SET007 Axioms: SET007+504.ax
%------------------------------------------------------------------------------
% File : SET007+504 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Algebra of Morphisms
% 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 : catalg_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 102 ( 14 unt; 0 def)
% Number of atoms : 610 ( 94 equ)
% Maximal formula atoms : 28 ( 5 avg)
% Number of connectives : 567 ( 59 ~; 5 |; 264 &)
% ( 18 <=>; 221 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 41 ( 39 usr; 1 prp; 0-4 aty)
% Number of functors : 74 ( 74 usr; 9 con; 0-6 aty)
% Number of variables : 311 ( 288 !; 23 ?)
% 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(cc1_catalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v5_msualg_1(B,A)
=> ~ v1_catalg_1(B,A) ) ) ) ).
fof(fc1_catalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& v2_relat_1(B)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v4_msualg_1(k11_msafree(A,B),A)
& v5_msualg_1(k11_msafree(A,B),A)
& v1_msafree1(k11_msafree(A,B),A)
& ~ v1_catalg_1(k11_msafree(A,B),A) ) ) ).
fof(rc1_catalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v1_msafree1(B,A)
& ~ v1_catalg_1(B,A) ) ) ).
fof(fc2_catalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v1_catalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v1_relat_1(u4_msualg_1(A,B))
& ~ v3_relat_1(u4_msualg_1(A,B))
& v1_funct_1(u4_msualg_1(A,B)) ) ) ).
fof(rc2_catalg_1,axiom,
? [A] :
( v1_relat_1(A)
& ~ v3_relat_1(A)
& v1_funct_1(A) ) ).
fof(fc3_catalg_1,axiom,
! [A] :
( v1_msualg_1(k2_catalg_1(A))
& v1_instalg1(k2_catalg_1(A)) ) ).
fof(fc4_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k2_catalg_1(A))
& v1_msualg_1(k2_catalg_1(A))
& ~ v2_msualg_1(k2_catalg_1(A))
& v1_instalg1(k2_catalg_1(A)) ) ) ).
fof(cc2_catalg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& v2_catalg_1(A) )
=> ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v1_instalg1(A) ) ) ) ).
fof(rc3_catalg_1,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_instalg1(A)
& v2_catalg_1(A) ) ).
fof(cc3_catalg_1,axiom,
! [A,B] :
( m1_catalg_1(B,A)
=> v2_catalg_1(B) ) ).
fof(cc4_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_catalg_1(B,A)
=> ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v1_instalg1(B)
& v2_catalg_1(B) ) ) ) ).
fof(rc4_catalg_1,axiom,
! [A] :
? [B] :
( m1_catalg_1(B,A)
& v1_msualg_1(B)
& v1_instalg1(B)
& v2_catalg_1(B) ) ).
fof(fc5_catalg_1,axiom,
! [A] :
( v1_msualg_1(k2_catalg_1(A))
& v1_instalg1(k2_catalg_1(A))
& v3_catalg_1(k2_catalg_1(A)) ) ).
fof(rc5_catalg_1,axiom,
? [A] :
( l1_msualg_1(A)
& ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v1_instalg1(A)
& v2_catalg_1(A)
& v3_catalg_1(A) ) ).
fof(rc6_catalg_1,axiom,
! [A] :
? [B] :
( m1_catalg_1(B,A)
& v1_msualg_1(B)
& v1_instalg1(B)
& v2_catalg_1(B)
& v3_catalg_1(B) ) ).
fof(fc6_catalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& v2_catalg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_relat_1(k2_mcart_1(B))
& v1_funct_1(k2_mcart_1(B)) ) ) ).
fof(fc7_catalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_catalg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_relat_1(k2_mcart_1(B))
& v1_funct_1(k2_mcart_1(B)) ) ) ).
fof(fc8_catalg_1,axiom,
! [A,B] :
( ( ~ v2_msualg_1(A)
& v3_catalg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> ( v1_relat_1(k2_mcart_1(B))
& v1_funct_1(k2_mcart_1(B)) ) ) ).
