SET007 Axioms: SET007+735.ax
%------------------------------------------------------------------------------
% File : SET007+735 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Order 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 : osalg_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 124 ( 5 unt; 0 def)
% Number of atoms : 1115 ( 65 equ)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 1213 ( 222 ~; 1 |; 669 &)
% ( 31 <=>; 290 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 1 prp; 0-4 aty)
% Number of functors : 42 ( 42 usr; 1 con; 0-6 aty)
% Number of variables : 345 ( 326 !; 19 ?)
% 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_osalg_1,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_finseq_1(C,A) )
=> ( v1_relat_1(k5_relat_1(C,B))
& v1_funct_1(k5_relat_1(C,B))
& v1_finseq_1(k5_relat_1(C,B)) ) ) ).
fof(rc1_osalg_1,axiom,
? [A] :
( l1_osalg_1(A)
& v1_osalg_1(A) ) ).
fof(rc2_osalg_1,axiom,
? [A] :
( l2_osalg_1(A)
& v2_osalg_1(A) ) ).
fof(rc3_osalg_1,axiom,
? [A] :
( l3_osalg_1(A)
& v3_osalg_1(A) ) ).
fof(fc2_osalg_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m1_relset_1(B,A,A)
& ~ v1_xboole_0(C)
& v3_relat_2(D)
& v8_relat_2(D)
& v1_partfun1(D,C,C)
& m1_relset_1(D,C,C)
& v1_funct_1(E)
& v1_funct_2(E,C,k3_finseq_2(A))
& m1_relset_1(E,C,k3_finseq_2(A))
& v1_funct_1(F)
& v1_funct_2(F,C,A)
& m1_relset_1(F,C,A) )
=> ( ~ v3_struct_0(g3_osalg_1(A,B,C,D,E,F))
& v2_orders_2(g3_osalg_1(A,B,C,D,E,F))
& v3_orders_2(g3_osalg_1(A,B,C,D,E,F))
& v4_orders_2(g3_osalg_1(A,B,C,D,E,F))
& v3_osalg_1(g3_osalg_1(A,B,C,D,E,F)) ) ) ).
fof(cc1_osalg_1,axiom,
! [A] :
( l3_osalg_1(A)
=> ( v4_osalg_1(A)
=> ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A) ) ) ) ).
fof(rc4_osalg_1,axiom,
? [A] :
( l3_osalg_1(A)
& ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v3_osalg_1(A)
& v4_osalg_1(A) ) ).
fof(rc5_osalg_1,axiom,
? [A] :
( l1_osalg_1(A)
& ~ v3_struct_0(A)
& ~ v2_msualg_1(A) ) ).
fof(rc6_osalg_1,axiom,
? [A] :
( l3_osalg_1(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_orders_3(A)
& ~ v2_msualg_1(A)
& v3_osalg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v6_osalg_1(A) ) ).
fof(cc2_osalg_1,axiom,
! [A] :
( l3_osalg_1(A)
=> ( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v6_osalg_1(A) )
=> ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v5_osalg_1(A) ) ) ) ).
fof(fc3_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ( ~ v3_struct_0(k2_osalg_1(A))
& v2_orders_2(k2_osalg_1(A))
& v3_orders_2(k2_osalg_1(A))
& v4_orders_2(k2_osalg_1(A))
& v1_orders_3(k2_osalg_1(A))
& ~ v2_msualg_1(k2_osalg_1(A))
& v3_osalg_1(k2_osalg_1(A))
& v4_osalg_1(k2_osalg_1(A))
& v5_osalg_1(k2_osalg_1(A))
& v6_osalg_1(k2_osalg_1(A)) ) ) ).
fof(rc7_osalg_1,axiom,
? [A] :
( l3_osalg_1(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A) ) ).
fof(rc8_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& l3_osalg_1(A) )
=> ? [B] :
( m1_subset_1(B,u1_msualg_1(A))
& v7_osalg_1(B,A) ) ) ).
fof(cc3_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> v7_osalg_1(B,A) ) ) ).
fof(cc4_osalg_1,axiom,
! [A] :
( l3_osalg_1(A)
=> ( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v6_osalg_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A) ) ) ) ).
fof(rc9_osalg_1,axiom,
? [A] :
( l3_osalg_1(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A) ) ).
