SET007 Axioms: SET007+400.ax
%------------------------------------------------------------------------------
% File : SET007+400 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Many Sorted Quotient 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 59 ( 1 unt; 0 def)
% Number of atoms : 594 ( 36 equ)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 634 ( 99 ~; 0 |; 339 &)
% ( 20 <=>; 176 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-4 aty)
% Number of functors : 49 ( 49 usr; 2 con; 0-6 aty)
% Number of variables : 257 ( 253 !; 4 ?)
% 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_4,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_msualg_4(B) ) ).
fof(cc1_msualg_4,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ! [D] :
( m1_msualg_4(D,A,B,C)
=> v1_msualg_4(D) ) ) ).
fof(rc2_msualg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(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))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_msualg_4(C)
& v3_msualg_4(C,A,B) ) ) ).
fof(rc3_msualg_4,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_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_msualg_4(C)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B) ) ) ).
fof(fc1_msualg_4,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)
& 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)) )
=> ( v4_msualg_1(k14_msualg_4(A,B,C),A)
& v5_msualg_1(k14_msualg_4(A,B,C),A) ) ) ).
fof(d1_msualg_4,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_msualg_4(A)
<=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> v1_relat_1(k1_funct_1(A,B)) ) ) ) ).
fof(d2_msualg_4,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ( m1_msualg_4(D,A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ).
fof(d3_msualg_4,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_msualg_4(C,A,B,B)
=> ( v2_msualg_4(C,A,B)
<=> ! [D,E] :
( m2_relset_1(E,k1_funct_1(B,D),k1_funct_1(B,D))
=> ( ( r2_hidden(D,A)
& k1_funct_1(C,D) = E )
=> ( v3_relat_2(E)
& v8_relat_2(E)
& v1_partfun1(E,k1_funct_1(B,D),k1_funct_1(B,D))
& m2_relset_1(E,k1_funct_1(B,D),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(d4_msualg_4,axiom,
$true ).
fof(d5_msualg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( 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)
<=> v2_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ) ) ).
fof(t1_msualg_4,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] :
( ( v3_msualg_4(D,A,B)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v3_relat_2(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C))
& v8_relat_2(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C))
& v1_partfun1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),C))
& m2_relset_1(k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),D,C),k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),C)) ) ) ) ) ) ).
fof(d6_msualg_4,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)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ( v4_msualg_4(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_subset_1(E,k3_msualg_1(A,D,B))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,D,B))
=> ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k1_relat_1(E))
=> r2_hidden(k4_tarski(k1_funct_1(E,G),k1_funct_1(F,G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),G))) ) )
=> r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),E),k8_funct_2(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),F)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B),C,k2_msualg_1(A,D))) ) ) ) ) ) ) ) ) ).
fof(d7_msualg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D))
=> k3_msualg_4(A,B,C,D,E) = k6_eqrel_1(k1_funct_1(u4_msualg_1(A,B),D),k2_msualg_4(A,B,C,D),E) ) ) ) ) ) ).
fof(d8_msualg_4,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] :
( ( v2_relat_1(D)
& m1_pboole(D,u1_struct_0(A)) )
=> ( D = k4_msualg_4(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_funct_1(D,E) = k8_eqrel_1(k1_funct_1(u4_msualg_1(A,B),E),k2_msualg_4(A,B,C,E)) ) ) ) ) ) ) ).
fof(d9_msualg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ! [E] :
( m1_subset_1(E,k3_msualg_1(A,B,C))
=> ! [F] :
( m1_subset_1(F,k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k4_msualg_4(A,C,D))))
=> ( F = k7_msualg_4(A,B,C,D,E)
<=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,B)))
=> k1_funct_1(F,G) = k6_eqrel_1(k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G)),k2_msualg_4(A,C,D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G)),k1_funct_1(E,G)) ) ) ) ) ) ) ) ) ) ).
fof(d10_msualg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
& m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) )
=> ( E = k8_msualg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,C),k2_msualg_1(A,B)))
=> k1_funct_1(E,F) = k3_msualg_4(A,C,D,k2_msualg_1(A,B),F) ) ) ) ) ) ) ) ).
fof(d11_msualg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
& m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B)) )
=> ( E = k9_msualg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,B,C))
=> k1_funct_1(E,F) = k7_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(d12_msualg_4,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] :
( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)))
=> ( D = k10_msualg_4(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> k5_msualg_4(A,k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)),D,E) = k8_msualg_4(A,E,B,C) ) ) ) ) ) ) ).
fof(d13_msualg_4,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] :
( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))))
=> ( D = k11_msualg_4(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),D,E) = k9_msualg_4(A,E,B,C) ) ) ) ) ) ) ).