fof(fc9_catalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& v2_catalg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_relat_1(k2_mcart_1(B))
& v1_funct_1(k2_mcart_1(B))
& v1_finset_1(k2_mcart_1(B))
& v1_finseq_1(k2_mcart_1(B)) ) ) ).
fof(fc10_catalg_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_catalg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_relat_1(k2_mcart_1(B))
& v1_funct_1(k2_mcart_1(B))
& v1_finset_1(k2_mcart_1(B))
& v1_finseq_1(k2_mcart_1(B)) ) ) ).
fof(fc11_catalg_1,axiom,
! [A,B] :
( ( ~ v2_msualg_1(A)
& v3_catalg_1(A)
& l1_msualg_1(A)
& m1_subset_1(B,u1_msualg_1(A)) )
=> ( v1_relat_1(k2_mcart_1(B))
& v1_funct_1(k2_mcart_1(B))
& v1_finset_1(k2_mcart_1(B))
& v1_finseq_1(k2_mcart_1(B)) ) ) ).
fof(fc12_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v4_msualg_1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A)))
& v1_msualg_6(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A)))
& v1_msafree1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A))) ) ) ).
fof(d1_catalg_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_funcop_1(D)
& m1_pboole(D,A) )
=> ( D = k1_catalg_1(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k1_funct_1(D,E) = k7_relat_1(C,k1_funct_1(B,E)) ) ) ) ) ) ).
fof(t1_catalg_1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> r6_pboole(A,k1_catalg_1(A,B,k6_relat_1(k3_card_3(B))),k2_msualg_3(A,B)) ) ).
fof(t2_catalg_1,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_pboole(A,k2_extens_1(A,k1_catalg_1(A,B,D)),C)
=> k1_catalg_1(A,B,k5_relat_1(D,E)) = k13_pboole(k1_catalg_1(A,B,D),k1_catalg_1(A,C,E)) ) ) ) ) ) ).
fof(t3_catalg_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( m1_pboole(C,B)
=> ! [D] :
( m1_pboole(D,B)
=> ( ! [E] :
( r2_hidden(E,B)
=> ( r1_tarski(k1_funct_1(C,E),k1_relat_1(A))
& r1_tarski(k9_relat_1(A,k1_funct_1(C,E)),k1_funct_1(D,E)) ) )
=> m3_pboole(k1_catalg_1(B,C,A),B,C,D) ) ) ) ) ).
fof(t4_catalg_1,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( r2_hidden(C,k4_finseq_2(B,A))
<=> ( k3_finseq_1(C) = B
& r1_tarski(k2_relat_1(C),A) ) ) ) ) ).
fof(t5_catalg_1,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,A)
=> ( r2_hidden(C,k4_finseq_2(B,A))
<=> k3_finseq_1(C) = B ) ) ) ).
fof(t6_catalg_1,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)) ) ).
fof(t7_catalg_1,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( B != np__0
& A = k1_xboole_0 )
<=> k4_finseq_2(B,A) = k1_xboole_0 ) ) ).
fof(t8_catalg_1,axiom,
! [A,B] :
( r2_hidden(B,k4_finseq_2(np__1,A))
<=> ? [C] :
( r2_hidden(C,A)
& B = k9_finseq_1(C) ) ) ).
fof(t9_catalg_1,axiom,
! [A,B] :
( r2_hidden(k9_finseq_1(B),k4_finseq_2(np__1,A))
=> r2_hidden(B,A) ) ).
fof(t10_catalg_1,axiom,
! [A,B] :
( r2_hidden(B,k4_finseq_2(np__2,A))
<=> ? [C,D] :
( r2_hidden(C,A)
& r2_hidden(D,A)
& B = k10_finseq_1(C,D) ) ) ).
