SET007 Axioms: SET007+333.ax
%------------------------------------------------------------------------------
% File : SET007+333 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Products and Coproducts in Categories
% 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 : cat_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 130 ( 7 unt; 0 def)
% Number of atoms : 1019 ( 155 equ)
% Maximal formula atoms : 21 ( 7 avg)
% Number of connectives : 933 ( 44 ~; 4 |; 362 &)
% ( 34 <=>; 489 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-4 aty)
% Number of functors : 39 ( 39 usr; 5 con; 0-6 aty)
% Number of variables : 547 ( 539 !; 8 ?)
% 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(d1_cat_3,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( r2_hidden(D,A)
=> k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ) ).
fof(t1_cat_3,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( ! [E] :
( r2_hidden(E,A)
=> k4_finseq_4(A,B,C,E) = k4_finseq_4(A,B,D,E) )
=> C = D ) ) ) ) ).
fof(t2_cat_3,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ( r2_hidden(B,A)
=> k4_finseq_4(A,C,k1_cat_3(C,A,D),B) = D ) ) ) ).
fof(t3_cat_3,axiom,
$true ).
fof(t4_cat_3,axiom,
$true ).
fof(t5_cat_3,axiom,
$true ).
fof(t6_cat_3,axiom,
$true ).
fof(t7_cat_3,axiom,
! [A,B,C] :
( ~ v1_xboole_0(C)
=> ( A != B
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( m1_subset_1(E,C)
=> ( k4_finseq_4(k2_tarski(A,B),C,k5_funct_4(C,A,B,D,E),A) = D
& k4_finseq_4(k2_tarski(A,B),C,k5_funct_4(C,A,B,D,E),B) = E ) ) ) ) ) ).
fof(d2_cat_3,axiom,
$true ).
fof(d3_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m2_relset_1(C,B,u2_cat_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_cat_1(A))
& m2_relset_1(D,B,u1_cat_1(A)) )
=> ( D = k3_cat_3(A,B,C)
<=> ! [E] :
( r2_hidden(E,B)
=> k4_finseq_4(B,u1_cat_1(A),D,E) = k2_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ).
fof(d4_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m2_relset_1(C,B,u2_cat_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u1_cat_1(A))
& m2_relset_1(D,B,u1_cat_1(A)) )
=> ( D = k4_cat_3(A,B,C)
<=> ! [E] :
( r2_hidden(E,B)
=> k4_finseq_4(B,u1_cat_1(A),D,E) = k3_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ).
fof(t8_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> k3_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C)) = k1_cat_3(u1_cat_1(B),A,k2_cat_1(B,C)) ) ) ).
fof(t9_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> k4_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C)) = k1_cat_3(u1_cat_1(B),A,k3_cat_1(B,C)) ) ) ).
fof(t10_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> k3_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E)) = k5_funct_4(u1_cat_1(C),A,B,k2_cat_1(C,D),k2_cat_1(C,E)) ) ) ) ).
fof(t11_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> k4_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E)) = k5_funct_4(u1_cat_1(C),A,B,k3_cat_1(C,D),k3_cat_1(C,E)) ) ) ) ).
fof(d5_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m2_relset_1(C,B,u2_cat_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u2_cat_1(k2_oppcat_1(A)))
& m2_relset_1(D,B,u2_cat_1(k2_oppcat_1(A))) )
=> ( D = k5_cat_3(A,B,C)
<=> ! [E] :
( r2_hidden(E,B)
=> k4_finseq_4(B,u2_cat_1(k2_oppcat_1(A)),D,E) = k5_oppcat_1(A,k4_finseq_4(B,u2_cat_1(A),C,E)) ) ) ) ) ) ).
fof(t12_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> k5_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C)) = k1_cat_3(u2_cat_1(k2_oppcat_1(B)),A,k5_oppcat_1(B,C)) ) ) ).
fof(t13_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ( A != B
=> k5_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E)) = k5_funct_4(u2_cat_1(k2_oppcat_1(C)),A,B,k5_oppcat_1(C,D),k5_oppcat_1(C,E)) ) ) ) ) ).
fof(t14_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u2_cat_1(B))
& m2_relset_1(C,A,u2_cat_1(B)) )
=> k5_cat_3(k2_oppcat_1(B),A,k5_cat_3(B,A,C)) = C ) ) ).