fof(cc5_osalg_1,axiom,
! [A] :
( l3_osalg_1(A)
=> ( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v6_osalg_1(A)
& v8_osalg_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A) ) ) ) ).
fof(cc6_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ( v7_osalg_1(B,A)
& v9_osalg_1(B,A) ) ) ) ).
fof(rc10_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_pboole(B,u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v11_osalg_1(B,A) ) ) ).
fof(rc11_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_pboole(B,u1_struct_0(A))
& v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B)
& v11_osalg_1(B,A) ) ) ).
fof(rc12_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A) ) ) ).
fof(fc4_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& ~ v1_xboole_0(B)
& m3_pboole(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),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B))) )
=> ( v4_msualg_1(k6_osalg_1(A,B,C),A)
& v5_msualg_1(k6_osalg_1(A,B,C),A)
& v12_osalg_1(k6_osalg_1(A,B,C),A) ) ) ).
fof(cc7_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_orders_3(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> v12_osalg_1(B,A) ) ) ).
fof(rc13_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& v13_osalg_1(B,A) ) ) ).
fof(fc5_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,B) )
=> ( v4_msualg_1(k8_osalg_1(A,B,C),A)
& v5_msualg_1(k8_osalg_1(A,B,C),A)
& v12_osalg_1(k8_osalg_1(A,B,C),A)
& v13_osalg_1(k8_osalg_1(A,B,C),A) ) ) ).
fof(cc8_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,k9_osalg_1(A))
=> ~ v1_xboole_0(B) ) ) ).
fof(t1_osalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v3_relat_2(D)
& v8_relat_2(D)
& v1_partfun1(D,B,B)
& m2_relset_1(D,B,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,k3_finseq_2(A))
& m2_relset_1(E,B,k3_finseq_2(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,A)
& m2_relset_1(F,B,A) )
=> ( ~ v3_struct_0(g3_osalg_1(A,C,B,D,E,F))
& ~ v2_msualg_1(g3_osalg_1(A,C,B,D,E,F))
& v2_orders_2(g3_osalg_1(A,C,B,D,E,F))
& v3_orders_2(g3_osalg_1(A,C,B,D,E,F))
& v4_orders_2(g3_osalg_1(A,C,B,D,E,F)) ) ) ) ) ) ) ) ).
fof(d1_osalg_1,axiom,
$true ).
fof(d2_osalg_1,axiom,
! [A] :
( l3_osalg_1(A)
=> ( v4_osalg_1(A)
<=> ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A) ) ) ) ).
fof(d3_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( r1_osalg_1(A,B,C)
<=> r2_hidden(k4_tarski(B,C),u1_osalg_1(A)) ) ) ) ) ).
fof(t2_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( ( r1_osalg_1(A,B,C)
& r1_osalg_1(A,C,D) )
=> r1_osalg_1(A,B,D) ) ) ) ) ) ).
fof(d4_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A) )
=> ( v5_osalg_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( ( r1_osalg_1(A,B,C)
& k1_msualg_1(A,B) = k1_msualg_1(A,C)
& k1_osalg_1(A,B) = k1_osalg_1(A,C) )
=> B = C ) ) ) ) ) ).
fof(d5_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A) )
=> ( v6_osalg_1(A)
<=> u1_osalg_1(A) = k6_partfun1(u1_msualg_1(A)) ) ) ).
fof(t3_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A) )
=> ( v6_osalg_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( r1_osalg_1(A,B,C)
=> B = C ) ) ) ) ) ).
fof(t4_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A) )
=> ( v6_osalg_1(A)
=> v5_osalg_1(A) ) ) ).
fof(d6_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v3_osalg_1(B)
& v4_osalg_1(B)
& l3_osalg_1(B) )
=> ( B = k2_osalg_1(A)
<=> ( u1_struct_0(A) = u1_struct_0(B)
& k6_partfun1(u1_struct_0(A)) = u1_orders_2(B)
& u1_msualg_1(A) = u1_msualg_1(B)
& k6_partfun1(u1_msualg_1(A)) = u1_osalg_1(B)
& u2_msualg_1(A) = u2_msualg_1(B)
& u3_msualg_1(A) = u3_msualg_1(B) ) ) ) ) ).