fof(t11_catalg_1,axiom,
! [A,B,C] :
( r2_hidden(k10_finseq_1(B,C),k4_finseq_2(np__2,A))
=> ( r2_hidden(B,A)
& r2_hidden(C,A) ) ) ).
fof(t12_catalg_1,axiom,
! [A,B] :
( r2_hidden(B,k4_finseq_2(np__3,A))
<=> ? [C,D,E] :
( r2_hidden(C,A)
& r2_hidden(D,A)
& r2_hidden(E,A)
& B = k11_finseq_1(C,D,E) ) ) ).
fof(t13_catalg_1,axiom,
! [A,B,C,D] :
( r2_hidden(k11_finseq_1(B,C,D),k4_finseq_2(np__3,A))
=> ( r2_hidden(B,A)
& r2_hidden(C,A)
& r2_hidden(D,A) ) ) ).
fof(d2_catalg_1,axiom,
$true ).
fof(d3_catalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ( v1_catalg_1(B,A)
<=> v3_relat_1(u4_msualg_1(A,B)) ) ) ) ).
fof(d4_catalg_1,axiom,
$true ).
fof(d5_catalg_1,axiom,
! [A,B] :
( ( v1_msualg_1(B)
& l1_msualg_1(B) )
=> ( B = k2_catalg_1(A)
<=> ( u1_struct_0(B) = k2_zfmisc_1(k1_tarski(np__0),k4_finseq_2(np__2,A))
& u1_msualg_1(B) = k2_xboole_0(k2_zfmisc_1(k1_tarski(np__1),k4_finseq_2(np__1,A)),k2_zfmisc_1(k1_tarski(np__2),k4_finseq_2(np__3,A)))
& ! [C] :
( r2_hidden(C,A)
=> ( k1_funct_1(u2_msualg_1(B),k4_tarski(np__1,k9_finseq_1(C))) = k1_xboole_0
& k1_funct_1(u3_msualg_1(B),k4_tarski(np__1,k9_finseq_1(C))) = k4_tarski(np__0,k10_finseq_1(C,C)) ) )
& ! [C,D,E] :
( ( r2_hidden(C,A)
& r2_hidden(D,A)
& r2_hidden(E,A) )
=> ( k1_funct_1(u2_msualg_1(B),k4_tarski(np__2,k11_finseq_1(C,D,E))) = k10_finseq_1(k4_tarski(np__0,k10_finseq_1(D,E)),k4_tarski(np__0,k10_finseq_1(C,D)))
& k1_funct_1(u3_msualg_1(B),k4_tarski(np__2,k11_finseq_1(C,D,E))) = k4_tarski(np__0,k10_finseq_1(C,E)) ) ) ) ) ) ).
fof(d6_catalg_1,axiom,
! [A] :
( ( v1_instalg1(A)
& l1_msualg_1(A) )
=> ( v2_catalg_1(A)
<=> ? [B] :
( m1_instalg1(k2_catalg_1(B),A)
& u1_struct_0(A) = k2_zfmisc_1(k1_tarski(np__0),k4_finseq_2(np__2,B)) ) ) ) ).
fof(d7_catalg_1,axiom,
! [A,B] :
( ( v1_instalg1(B)
& l1_msualg_1(B) )
=> ( m1_catalg_1(B,A)
<=> ( m1_instalg1(k2_catalg_1(A),B)
& u1_struct_0(B) = k2_zfmisc_1(k1_tarski(np__0),k4_finseq_2(np__2,A)) ) ) ) ).
fof(t14_catalg_1,axiom,
! [A,B,C] :
( m1_catalg_1(C,A)
=> ( m1_catalg_1(C,B)
=> A = B ) ) ).
fof(d8_catalg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( B = k4_catalg_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D,E] :
( v1_relat_1(E)
& v1_funct_1(E)
& r2_hidden(k4_tarski(D,E),k2_xboole_0(u1_struct_0(A),u1_msualg_1(A)))
& r2_hidden(C,k2_relat_1(E)) ) ) ) ) ).