fof(d6_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(k2_oppcat_1(A)))
& m2_relset_1(C,B,u2_cat_1(k2_oppcat_1(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u2_cat_1(A))
& m2_relset_1(D,B,u2_cat_1(A)) )
=> ( D = k6_cat_3(A,B,C)
<=> ! [E] :
( r2_hidden(E,B)
=> k4_finseq_4(B,u2_cat_1(A),D,E) = k6_oppcat_1(A,k4_finseq_4(B,u2_cat_1(k2_oppcat_1(A)),C,E)) ) ) ) ) ) ).
fof(t15_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k2_oppcat_1(B)))
=> k6_cat_3(B,A,k1_cat_3(u2_cat_1(k2_oppcat_1(B)),A,C)) = k1_cat_3(u2_cat_1(B),A,k6_oppcat_1(B,C)) ) ) ).
fof(t16_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ( A != B
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k2_oppcat_1(C)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k2_oppcat_1(C)))
=> k6_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(k2_oppcat_1(C)),A,B,D,E)) = k5_funct_4(u2_cat_1(C),A,B,k6_oppcat_1(C,D),k6_oppcat_1(C,E)) ) ) ) ) ).
fof(t17_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u2_cat_1(B))
& m2_relset_1(C,A,u2_cat_1(B)) )
=> k6_cat_3(B,A,k5_cat_3(B,A,C)) = C ) ) ).
fof(d7_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m2_relset_1(C,B,u2_cat_1(A)) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u2_cat_1(A))
& m2_relset_1(E,B,u2_cat_1(A)) )
=> ( E = k7_cat_3(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,B)
=> k4_finseq_4(B,u2_cat_1(A),E,F) = k4_cat_1(A,D,k4_finseq_4(B,u2_cat_1(A),C,F)) ) ) ) ) ) ) ).
fof(d8_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m2_relset_1(C,B,u2_cat_1(A)) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u2_cat_1(A))
& m2_relset_1(E,B,u2_cat_1(A)) )
=> ( E = k8_cat_3(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,B)
=> k4_finseq_4(B,u2_cat_1(A),E,F) = k4_cat_1(A,k4_finseq_4(B,u2_cat_1(A),C,F),D) ) ) ) ) ) ) ).
fof(t18_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(C))
=> ( A != B
=> k7_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E),F) = k5_funct_4(u2_cat_1(C),A,B,k4_cat_1(C,F,D),k4_cat_1(C,F,E)) ) ) ) ) ) ).
fof(t19_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(C))
=> ( A != B
=> k8_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,E,F),D) = k5_funct_4(u2_cat_1(C),A,B,k4_cat_1(C,E,D),k4_cat_1(C,F,D)) ) ) ) ) ) ).
fof(t20_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> ( k3_cat_3(B,A,D) = k1_cat_3(u1_cat_1(B),A,k3_cat_1(B,C))
=> ( k3_cat_3(B,A,k7_cat_3(B,A,D,C)) = k1_cat_3(u1_cat_1(B),A,k2_cat_1(B,C))
& k4_cat_3(B,A,k7_cat_3(B,A,D,C)) = k4_cat_3(B,A,D) ) ) ) ) ) ).
fof(t21_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> ( k4_cat_3(B,A,D) = k1_cat_3(u1_cat_1(B),A,k2_cat_1(B,C))
=> ( k3_cat_3(B,A,k8_cat_3(B,A,D,C)) = k3_cat_3(B,A,D)
& k4_cat_3(B,A,k8_cat_3(B,A,D,C)) = k1_cat_3(u1_cat_1(B),A,k3_cat_1(B,C)) ) ) ) ) ) ).
fof(d9_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m2_relset_1(C,B,u2_cat_1(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,u2_cat_1(A))
& m2_relset_1(D,B,u2_cat_1(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,u2_cat_1(A))
& m2_relset_1(E,B,u2_cat_1(A)) )
=> ( E = k9_cat_3(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,B)
=> k4_finseq_4(B,u2_cat_1(A),E,F) = k4_cat_1(A,k4_finseq_4(B,u2_cat_1(A),D,F),k4_finseq_4(B,u2_cat_1(A),C,F)) ) ) ) ) ) ) ).