fof(t5_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ( v1_orders_3(k2_osalg_1(A))
& v6_osalg_1(k2_osalg_1(A)) ) ) ).
fof(d7_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( r2_osalg_1(A,B,C)
<=> ( k3_finseq_1(B) = k3_finseq_1(C)
& ! [D] :
( r2_hidden(D,k4_finseq_1(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( E = k1_funct_1(B,D)
& F = k1_funct_1(C,D) )
=> r3_orders_2(A,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t6_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( ( r2_osalg_1(A,B,C)
& r2_osalg_1(A,C,B) )
=> B = C ) ) ) ) ).
fof(t7_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( ( v1_orders_3(A)
& r2_osalg_1(A,B,C) )
=> B = C ) ) ) ) ).
fof(t8_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( ( v1_orders_3(A)
& r1_osalg_1(A,B,C)
& r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C))
& r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C)) )
=> B = C ) ) ) ) ).
fof(d8_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ( v7_osalg_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( ( r1_osalg_1(A,B,C)
& r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C)) )
=> r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C)) ) ) ) ) ) ).
fof(d9_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ( v8_osalg_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> v7_osalg_1(B,A) ) ) ) ).
fof(t9_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ( v6_osalg_1(A)
=> v8_osalg_1(A) ) ) ).
fof(t10_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( ( v8_osalg_1(A)
& k1_msualg_1(A,B) = k1_xboole_0
& r1_osalg_1(A,B,C)
& k1_msualg_1(A,C) = k1_xboole_0 )
=> B = C ) ) ) ) ).
fof(d10_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( r3_osalg_1(A,B,C,D)
<=> ( r1_osalg_1(A,B,C)
& r2_osalg_1(A,D,k1_msualg_1(A,C))
& ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ( ( r1_osalg_1(A,B,E)
& r2_osalg_1(A,D,k1_msualg_1(A,E)) )
=> r2_osalg_1(A,k1_msualg_1(A,C),k1_msualg_1(A,E)) ) ) ) ) ) ) ) ) ).
fof(d11_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( r4_osalg_1(A,B,C,D)
<=> ( r1_osalg_1(A,B,C)
& r2_osalg_1(A,D,k1_msualg_1(A,C))
& ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ( ( r1_osalg_1(A,B,E)
& r2_osalg_1(A,D,k1_msualg_1(A,E)) )
=> r3_orders_2(A,k1_osalg_1(A,C),k1_osalg_1(A,E)) ) ) ) ) ) ) ) ) ).
fof(d12_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( r5_osalg_1(A,B,C,D)
<=> ( r3_osalg_1(A,B,C,D)
& r4_osalg_1(A,B,C,D) ) ) ) ) ) ) ).
fof(d13_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ( v9_osalg_1(B,A)
<=> ( v7_osalg_1(B,A)
& ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ~ ( r2_osalg_1(A,C,k1_msualg_1(A,B))
& ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ~ r3_osalg_1(A,B,D,C) ) ) ) ) ) ) ) ).
fof(d14_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& l3_osalg_1(A) )
=> ( v10_osalg_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> v9_osalg_1(B,A) ) ) ) ).
fof(t11_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& l3_osalg_1(A) )
=> ( v10_osalg_1(A)
<=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ~ ( r2_osalg_1(A,C,k1_msualg_1(A,B))
& ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ~ r5_osalg_1(A,B,D,C) ) ) ) ) ) ) ).
fof(t12_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& l3_osalg_1(A) )
=> ( v6_osalg_1(A)
=> v10_osalg_1(A) ) ) ).
fof(t13_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( ( r2_osalg_1(A,E,k1_msualg_1(A,B))
& r3_osalg_1(A,B,C,E)
& r3_osalg_1(A,B,D,E) )
=> C = D ) ) ) ) ) ) ).
fof(d15_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( r2_osalg_1(A,C,k1_msualg_1(A,B))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( D = k3_osalg_1(A,B,C)
<=> r3_osalg_1(A,B,D,C) ) ) ) ) ) ) ).
fof(t14_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( r2_osalg_1(A,C,k1_msualg_1(A,B))
=> r5_osalg_1(A,B,k3_osalg_1(A,B,C),C) ) ) ) ) ).
fof(d16_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> k4_osalg_1(A,B) = k10_pboole(u1_struct_0(A),B) ) ) ).