fof(t15_catalg_1,axiom,
! [A] : k4_catalg_1(k3_catalg_1(A)) = A ).
fof(d9_catalg_1,axiom,
! [A] :
( l1_msualg_1(A)
=> ( v3_catalg_1(A)
<=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k5_numbers)
& m2_relset_1(B,k5_numbers,k5_numbers)
& ! [C] :
~ ( r2_hidden(C,u1_struct_0(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ~ ( C = k4_tarski(D,E)
& k3_finseq_1(E) = k8_funct_2(k5_numbers,k5_numbers,B,D)
& r1_tarski(k2_zfmisc_1(k1_tarski(D),k4_finseq_2(k8_funct_2(k5_numbers,k5_numbers,B,D),k4_catalg_1(A))),u1_struct_0(A)) ) ) ) )
& ! [C] :
~ ( r2_hidden(C,u1_msualg_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ~ ( C = k4_tarski(D,E)
& k3_finseq_1(E) = k8_funct_2(k5_numbers,k5_numbers,B,D)
& r1_tarski(k2_zfmisc_1(k1_tarski(D),k4_finseq_2(k8_funct_2(k5_numbers,k5_numbers,B,D),k4_catalg_1(A))),u1_msualg_1(A)) ) ) ) ) ) ) ) ).
fof(t16_catalg_1,axiom,
! [A] :
( ( v3_catalg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
~ ( ( r2_hidden(B,u1_struct_0(A))
| r2_hidden(B,u1_msualg_1(A)) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ~ ( B = k4_tarski(C,D)
& r1_tarski(k2_relat_1(D),k4_catalg_1(A)) ) ) ) ) ) ).
fof(t17_catalg_1,axiom,
! [A] :
( ( v3_catalg_1(A)
& l1_msualg_1(A) )
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ( ( ( r2_hidden(k4_tarski(B,C),u1_struct_0(A))
& r2_hidden(k4_tarski(B,D),u1_struct_0(A)) )
| ( r2_hidden(k4_tarski(B,C),u1_msualg_1(A))
& r2_hidden(k4_tarski(B,D),u1_msualg_1(A)) ) )
=> k3_finseq_1(C) = k3_finseq_1(D) ) ) ) ) ).
fof(t18_catalg_1,axiom,
! [A] :
( ( v3_catalg_1(A)
& l1_msualg_1(A) )
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ( ( k3_finseq_1(D) = k3_finseq_1(C)
& r1_tarski(k2_relat_1(D),k4_catalg_1(A)) )
=> ( ( r2_hidden(k4_tarski(B,C),u1_struct_0(A))
=> r2_hidden(k4_tarski(B,D),u1_struct_0(A)) )
& ( r2_hidden(k4_tarski(B,C),u1_msualg_1(A))
=> r2_hidden(k4_tarski(B,D),u1_msualg_1(A)) ) ) ) ) ) ) ).
fof(t19_catalg_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_instalg1(A)
& v2_catalg_1(A)
& v3_catalg_1(A)
& l1_msualg_1(A) )
=> m1_catalg_1(A,k4_catalg_1(A)) ) ).
fof(d10_catalg_1,axiom,
! [A] : k5_catalg_1(A) = k4_tarski(np__1,k9_finseq_1(A)) ).
fof(d11_catalg_1,axiom,
! [A,B] : k6_catalg_1(A,B) = k4_tarski(np__0,k10_finseq_1(A,B)) ).
fof(d12_catalg_1,axiom,
! [A,B,C] : k7_catalg_1(A,B,C) = k4_tarski(np__2,k11_finseq_1(A,B,C)) ).
fof(t20_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_catalg_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( r2_hidden(k5_catalg_1(C),u1_msualg_1(B))
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(k6_catalg_1(C,D),u1_struct_0(B))
& ! [E] :
( m1_subset_1(E,A)
=> r2_hidden(k7_catalg_1(C,D,E),u1_msualg_1(B)) ) ) ) ) ) ) ) ).
