SET007 Axioms: SET007+397.ax
%------------------------------------------------------------------------------
% File : SET007+397 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Homomorphisms 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 : msualg_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 52 ( 2 unt; 0 def)
% Number of atoms : 474 ( 29 equ)
% Maximal formula atoms : 19 ( 9 avg)
% Number of connectives : 503 ( 81 ~; 0 |; 207 &)
% ( 16 <=>; 199 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 12 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-4 aty)
% Number of functors : 28 ( 28 usr; 3 con; 0-6 aty)
% Number of variables : 237 ( 235 !; 2 ?)
% 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_3,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B)
& v1_msualg_3(B) ) ).
fof(fc1_msualg_3,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)
& m1_subset_1(C,u1_msualg_1(A)) )
=> ( ~ v1_xboole_0(k3_msualg_1(A,C,B))
& v1_fraenkel(k3_msualg_1(A,C,B)) ) ) ).
fof(d1_msualg_3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m3_pboole(C,A,B,B)
=> ( C = k2_msualg_3(A,B)
<=> ! [D] :
( r2_hidden(D,A)
=> k1_funct_1(C,D) = k6_partfun1(k1_funct_1(B,D)) ) ) ) ) ).
fof(d2_msualg_3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_msualg_3(A)
<=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_hidden(B,k1_relat_1(A))
& k1_funct_1(A,B) = C )
=> v2_funct_1(C) ) ) ) ) ).
fof(t1_msualg_3,axiom,
! [A,B] :
( ( v1_funcop_1(B)
& m1_pboole(B,A) )
=> ( v1_msualg_3(B)
<=> ! [C] :
( r2_hidden(C,A)
=> v2_funct_1(k1_funct_1(B,C)) ) ) ) ).
fof(d3_msualg_3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,B,C)
=> ( v2_msualg_3(D,A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k2_relat_1(k1_funct_1(D,E)) = k1_funct_1(C,E) ) ) ) ) ) ).
fof(t2_msualg_3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m3_pboole(E,A,B,C)
=> ! [F] :
( m3_pboole(F,A,C,D)
=> ( k1_relat_1(k13_pboole(E,F)) = A
& ! [G] :
( r2_hidden(G,A)
=> k1_funct_1(k13_pboole(E,F),G) = k5_relat_1(k1_funct_1(E,G),k1_funct_1(F,G)) ) ) ) ) ) ) ) ).
fof(t3_msualg_3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,B,C)
=> k13_pboole(k2_msualg_3(A,B),D) = D ) ) ) ).
fof(t4_msualg_3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,B,C)
=> k13_pboole(D,k2_msualg_3(A,C)) = D ) ) ) ).
fof(d4_msualg_3,axiom,
$true ).
fof(d5_msualg_3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,B,C)
=> ( ( v1_msualg_3(D)
& v2_msualg_3(D,A,B,C) )
=> ! [E] :
( m3_pboole(E,A,C,B)
=> ( E = k4_msualg_3(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,A)
=> k1_funct_1(E,F) = k2_funct_1(k1_funct_1(D,F)) ) ) ) ) ) ) ) ).
fof(t5_msualg_3,axiom,
! [A,B] :
( ( v2_relat_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( m3_pboole(D,A,B,C)
=> ! [E] :
( m3_pboole(E,A,C,B)
=> ( ( v1_msualg_3(D)
& v2_msualg_3(D,A,B,C)
& r6_pboole(A,E,k4_msualg_3(A,B,C,D)) )
=> ( r6_pboole(A,k3_msualg_3(A,C,B,C,E,D),k2_msualg_3(A,C))
& r6_pboole(A,k3_msualg_3(A,B,C,B,D,E),k2_msualg_3(A,B)) ) ) ) ) ) ) ).
fof(t6_msualg_3,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] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,k3_msualg_1(A,B,C))
=> ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,B))
& ! [E] :
( r2_hidden(E,k1_relat_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C))))
=> r2_hidden(k1_funct_1(D,E),k1_funct_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)),E)) ) ) ) ) ) ) ) ).
fof(d6_msualg_3,axiom,
$true ).
fof(d7_msualg_3,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] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,D,B))
=> ~ ( k3_msualg_1(A,D,B) != k1_xboole_0
& k3_msualg_1(A,D,C) != k1_xboole_0
& k5_msualg_3(A,B,C,D,E,F) != k1_funct_1(k3_pralg_2(k5_relat_1(k1_msualg_1(A,D),E)),F) ) ) ) ) ) ) ) ).
