SET007 Axioms: SET007+447.ax
%------------------------------------------------------------------------------
% File : SET007+447 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Lattice of Congruences in Many Sorted Algebra
% 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 : msualg_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 39 ( 0 unt; 0 def)
% Number of atoms : 396 ( 25 equ)
% Maximal formula atoms : 35 ( 10 avg)
% Number of connectives : 403 ( 46 ~; 0 |; 207 &)
% ( 9 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 40 ( 39 usr; 0 prp; 1-4 aty)
% Number of functors : 43 ( 43 usr; 3 con; 0-5 aty)
% Number of variables : 158 ( 155 !; 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(rc1_msualg_5,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ? [C] :
( m1_msualg_4(C,A,B,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_msualg_4(C)
& v2_msualg_4(C,A,B) ) ) ).
fof(cc1_msualg_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( v3_msualg_4(C,A,B)
=> ( v1_msualg_4(C)
& v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ) ) ).
fof(fc1_msualg_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ( ~ v3_struct_0(k6_msualg_5(A,B))
& v3_lattices(k6_msualg_5(A,B))
& v4_lattices(k6_msualg_5(A,B))
& v5_lattices(k6_msualg_5(A,B))
& v6_lattices(k6_msualg_5(A,B))
& v7_lattices(k6_msualg_5(A,B))
& v8_lattices(k6_msualg_5(A,B))
& v9_lattices(k6_msualg_5(A,B))
& v10_lattices(k6_msualg_5(A,B))
& v13_lattices(k6_msualg_5(A,B))
& v14_lattices(k6_msualg_5(A,B))
& v15_lattices(k6_msualg_5(A,B)) ) ) ).
fof(t1_msualg_5,axiom,
! [A,B] :
( ( v1_partfun1(B,A,A)
& v3_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> k5_eqrel_1(A,k5_eqrel_1(A,B,C),D) = k5_eqrel_1(A,B,k5_eqrel_1(A,C,D)) ) ) ) ).
fof(d1_msualg_5,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ( C = k1_msualg_5(A,B)
<=> ( r1_tarski(B,C)
& ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ( r1_tarski(B,D)
=> r1_tarski(C,D) ) ) ) ) ) ) ).
fof(t2_msualg_5,axiom,
! [A,B] :
( ( v1_partfun1(B,A,A)
& v3_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> k5_eqrel_1(A,B,C) = k1_msualg_5(A,k3_eqrel_1(A,B,C)) ) ) ).
fof(t3_msualg_5,axiom,
! [A,B] :
( ( v1_partfun1(B,A,A)
& v3_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,A,A) )
=> k1_msualg_5(A,B) = B ) ).
fof(t4_msualg_5,axiom,
! [A,B] :
( m2_relset_1(B,A,A)
=> k3_eqrel_1(A,k1_eqrel_1(A),B) = k1_eqrel_1(A) ) ).
fof(d3_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_msualg_4(C,A,B,B)
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ( D = k3_msualg_5(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> k1_msualg_4(A,B,B,D,E) = k1_msualg_5(k1_funct_1(B,E),k1_msualg_4(A,B,B,C,E)) ) ) ) ) ) ) ).
fof(t5_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> r6_pboole(A,k3_msualg_5(A,B,C),C) ) ) ) ).
fof(d4_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ! [E] :
( ( v2_msualg_4(E,A,B)
& m1_msualg_4(E,A,B,B) )
=> ( E = k4_msualg_5(A,B,C,D)
<=> ? [F] :
( m1_msualg_4(F,A,B,B)
& r6_pboole(A,F,k2_pboole(A,C,D))
& r6_pboole(A,E,k3_msualg_5(A,B,F)) ) ) ) ) ) ) ) ).
fof(t6_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> r2_pboole(A,k2_pboole(A,C,D),k4_msualg_5(A,B,C,D)) ) ) ) ) ).
fof(t7_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ! [E] :
( ( v2_msualg_4(E,A,B)
& m1_msualg_4(E,A,B,B) )
=> ( r2_pboole(A,k2_pboole(A,C,D),E)
=> r2_pboole(A,k4_msualg_5(A,B,C,D),E) ) ) ) ) ) ) ).
fof(t8_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ! [E] :
( ( v2_msualg_4(E,A,B)
& m1_msualg_4(E,A,B,B) )
=> ( ( r2_pboole(A,k2_pboole(A,C,D),E)
& ! [F] :
( ( v2_msualg_4(F,A,B)
& m1_msualg_4(F,A,B,B) )
=> ( r2_pboole(A,k2_pboole(A,C,D),F)
=> r2_pboole(A,E,F) ) ) )
=> r6_pboole(A,E,k4_msualg_5(A,B,C,D)) ) ) ) ) ) ) ).
fof(t9_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> r6_pboole(A,k4_msualg_5(A,B,C,C),C) ) ) ) ).
fof(t10_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ! [E] :
( ( v2_msualg_4(E,A,B)
& m1_msualg_4(E,A,B,B) )
=> r6_pboole(A,k4_msualg_5(A,B,k4_msualg_5(A,B,C,D),E),k4_msualg_5(A,B,C,k4_msualg_5(A,B,D,E))) ) ) ) ) ) ).
