SET007 Axioms: SET007+468.ax
%------------------------------------------------------------------------------
% File : SET007+468 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Inverse Limits of Many Sorted Algebras
% 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 : msalimit [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 37 ( 2 unt; 0 def)
% Number of atoms : 370 ( 21 equ)
% Maximal formula atoms : 23 ( 10 avg)
% Number of connectives : 417 ( 84 ~; 1 |; 213 &)
% ( 13 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 12 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-4 aty)
% Number of functors : 22 ( 22 usr; 1 con; 0-6 aty)
% Number of variables : 143 ( 133 !; 10 ?)
% 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_msalimit,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m2_pralg_2(C,A,B)
& m1_subset_1(D,A)
& m1_subset_1(E,u1_msualg_1(B)) )
=> ( v1_relat_1(k1_funct_1(k1_funct_1(k12_pralg_2(A,B,C),D),E))
& v1_funct_1(k1_funct_1(k1_funct_1(k12_pralg_2(A,B,C),D),E)) ) ) ).
fof(fc2_msalimit,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m2_pralg_2(C,A,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k1_funct_1(k11_pralg_2(A,B,C),D))
& v1_fraenkel(k1_funct_1(k11_pralg_2(A,B,C),D)) ) ) ).
fof(fc3_msalimit,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m1_msalimit(C,A,B)
& m2_msalimit(D,A,B,C) )
=> ( v1_relat_1(k2_msalimit(A,B,C,D))
& v1_funct_1(k2_msalimit(A,B,C,D))
& v1_funcop_1(k2_msalimit(A,B,C,D))
& v1_msalimit(k2_msalimit(A,B,C,D),A,B,C) ) ) ).
fof(rc1_msalimit,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m1_msalimit(C,A,B) )
=> ? [D] :
( m2_msalimit(D,A,B,C)
& v1_relat_1(D)
& v1_funct_1(D)
& v1_funcop_1(D)
& v1_msalimit(D,A,B,C) ) ) ).
fof(rc2_msalimit,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v2_msalimit(A) ) ).
fof(fc4_msalimit,axiom,
( v3_struct_0(k4_msalimit)
& v1_msualg_1(k4_msalimit)
& v2_msualg_1(k4_msalimit) ) ).
fof(rc3_msalimit,axiom,
? [A] :
( l1_msualg_1(A)
& v3_struct_0(A)
& v1_msualg_1(A)
& v2_msualg_1(A) ) ).
fof(fc5_msalimit,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v1_xboole_0(k5_msalimit(A))
& v2_msalimit(k5_msalimit(A)) ) ) ).
fof(d1_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m2_pralg_2(C,u1_struct_0(A),B)
=> ( m1_msalimit(C,A,B)
<=> ? [D] :
( v1_funcop_1(D)
& m1_pboole(D,u1_orders_2(A))
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( r1_orders_2(A,F,E)
& r1_orders_2(A,G,F)
& ! [H] :
( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)))
=> ! [I] :
( m3_pboole(I,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)))
=> ~ ( H = k1_binop_1(D,F,E)
& I = k1_binop_1(D,G,F)
& k1_binop_1(D,G,E) = k3_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)),H,I)
& r1_msualg_3(B,k6_pralg_2(u1_struct_0(A),B,C,E),k6_pralg_2(u1_struct_0(A),B,C,F),H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( ( v1_funcop_1(D)
& m1_pboole(D,u1_orders_2(A)) )
=> ( m2_msalimit(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( r1_orders_2(A,F,E)
& r1_orders_2(A,G,F)
& ! [H] :
( m3_pboole(H,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)))
=> ! [I] :
( m3_pboole(I,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)))
=> ~ ( H = k1_binop_1(D,F,E)
& I = k1_binop_1(D,G,F)
& k1_binop_1(D,G,E) = k3_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)),H,I)
& r1_msualg_3(B,k6_pralg_2(u1_struct_0(A),B,C,E),k6_pralg_2(u1_struct_0(A),B,C,F),H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( m2_msalimit(D,A,B,C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_orders_2(A,F,E)
=> k1_msalimit(A,B,C,D,E,F) = k1_binop_1(D,F,E) ) ) ) ) ) ) ) ).
