SET007 Axioms: SET007+395.ax
%------------------------------------------------------------------------------
% File : SET007+395 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subalgebras of Many Sorted Algebra. Lattice of Subalgebras
% 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 99 ( 7 unt; 0 def)
% Number of atoms : 764 ( 56 equ)
% Maximal formula atoms : 18 ( 7 avg)
% Number of connectives : 853 ( 188 ~; 0 |; 362 &)
% ( 26 <=>; 277 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 1 prp; 0-4 aty)
% Number of functors : 48 ( 48 usr; 1 con; 0-6 aty)
% Number of variables : 321 ( 312 !; 9 ?)
% 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_msualg_2,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A) )
=> ( v1_relat_1(k2_pboole(A,B,C))
& v2_relat_1(k2_pboole(A,B,C))
& v1_funct_1(k2_pboole(A,B,C)) ) ) ).
fof(fc2_msualg_2,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A) )
=> ( v1_relat_1(k2_pboole(A,C,B))
& v2_relat_1(k2_pboole(A,C,B))
& v1_funct_1(k2_pboole(A,C,B)) ) ) ).
fof(fc3_msualg_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(C)
& v1_funct_2(C,B,k3_finseq_2(A))
& m1_relset_1(C,B,k3_finseq_2(A))
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A) )
=> ( ~ v3_struct_0(g1_msualg_1(A,B,C,D))
& v1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ).
fof(rc1_msualg_2,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v2_msualg_2(A) ) ).
fof(fc4_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msualg_2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> ~ v1_xboole_0(k1_msualg_2(A,B,C)) ) ).
fof(fc5_msualg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msualg_2(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v1_relat_1(k2_msualg_2(A,B))
& v2_relat_1(k2_msualg_2(A,B))
& ~ v3_relat_1(k2_msualg_2(A,B))
& v1_funct_1(k2_msualg_2(A,B)) ) ) ).
fof(rc2_msualg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_msualg_2(C,A,B)
& v4_msualg_1(C,A) ) ) ).
fof(fc6_msualg_2,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) )
=> ( v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A)
& v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ).
fof(rc3_msualg_2,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) )
=> ? [C] :
( m1_msualg_2(C,A,B)
& v4_msualg_1(C,A)
& v5_msualg_1(C,A) ) ) ).
fof(fc7_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
=> ~ v1_xboole_0(k5_msualg_2(A,B,C)) ) ).
fof(fc8_msualg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ~ v1_xboole_0(k6_msualg_2(A,B)) ) ).
fof(fc9_msualg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
& m1_subset_1(D,u1_struct_0(A)) )
=> ~ v1_xboole_0(k8_msualg_2(A,B,C,D)) ) ).
fof(fc10_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v2_relat_1(C)
& m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
=> ( v4_msualg_1(k12_msualg_2(A,B,C),A)
& v5_msualg_1(k12_msualg_2(A,B,C),A) ) ) ).
fof(fc11_msualg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ~ v1_xboole_0(k14_msualg_2(A,B)) ) ).
fof(fc12_msualg_2,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(k17_msualg_2(A,B))
& v3_lattices(k17_msualg_2(A,B))
& v4_lattices(k17_msualg_2(A,B))
& v5_lattices(k17_msualg_2(A,B))
& v6_lattices(k17_msualg_2(A,B))
& v7_lattices(k17_msualg_2(A,B))
& v8_lattices(k17_msualg_2(A,B))
& v9_lattices(k17_msualg_2(A,B))
& v10_lattices(k17_msualg_2(A,B))
& v13_lattices(k17_msualg_2(A,B))
& v14_lattices(k17_msualg_2(A,B))
& v15_lattices(k17_msualg_2(A,B)) ) ) ).
fof(t1_msualg_2,axiom,
$true ).
fof(t2_msualg_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m2_finseq_2(D,A,k3_finseq_2(A))
=> k4_card_3(k5_relat_1(D,k3_pboole(A,B,C))) = k3_xboole_0(k4_card_3(k5_relat_1(D,B)),k4_card_3(k5_relat_1(D,C))) ) ) ) ) ).