fof(t22_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u2_cat_1(B))
& m2_relset_1(C,A,u2_cat_1(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> ( k3_cat_3(B,A,C) = k4_cat_3(B,A,D)
=> ( k3_cat_3(B,A,k9_cat_3(B,A,C,D)) = k3_cat_3(B,A,D)
& k4_cat_3(B,A,k9_cat_3(B,A,C,D)) = k4_cat_3(B,A,C) ) ) ) ) ) ).
fof(t23_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u2_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(C))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(C))
=> ( A != B
=> k9_cat_3(C,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,D,E),k5_funct_4(u2_cat_1(C),A,B,F,G)) = k5_funct_4(u2_cat_1(C),A,B,k4_cat_1(C,F,D),k4_cat_1(C,G,E)) ) ) ) ) ) ) ).
fof(t24_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> k7_cat_3(B,A,D,C) = k9_cat_3(B,A,D,k1_cat_3(u2_cat_1(B),A,C)) ) ) ) ).
fof(t25_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> k8_cat_3(B,A,D,C) = k9_cat_3(B,A,k1_cat_3(u2_cat_1(B),A,C),D) ) ) ) ).
fof(d10_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v1_cat_3(B,A)
<=> ? [C] :
( m1_subset_1(C,u2_cat_1(A))
& k3_cat_1(A,C) = k2_cat_1(A,B)
& k4_cat_1(A,C,B) = k10_cat_1(A,k3_cat_1(A,B)) ) ) ) ) ).
fof(d11_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v2_cat_3(B,A)
<=> ? [C] :
( m1_subset_1(C,u2_cat_1(A))
& k2_cat_1(A,C) = k3_cat_1(A,B)
& k4_cat_1(A,B,C) = k10_cat_1(A,k2_cat_1(A,B)) ) ) ) ) ).
fof(t26_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v1_cat_3(B,A)
=> v4_cat_1(B,A) ) ) ) ).
fof(t27_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v2_cat_3(B,A)
=> v3_cat_1(B,A) ) ) ) ).
fof(t28_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( ( v1_cat_3(B,A)
& v1_cat_3(C,A)
& k2_cat_1(A,C) = k3_cat_1(A,B) )
=> v1_cat_3(k4_cat_1(A,B,C),A) ) ) ) ) ).
fof(t29_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( ( v2_cat_3(B,A)
& v2_cat_3(C,A)
& k2_cat_1(A,C) = k3_cat_1(A,B) )
=> v2_cat_3(k4_cat_1(A,B,C),A) ) ) ) ) ).
fof(t30_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( ( k2_cat_1(A,B) = k3_cat_1(A,C)
& v1_cat_3(k4_cat_1(A,C,B),A) )
=> v1_cat_3(B,A) ) ) ) ) ).
fof(t31_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( ( k2_cat_1(A,B) = k3_cat_1(A,C)
& v2_cat_3(k4_cat_1(A,C,B),A) )
=> v2_cat_3(C,A) ) ) ) ) ).
fof(t32_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( ( v1_cat_3(B,A)
& v3_cat_1(B,A) )
=> v5_cat_1(B,A) ) ) ) ).
fof(t33_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( ( v2_cat_3(B,A)
& v4_cat_1(B,A) )
=> v5_cat_1(B,A) ) ) ) ).
fof(t34_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v5_cat_1(B,A)
<=> ( v1_cat_3(B,A)
& v2_cat_3(B,A) ) ) ) ) ).
fof(t35_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m2_cat_1(D,A,B)
=> ( v1_cat_3(C,A)
=> v1_cat_3(k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,C),B) ) ) ) ) ) ).
fof(t36_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m2_cat_1(D,A,B)
=> ( v2_cat_3(C,A)
=> v2_cat_3(k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,C),B) ) ) ) ) ) ).
fof(t37_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v1_cat_3(B,A)
<=> v2_cat_3(k5_oppcat_1(A,B),k2_oppcat_1(A)) ) ) ) ).
fof(t38_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ( v2_cat_3(B,A)
<=> v1_cat_3(k5_oppcat_1(A,B),k2_oppcat_1(A)) ) ) ) ).
fof(d12_cat_3,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))
=> ( v6_cat_1(C,A)
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> D = k10_cat_3(A,B,C) ) ) ) ) ) ).