fof(t11_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> r6_pboole(A,k3_pboole(A,C,k4_msualg_5(A,B,C,D)),C) ) ) ) ) ).
fof(t12_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ! [E] :
( ( v2_msualg_4(E,A,B)
& m1_msualg_4(E,A,B,B) )
=> ( r6_pboole(A,E,k3_pboole(A,C,D))
=> r6_pboole(A,k4_msualg_5(A,B,C,E),C) ) ) ) ) ) ) ).
fof(t13_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B) )
=> ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ( v2_msualg_4(k3_pboole(A,C,D),A,B)
& m1_msualg_4(k3_pboole(A,C,D),A,B,B) ) ) ) ) ) ).
fof(d5_msualg_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_lattices(C)
& v10_lattices(C)
& l3_lattices(C) )
=> ( C = k5_msualg_5(A,B)
<=> ( ! [D] :
( r2_hidden(D,u1_struct_0(C))
<=> ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) ) )
& ! [D] :
( ( v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ! [E] :
( ( v2_msualg_4(E,A,B)
& m1_msualg_4(E,A,B,B) )
=> ( k1_binop_1(u1_lattices(C),D,E) = k3_pboole(A,D,E)
& k1_binop_1(u2_lattices(C),D,E) = k4_msualg_5(A,B,D,E) ) ) ) ) ) ) ) ) ).
fof(t14_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v3_msualg_4(D,A,B)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [E] :
( ( v3_msualg_4(E,A,B)
& v4_msualg_4(E,A,B)
& m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [F,G,H] :
( ( v1_relat_1(H)
& v1_funct_1(H)
& v1_finseq_1(H) )
=> ! [I] :
( ( v1_relat_1(I)
& v1_funct_1(I)
& v1_finseq_1(I) )
=> ( r2_hidden(k4_tarski(F,G),k3_eqrel_1(k1_funct_1(u4_msualg_1(A,B),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),k1_nat_1(k3_finseq_1(H),np__1))),k2_msualg_4(A,B,D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),k1_nat_1(k3_finseq_1(H),np__1))),k2_msualg_4(A,B,E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),k1_nat_1(k3_finseq_1(H),np__1)))))
=> ! [J] :
( m1_subset_1(J,k3_msualg_1(A,C,B))
=> ! [K] :
( m1_subset_1(K,k3_msualg_1(A,C,B))
=> ( ( J = k7_finseq_1(k7_finseq_1(H,k9_finseq_1(F)),I)
& K = k7_finseq_1(k7_finseq_1(H,k9_finseq_1(G)),I) )
=> r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),J),k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),K)),k3_eqrel_1(k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C)),k2_msualg_4(A,B,D,k2_msualg_1(A,C)),k2_msualg_4(A,B,E,k2_msualg_1(A,C)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v3_msualg_4(D,A,B)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [E] :
( ( v3_msualg_4(E,A,B)
& v4_msualg_4(E,A,B)
& m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [F] :
( ( v3_msualg_4(F,A,B)
& m1_msualg_4(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( r6_pboole(u1_struct_0(A),F,k4_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),D,E))
=> ! [G,H,I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ! [J] :
( ( v1_relat_1(J)
& v1_funct_1(J)
& v1_finseq_1(J) )
=> ! [K] :
( ( v1_relat_1(K)
& v1_funct_1(K)
& v1_finseq_1(K) )
=> ! [L] :
( ( v1_relat_1(L)
& v1_funct_1(L)
& v1_finseq_1(L) )
=> ( ( k3_finseq_1(J) = I
& k3_finseq_1(J) = k3_finseq_1(K)
& ! [M] :
( m2_subset_1(M,k1_numbers,k5_numbers)
=> ( r2_hidden(M,k4_finseq_1(J))
=> r2_hidden(k4_tarski(k1_funct_1(J,M),k1_funct_1(K,M)),k2_msualg_4(A,B,F,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),M))) ) )
& r2_hidden(k4_tarski(k1_funct_1(k5_msualg_1(A,C,B),k7_finseq_1(k7_finseq_1(J,k9_finseq_1(G)),L)),k1_funct_1(k5_msualg_1(A,C,B),k7_finseq_1(k7_finseq_1(K,k9_finseq_1(G)),L))),k2_msualg_4(A,B,F,k2_msualg_1(A,C)))
& r2_hidden(k4_tarski(G,H),k2_msualg_4(A,B,F,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),k1_nat_1(I,np__1)))) )
=> ! [M] :
( m1_subset_1(M,k3_msualg_1(A,C,B))
=> ( M = k7_finseq_1(k7_finseq_1(J,k9_finseq_1(G)),L)
=> r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),M),k1_funct_1(k5_msualg_1(A,C,B),k7_finseq_1(k7_finseq_1(K,k9_finseq_1(H)),L))),k2_msualg_4(A,B,F,k2_msualg_1(A,C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v3_msualg_4(D,A,B)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [E] :
( ( v3_msualg_4(E,A,B)
& v4_msualg_4(E,A,B)
& m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [F] :
( ( v3_msualg_4(F,A,B)
& m1_msualg_4(F,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( r6_pboole(u1_struct_0(A),F,k4_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),D,E))
=> ! [G] :
( m1_subset_1(G,k3_msualg_1(A,C,B))
=> ! [H] :
( m1_subset_1(H,k3_msualg_1(A,C,B))
=> ( ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ( r2_hidden(I,k1_relat_1(G))
=> r2_hidden(k4_tarski(k1_funct_1(G,I),k1_funct_1(H,I)),k2_msualg_4(A,B,F,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),I))) ) )
=> r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),G),k8_funct_2(k3_msualg_1(A,C,B),k4_msualg_1(A,C,B),k5_msualg_1(A,C,B),H)),k2_msualg_4(A,B,F,k2_msualg_1(A,C))) ) ) ) ) ) ) ) ) ) ) ).