fof(t2_msualg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ! [E] :
~ ( r2_hidden(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
& ! [F] :
( m1_subset_1(F,k3_msualg_1(A,B,C))
=> E != k7_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ).
fof(d14_msualg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
& m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) )
=> ( E = k12_msualg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,B,C))
=> ( r2_hidden(k7_msualg_4(A,B,C,D,F),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
=> k1_funct_1(E,k7_msualg_4(A,B,C,D,F)) = k1_funct_1(k1_partfun1(k3_msualg_1(A,B,C),k4_msualg_1(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B),k5_msualg_1(A,B,C),k8_msualg_4(A,B,C,D)),F) ) ) ) ) ) ) ) ) ).
fof(d15_msualg_4,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] :
( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)))
=> ( D = k13_msualg_4(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C)),D,E) = k12_msualg_4(A,E,B,C) ) ) ) ) ) ) ).
fof(d16_msualg_4,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)) )
=> k14_msualg_4(A,B,C) = g3_msualg_1(A,k4_msualg_4(A,B,C),k13_msualg_4(A,B,C)) ) ) ) ).
fof(d17_msualg_4,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] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D))
& m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D)) )
=> ( E = k15_msualg_4(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,k1_funct_1(u4_msualg_1(A,B),D))
=> k1_funct_1(E,F) = k6_eqrel_1(k1_funct_1(u4_msualg_1(A,B),D),k2_msualg_4(A,B,C,D),F) ) ) ) ) ) ) ) ).
fof(d18_msualg_4,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] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)))
=> ( D = k16_msualg_4(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C)),D,E) = k15_msualg_4(A,B,C,E) ) ) ) ) ) ) ).
fof(t3_msualg_4,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)) )
=> r2_msualg_3(A,B,k14_msualg_4(A,B,C),k16_msualg_4(A,B,C)) ) ) ) ).
fof(d19_msualg_4,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] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v3_relat_2(F)
& v8_relat_2(F)
& v1_partfun1(F,k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E))
& m2_relset_1(F,k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) )
=> ( F = k17_msualg_4(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
=> ! [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),E))
=> ( r2_hidden(k4_tarski(G,H),F)
<=> k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),G) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),H) ) ) ) ) ) ) ) ) ) ) ).
fof(d20_msualg_4,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] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r1_msualg_3(A,B,C,D)
=> ! [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)) )
=> ( E = k18_msualg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k2_msualg_4(A,B,E,F) = k17_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ) ) ).
fof(d21_msualg_4,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] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_msualg_3(A,B,C,D)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E))
& m2_relset_1(F,k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) )
=> ( F = k19_msualg_4(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
=> k1_funct_1(F,k6_eqrel_1(k1_funct_1(u4_msualg_1(A,B),E),k17_msualg_4(A,B,C,D,E),G)) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),G) ) ) ) ) ) ) ) ) ) ).
fof(d22_msualg_4,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] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C))
=> ( E = k20_msualg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C),E,F) = k19_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t4_msualg_4,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] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r1_msualg_3(A,B,C,D)
=> r3_msualg_3(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D)),C,k20_msualg_4(A,B,C,D)) ) ) ) ) ) ).
fof(t5_msualg_4,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] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r2_msualg_3(A,B,C,D)
=> r4_msualg_3(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D)),C,k20_msualg_4(A,B,C,D)) ) ) ) ) ) ).
fof(t6_msualg_4,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] :
( ( v5_msualg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r2_msualg_3(A,B,C,D)
=> r6_msualg_3(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D)),C) ) ) ) ) ) ).
fof(dt_m1_msualg_4,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ! [D] :
( m1_msualg_4(D,A,B,C)
=> m1_pboole(D,A) ) ) ).
fof(existence_m1_msualg_4,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ? [D] : m1_msualg_4(D,A,B,C) ) ).
fof(dt_k1_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& m1_pboole(C,A)
& m1_msualg_4(D,A,B,C)
& m1_subset_1(E,A) )
=> m2_relset_1(k1_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ).
fof(redefinition_k1_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& m1_pboole(C,A)
& m1_msualg_4(D,A,B,C)
& m1_subset_1(E,A) )
=> k1_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ).
fof(dt_k2_msualg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
& m1_subset_1(D,u1_struct_0(A)) )
=> ( v3_relat_2(k2_msualg_4(A,B,C,D))
& v8_relat_2(k2_msualg_4(A,B,C,D))
& v1_partfun1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D))
& m2_relset_1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ).
