_scmring1(C)
& l3_vectsp_1(C) )
=> ! [D] :
( m1_scmring2(D,C)
=> ! [E] :
( m1_scmring2(E,C)
=> ( r2_hidden(B,k2_enumset1(np__1,np__2,np__3,np__4))
=> r2_hidden(k4_tarski(B,k10_finseq_1(D,E)),k1_scmring1(A)) ) ) ) ) ) ).
fof(t5_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v1_scmring1(C)
& l3_vectsp_1(C) )
=> ! [D] :
( m1_scmring2(D,C)
=> r2_hidden(k4_tarski(np__5,k10_finseq_1(D,B)),k1_scmring1(A)) ) ) ) ) ).
fof(t6_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& v1_scmring1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_struct_0(C,k1_scmring2(B),u2_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)))
=> r2_hidden(k4_tarski(np__6,k12_finseq_1(u2_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)),C)),k1_scmring1(A)) ) ) ) ).
fof(t7_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& v1_scmring1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_scmring2(C,B)
=> ! [D] :
( m1_struct_0(D,k1_scmring2(B),u2_ami_1(k1_tarski(u1_struct_0(B)),k1_scmring2(B)))
=> r2_hidden(k4_tarski(np__7,k10_finseq_1(D,C)),k1_scmring1(A)) ) ) ) ) ).
fof(d3_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_scmring2(A,B,C) = k4_tarski(np__1,k10_finseq_1(B,C)) ) ) ) ).
fof(d4_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)
=> k5_scmring2(A,B,C) = k4_tarski(np__2,k10_finseq_1(B,C)) ) ) ) ).
fof(d5_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)
=> k6_scmring2(A,B,C) = k4_tarski(np__3,k10_finseq_1(B,C)) ) ) ) ).
fof(d6_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)
=> k7_scmring2(A,B,C) = k4_tarski(np__4,k10_finseq_1(B,C)) ) ) ) ).
fof(d7_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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,u1_struct_0(A))
=> k8_scmring2(A,B,C) = k4_tarski(np__5,k10_finseq_1(B,C)) ) ) ) ).
fof(d8_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
=> k9_scmring2(A,B) = k4_tarski(np__6,k12_finseq_1(u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B)) ) ) ).
fof(d9_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_scmring2(C,A)
=> k10_scmring2(A,B,C) = k4_tarski(np__7,k10_finseq_1(B,C)) ) ) ) ).
fof(t8_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
<=> ~ ( B != k4_tarski(np__0,k1_xboole_0)
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k4_scmring2(A,C,D) ) )
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k5_scmring2(A,C,D) ) )
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k6_scmring2(A,C,D) ) )
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_scmring2(D,A)
=> B != k7_scmring2(A,C,D) ) )
& ! [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) )
& ! [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) ) )
& ! [C] :
( m1_scmring2(C,A)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> B != k8_scmring2(A,C,D) ) ) ) ) ) ).
fof(t9_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) = np__0 ) ).
fof(t10_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ! [C] :
( m1_subset_1(C,k4_card_3(k2_scmring1(A)))
=> ( C = B
=> k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = k3_scmring1(A,C) ) ) ) ) ).
fof(d10_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
=> ( C = k11_scmring2(A,B)
<=> ? [D] :
( m2_subset_1(D,k5_numbers,k3_ami_2)
& D = B
& C = k15_ami_2(D) ) ) ) ) ) ).
fof(t11_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
=> ( C = B
=> k15_ami_2(C) = k11_scmring2(A,B) ) ) ) ) ).
fof(t12_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ! [C] :
( m2_subset_1(C,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)))
=> ! [D] :
( m1_subset_1(D,k1_scmring1(A))
=> ( D = C
=> ! [E] :
( m1_subset_1(E,k4_card_3(k2_scmring1(A)))
=> ( E = B
=> k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C,B) = k15_scmring1(A,D,E) ) ) ) ) ) ) ) ).
fof(t13_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C),D),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k11_scmring2(A,k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D))
& k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C),D),B) = k3_scmring2(A,D,C)
& ! [E] :
( m1_scmring2(E,A)
=> ( E != B
=> k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C),D),E) = k3_scmring2(A,D,E) ) ) ) ) ) ) ) ).
fof(t14_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C),D),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k11_scmring2(A,k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D))
& k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C),D),B) = k4_rlvect_1(A,k3_scmring2(A,D,B),k3_scmring2(A,D,C))
& ! [E] :
( m1_scmring2(E,A)
=> ( E != B
=> k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C),D),E) = k3_scmring2(A,D,E) ) ) ) ) ) ) ) ).