fof(d1_msualg_2,axiom,
$true ).
fof(d2_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_msualg_2(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_msualg_1(A))
& k1_funct_1(u2_msualg_1(A),C) = k1_xboole_0
& k1_funct_1(u3_msualg_1(A),C) = B ) ) ) ) ).
fof(d3_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ( v2_msualg_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v1_msualg_2(B,A) ) ) ) ).
fof(d5_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( C = k2_msualg_2(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k1_msualg_2(A,B,D) ) ) ) ) ) ).
fof(d6_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r1_msualg_2(A,B,C,D)
<=> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) ) ) ) ) ) ).
fof(d7_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( v3_msualg_2(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> r1_msualg_2(A,B,D,C) ) ) ) ) ) ).
fof(t3_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
=> ! [E] :
( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C))
=> ( r2_pboole(u1_struct_0(A),D,E)
=> r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B)) ) ) ) ) ) ) ).
fof(d8_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r1_msualg_2(A,B,C,D)
=> k3_msualg_2(A,B,C,D) = k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C)) ) ) ) ) ) ).
fof(d9_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ! [D] :
( m3_pboole(D,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C))
=> ( D = k4_msualg_2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> k1_funct_1(D,E) = k3_msualg_2(A,B,E,C) ) ) ) ) ) ) ).
fof(t4_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
=> ( v3_msualg_2(C,A,B)
& ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> k3_msualg_2(A,B,D,C) = k5_msualg_1(A,D,B) ) ) ) ) ) ) ).
fof(t5_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
=> r6_pboole(u1_msualg_1(A),k4_msualg_2(A,B,C),u5_msualg_1(A,B)) ) ) ) ) ).
fof(d10_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( l3_msualg_1(C,A)
=> ( m1_msualg_2(C,A,B)
<=> ( m4_pboole(u4_msualg_1(A,C),u1_struct_0(A),u4_msualg_1(A,B))
& ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
=> ( v3_msualg_2(D,A,B)
& r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) ) ) ) ) ) ) ) ) ).
fof(t6_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> m1_msualg_2(B,A,B) ) ) ).
fof(t7_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( l3_msualg_1(D,A)
=> ( ( m1_msualg_2(B,A,C)
& m1_msualg_2(C,A,D) )
=> m1_msualg_2(B,A,D) ) ) ) ) ) ).
fof(t8_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( l3_msualg_1(C,A)
=> ( ( v4_msualg_1(B,A)
& m1_msualg_2(B,A,C)
& v4_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> B = C ) ) ) ) ).
fof(t9_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_2(C,A,B)
=> ! [D] :
( m1_msualg_2(D,A,B)
=> ( r2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> m1_msualg_2(C,A,D) ) ) ) ) ) ).
fof(t10_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( ( v4_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v4_msualg_1(D,A)
& m1_msualg_2(D,A,B) )
=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> C = D ) ) ) ) ) ).
fof(t11_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_2(C,A,B)
=> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)) ) ) ) ).
fof(t12_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msualg_2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ( v2_relat_1(k2_msualg_2(A,B))
& m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)) ) ) ) ) ).
fof(t13_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v2_msualg_2(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v5_msualg_1(D,A)
& m1_msualg_2(D,A,B) )
=> v2_relat_1(k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))) ) ) ) ) ).
fof(d11_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ! [D] :
( D = k5_msualg_2(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> ( r2_hidden(E,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B)))))
& m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B))
& ! [F] :
( m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B))
=> ( F = E
=> ( v3_msualg_2(F,A,B)
& r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),F)
& r2_pboole(u1_struct_0(A),C,F) ) ) ) ) ) ) ) ) ) ).
fof(d12_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( C = k6_msualg_2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B)))))
& m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
& ! [E] :
( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B))
=> ( E = D
=> v3_msualg_2(E,A,B) ) ) ) ) ) ) ) ).
