SET007 Axioms: SET007+738.ax
%------------------------------------------------------------------------------
% File : SET007+738 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Order 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 : osalg_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 103 ( 4 unt; 0 def)
% Number of atoms : 1354 ( 49 equ)
% Maximal formula atoms : 26 ( 13 avg)
% Number of connectives : 1433 ( 182 ~; 0 |; 915 &)
% ( 28 <=>; 308 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 56 ( 54 usr; 1 prp; 0-4 aty)
% Number of functors : 66 ( 66 usr; 5 con; 0-6 aty)
% Number of variables : 388 ( 373 !; 15 ?)
% 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_osalg_4,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)
& v1_msualg_4(B) ) ) ).
fof(rc2_osalg_4,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_pboole(B,u1_struct_0(A))
& m1_pboole(C,u1_struct_0(A)) )
=> ? [D] :
( m1_msualg_4(D,u1_struct_0(A),B,C)
& v1_relat_1(D)
& v1_funct_1(D)
& v1_msualg_4(D)
& v1_osalg_4(D,A,B,C) ) ) ).
fof(cc1_osalg_4,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_pboole(B,u1_struct_0(A))
& m1_pboole(C,u1_struct_0(A)) )
=> ! [D] :
( m1_msualg_4(D,u1_struct_0(A),B,C)
=> ( v1_osalg_4(D,A,B,C)
=> ( v11_osalg_1(D,A)
& v1_msualg_4(D) ) ) ) ) ).
fof(rc3_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_osalg_4(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_msualg_4(C)
& v3_msualg_4(C,A,B) ) ) ).
fof(rc4_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_osalg_4(C,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(cc2_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k2_osalg_4(A))
=> ~ v1_xboole_0(B) ) ) ).
fof(rc5_osalg_4,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_osalg_4(A) ) ).
fof(rc6_osalg_4,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)
& v2_osalg_4(A) ) ).
fof(cc3_osalg_4,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_orders_3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_osalg_4(A) ) ) ) ).
fof(cc4_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_osalg_4(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k2_osalg_4(A))
=> ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A) ) ) ) ).
fof(fc1_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B)
& m1_subset_1(D,u1_struct_0(A)) )
=> ~ v1_xboole_0(k6_osalg_4(A,B,C,D)) ) ).
fof(fc2_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( v1_relat_1(k7_osalg_4(A,B,C))
& v2_relat_1(k7_osalg_4(A,B,C))
& ~ v3_relat_1(k7_osalg_4(A,B,C))
& v1_funct_1(k7_osalg_4(A,B,C))
& v11_osalg_1(k7_osalg_4(A,B,C),A) ) ) ).
fof(fc3_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( v4_msualg_1(k16_osalg_4(A,B,C),A)
& v5_msualg_1(k16_osalg_4(A,B,C),A)
& v12_osalg_1(k16_osalg_4(A,B,C),A) ) ) ).
fof(rc7_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_osalg_4(C,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)
& v3_osalg_4(C,A,B) ) ) ).
fof(rc8_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_osalg_4(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_msualg_4(C)
& v3_msualg_4(C,A,B)
& v3_osalg_4(C,A,B) ) ) ).
fof(cc5_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_osalg_4(C,A,B)
=> ( ( v3_msualg_4(C,A,B)
& v3_osalg_4(C,A,B) )
=> ( v1_msualg_4(C)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B) ) ) ) ) ).
fof(cc6_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& v13_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_osalg_4(C,A,B)
=> ( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B) )
=> ( v1_msualg_4(C)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& v3_osalg_4(C,A,B) ) ) ) ) ).
fof(fc4_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& v3_osalg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( v4_msualg_1(k16_osalg_4(A,B,C),A)
& v5_msualg_1(k16_osalg_4(A,B,C),A)
& v12_osalg_1(k16_osalg_4(A,B,C),A)
& v13_osalg_1(k16_osalg_4(A,B,C),A) ) ) ).