fof(t15_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C),D),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k11_scmring2(A,k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D))
& k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C),D),B) = k6_rlvect_1(A,k3_scmring2(A,D,B),k3_scmring2(A,D,C))
& ! [E] :
( m1_scmring2(E,A)
=> ( E != B
=> k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C),D),E) = k3_scmring2(A,D,E) ) ) ) ) ) ) ) ).
fof(t16_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C),D),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k11_scmring2(A,k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D))
& k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C),D),B) = k1_group_1(A,k3_scmring2(A,D,B),k3_scmring2(A,D,C))
& ! [E] :
( m1_scmring2(E,A)
=> ( E != B
=> k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C),D),E) = k3_scmring2(A,D,E) ) ) ) ) ) ) ) ).
fof(t17_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,C),D),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = C
& k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,C),D),B) = k3_scmring2(A,D,B) ) ) ) ) ) ).
fof(t18_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( ( k3_scmring2(A,E,B) = k1_rlvect_1(A)
=> k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,D,B),E),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = D )
& ( k3_scmring2(A,E,B) != k1_rlvect_1(A)
=> k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,D,B),E),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k11_scmring2(A,k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),E)) )
& k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,D,B),E),C) = k3_scmring2(A,E,C) ) ) ) ) ) ) ).
fof(t19_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
=> ( k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B),D),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k11_scmring2(A,k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D))
& k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B),D),C) = B
& ! [E] :
( m1_scmring2(E,A)
=> ( E != C
=> k3_scmring2(A,k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B),D),E) = k3_scmring2(A,D,E) ) ) ) ) ) ) ) ).
fof(t20_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
=> ~ ( ? [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& k1_funct_1(k4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B,C),k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k11_scmring2(A,k6_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C)) )
& v3_ami_1(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ) ).
fof(t21_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
=> ( B = k4_tarski(np__0,k1_xboole_0)
=> v3_ami_1(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ) ).
fof(t22_scmring2,axiom,
$true ).
fof(t23_scmring2,axiom,
$true ).
fof(t24_scmring2,axiom,
$true ).
fof(t25_scmring2,axiom,
$true ).
fof(t26_scmring2,axiom,
$true ).
fof(t27_scmring2,axiom,
$true ).
fof(t28_scmring2,axiom,
$true ).
fof(t29_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
=> ( v3_ami_1(B,k1_tarski(u1_struct_0(A)),k1_scmring2(A))
=> B = k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ) ).
fof(t30_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) = k4_tarski(np__0,k1_xboole_0) ) ).
fof(dt_m1_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)
=> m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) ) ).
fof(existence_m1_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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) ) ).
fof(dt_k1_scmring2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v1_scmring1(A)
& l3_vectsp_1(A) )
=> ( v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
& l1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) ).
fof(dt_k2_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& m1_subset_1(C,k2_ami_2) )
=> m1_subset_1(k2_scmring2(A,B,C),u1_struct_0(A)) ) ).
fof(redefinition_k2_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& m1_subset_1(C,k2_ami_2) )
=> k2_scmring2(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k3_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& m1_scmring2(C,A) )
=> m1_subset_1(k3_scmring2(A,B,C),u1_struct_0(A)) ) ).
fof(redefinition_k3_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
& m1_scmring2(C,A) )
=> k3_scmring2(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k4_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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) )
=> m2_subset_1(k4_scmring2(A,B,C),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))) ) ).
fof(dt_k5_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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) )
=> m2_subset_1(k5_scmring2(A,B,C),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))) ) ).
fof(dt_k6_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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) )
=> m2_subset_1(k6_scmring2(A,B,C),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))) ) ).
fof(dt_k7_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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) )
=> m2_subset_1(k7_scmring2(A,B,C),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))) ) ).
fof(dt_k8_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)) )
=> m2_subset_1(k8_scmring2(A,B,C),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))) ) ).
fof(dt_k9_scmring2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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))) )
=> m2_subset_1(k9_scmring2(A,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))) ) ).
fof(dt_k10_scmring2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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)))
& m1_scmring2(C,A) )
=> m2_subset_1(k10_scmring2(A,B,C),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))) ) ).
fof(dt_k11_scmring2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_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))) )
=> m1_struct_0(k11_scmring2(A,B),k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) ) ).
%------------------------------------------------------------------------------