fof(t15_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( v2_relat_1(k4_osalg_1(A,B))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_orders_2(A,C,D)
=> r1_tarski(k1_funct_1(k4_osalg_1(A,B),C),k1_funct_1(k4_osalg_1(A,B),D)) ) ) ) ) ) ) ).
fof(d17_osalg_1,axiom,
$true ).
fof(d18_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ( v11_osalg_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_orders_2(A,C,D)
=> r1_tarski(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(t16_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> v11_osalg_1(k4_osalg_1(A,B),A) ) ) ).
fof(d19_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v12_osalg_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r3_orders_2(A,C,D)
=> r1_tarski(k1_funct_1(u4_msualg_1(A,B),C),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ) ) ) ) ).
fof(t17_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v12_osalg_1(B,A)
<=> ( v11_osalg_1(u4_msualg_1(A,B),A)
& m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ) ) ) ).
fof(d20_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m3_pboole(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),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B)))
=> ! [D] :
( ( v4_msualg_1(D,A)
& v5_msualg_1(D,A)
& l3_msualg_1(D,A) )
=> ( D = k6_osalg_1(A,B,C)
<=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,D),k5_osalg_1(A,B))
& r6_pboole(u1_msualg_1(A),u5_msualg_1(A,D),C) ) ) ) ) ) ) ).
fof(t18_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m3_pboole(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),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B)))
=> v12_osalg_1(k6_osalg_1(A,B,C),A) ) ) ) ).
fof(t19_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_orders_3(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> v12_osalg_1(B,A) ) ) ).
fof(t20_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ! [D] :
( ( v12_osalg_1(D,A)
& l3_msualg_1(D,A) )
=> ( r2_osalg_1(A,B,C)
=> r1_tarski(k1_funct_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,D)),B),k1_funct_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,D)),C)) ) ) ) ) ) ).
fof(d21_osalg_1,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,k2_osalg_1(A))
& v12_osalg_1(C,k2_osalg_1(A))
& l3_msualg_1(C,k2_osalg_1(A)) )
=> ( C = k7_osalg_1(A,B)
<=> ( u4_msualg_1(k2_osalg_1(A),C) = u4_msualg_1(A,B)
& u5_msualg_1(k2_osalg_1(A),C) = u5_msualg_1(A,B) ) ) ) ) ) ).
fof(t21_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( ( r2_osalg_1(A,B,C)
& r2_osalg_1(A,C,D) )
=> r2_osalg_1(A,B,D) ) ) ) ) ) ).
fof(d22_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( r6_osalg_1(A,B,C)
<=> ( r1_osalg_1(A,B,C)
& r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C))
& r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C)) ) ) ) ) ) ).
fof(t22_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( ( r6_osalg_1(A,B,C)
& r6_osalg_1(A,C,B) )
=> B = C ) ) ) ) ).
fof(t23_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( ( r6_osalg_1(A,B,C)
& r6_osalg_1(A,C,D) )
=> r6_osalg_1(A,B,D) ) ) ) ) ) ).
fof(t24_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v12_osalg_1(D,A)
& l3_msualg_1(D,A) )
=> ( r3_orders_2(A,k1_osalg_1(A,B),k1_osalg_1(A,C))
=> r1_tarski(k4_msualg_1(A,B,D),k4_msualg_1(A,C,D)) ) ) ) ) ) ).
fof(t25_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v12_osalg_1(D,A)
& l3_msualg_1(D,A) )
=> ( r2_osalg_1(A,k1_msualg_1(A,B),k1_msualg_1(A,C))
=> r1_tarski(k3_msualg_1(A,B,D),k3_msualg_1(A,C,D)) ) ) ) ) ) ).
fof(t26_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( ( v12_osalg_1(D,A)
& l3_msualg_1(D,A) )
=> ( r6_osalg_1(A,B,C)
=> ( r1_tarski(k3_msualg_1(A,B,D),k3_msualg_1(A,C,D))
& r1_tarski(k4_msualg_1(A,B,D),k4_msualg_1(A,C,D)) ) ) ) ) ) ) ).
fof(d23_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v13_osalg_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( r6_osalg_1(A,C,D)
=> k2_partfun1(k3_msualg_1(A,D,B),k4_msualg_1(A,D,B),k5_msualg_1(A,D,B),k3_msualg_1(A,C,B)) = k5_msualg_1(A,C,B) ) ) ) ) ) ) ).