fof(t17_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [D] :
( ( v3_msualg_4(D,A,B)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v3_msualg_4(k4_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),C,D),A,B)
& v4_msualg_4(k4_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),C,D),A,B)
& m1_msualg_4(k4_msualg_5(u1_struct_0(A),u4_msualg_1(A,B),C,D),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ).
fof(t18_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [D] :
( ( v3_msualg_4(D,A,B)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v3_msualg_4(k3_pboole(u1_struct_0(A),C,D),A,B)
& v4_msualg_4(k3_pboole(u1_struct_0(A),C,D),A,B)
& m1_msualg_4(k3_pboole(u1_struct_0(A),C,D),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ).
fof(d6_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_lattices(C)
& m2_nat_lat(C,k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) )
=> ( C = k6_msualg_5(A,B)
<=> ! [D] :
( r2_hidden(D,u1_struct_0(C))
<=> ( v3_msualg_4(D,A,B)
& v4_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ) ) ).
fof(t19_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v3_msualg_4(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)),A,B)
& v4_msualg_4(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)),A,B)
& m1_msualg_4(k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ).
fof(t20_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v3_msualg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B)
& v4_msualg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B)
& m1_msualg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ).
fof(t21_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> k5_lattices(k6_msualg_5(A,B)) = k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)) ) ) ).
fof(t22_msualg_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> k6_lattices(k6_msualg_5(A,B)) = k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(dt_k1_msualg_5,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ( v1_partfun1(k1_msualg_5(A,B),A,A)
& v3_relat_2(k1_msualg_5(A,B))
& v8_relat_2(k1_msualg_5(A,B))
& m2_relset_1(k1_msualg_5(A,B),A,A) ) ) ).
fof(dt_k2_msualg_5,axiom,
! [A] :
( ~ v3_struct_0(k2_msualg_5(A))
& v3_lattices(k2_msualg_5(A))
& v10_lattices(k2_msualg_5(A))
& l3_lattices(k2_msualg_5(A)) ) ).
fof(dt_k3_msualg_5,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& m1_msualg_4(C,A,B,B) )
=> ( v2_msualg_4(k3_msualg_5(A,B,C),A,B)
& m1_msualg_4(k3_msualg_5(A,B,C),A,B,B) ) ) ).
fof(dt_k4_msualg_5,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B)
& v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> ( v2_msualg_4(k4_msualg_5(A,B,C,D),A,B)
& m1_msualg_4(k4_msualg_5(A,B,C,D),A,B,B) ) ) ).
fof(commutativity_k4_msualg_5,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& v2_msualg_4(C,A,B)
& m1_msualg_4(C,A,B,B)
& v2_msualg_4(D,A,B)
& m1_msualg_4(D,A,B,B) )
=> k4_msualg_5(A,B,C,D) = k4_msualg_5(A,B,D,C) ) ).
fof(dt_k5_msualg_5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k5_msualg_5(A,B))
& v3_lattices(k5_msualg_5(A,B))
& v10_lattices(k5_msualg_5(A,B))
& l3_lattices(k5_msualg_5(A,B)) ) ) ).
fof(dt_k6_msualg_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v3_lattices(k6_msualg_5(A,B))
& m2_nat_lat(k6_msualg_5(A,B),k5_msualg_5(u1_struct_0(A),u4_msualg_1(A,B))) ) ) ).
fof(d2_msualg_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_lattices(B)
& v10_lattices(B)
& l3_lattices(B) )
=> ( B = k2_msualg_5(A)
<=> ( u1_struct_0(B) = a_1_0_msualg_5(A)
& ! [C] :
( ( v1_partfun1(C,A,A)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_partfun1(D,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& m2_relset_1(D,A,A) )
=> ( k1_binop_1(u1_lattices(B),C,D) = k4_eqrel_1(A,C,D)
& k1_binop_1(u2_lattices(B),C,D) = k5_eqrel_1(A,C,D) ) ) ) ) ) ) ).
fof(fraenkel_a_1_0_msualg_5,axiom,
! [A,B] :
( r2_hidden(A,a_1_0_msualg_5(B))
<=> ? [C] :
( m2_relset_1(C,B,B)
& A = C
& v1_partfun1(C,B,B)
& v3_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,B,B) ) ) ).
%------------------------------------------------------------------------------