fof(d13_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_subset_1(C,k6_msualg_2(A,B))
=> k7_msualg_2(A,B,C) = C ) ) ) ).
fof(t14_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r2_hidden(D,k5_msualg_2(A,B,C))
<=> ( v3_msualg_2(D,A,B)
& r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),D)
& r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) ) ).
fof(t15_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r2_hidden(C,k6_msualg_2(A,B))
<=> v3_msualg_2(C,A,B) ) ) ) ) ).
fof(d14_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( E = k8_msualg_2(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,E)
<=> ? [G] :
( m4_pboole(G,u1_struct_0(A),u4_msualg_1(A,B))
& r2_hidden(G,k5_msualg_2(A,B,C))
& F = k1_funct_1(G,D) ) ) ) ) ) ) ) ).
fof(d15_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ( D = k9_msualg_2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_funct_1(D,E) = k1_setfam_1(k8_msualg_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t16_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> r2_pboole(u1_struct_0(A),k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C),k9_msualg_2(A,B,C)) ) ) ) ).
fof(t17_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( v2_relat_1(k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C))
=> v2_relat_1(k9_msualg_2(A,B,C)) ) ) ) ) ).
fof(t18_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
=> ! [E] :
( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C))
=> ( r2_hidden(E,k5_msualg_2(A,C,D))
=> r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B)) ) ) ) ) ) ) ).
fof(t19_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
=> ! [E] :
( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C))
=> ( r2_hidden(E,k5_msualg_2(A,C,D))
=> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),E),B)) ) ) ) ) ) ) ).
fof(t20_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( l3_msualg_1(C,A)
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C))
=> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k9_msualg_2(A,C,D)),B)) ) ) ) ) ).
fof(t21_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( v3_msualg_2(k9_msualg_2(A,B,C),A,B)
& r2_pboole(u1_struct_0(A),C,k9_msualg_2(A,B,C)) ) ) ) ) ).
fof(d16_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( v3_msualg_2(C,A,B)
=> k10_msualg_2(A,B,C) = g3_msualg_1(A,C,k4_msualg_2(A,B,C)) ) ) ) ) ).
fof(d17_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_msualg_2(C,A,B)
=> ! [D] :
( m1_msualg_2(D,A,B)
=> ! [E] :
( ( v4_msualg_1(E,A)
& m1_msualg_2(E,A,B) )
=> ( E = k11_msualg_2(A,B,C,D)
<=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,E),k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)))
& ! [F] :
( m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),F,u4_msualg_1(A,E))
=> ( v3_msualg_2(F,A,B)
& r6_pboole(u1_msualg_1(A),u5_msualg_1(A,E),k4_msualg_2(A,B,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(d18_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ! [D] :
( ( v4_msualg_1(D,A)
& m1_msualg_2(D,A,B) )
=> ( D = k12_msualg_2(A,B,C)
<=> ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,D))
& ! [E] :
( m1_msualg_2(E,A,B)
=> ( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,E))
=> m1_msualg_2(D,A,E) ) ) ) ) ) ) ) ) ).
fof(t22_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
=> k12_msualg_2(A,B,C) = B ) ) ) ) ).
fof(t23_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( ( v4_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
=> k12_msualg_2(A,B,D) = C ) ) ) ) ) ).
fof(t24_msualg_2,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_msualg_2(C,A,B)
=> k11_msualg_2(A,B,k12_msualg_2(A,B,k2_msualg_2(A,B)),C) = k12_msualg_2(A,B,k2_msualg_2(A,B)) ) ) ) ).
fof(d19_msualg_2,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_msualg_2(C,A,B)
=> ! [D] :
( m1_msualg_2(D,A,B)
=> ! [E] :
( ( v4_msualg_1(E,A)
& m1_msualg_2(E,A,B) )
=> ( E = k13_msualg_2(A,B,C,D)
<=> ! [F] :
( m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),F,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)))
=> E = k12_msualg_2(A,B,F) ) ) ) ) ) ) ) ) ).