fof(d1_osalg_4,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))
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> ! [D] :
( m1_msualg_4(D,u1_struct_0(A),B,C)
=> ( v1_osalg_4(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r3_orders_2(A,E,F)
=> ! [G,H] :
( ( r2_hidden(G,k1_funct_1(B,E))
& r2_hidden(H,k1_funct_1(C,E)) )
=> ( r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),B,C,D,E))
<=> r2_hidden(k4_tarski(G,H),k1_msualg_4(u1_struct_0(A),B,C,D,F)) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_osalg_4,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))
=> ! [C] :
( m1_pboole(C,u1_struct_0(A))
=> ! [D] :
( m1_msualg_4(D,u1_struct_0(A),B,C)
=> ( v1_osalg_4(D,A,B,C)
=> ( v11_osalg_1(D,A)
& m1_pboole(D,u1_struct_0(A)) ) ) ) ) ) ) ).
fof(d2_osalg_4,axiom,
$true ).
fof(d3_osalg_4,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) )
=> ! [C] :
( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B))
=> ( m1_osalg_4(C,A,B)
<=> v1_osalg_4(C,A,u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) ) ).
fof(d4_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v3_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( B = k1_osalg_4(A)
<=> ! [C,D] :
( r2_hidden(k4_tarski(C,D),B)
<=> ( r2_hidden(C,u1_struct_0(A))
& r2_hidden(D,u1_struct_0(A))
& ? [E] :
( m2_finseq_1(E,u1_struct_0(A))
& ~ r1_xreal_0(k3_finseq_1(E),np__1)
& k1_funct_1(E,np__1) = C
& k1_funct_1(E,k3_finseq_1(E)) = D
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__2,F)
& r1_xreal_0(F,k3_finseq_1(E))
& ~ r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k6_xcmplx_0(F,np__1))),u1_orders_2(A))
& ~ r2_hidden(k4_tarski(k1_funct_1(E,k6_xcmplx_0(F,np__1)),k1_funct_1(E,F)),u1_orders_2(A)) ) ) ) ) ) ) ) ) ).
fof(t2_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> r2_hidden(k4_tarski(B,C),k1_osalg_4(A)) ) ) ) ) ).
fof(d5_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_osalg_4(A,B,C)
<=> r2_hidden(k4_tarski(B,C),k1_osalg_4(A)) ) ) ) ) ).
fof(t3_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_osalg_4(A,B,C)
& r1_osalg_4(A,C,D) )
=> r1_osalg_4(A,B,D) ) ) ) ) ) ).
fof(d6_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> k2_osalg_4(A) = k8_eqrel_1(u1_struct_0(A),k1_osalg_4(A)) ) ).
fof(d7_osalg_4,axiom,
$true ).
fof(d8_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_osalg_4(A,B) = k6_eqrel_1(u1_struct_0(A),k1_osalg_4(A),B) ) ) ).
fof(t4_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_hidden(B,k3_osalg_4(A,B)) ) ) ).
fof(t5_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> k3_osalg_4(A,B) = k3_osalg_4(A,C) ) ) ) ) ).
fof(t6_osalg_4,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))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( r2_hidden(D,k1_funct_1(B,C))
=> r2_hidden(D,k4_osalg_4(A,B,k3_osalg_4(A,C))) ) ) ) ) ).
fof(d10_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v2_osalg_4(A)
<=> ! [B] :
( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
=> v1_waybel_0(B,A) ) ) ) ).
fof(t7_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_orders_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(B,C),k1_osalg_4(A))
=> B = C ) ) ) ) ).
fof(t8_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_orders_3(A)
& l1_orders_2(A) )
=> ! [B] :
( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& B = k1_struct_0(A,C) ) ) ) ).
fof(t9_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_orders_3(A)
& l1_orders_2(A) )
=> v2_osalg_4(A) ) ).
fof(t10_osalg_4,axiom,
( v1_partfun1(k1_xboole_0,k1_xboole_0,k1_xboole_0)
& v3_relat_2(k1_xboole_0)
& v8_relat_2(k1_xboole_0)
& m2_relset_1(k1_xboole_0,k1_xboole_0,k1_xboole_0) ) ).