fof(t27_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v13_osalg_1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ( r6_osalg_1(A,C,D)
=> r1_tarski(k5_msualg_1(A,C,B),k5_msualg_1(A,D,B)) ) ) ) ) ) ) ).
fof(t28_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( ( v1_orders_3(A)
| v6_osalg_1(A) )
=> v13_osalg_1(B,A) ) ) ) ).
fof(d24_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v4_msualg_1(D,A)
& v12_osalg_1(D,A)
& l3_msualg_1(D,A) )
=> ( D = k8_osalg_1(A,B,C)
<=> ( r6_pboole(u1_struct_0(A),u4_msualg_1(A,D),k5_osalg_1(A,B))
& ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> k5_msualg_1(A,E,D) = k10_pboole(k3_msualg_1(A,E,D),C) ) ) ) ) ) ) ) ).
fof(t29_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ( v5_msualg_1(k8_osalg_1(A,B,C),A)
& v13_osalg_1(k8_osalg_1(A,B,C),A) ) ) ) ) ).
fof(d25_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> k9_osalg_1(A) = k8_eqrel_1(u1_msualg_1(A),u1_osalg_1(A)) ) ).
fof(d26_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> k10_osalg_1(A,B) = k6_eqrel_1(u1_msualg_1(A),u1_osalg_1(A),B) ) ) ).
fof(t30_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( r1_osalg_1(A,B,C)
<=> r2_hidden(C,k6_eqrel_1(u1_msualg_1(A),u1_osalg_1(A),B)) ) ) ) ) ).
fof(t31_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( r1_osalg_1(A,B,C)
<=> k10_osalg_1(A,B) = k10_osalg_1(A,C) ) ) ) ) ).
fof(t32_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A))
<=> ? [C] :
( m1_subset_1(C,u1_msualg_1(A))
& B = k10_osalg_1(A,C) ) ) ) ).
fof(t33_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ( m1_osalg_1(C,A,B)
<=> k10_osalg_1(A,C) = B ) ) ) ) ).
fof(t34_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( ( r1_osalg_1(A,B,C)
& k3_finseq_1(k1_msualg_1(A,B)) = k3_finseq_1(k1_msualg_1(A,C))
& r2_osalg_1(A,D,k1_msualg_1(A,B))
& r2_osalg_1(A,D,k1_msualg_1(A,C)) )
=> k3_osalg_1(A,B,D) = k3_osalg_1(A,C,D) ) ) ) ) ) ).
fof(d27_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( ? [D] :
( m1_osalg_1(D,A,B)
& r2_osalg_1(A,C,k1_msualg_1(A,D)) )
=> ! [D] :
( m1_osalg_1(D,A,B)
=> ( D = k11_osalg_1(A,B,C)
<=> ! [E] :
( m1_osalg_1(E,A,B)
=> ( r2_osalg_1(A,C,k1_msualg_1(A,E))
=> D = k3_osalg_1(A,E,C) ) ) ) ) ) ) ) ) ).
fof(t35_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> ( r2_osalg_1(A,C,k1_msualg_1(A,B))
=> r6_osalg_1(A,k3_osalg_1(A,B,C),B) ) ) ) ) ).
fof(dt_m1_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_subset_1(B,k9_osalg_1(A)) )
=> ! [C] :
( m1_osalg_1(C,A,B)
=> m1_subset_1(C,u1_msualg_1(A)) ) ) ).
fof(existence_m1_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_subset_1(B,k9_osalg_1(A)) )
=> ? [C] : m1_osalg_1(C,A,B) ) ).
fof(redefinition_m1_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_subset_1(B,k9_osalg_1(A)) )
=> ! [C] :
( m1_osalg_1(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_l1_osalg_1,axiom,
! [A] :
( l1_osalg_1(A)
=> l1_msualg_1(A) ) ).
fof(existence_l1_osalg_1,axiom,
? [A] : l1_osalg_1(A) ).
fof(dt_l2_osalg_1,axiom,
! [A] :
( l2_osalg_1(A)
=> ( l1_msualg_1(A)
& l1_orders_2(A) ) ) ).