fof(t25_msualg_2,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_msualg_2(C,A,B)
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ! [E] :
( m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),E,k2_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)))
=> k13_msualg_2(A,B,k12_msualg_2(A,B,D),C) = k12_msualg_2(A,B,E) ) ) ) ) ) ) ).
fof(t26_msualg_2,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_msualg_2(C,A,B)
=> ! [D] :
( m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,B))
=> k13_msualg_2(A,B,k12_msualg_2(A,B,D),C) = k12_msualg_2(A,B,D) ) ) ) ) ) ).
fof(t27_msualg_2,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_msualg_2(C,A,B)
=> ! [D] :
( m1_msualg_2(D,A,B)
=> k13_msualg_2(A,B,C,D) = k13_msualg_2(A,B,D,C) ) ) ) ) ).
fof(t28_msualg_2,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] :
( ( v4_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v4_msualg_1(D,A)
& m1_msualg_2(D,A,B) )
=> k11_msualg_2(A,B,C,k13_msualg_2(A,B,C,D)) = C ) ) ) ) ).
fof(t29_msualg_2,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] :
( ( v4_msualg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v4_msualg_1(D,A)
& m1_msualg_2(D,A,B) )
=> k13_msualg_2(A,B,k11_msualg_2(A,B,C,D),D) = D ) ) ) ) ).
fof(d20_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( C = k14_msualg_2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( v4_msualg_1(D,A)
& m1_msualg_2(D,A,B) ) ) ) ) ) ).
fof(d21_msualg_2,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
& m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) )
=> ( C = k15_msualg_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k14_msualg_2(A,B))
=> ! [E] :
( m1_subset_1(E,k14_msualg_2(A,B))
=> ! [F] :
( ( v4_msualg_1(F,A)
& m1_msualg_2(F,A,B) )
=> ! [G] :
( ( v4_msualg_1(G,A)
& m1_msualg_2(G,A,B) )
=> ( ( D = F
& E = G )
=> k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E) = k13_msualg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) ).
fof(d22_msualg_2,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
& m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) )
=> ( C = k16_msualg_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k14_msualg_2(A,B))
=> ! [E] :
( m1_subset_1(E,k14_msualg_2(A,B))
=> ! [F] :
( ( v4_msualg_1(F,A)
& m1_msualg_2(F,A,B) )
=> ! [G] :
( ( v4_msualg_1(G,A)
& m1_msualg_2(G,A,B) )
=> ( ( D = F
& E = G )
=> k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E) = k11_msualg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t30_msualg_2,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) )
=> v1_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)) ) ) ).
fof(t31_msualg_2,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) )
=> v2_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)) ) ) ).
fof(t32_msualg_2,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) )
=> v1_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)) ) ) ).
fof(t33_msualg_2,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) )
=> v2_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)) ) ) ).
fof(d23_msualg_2,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) )
=> k17_msualg_2(A,B) = g3_lattices(k14_msualg_2(A,B),k15_msualg_2(A,B),k16_msualg_2(A,B)) ) ) ).
fof(t34_msualg_2,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) )
=> v15_lattices(k17_msualg_2(A,B)) ) ) ).
fof(t35_msualg_2,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(k17_msualg_2(A,B)) = k12_msualg_2(A,B,k2_msualg_2(A,B)) ) ) ).
fof(t36_msualg_2,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] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
=> k6_lattices(k17_msualg_2(A,B)) = k12_msualg_2(A,B,C) ) ) ) ) ).
fof(t37_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A) )
=> k6_lattices(k17_msualg_2(A,B)) = B ) ) ).
fof(t38_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> m1_msualg_2(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A,B) ) ) ).
fof(t39_msualg_2,axiom,
$true ).
fof(t40_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> r2_hidden(u4_msualg_1(A,B),k5_msualg_2(A,B,C)) ) ) ) ).
fof(t41_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> r1_tarski(k5_msualg_2(A,B,C),k6_msualg_2(A,B)) ) ) ) ).
fof(dt_m1_msualg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_msualg_2(C,A,B)
=> l3_msualg_1(C,A) ) ) ).