fof(d11_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
=> ! [E] :
( ( v1_partfun1(E,k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D))
& v3_relat_2(E)
& v8_relat_2(E)
& m2_relset_1(E,k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) )
=> ( E = k5_osalg_4(A,B,C,D)
<=> ! [F,G] :
( r2_hidden(k4_tarski(F,G),E)
<=> ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& r2_hidden(H,D)
& r2_hidden(k4_tarski(F,G),k2_msualg_4(A,B,C,H)) ) ) ) ) ) ) ) ) ).
fof(d12_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k8_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)))))
=> ( E = k6_osalg_4(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,E)
<=> ? [G] :
( r2_hidden(G,k1_funct_1(u4_msualg_1(A,B),D))
& F = k6_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)),G) ) ) ) ) ) ) ) ) ).
fof(t11_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r3_orders_2(A,D,E)
=> r1_tarski(k6_osalg_4(A,B,C,D),k6_osalg_4(A,B,C,E)) ) ) ) ) ) ) ).
fof(d13_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ! [D] :
( ( v11_osalg_1(D,A)
& m1_pboole(D,u1_struct_0(A)) )
=> ( D = k7_osalg_4(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_funct_1(D,E) = k6_osalg_4(A,B,C,E) ) ) ) ) ) ) ).
fof(d14_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,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))
=> k8_osalg_4(A,B,C,D,E) = k6_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)),E) ) ) ) ) ) ).
fof(t12_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_osalg_4(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r3_orders_2(A,D,B)
& r3_orders_2(A,D,C) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r3_orders_2(A,B,D)
& r3_orders_2(A,C,D) ) ) ) ) ) ) ).
fof(t13_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,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))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ( k8_osalg_4(A,B,C,D,E) = k8_osalg_4(A,B,C,D,F)
<=> r2_hidden(k4_tarski(E,F),k2_msualg_4(A,B,C,D)) ) ) ) ) ) ) ) ).
fof(t14_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> ( r3_orders_2(A,D,E)
=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
=> ( G = F
=> k8_osalg_4(A,B,C,D,F) = k8_osalg_4(A,B,C,E,G) ) ) ) ) ) ) ) ) ) ).
fof(d15_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,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),k7_osalg_4(A,C,D))))
=> ( F = k9_osalg_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)))
& ! [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G)))
=> ~ ( H = k1_funct_1(E,G)
& k1_funct_1(F,G) = k8_osalg_4(A,C,D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G),H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d16_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,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),k7_osalg_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),k7_osalg_4(A,C,D)),B)) )
=> ( E = k10_osalg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,C),k1_osalg_1(A,B)))
=> k1_funct_1(E,F) = k8_osalg_4(A,C,D,k1_osalg_1(A,B),F) ) ) ) ) ) ) ) ).
fof(d17_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,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),k7_osalg_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),k7_osalg_4(A,C,D))),B)) )
=> ( E = k11_osalg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,B,C))
=> k1_funct_1(E,F) = k9_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(d18_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,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),k7_osalg_4(A,B,C)))
=> ( D = k12_osalg_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),k7_osalg_4(A,B,C)),D,E) = k10_osalg_4(A,E,B,C) ) ) ) ) ) ) ).
fof(d19_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,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),k7_osalg_4(A,B,C))))
=> ( D = k13_osalg_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),k7_osalg_4(A,B,C))),D,E) = k11_osalg_4(A,E,B,C) ) ) ) ) ) ) ).
fof(t15_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,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),k7_osalg_4(A,C,D))),B))
& ! [F] :
( m1_subset_1(F,k3_msualg_1(A,B,C))
=> E != k9_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ).
fof(d20_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(A))
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A) )
=> ! [D] :
( ( v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) )
=> ( E = k14_osalg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,B,C))
=> ( r2_hidden(k9_osalg_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),k7_osalg_4(A,C,D))),B))
=> k1_funct_1(E,k9_osalg_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),k7_osalg_4(A,C,D)),B),k5_msualg_1(A,B,C),k10_osalg_4(A,B,C,D)),F) ) ) ) ) ) ) ) ) ).