fof(t21_catalg_1,axiom,
! [A,B] :
( k5_catalg_1(A) = k5_catalg_1(B)
=> A = B ) ).
fof(t22_catalg_1,axiom,
! [A,B,C,D] :
( k6_catalg_1(A,C) = k6_catalg_1(B,D)
=> ( A = B
& C = D ) ) ).
fof(t23_catalg_1,axiom,
! [A,B,C,D,E,F] :
( k7_catalg_1(A,C,E) = k7_catalg_1(B,D,F)
=> ( A = B
& C = D
& E = F ) ) ).
fof(t24_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_catalg_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ? [D] :
( m1_subset_1(D,A)
& ? [E] :
( m1_subset_1(E,A)
& C = k9_catalg_1(A,D,E) ) ) ) ) ) ).
fof(t25_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(k3_catalg_1(A)))
=> ( ( k1_mcart_1(B) = np__1
& k3_finseq_1(k2_mcart_1(B)) = np__1 )
| ( k1_mcart_1(B) = np__2
& k3_finseq_1(k2_mcart_1(B)) = np__3 ) ) ) ) ).
fof(t26_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(k3_catalg_1(A)))
=> ~ ( ( k1_mcart_1(B) = np__1
| k3_finseq_1(k2_mcart_1(B)) = np__1 )
& ! [C] :
( m1_subset_1(C,A)
=> B != k8_catalg_1(A,C) ) ) ) ) ).
fof(t27_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_msualg_1(k3_catalg_1(A)))
=> ~ ( ( k1_mcart_1(B) = np__2
| k3_finseq_1(k2_mcart_1(B)) = np__3 )
& ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> B != k10_catalg_1(A,C,D,E) ) ) ) ) ) ) ).
fof(t28_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( k1_msualg_1(k3_catalg_1(A),k8_catalg_1(A,B)) = k1_xboole_0
& k2_msualg_1(k3_catalg_1(A),k8_catalg_1(A,B)) = k9_catalg_1(A,B,B) ) ) ) ).
fof(t29_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ( k1_msualg_1(k3_catalg_1(A),k10_catalg_1(A,B,C,D)) = k2_finseq_4(u1_struct_0(k3_catalg_1(A)),k9_catalg_1(A,C,D),k9_catalg_1(A,B,C))
& k2_msualg_1(k3_catalg_1(A),k10_catalg_1(A,B,C,D)) = k9_catalg_1(A,B,D) ) ) ) ) ) ).
fof(d13_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))))
& m2_relset_1(D,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B)))) )
=> ( D = k11_catalg_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_catalg_1(u1_cat_1(A))))
=> k8_funct_2(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))),D,E) = k4_tarski(np__0,k5_relat_1(k2_mcart_1(E),k12_cat_1(A,B,C))) ) ) ) ) ) ) ).
fof(d14_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))))
& m2_relset_1(D,u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B)))) )
=> ( D = k12_catalg_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_msualg_1(k3_catalg_1(u1_cat_1(A))))
=> k8_funct_2(u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))),D,E) = k4_tarski(k1_mcart_1(E),k5_relat_1(k2_mcart_1(E),k12_cat_1(A,B,C))) ) ) ) ) ) ) ).
fof(t30_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> k8_funct_2(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))),k11_catalg_1(A,B,C),k9_catalg_1(u1_cat_1(A),D,E)) = k9_catalg_1(u1_cat_1(B),k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) ) ) ) ) ) ).
fof(t31_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k8_funct_2(u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))),k12_catalg_1(A,B,C),k8_catalg_1(u1_cat_1(A),D)) = k8_catalg_1(u1_cat_1(B),k13_cat_1(A,B,C,D)) ) ) ) ) ).