fof(existence_l2_osalg_1,axiom,
? [A] : l2_osalg_1(A) ).
fof(dt_l3_osalg_1,axiom,
! [A] :
( l3_osalg_1(A)
=> ( l1_osalg_1(A)
& l2_osalg_1(A) ) ) ).
fof(existence_l3_osalg_1,axiom,
? [A] : l3_osalg_1(A) ).
fof(abstractness_v1_osalg_1,axiom,
! [A] :
( l1_osalg_1(A)
=> ( v1_osalg_1(A)
=> A = g1_osalg_1(u1_struct_0(A),u1_msualg_1(A),u1_osalg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ).
fof(abstractness_v2_osalg_1,axiom,
! [A] :
( l2_osalg_1(A)
=> ( v2_osalg_1(A)
=> A = g2_osalg_1(u1_struct_0(A),u1_orders_2(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ).
fof(abstractness_v3_osalg_1,axiom,
! [A] :
( l3_osalg_1(A)
=> ( v3_osalg_1(A)
=> A = g3_osalg_1(u1_struct_0(A),u1_orders_2(A),u1_msualg_1(A),u1_osalg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ).
fof(symmetry_r1_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> ( r1_osalg_1(A,B,C)
=> r1_osalg_1(A,C,B) ) ) ).
fof(reflexivity_r1_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> r1_osalg_1(A,B,B) ) ).
fof(reflexivity_r2_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,k3_finseq_2(u1_struct_0(A)))
& m1_subset_1(C,k3_finseq_2(u1_struct_0(A))) )
=> r2_osalg_1(A,B,B) ) ).
fof(reflexivity_r6_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& m1_subset_1(C,u1_msualg_1(A)) )
=> r6_osalg_1(A,B,B) ) ).
fof(dt_k1_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> m1_subset_1(k1_osalg_1(A,B),u1_struct_0(A)) ) ).
fof(redefinition_k1_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> k1_osalg_1(A,B) = k2_msualg_1(A,B) ) ).
fof(dt_k2_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ( ~ v3_struct_0(k2_osalg_1(A))
& ~ v2_msualg_1(k2_osalg_1(A))
& v3_osalg_1(k2_osalg_1(A))
& v4_osalg_1(k2_osalg_1(A))
& l3_osalg_1(k2_osalg_1(A)) ) ) ).
fof(dt_k3_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& m1_subset_1(C,k3_finseq_2(u1_struct_0(A))) )
=> m1_subset_1(k3_osalg_1(A,B,C),u1_msualg_1(A)) ) ).
fof(dt_k4_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B) )
=> m1_pboole(k4_osalg_1(A,B),u1_struct_0(A)) ) ).
fof(dt_k5_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B) )
=> ( v11_osalg_1(k5_osalg_1(A,B),A)
& m1_pboole(k5_osalg_1(A,B),u1_struct_0(A)) ) ) ).
fof(redefinition_k5_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B) )
=> k5_osalg_1(A,B) = k4_osalg_1(A,B) ) ).
fof(dt_k6_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& ~ v1_xboole_0(B)
& m3_pboole(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),k5_osalg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osalg_1(A,B))) )
=> ( v4_msualg_1(k6_osalg_1(A,B,C),A)
& v5_msualg_1(k6_osalg_1(A,B,C),A)
& l3_msualg_1(k6_osalg_1(A,B,C),A) ) ) ).
fof(dt_k7_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& l3_msualg_1(B,A) )
=> ( v4_msualg_1(k7_osalg_1(A,B),k2_osalg_1(A))
& v12_osalg_1(k7_osalg_1(A,B),k2_osalg_1(A))
& l3_msualg_1(k7_osalg_1(A,B),k2_osalg_1(A)) ) ) ).
fof(dt_k8_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(C,B) )
=> ( v4_msualg_1(k8_osalg_1(A,B,C),A)
& v12_osalg_1(k8_osalg_1(A,B,C),A)
& l3_msualg_1(k8_osalg_1(A,B,C),A) ) ) ).
fof(dt_k9_osalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ( ~ v1_xboole_0(k9_osalg_1(A))
& m1_subset_1(k9_osalg_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_msualg_1(A)))) ) ) ).
fof(dt_k10_osalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> m2_subset_1(k10_osalg_1(A,B),k1_zfmisc_1(u1_msualg_1(A)),k9_osalg_1(A)) ) ).