fof(d21_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,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),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C)))
=> ( D = k15_osalg_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),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C)),D,E) = k14_osalg_4(A,E,B,C) ) ) ) ) ) ) ).
fof(d22_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> k16_osalg_4(A,B,C) = g3_msualg_1(A,k7_osalg_4(A,B,C),k15_osalg_4(A,B,C)) ) ) ) ).
fof(d23_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,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),k6_osalg_4(A,B,C,D))
& m2_relset_1(E,k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) )
=> ( E = k17_osalg_4(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D))
=> k8_funct_2(k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D),E,F) = k8_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(d24_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ! [D] :
( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C)))
=> ( D = k18_osalg_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,k16_osalg_4(A,B,C)),D,E) = k17_osalg_4(A,B,C,E) ) ) ) ) ) ) ).
fof(t16_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( r2_msualg_3(A,B,k16_osalg_4(A,B,C),k18_osalg_4(A,B,C))
& v1_osalg_3(k18_osalg_4(A,B,C),A) ) ) ) ) ).
fof(t17_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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)
& v1_osalg_3(D,A) )
=> ( 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_osalg_4(k18_msualg_4(A,B,C,D),A,B) ) ) ) ) ) ) ).
fof(d25_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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)
& v1_osalg_3(D,A) )
=> k19_osalg_4(A,B,C,D) = k18_msualg_4(A,B,C,D) ) ) ) ) ) ).
fof(d26_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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)
& v1_osalg_3(D,A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_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,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) )
=> ( F = k20_osalg_4(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E))
=> k1_funct_1(F,k8_osalg_4(A,B,k19_osalg_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(d27_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C))
=> ( E = k21_osalg_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,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C),E,F) = k20_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t18_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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)
& v1_osalg_3(D,A) )
=> ( r3_msualg_3(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D)),C,k21_osalg_4(A,B,C,D))
& v1_osalg_3(k21_osalg_4(A,B,C,D),A) ) ) ) ) ) ) ).
fof(t19_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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)
& v1_osalg_3(D,A) )
=> r4_msualg_3(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D)),C,k21_osalg_4(A,B,C,D)) ) ) ) ) ) ).
fof(t20_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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)
& v1_osalg_3(D,A) )
=> r6_msualg_3(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D)),C) ) ) ) ) ) ).
fof(d28_osalg_4,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) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( v3_osalg_4(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_msualg_1(A))
=> ! [E] :
( m1_subset_1(E,u1_msualg_1(A))
=> ( r6_osalg_1(A,D,E)
=> ! [F] :
( m1_subset_1(F,k3_msualg_1(A,D,B))
=> ! [G] :
( m1_subset_1(G,k3_msualg_1(A,E,B))
=> ( ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( r2_hidden(H,k1_relat_1(F))
=> r2_hidden(k4_tarski(k1_funct_1(F,H),k1_funct_1(G,H)),k2_msualg_4(A,B,C,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,E),H))) ) )
=> 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),F),k8_funct_2(k3_msualg_1(A,E,B),k4_msualg_1(A,E,B),k5_msualg_1(A,E,B),G)),k2_msualg_4(A,B,C,k1_osalg_1(A,E))) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_osalg_4,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) )
=> ( v3_msualg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B)
& v4_msualg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B)
& m1_osalg_4(k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)),A,B) ) ) ) ).
fof(t22_osalg_4,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) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( r6_pboole(u1_struct_0(A),C,k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)))
=> v3_osalg_4(C,A,B) ) ) ) ) ).
fof(t23_osalg_4,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) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v3_osalg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> v4_msualg_4(C,A,B) ) ) ) ).
fof(t24_osalg_4,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)
& v13_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> v3_osalg_4(C,A,B) ) ) ) ).
fof(t25_osalg_4,axiom,
$true ).
fof(t26_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& v13_osalg_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)
& v1_osalg_3(D,A) )
=> v3_osalg_4(k19_osalg_4(A,B,C,D),A,B) ) ) ) ) ) ).