fof(t1_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( ~ v3_struct_0(E)
& ~ v2_msualg_1(E)
& l1_msualg_1(E) )
=> ! [F] :
( m1_msalimit(F,A,E)
=> ! [G] :
( m2_msalimit(G,A,E,F)
=> ( ( r1_orders_2(A,C,B)
& r1_orders_2(A,D,C) )
=> r6_pboole(u1_struct_0(E),k3_msualg_3(u1_struct_0(E),u4_msualg_1(E,k6_pralg_2(u1_struct_0(A),E,F,B)),u4_msualg_1(E,k6_pralg_2(u1_struct_0(A),E,F,C)),u4_msualg_1(E,k6_pralg_2(u1_struct_0(A),E,F,D)),k1_msalimit(A,E,F,G,B,C),k1_msalimit(A,E,F,G,C,D)),k1_msalimit(A,E,F,G,B,D)) ) ) ) ) ) ) ) ) ).
fof(d4_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( m2_msalimit(D,A,B,C)
=> ( v1_msalimit(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_binop_1(D,E,E) = k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E))) ) ) ) ) ) ) ).
fof(t2_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( m2_msalimit(D,A,B,C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_orders_2(A,F,E)
=> ! [G] :
( m3_pboole(G,u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)))
=> ( r6_pboole(u1_struct_0(B),G,k1_msalimit(A,B,C,D,E,F))
=> r1_msualg_3(B,k6_pralg_2(u1_struct_0(A),B,C,E),k6_pralg_2(u1_struct_0(A),B,C,F),G) ) ) ) ) ) ) ) ) ) ).
fof(d5_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( m2_msalimit(D,A,B,C)
=> ! [E] :
( m2_msalimit(E,A,B,C)
=> ( E = k2_msalimit(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( r1_orders_2(A,G,F)
=> k1_binop_1(E,G,F) = k1_cqc_lang(G,F,k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F))),k3_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,G)),k2_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F))),k1_msalimit(A,B,C,D,F,G))) ) ) ) ) ) ) ) ) ) ).
fof(t3_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( m2_msalimit(D,A,B,C)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_orders_2(A,F,E)
=> ( E = F
| k1_binop_1(D,F,E) = k1_binop_1(k2_msalimit(A,B,C,D),F,E) ) ) ) ) ) ) ) ) ).
fof(t4_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( ( v1_msalimit(D,A,B,C)
& m2_msalimit(D,A,B,C) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_orders_2(A,F,E)
=> k1_binop_1(k2_msalimit(A,B,C,D),F,E) = k1_binop_1(D,F,E) ) ) ) ) ) ) ) ).
fof(d6_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( m2_msalimit(D,A,B,C)
=> ! [E] :
( ( v4_msualg_1(E,B)
& m1_msualg_2(E,B,k15_pralg_2(u1_struct_0(A),B,C)) )
=> ( E = k3_msalimit(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,k1_funct_1(k11_pralg_2(u1_struct_0(A),B,C),F))
=> ( r2_hidden(G,k1_funct_1(u4_msualg_1(B,E),F))
<=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( r1_orders_2(A,I,H)
=> k1_funct_1(k1_msualg_3(u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,H)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,I)),k1_msalimit(A,B,C,D,H,I),F),k1_funct_1(G,H)) = k1_funct_1(G,I) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_msalimit,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_orders_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> ! [D] :
( ( v1_msalimit(D,A,B,C)
& m2_msalimit(D,A,B,C) )
=> k3_msalimit(A,B,C,D) = k15_pralg_2(u1_struct_0(A),B,C) ) ) ) ) ).