fof(d8_msualg_3,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] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,D,B))
=> ! [G] :
( m1_subset_1(G,k3_msualg_1(A,D,C))
=> ( G = k6_msualg_3(A,B,C,D,E,F)
<=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( r2_hidden(H,k1_relat_1(F))
=> k1_funct_1(G,H) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),H)),k1_funct_1(F,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_msualg_3,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)
=> ( k3_msualg_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k3_msualg_1(A,B,C))
=> D = k5_msualg_3(A,C,C,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)),D) ) ) ) ) ) ).
fof(t8_msualg_3,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] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( ( v5_msualg_1(E,A)
& l3_msualg_1(E,A) )
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ! [G] :
( m3_pboole(G,u1_struct_0(A),u4_msualg_1(A,D),u4_msualg_1(A,E))
=> ! [H] :
( m1_subset_1(H,k3_msualg_1(A,B,C))
=> k6_msualg_3(A,C,E,B,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D),u4_msualg_1(A,E),F,G),H) = k6_msualg_3(A,D,E,B,G,k6_msualg_3(A,C,D,B,F,H)) ) ) ) ) ) ) ) ) ).
fof(d9_msualg_3,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] :
( 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] :
( m1_subset_1(E,u1_msualg_1(A))
=> ( k3_msualg_1(A,E,B) != k1_xboole_0
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,E,B))
=> k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,B),F)) = k1_funct_1(k5_msualg_1(A,E,C),k5_msualg_3(A,B,C,E,D,F)) ) ) ) ) ) ) ) ) ).
fof(t9_msualg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> r1_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B))) ) ) ).
fof(t10_msualg_3,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] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ( ( r1_msualg_3(A,B,C,E)
& r1_msualg_3(A,C,D,F) )
=> r1_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ).
fof(d10_msualg_3,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] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r2_msualg_3(A,B,C,D)
<=> ( r1_msualg_3(A,B,C,D)
& v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) ) ) ) ) ) ).
fof(t11_msualg_3,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] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ( ( r2_msualg_3(A,B,C,E)
& r2_msualg_3(A,C,D,F) )
=> r2_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ).
fof(d11_msualg_3,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] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r3_msualg_3(A,B,C,D)
<=> ( r1_msualg_3(A,B,C,D)
& v1_msualg_3(D) ) ) ) ) ) ) ).
fof(t12_msualg_3,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] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ( ( r3_msualg_3(A,B,C,E)
& r3_msualg_3(A,C,D,F) )
=> r3_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ).
fof(d12_msualg_3,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] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r4_msualg_3(A,B,C,D)
<=> ( r2_msualg_3(A,B,C,D)
& r3_msualg_3(A,B,C,D) ) ) ) ) ) ) ).
fof(t13_msualg_3,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] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ( r4_msualg_3(A,B,C,D)
<=> ( r1_msualg_3(A,B,C,D)
& v2_msualg_3(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
& v1_msualg_3(D) ) ) ) ) ) ) ).
fof(t14_msualg_3,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,C),u4_msualg_1(A,B))
=> ( ( r4_msualg_3(A,B,C,D)
& r6_pboole(u1_struct_0(A),E,k4_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D)) )
=> r4_msualg_3(A,C,B,E) ) ) ) ) ) ) ).
fof(t15_msualg_3,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] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))
=> ( ( r4_msualg_3(A,B,C,E)
& r4_msualg_3(A,C,D,F) )
=> r4_msualg_3(A,B,D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u4_msualg_1(A,D),E,F)) ) ) ) ) ) ) ) ).
fof(d13_msualg_3,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)
=> ( r5_msualg_3(A,B,C)
<=> ? [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
& r4_msualg_3(A,B,C,D) ) ) ) ) ) ).
fof(t16_msualg_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( r4_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,B)))
& r5_msualg_3(A,B,B) ) ) ) ).
fof(t17_msualg_3,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) )
=> ( r6_msualg_3(A,B,C)
=> r6_msualg_3(A,C,B) ) ) ) ) ).
fof(t18_msualg_3,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] :
( ( v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ( ( r6_msualg_3(A,B,C)
& r6_msualg_3(A,C,D) )
=> r6_msualg_3(A,B,D) ) ) ) ) ) ).
fof(d14_msualg_3,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] :
( ( v4_msualg_1(E,A)
& v5_msualg_1(E,A)
& m1_msualg_2(E,A,C) )
=> ( E = k7_msualg_3(A,B,C,D)
<=> r6_pboole(u1_struct_0(A),u4_msualg_1(A,E),k14_pboole(u1_struct_0(A),u4_msualg_1(A,B),D)) ) ) ) ) ) ) ) ).
fof(t19_msualg_3,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)
& 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)
=> ( r2_msualg_3(A,B,C,D)
<=> k7_msualg_3(A,B,C,D) = C ) ) ) ) ) ) ).