fof(d29_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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] :
( ( v3_msualg_4(E,A,B)
& v4_msualg_4(E,A,B)
& m1_osalg_4(E,A,B) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r1_msualg_3(A,B,C,D)
& v1_osalg_3(D,A)
& r2_pboole(u1_struct_0(A),E,k19_osalg_4(A,B,C,D)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F))
& m2_relset_1(G,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) )
=> ( G = k22_osalg_4(A,B,C,D,E,F)
<=> ! [H] :
( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),F))
=> k1_funct_1(G,k8_osalg_4(A,B,E,F,H)) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),F),k1_funct_1(u4_msualg_1(A,C),F),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,F),H) ) ) ) ) ) ) ) ) ) ) ).
fof(d30_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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] :
( ( v3_msualg_4(E,A,B)
& v4_msualg_4(E,A,B)
& m1_osalg_4(E,A,B) )
=> ! [F] :
( m3_pboole(F,u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C))
=> ( F = k23_osalg_4(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C),F,G) = k22_osalg_4(A,B,C,D,E,G) ) ) ) ) ) ) ) ) ).
fof(t27_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_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] :
( ( v3_msualg_4(E,A,B)
& v4_msualg_4(E,A,B)
& m1_osalg_4(E,A,B) )
=> ( ( r1_msualg_3(A,B,C,D)
& v1_osalg_3(D,A)
& r2_pboole(u1_struct_0(A),E,k19_osalg_4(A,B,C,D)) )
=> ( r1_msualg_3(A,k16_osalg_4(A,B,E),C,k23_osalg_4(A,B,C,D,E))
& v1_osalg_3(k23_osalg_4(A,B,C,D,E),A) ) ) ) ) ) ) ) ).
fof(dt_m1_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_osalg_4(C,A,B)
=> m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ).
fof(existence_m1_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] : m1_osalg_4(C,A,B) ) ).
fof(symmetry_r1_osalg_4,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,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_osalg_4(A,B,C)
=> r1_osalg_4(A,C,B) ) ) ).
fof(reflexivity_r1_osalg_4,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,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r1_osalg_4(A,B,B) ) ).
fof(dt_k1_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_partfun1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A))
& v3_relat_2(k1_osalg_4(A))
& v8_relat_2(k1_osalg_4(A))
& m2_relset_1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k2_osalg_4,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_osalg_4(A))
& m1_subset_1(k2_osalg_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
fof(dt_k3_osalg_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m2_subset_1(k3_osalg_4(A,B),k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) ) ).
fof(dt_k4_osalg_4,axiom,
$true ).
fof(dt_k5_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B)
& m1_subset_1(D,k2_osalg_4(A)) )
=> ( v1_partfun1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D))
& v3_relat_2(k5_osalg_4(A,B,C,D))
& v8_relat_2(k5_osalg_4(A,B,C,D))
& m2_relset_1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) ) ) ).
fof(dt_k6_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B)
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k6_osalg_4(A,B,C,D),k1_zfmisc_1(k8_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D))))) ) ).
fof(dt_k7_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( v11_osalg_1(k7_osalg_4(A,B,C),A)
& m1_pboole(k7_osalg_4(A,B,C),u1_struct_0(A)) ) ) ).
fof(dt_k8_osalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& m1_osalg_4(C,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(k8_osalg_4(A,B,C,D,E),k6_osalg_4(A,B,C,D)) ) ).
fof(dt_k9_osalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,A,C)
& m1_subset_1(E,k3_msualg_1(A,B,C)) )
=> m1_subset_1(k9_osalg_4(A,B,C,D,E),k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k7_osalg_4(A,C,D)))) ) ).
fof(dt_k10_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,A,C) )
=> ( v1_funct_1(k10_osalg_4(A,B,C,D))
& v1_funct_2(k10_osalg_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),k7_osalg_4(A,C,D)),B))
& m2_relset_1(k10_osalg_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),k7_osalg_4(A,C,D)),B)) ) ) ).