fof(dt_k11_osalg_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v8_osalg_1(A)
& v10_osalg_1(A)
& l3_osalg_1(A)
& m1_subset_1(B,k9_osalg_1(A))
& m1_subset_1(C,k3_finseq_2(u1_struct_0(A))) )
=> m1_osalg_1(k11_osalg_1(A,B,C),A,B) ) ).
fof(dt_u1_osalg_1,axiom,
! [A] :
( l1_osalg_1(A)
=> ( v3_relat_2(u1_osalg_1(A))
& v8_relat_2(u1_osalg_1(A))
& v1_partfun1(u1_osalg_1(A),u1_msualg_1(A),u1_msualg_1(A))
& m2_relset_1(u1_osalg_1(A),u1_msualg_1(A),u1_msualg_1(A)) ) ) ).
fof(dt_g1_osalg_1,axiom,
! [A,B,C,D,E] :
( ( v3_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,B,B)
& m1_relset_1(C,B,B)
& v1_funct_1(D)
& v1_funct_2(D,B,k3_finseq_2(A))
& m1_relset_1(D,B,k3_finseq_2(A))
& v1_funct_1(E)
& v1_funct_2(E,B,A)
& m1_relset_1(E,B,A) )
=> ( v1_osalg_1(g1_osalg_1(A,B,C,D,E))
& l1_osalg_1(g1_osalg_1(A,B,C,D,E)) ) ) ).
fof(free_g1_osalg_1,axiom,
! [A,B,C,D,E] :
( ( v3_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,B,B)
& m1_relset_1(C,B,B)
& v1_funct_1(D)
& v1_funct_2(D,B,k3_finseq_2(A))
& m1_relset_1(D,B,k3_finseq_2(A))
& v1_funct_1(E)
& v1_funct_2(E,B,A)
& m1_relset_1(E,B,A) )
=> ! [F,G,H,I,J] :
( g1_osalg_1(A,B,C,D,E) = g1_osalg_1(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(dt_g2_osalg_1,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(B,A,A)
& v1_funct_1(D)
& v1_funct_2(D,C,k3_finseq_2(A))
& m1_relset_1(D,C,k3_finseq_2(A))
& v1_funct_1(E)
& v1_funct_2(E,C,A)
& m1_relset_1(E,C,A) )
=> ( v2_osalg_1(g2_osalg_1(A,B,C,D,E))
& l2_osalg_1(g2_osalg_1(A,B,C,D,E)) ) ) ).
fof(free_g2_osalg_1,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(B,A,A)
& v1_funct_1(D)
& v1_funct_2(D,C,k3_finseq_2(A))
& m1_relset_1(D,C,k3_finseq_2(A))
& v1_funct_1(E)
& v1_funct_2(E,C,A)
& m1_relset_1(E,C,A) )
=> ! [F,G,H,I,J] :
( g2_osalg_1(A,B,C,D,E) = g2_osalg_1(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(dt_g3_osalg_1,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(B,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& v1_partfun1(D,C,C)
& m1_relset_1(D,C,C)
& v1_funct_1(E)
& v1_funct_2(E,C,k3_finseq_2(A))
& m1_relset_1(E,C,k3_finseq_2(A))
& v1_funct_1(F)
& v1_funct_2(F,C,A)
& m1_relset_1(F,C,A) )
=> ( v3_osalg_1(g3_osalg_1(A,B,C,D,E,F))
& l3_osalg_1(g3_osalg_1(A,B,C,D,E,F)) ) ) ).
fof(free_g3_osalg_1,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(B,A,A)
& v3_relat_2(D)
& v8_relat_2(D)
& v1_partfun1(D,C,C)
& m1_relset_1(D,C,C)
& v1_funct_1(E)
& v1_funct_2(E,C,k3_finseq_2(A))
& m1_relset_1(E,C,k3_finseq_2(A))
& v1_funct_1(F)
& v1_funct_2(F,C,A)
& m1_relset_1(F,C,A) )
=> ! [G,H,I,J,K,L] :
( g3_osalg_1(A,B,C,D,E,F) = g3_osalg_1(G,H,I,J,K,L)
=> ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
%------------------------------------------------------------------------------