fof(t32_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> k8_funct_2(u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))),k12_catalg_1(A,B,C),k10_catalg_1(u1_cat_1(A),D,E,F)) = k10_catalg_1(u1_cat_1(B),k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E),k13_cat_1(A,B,C,F)) ) ) ) ) ) ) ).
fof(t33_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> r3_pua2mss1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)) ) ) ) ).
fof(t34_catalg_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( l3_msualg_1(B,k3_catalg_1(A))
=> ! [C] :
( m1_subset_1(C,A)
=> k3_msualg_1(k3_catalg_1(A),k8_catalg_1(A,C),B) = k1_tarski(k1_xboole_0) ) ) ) ).
fof(d15_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,k3_catalg_1(u1_cat_1(A)))
& l3_msualg_1(B,k3_catalg_1(u1_cat_1(A))) )
=> ( B = k13_catalg_1(A)
<=> ( ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k1_funct_1(u4_msualg_1(k3_catalg_1(u1_cat_1(A)),B),k9_catalg_1(u1_cat_1(A),C,D)) = k6_cat_1(A,C,D) ) )
& ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k8_catalg_1(u1_cat_1(A),C),B),k1_xboole_0) = k10_cat_1(A,C) )
& ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ( ( k2_cat_1(A,F) = C
& k3_cat_1(A,F) = D
& k2_cat_1(A,G) = D
& k3_cat_1(A,G) = E )
=> k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),C,D,E),B),k2_finseq_4(u2_cat_1(A),G,F)) = k4_cat_1(A,F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_catalg_1,axiom,
$true ).
fof(t36_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k4_msualg_1(k3_catalg_1(u1_cat_1(A)),k8_catalg_1(u1_cat_1(A),B),k13_catalg_1(A)) = k6_cat_1(A,B,B) ) ) ).
fof(t37_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ( k3_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)) = k4_card_3(k2_finseq_4(k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,C,D),k6_cat_1(A,B,C)))
& k4_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)) = k6_cat_1(A,B,D) ) ) ) ) ) ).
fof(t38_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> m3_pboole(k1_catalg_1(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),C),u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)))) ) ) ) ).
fof(t39_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( r2_hidden(E,k3_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)))
<=> ? [F] :
( m1_subset_1(F,u2_cat_1(A))
& ? [G] :
( m1_subset_1(G,u2_cat_1(A))
& E = k2_finseq_4(u2_cat_1(A),F,G)
& k2_cat_1(A,G) = B
& k3_cat_1(A,G) = C
& k2_cat_1(A,F) = C
& k3_cat_1(A,F) = D ) ) ) ) ) ) ) ).
fof(t40_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ! [H] :
( m1_subset_1(H,u2_cat_1(A))
=> ( ( r2_hidden(G,k6_cat_1(A,D,E))
& r2_hidden(H,k6_cat_1(A,E,F)) )
=> ! [I] :
( m1_subset_1(I,k3_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),D,E,F),k13_catalg_1(A)))
=> ( I = k2_finseq_4(u2_cat_1(A),H,G)
=> ! [J] :
( m3_pboole(J,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C))))
=> ( r6_pboole(u1_struct_0(k3_catalg_1(u1_cat_1(A))),J,k1_catalg_1(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),C))
=> k5_msualg_3(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)),k10_catalg_1(u1_cat_1(A),D,E,F),J,I) = k2_finseq_4(u2_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,H),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_catalg_1,axiom,
$true ).
fof(t42_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ( ( r2_hidden(E,k6_cat_1(A,B,C))
& r2_hidden(F,k6_cat_1(A,C,D)) )
=> k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),F,E)) = k4_cat_1(A,E,F) ) ) ) ) ) ) ) ).
fof(t43_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ! [H] :
( m1_subset_1(H,u2_cat_1(A))
=> ( ( r2_hidden(F,k6_cat_1(A,B,C))
& r2_hidden(G,k6_cat_1(A,C,D))
& r2_hidden(H,k6_cat_1(A,D,E)) )
=> k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,D,E),k13_catalg_1(A)),k10_finseq_1(H,k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,D),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),G,F)))) = k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,E),k13_catalg_1(A)),k10_finseq_1(k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),C,D,E),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),H,G)),F)) ) ) ) ) ) ) ) ) ) ).