fof(d7_msalimit,axiom,
! [A] :
( v2_msalimit(A)
<=> ! [B] :
( r2_hidden(B,A)
=> ( ~ v3_struct_0(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) ) ) ) ).
fof(d8_msalimit,axiom,
! [A] :
( ( v1_msualg_1(A)
& l1_msualg_1(A) )
=> ( A = k4_msalimit
<=> ( v3_struct_0(A)
& v2_msualg_1(A) ) ) ) ).
fof(t6_msalimit,axiom,
! [A] :
( ( v2_msualg_1(A)
& l1_msualg_1(A) )
=> r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) ) ).
fof(d9_msalimit,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( B = k5_msalimit(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( ~ v3_struct_0(D)
& v1_msualg_1(D)
& ~ v2_msualg_1(D)
& l1_msualg_1(D)
& C = D
& r1_tarski(u1_struct_0(D),A)
& r1_tarski(u1_msualg_1(D),A) ) ) ) ) ).
fof(d10_msalimit,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( l1_msualg_1(B)
=> ! [C] :
( C = k6_msalimit(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v1_relat_1(E)
& v1_funct_1(E)
& ? [F] :
( v1_relat_1(F)
& v1_funct_1(F)
& D = k4_tarski(E,F)
& r3_pua2mss1(A,B,E,F) ) ) ) ) ) ) ).
fof(dt_m1_msalimit,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( m1_msalimit(C,A,B)
=> m2_pralg_2(C,u1_struct_0(A),B) ) ) ).
fof(existence_m1_msalimit,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ? [C] : m1_msalimit(C,A,B) ) ).
fof(dt_m2_msalimit,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m1_msalimit(C,A,B) )
=> ! [D] :
( m2_msalimit(D,A,B,C)
=> ( v1_funcop_1(D)
& m1_pboole(D,u1_orders_2(A)) ) ) ) ).
fof(existence_m2_msalimit,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m1_msalimit(C,A,B) )
=> ? [D] : m2_msalimit(D,A,B,C) ) ).
fof(dt_m3_msalimit,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_msalimit(A) )
=> ! [B] :
( m3_msalimit(B,A)
=> ( ~ v3_struct_0(B)
& v1_msualg_1(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) ) ) ) ).
fof(existence_m3_msalimit,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_msalimit(A) )
=> ? [B] : m3_msalimit(B,A) ) ).
fof(redefinition_m3_msalimit,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_msalimit(A) )
=> ! [B] :
( m3_msalimit(B,A)
<=> m1_subset_1(B,A) ) ) ).
fof(dt_k1_msalimit,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m1_msalimit(C,A,B)
& m2_msalimit(D,A,B,C)
& m1_subset_1(E,u1_struct_0(A))
& m1_subset_1(F,u1_struct_0(A)) )
=> m3_pboole(k1_msalimit(A,B,C,D,E,F),u1_struct_0(B),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,E)),u4_msualg_1(B,k6_pralg_2(u1_struct_0(A),B,C,F))) ) ).
fof(dt_k2_msalimit,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m1_msalimit(C,A,B)
& m2_msalimit(D,A,B,C) )
=> m2_msalimit(k2_msalimit(A,B,C,D),A,B,C) ) ).
fof(dt_k3_msalimit,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& m1_msalimit(C,A,B)
& m2_msalimit(D,A,B,C) )
=> ( v4_msualg_1(k3_msalimit(A,B,C,D),B)
& m1_msualg_2(k3_msalimit(A,B,C,D),B,k15_pralg_2(u1_struct_0(A),B,C)) ) ) ).
fof(dt_k4_msalimit,axiom,
( v1_msualg_1(k4_msalimit)
& l1_msualg_1(k4_msalimit) ) ).
fof(dt_k5_msalimit,axiom,
$true ).
fof(dt_k6_msalimit,axiom,
$true ).
%------------------------------------------------------------------------------