fof(existence_m1_msualg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ? [C] : m1_msualg_2(C,A,B) ) ).
fof(dt_k1_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_msualg_2(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))) ) ).
fof(dt_k2_msualg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) ) ).
fof(dt_k3_msualg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_msualg_1(A))
& m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) )
=> ( v1_funct_1(k3_msualg_2(A,B,C,D))
& v1_funct_2(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C))
& m2_relset_1(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) ) ) ).
fof(dt_k4_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
=> m3_pboole(k4_msualg_2(A,B,C),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C)) ) ).
fof(dt_k5_msualg_2,axiom,
$true ).
fof(dt_k6_msualg_2,axiom,
$true ).
fof(dt_k7_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m1_subset_1(C,k6_msualg_2(A,B)) )
=> m4_pboole(k7_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)) ) ).
fof(dt_k8_msualg_2,axiom,
$true ).
fof(dt_k9_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
=> m4_pboole(k9_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)) ) ).
fof(dt_k10_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
=> ( v4_msualg_1(k10_msualg_2(A,B,C),A)
& m1_msualg_2(k10_msualg_2(A,B,C),A,B) ) ) ).
fof(dt_k11_msualg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m1_msualg_2(C,A,B)
& m1_msualg_2(D,A,B) )
=> ( v4_msualg_1(k11_msualg_2(A,B,C,D),A)
& m1_msualg_2(k11_msualg_2(A,B,C,D),A,B) ) ) ).
fof(dt_k12_msualg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) )
=> ( v4_msualg_1(k12_msualg_2(A,B,C),A)
& m1_msualg_2(k12_msualg_2(A,B,C),A,B) ) ) ).
fof(dt_k13_msualg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& m1_msualg_2(C,A,B)
& m1_msualg_2(D,A,B) )
=> ( v4_msualg_1(k13_msualg_2(A,B,C,D),A)
& m1_msualg_2(k13_msualg_2(A,B,C,D),A,B) ) ) ).
fof(dt_k14_msualg_2,axiom,
$true ).
fof(dt_k15_msualg_2,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) )
=> ( v1_funct_1(k15_msualg_2(A,B))
& v1_funct_2(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
& m2_relset_1(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) ) ) ).
fof(dt_k16_msualg_2,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) )
=> ( v1_funct_1(k16_msualg_2(A,B))
& v1_funct_2(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B))
& m2_relset_1(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) ) ) ).
fof(dt_k17_msualg_2,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(k17_msualg_2(A,B))
& v3_lattices(k17_msualg_2(A,B))
& v10_lattices(k17_msualg_2(A,B))
& l3_lattices(k17_msualg_2(A,B)) ) ) ).
fof(d4_msualg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C)))
=> ( ( k1_funct_1(u4_msualg_1(A,B),C) != k1_xboole_0
=> ( D = k1_msualg_2(A,B,C)
<=> ? [E] :
( ~ v1_xboole_0(E)
& E = k1_funct_1(u4_msualg_1(A,B),C)
& D = a_4_0_msualg_2(A,B,C,E) ) ) )
& ( k1_funct_1(u4_msualg_1(A,B),C) = k1_xboole_0
=> ( D = k1_msualg_2(A,B,C)
<=> D = k1_xboole_0 ) ) ) ) ) ) ) ).
fof(fraenkel_a_4_0_msualg_2,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B)
& l3_msualg_1(C,B)
& m1_subset_1(D,u1_struct_0(B))
& ~ v1_xboole_0(E) )
=> ( r2_hidden(A,a_4_0_msualg_2(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,E)
& A = F
& ? [G] :
( m1_subset_1(G,u1_msualg_1(B))
& k1_funct_1(u2_msualg_1(B),G) = k1_xboole_0
& k1_funct_1(u3_msualg_1(B),G) = D
& r2_hidden(F,k2_relat_1(k5_msualg_1(B,G,C))) ) ) ) ) ).
%------------------------------------------------------------------------------