fof(t44_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r2_hidden(D,k6_cat_1(A,B,C))
=> ( k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,C,C),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),k10_cat_1(A,C),D)) = D
& k1_funct_1(k5_msualg_1(k3_catalg_1(u1_cat_1(A)),k10_catalg_1(u1_cat_1(A),B,B,C),k13_catalg_1(A)),k2_finseq_4(u2_cat_1(A),D,k10_cat_1(A,B))) = D ) ) ) ) ) ) ).
fof(t45_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ? [D] :
( m3_pboole(D,u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C))))
& r6_pboole(u1_struct_0(k3_catalg_1(u1_cat_1(A))),D,k1_catalg_1(u1_struct_0(k3_catalg_1(u1_cat_1(A))),u4_msualg_1(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A)),C))
& r1_msualg_3(k3_catalg_1(u1_cat_1(A)),k13_catalg_1(A),k1_instalg1(k3_catalg_1(u1_cat_1(A)),k3_catalg_1(u1_cat_1(B)),k13_catalg_1(B),k11_catalg_1(A,B,C),k12_catalg_1(A,B,C)),D) ) ) ) ) ).
fof(s1_catalg_1,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s1_catalg_1)
=> ! [B] :
( m1_subset_1(B,f1_s1_catalg_1)
=> r1_tarski(f3_s1_catalg_1(A,B),f2_s1_catalg_1) ) )
& ! [A] :
( m1_subset_1(A,f1_s1_catalg_1)
=> r2_hidden(f5_s1_catalg_1(A),f3_s1_catalg_1(A,A)) )
& ! [A] :
( m1_subset_1(A,f1_s1_catalg_1)
=> ! [B] :
( m1_subset_1(B,f1_s1_catalg_1)
=> ! [C] :
( m1_subset_1(C,f1_s1_catalg_1)
=> ! [D] :
( m1_subset_1(D,f2_s1_catalg_1)
=> ! [E] :
( m1_subset_1(E,f2_s1_catalg_1)
=> ( ( r2_hidden(D,f3_s1_catalg_1(A,B))
& r2_hidden(E,f3_s1_catalg_1(B,C)) )
=> r2_hidden(f4_s1_catalg_1(A,B,C,E,D),f3_s1_catalg_1(A,C)) ) ) ) ) ) ) )
=> ? [A] :
( v4_msualg_1(A,k3_catalg_1(f1_s1_catalg_1))
& l3_msualg_1(A,k3_catalg_1(f1_s1_catalg_1))
& ! [B] :
( m1_subset_1(B,f1_s1_catalg_1)
=> ! [C] :
( m1_subset_1(C,f1_s1_catalg_1)
=> k1_funct_1(u4_msualg_1(k3_catalg_1(f1_s1_catalg_1),A),k9_catalg_1(f1_s1_catalg_1,B,C)) = f3_s1_catalg_1(B,C) ) )
& ! [B] :
( m1_subset_1(B,f1_s1_catalg_1)
=> k1_funct_1(k5_msualg_1(k3_catalg_1(f1_s1_catalg_1),k8_catalg_1(f1_s1_catalg_1,B),A),k1_xboole_0) = f5_s1_catalg_1(B) )
& ! [B] :
( m1_subset_1(B,f1_s1_catalg_1)
=> ! [C] :
( m1_subset_1(C,f1_s1_catalg_1)
=> ! [D] :
( m1_subset_1(D,f1_s1_catalg_1)
=> ! [E] :
( m1_subset_1(E,f2_s1_catalg_1)
=> ! [F] :
( m1_subset_1(F,f2_s1_catalg_1)
=> ( ( r2_hidden(E,f3_s1_catalg_1(B,C))
& r2_hidden(F,f3_s1_catalg_1(C,D)) )
=> k1_funct_1(k5_msualg_1(k3_catalg_1(f1_s1_catalg_1),k10_catalg_1(f1_s1_catalg_1,B,C,D),A),k2_finseq_4(f2_s1_catalg_1,F,E)) = f4_s1_catalg_1(B,C,D,F,E) ) ) ) ) ) ) ) ) ).