fof(redefinition_k2_msualg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
& m1_subset_1(D,u1_struct_0(A)) )
=> k2_msualg_4(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k3_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) )
=> m1_subset_1(k3_msualg_4(A,B,C,D,E),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),D))) ) ).
fof(dt_k4_msualg_4,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)
& 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)) )
=> ( v2_relat_1(k4_msualg_4(A,B,C))
& m1_pboole(k4_msualg_4(A,B,C),u1_struct_0(A)) ) ) ).
fof(dt_k5_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_pboole(B,u1_msualg_1(A))
& m1_pboole(C,u1_msualg_1(A))
& m3_pboole(D,u1_msualg_1(A),B,C)
& m1_subset_1(E,u1_msualg_1(A)) )
=> ( v1_funct_1(k5_msualg_4(A,B,C,D,E))
& v1_funct_2(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E))
& m2_relset_1(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ).
fof(redefinition_k5_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_pboole(B,u1_msualg_1(A))
& m1_pboole(C,u1_msualg_1(A))
& m3_pboole(D,u1_msualg_1(A),B,C)
& m1_subset_1(E,u1_msualg_1(A)) )
=> k5_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ).
fof(dt_k6_msualg_4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& v2_relat_1(C)
& m1_pboole(C,A) )
=> ( v2_relat_1(k6_msualg_4(A,B,C))
& m1_pboole(k6_msualg_4(A,B,C),k4_finseq_1(B)) ) ) ).
fof(redefinition_k6_msualg_4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& v2_relat_1(C)
& m1_pboole(C,A) )
=> k6_msualg_4(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k7_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C))
& m1_subset_1(E,k3_msualg_1(A,B,C)) )
=> m1_subset_1(k7_msualg_4(A,B,C,D,E),k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k4_msualg_4(A,C,D)))) ) ).
fof(dt_k8_msualg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ( v1_funct_1(k8_msualg_4(A,B,C,D))
& v1_funct_2(k8_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
& m2_relset_1(k8_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) ) ) ).
fof(dt_k9_msualg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ( v1_funct_1(k9_msualg_4(A,B,C,D))
& v1_funct_2(k9_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B))
& m2_relset_1(k9_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B)) ) ) ).
fof(dt_k10_msualg_4,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)
& 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)) )
=> m3_pboole(k10_msualg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B)),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C))) ) ).
fof(dt_k11_msualg_4,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)
& 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)) )
=> m3_pboole(k11_msualg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C)))) ) ).
fof(dt_k12_msualg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,C)) )
=> ( v1_funct_1(k12_msualg_4(A,B,C,D))
& v1_funct_2(k12_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B))
& m2_relset_1(k12_msualg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,C,D)),B)) ) ) ).
fof(dt_k13_msualg_4,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)
& 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)) )
=> m3_pboole(k13_msualg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k4_msualg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k4_msualg_4(A,B,C))) ) ).
fof(dt_k14_msualg_4,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)
& 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)) )
=> l3_msualg_1(k14_msualg_4(A,B,C),A) ) ).
fof(dt_k15_msualg_4,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)
& 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))
& m1_subset_1(D,u1_struct_0(A)) )
=> ( v1_funct_1(k15_msualg_4(A,B,C,D))
& v1_funct_2(k15_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D))
& m2_relset_1(k15_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(k4_msualg_4(A,B,C),D)) ) ) ).
fof(dt_k16_msualg_4,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)
& 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)) )
=> m3_pboole(k16_msualg_4(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k14_msualg_4(A,B,C))) ) ).
fof(dt_k17_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v3_relat_2(k17_msualg_4(A,B,C,D,E))
& v8_relat_2(k17_msualg_4(A,B,C,D,E))
& v1_partfun1(k17_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E))
& m2_relset_1(k17_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) ) ) ).
fof(dt_k18_msualg_4,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)
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
=> ( v3_msualg_4(k18_msualg_4(A,B,C,D),A,B)
& v4_msualg_4(k18_msualg_4(A,B,C,D),A,B)
& m1_msualg_4(k18_msualg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(dt_k19_msualg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v5_msualg_1(B,A)
& l3_msualg_1(B,A)
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_funct_1(k19_msualg_4(A,B,C,D,E))
& v1_funct_2(k19_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E))
& m2_relset_1(k19_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) ) ) ).
fof(dt_k20_msualg_4,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)
& v5_msualg_1(C,A)
& l3_msualg_1(C,A)
& m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) )
=> m3_pboole(k20_msualg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,k14_msualg_4(A,B,k18_msualg_4(A,B,C,D))),u4_msualg_1(A,C)) ) ).
%------------------------------------------------------------------------------