fof(t20_msualg_3,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,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
=> ( ( r6_pboole(u1_struct_0(A),D,E)
& r1_msualg_3(A,B,C,D) )
=> r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E) ) ) ) ) ) ) ).
fof(t21_msualg_3,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] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
=> ~ ( r6_pboole(u1_struct_0(A),D,E)
& r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E) ) ) ) ) ) ) ) ).
fof(t22_msualg_3,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)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,B))
=> ( r6_pboole(u1_struct_0(A),D,k2_msualg_3(u1_struct_0(A),u4_msualg_1(A,C)))
=> r3_msualg_3(A,C,B,D) ) ) ) ) ) ).
fof(t23_msualg_3,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] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)))
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k7_msualg_3(A,B,C,D)),u4_msualg_1(A,C))
=> ~ ( r2_msualg_3(A,B,k7_msualg_3(A,B,C,D),E)
& r3_msualg_3(A,k7_msualg_3(A,B,C,D),C,F)
& r6_pboole(u1_struct_0(A),D,k3_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k7_msualg_3(A,B,C,D)),u4_msualg_1(A,C),E,F)) ) ) ) ) ) ) ) ) ).
fof(t24_msualg_3,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] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,D,B))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H) )
=> ( ( F = G
& r2_hidden(F,k3_msualg_1(A,D,B))
& r2_hidden(H,k3_msualg_1(A,D,C)) )
=> ( H = k5_msualg_3(A,B,C,D,E,F)
<=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ( r2_hidden(I,k1_relat_1(G))
=> k1_funct_1(H,I) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),I)),k1_funct_1(G,I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(reflexivity_r6_msualg_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& l3_msualg_1(C,A) )
=> r6_msualg_3(A,B,B) ) ).
fof(redefinition_r6_msualg_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& l3_msualg_1(C,A) )
=> ( r6_msualg_3(A,B,C)
<=> r5_msualg_3(A,B,C) ) ) ).
fof(dt_k1_msualg_3,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& m1_pboole(C,A)
& m3_pboole(D,A,B,C)
& m1_subset_1(E,A) )
=> ( v1_funct_1(k1_msualg_3(A,B,C,D,E))
& v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E))
& m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ).
fof(redefinition_k1_msualg_3,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& m1_pboole(C,A)
& m3_pboole(D,A,B,C)
& m1_subset_1(E,A) )
=> k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) ).
fof(dt_k2_msualg_3,axiom,
! [A,B] :
( m1_pboole(B,A)
=> m3_pboole(k2_msualg_3(A,B),A,B,B) ) ).
fof(dt_k3_msualg_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A)
& v2_relat_1(D)
& m1_pboole(D,A)
& m3_pboole(E,A,B,C)
& m3_pboole(F,A,C,D) )
=> m3_pboole(k3_msualg_3(A,B,C,D,E,F),A,B,D) ) ).
fof(redefinition_k3_msualg_3,axiom,
! [A,B,C,D,E,F] :
( ( m1_pboole(B,A)
& v2_relat_1(C)
& m1_pboole(C,A)
& v2_relat_1(D)
& m1_pboole(D,A)
& m3_pboole(E,A,B,C)
& m3_pboole(F,A,C,D) )
=> k3_msualg_3(A,B,C,D,E,F) = k13_pboole(E,F) ) ).
fof(dt_k4_msualg_3,axiom,
! [A,B,C,D] :
( ( m1_pboole(B,A)
& m1_pboole(C,A)
& m3_pboole(D,A,B,C) )
=> m3_pboole(k4_msualg_3(A,B,C,D),A,C,B) ) ).
fof(dt_k5_msualg_3,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A)
& l3_msualg_1(C,A)
& m1_subset_1(D,u1_msualg_1(A))
& m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
& m1_subset_1(F,k3_msualg_1(A,D,B)) )
=> m1_subset_1(k5_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ).
fof(dt_k6_msualg_3,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& m1_subset_1(D,u1_msualg_1(A))
& m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
& m1_subset_1(F,k3_msualg_1(A,D,B)) )
=> m1_subset_1(k6_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ).
fof(redefinition_k6_msualg_3,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& m1_subset_1(D,u1_msualg_1(A))
& m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C))
& m1_subset_1(F,k3_msualg_1(A,D,B)) )
=> k6_msualg_3(A,B,C,D,E,F) = k5_msualg_3(A,B,C,D,E,F) ) ).
fof(dt_k7_msualg_3,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)) )
=> ( v4_msualg_1(k7_msualg_3(A,B,C,D),A)
& v5_msualg_1(k7_msualg_3(A,B,C,D),A)
& m1_msualg_2(k7_msualg_3(A,B,C,D),A,C) ) ) ).
%------------------------------------------------------------------------------