fof(dt_m1_catalg_1,axiom,
! [A,B] :
( m1_catalg_1(B,A)
=> ( v1_instalg1(B)
& l1_msualg_1(B) ) ) ).
fof(existence_m1_catalg_1,axiom,
! [A] :
? [B] : m1_catalg_1(B,A) ).
fof(dt_k1_catalg_1,axiom,
! [A,B,C] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_relat_1(C)
& v1_funct_1(C) )
=> ( v1_funcop_1(k1_catalg_1(A,B,C))
& m1_pboole(k1_catalg_1(A,B,C),A) ) ) ).
fof(dt_k2_catalg_1,axiom,
! [A] :
( v1_msualg_1(k2_catalg_1(A))
& l1_msualg_1(k2_catalg_1(A)) ) ).
fof(dt_k3_catalg_1,axiom,
! [A] :
( v1_msualg_1(k3_catalg_1(A))
& m1_catalg_1(k3_catalg_1(A),A) ) ).
fof(redefinition_k3_catalg_1,axiom,
! [A] : k3_catalg_1(A) = k2_catalg_1(A) ).
fof(dt_k4_catalg_1,axiom,
$true ).
fof(dt_k5_catalg_1,axiom,
$true ).
fof(dt_k6_catalg_1,axiom,
$true ).
fof(dt_k7_catalg_1,axiom,
$true ).
fof(dt_k8_catalg_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A) )
=> m1_subset_1(k8_catalg_1(A,B),u1_msualg_1(k3_catalg_1(A))) ) ).
fof(redefinition_k8_catalg_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A) )
=> k8_catalg_1(A,B) = k5_catalg_1(B) ) ).
fof(dt_k9_catalg_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> m1_subset_1(k9_catalg_1(A,B,C),u1_struct_0(k3_catalg_1(A))) ) ).
fof(redefinition_k9_catalg_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A) )
=> k9_catalg_1(A,B,C) = k6_catalg_1(B,C) ) ).
fof(dt_k10_catalg_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A) )
=> m1_subset_1(k10_catalg_1(A,B,C,D),u1_msualg_1(k3_catalg_1(A))) ) ).
fof(redefinition_k10_catalg_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& m1_subset_1(C,A)
& m1_subset_1(D,A) )
=> k10_catalg_1(A,B,C,D) = k7_catalg_1(B,C,D) ) ).
fof(dt_k11_catalg_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m2_cat_1(C,A,B) )
=> ( v1_funct_1(k11_catalg_1(A,B,C))
& v1_funct_2(k11_catalg_1(A,B,C),u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B))))
& m2_relset_1(k11_catalg_1(A,B,C),u1_struct_0(k3_catalg_1(u1_cat_1(A))),u1_struct_0(k3_catalg_1(u1_cat_1(B)))) ) ) ).
fof(dt_k12_catalg_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m2_cat_1(C,A,B) )
=> ( v1_funct_1(k12_catalg_1(A,B,C))
& v1_funct_2(k12_catalg_1(A,B,C),u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B))))
& m2_relset_1(k12_catalg_1(A,B,C),u1_msualg_1(k3_catalg_1(u1_cat_1(A))),u1_msualg_1(k3_catalg_1(u1_cat_1(B)))) ) ) ).
fof(dt_k13_catalg_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v4_msualg_1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A)))
& l3_msualg_1(k13_catalg_1(A),k3_catalg_1(u1_cat_1(A))) ) ) ).
%------------------------------------------------------------------------------