fof(dt_k11_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,A,C) )
=> ( v1_funct_1(k11_osalg_4(A,B,C,D))
& v1_funct_2(k11_osalg_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),k7_osalg_4(A,C,D))),B))
& m2_relset_1(k11_osalg_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),k7_osalg_4(A,C,D))),B)) ) ) ).
fof(dt_k12_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> m3_pboole(k12_osalg_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),k7_osalg_4(A,B,C))) ) ).
fof(dt_k13_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> m3_pboole(k13_osalg_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),k7_osalg_4(A,B,C)))) ) ).
fof(dt_k14_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& m1_subset_1(B,u1_msualg_1(A))
& v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& l3_msualg_1(C,A)
& v3_msualg_4(D,A,C)
& v4_msualg_4(D,A,C)
& m1_osalg_4(D,A,C) )
=> ( v1_funct_1(k14_osalg_4(A,B,C,D))
& v1_funct_2(k14_osalg_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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B))
& m2_relset_1(k14_osalg_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),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) ) ) ).
fof(dt_k15_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> m3_pboole(k15_osalg_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),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C))) ) ).
fof(dt_k16_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> ( v12_osalg_1(k16_osalg_4(A,B,C),A)
& l3_msualg_1(k16_osalg_4(A,B,C),A) ) ) ).
fof(dt_k17_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B)
& m1_subset_1(D,u1_struct_0(A)) )
=> ( v1_funct_1(k17_osalg_4(A,B,C,D))
& v1_funct_2(k17_osalg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D))
& m2_relset_1(k17_osalg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k6_osalg_4(A,B,C,D)) ) ) ).
fof(dt_k18_osalg_4,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_4(C,A,B)
& v4_msualg_4(C,A,B)
& m1_osalg_4(C,A,B) )
=> m3_pboole(k18_osalg_4(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,k16_osalg_4(A,B,C))) ) ).
fof(dt_k19_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v5_msualg_1(C,A)
& v12_osalg_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(k19_osalg_4(A,B,C,D),A,B)
& v4_msualg_4(k19_osalg_4(A,B,C,D),A,B)
& m1_osalg_4(k19_osalg_4(A,B,C,D),A,B) ) ) ).
fof(dt_k20_osalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v5_msualg_1(C,A)
& v12_osalg_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(k20_osalg_4(A,B,C,D,E))
& v1_funct_2(k20_osalg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E))
& m2_relset_1(k20_osalg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) ) ) ).
fof(dt_k21_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v5_msualg_1(C,A)
& v12_osalg_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(k21_osalg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C)) ) ).
fof(dt_k22_osalg_4,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v5_msualg_1(C,A)
& v12_osalg_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(E,A,B)
& v4_msualg_4(E,A,B)
& m1_osalg_4(E,A,B)
& m1_subset_1(F,u1_struct_0(A)) )
=> ( v1_funct_1(k22_osalg_4(A,B,C,D,E,F))
& v1_funct_2(k22_osalg_4(A,B,C,D,E,F),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F))
& m2_relset_1(k22_osalg_4(A,B,C,D,E,F),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,E)),F),k1_funct_1(u4_msualg_1(A,C),F)) ) ) ).
fof(dt_k23_osalg_4,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_osalg_4(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v5_msualg_1(C,A)
& v12_osalg_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(E,A,B)
& v4_msualg_4(E,A,B)
& m1_osalg_4(E,A,B) )
=> m3_pboole(k23_osalg_4(A,B,C,D,E),u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,E)),u4_msualg_1(A,C)) ) ).
fof(d9_osalg_4,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))
=> ! [C] :
( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A))
=> k4_osalg_4(A,B,C) = k3_tarski(a_3_0_osalg_4(A,B,C)) ) ) ) ).
fof(fraenkel_a_3_0_osalg_4,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& m1_pboole(C,u1_struct_0(B))
& m2_subset_1(D,k1_zfmisc_1(u1_struct_0(B)),k2_osalg_4(B)) )
=> ( r2_hidden(A,a_3_0_osalg_4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k1_funct_1(C,E)
& r2_hidden(E,D) ) ) ) ).
%------------------------------------------------------------------------------