fof(t39_cat_3,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))
=> ( v6_cat_1(B,A)
=> ( k2_cat_1(A,k10_cat_3(A,C,B)) = C
& k3_cat_1(A,k10_cat_3(A,C,B)) = B ) ) ) ) ) ).
fof(t40_cat_3,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))
=> ( ( v6_cat_1(B,A)
& k2_cat_1(A,D) = C
& k3_cat_1(A,D) = B )
=> k10_cat_3(A,C,B) = D ) ) ) ) ) ).
fof(t41_cat_3,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_cat_1(D,A,B,C)
=> ( v6_cat_1(C,A)
=> k10_cat_3(A,B,C) = D ) ) ) ) ) ).
fof(d13_cat_3,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))
=> ( v7_cat_1(B,A)
=> ! [D] :
( m1_cat_1(D,A,B,C)
=> D = k11_cat_3(A,B,C) ) ) ) ) ) ).
fof(t42_cat_3,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))
=> ( v7_cat_1(B,A)
=> ( k2_cat_1(A,k11_cat_3(A,B,C)) = B
& k3_cat_1(A,k11_cat_3(A,B,C)) = C ) ) ) ) ) ).
fof(t43_cat_3,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))
=> ( ( v7_cat_1(B,A)
& k2_cat_1(A,D) = B
& k3_cat_1(A,D) = C )
=> k11_cat_3(A,B,C) = D ) ) ) ) ) ).
fof(t44_cat_3,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_cat_1(D,A,B,C)
=> ( v7_cat_1(B,A)
=> k11_cat_3(A,B,C) = D ) ) ) ) ) ).
fof(d14_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u2_cat_1(A))
& m2_relset_1(D,C,u2_cat_1(A)) )
=> ( m1_cat_3(D,A,B,C)
<=> k3_cat_3(A,C,D) = k1_cat_3(u1_cat_1(A),C,B) ) ) ) ) ).
fof(t45_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(C))
=> ! [E] :
( m1_cat_3(E,C,D,A)
=> ( r2_hidden(B,A)
=> k2_cat_1(C,k4_finseq_4(A,u2_cat_1(C),E,B)) = D ) ) ) ) ).
fof(t46_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
& m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
=> m1_cat_3(C,A,B,k1_xboole_0) ) ) ) ).
fof(t47_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(B))
=> ( k2_cat_1(B,D) = C
=> m1_cat_3(k2_cat_3(u2_cat_1(B),A,D),B,C,k1_tarski(A)) ) ) ) ) ).
fof(t48_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(C))
=> ( ( k2_cat_1(C,E) = D
& k2_cat_1(C,F) = D )
=> m1_cat_3(k5_funct_4(u2_cat_1(C),A,B,E,F),C,D,k2_tarski(A,B)) ) ) ) ) ) ).
fof(t49_cat_3,axiom,
$true ).
fof(t50_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(B))
=> ! [E] :
( m1_cat_3(E,B,C,A)
=> ( k3_cat_1(B,D) = C
=> m1_cat_3(k7_cat_3(B,A,E,D),B,k2_cat_1(B,D),A) ) ) ) ) ) ).
fof(t51_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> ! [E] :
( m1_cat_3(E,B,C,A)
=> ( k3_cat_3(B,A,D) = k4_cat_3(B,A,E)
=> m1_cat_3(k9_cat_3(B,A,D,E),B,C,A) ) ) ) ) ) ).
fof(t52_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> ! [D] :
( m1_cat_3(D,B,k3_cat_1(B,C),A)
=> k8_cat_3(k2_oppcat_1(B),A,k5_cat_3(B,A,D),k5_oppcat_1(B,C)) = k5_cat_3(B,A,k7_cat_3(B,A,D,C)) ) ) ) ).
fof(d15_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u2_cat_1(A))
& m2_relset_1(D,C,u2_cat_1(A)) )
=> ( r1_cat_3(A,B,C,D)
<=> ( m1_cat_3(D,A,B,C)
& ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_cat_3(F,A,E,C)
=> ~ ( k4_cat_3(A,C,D) = k4_cat_3(A,C,F)
& ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ~ ( r2_hidden(G,k6_cat_1(A,E,B))
& ! [H] :
( m1_subset_1(H,u2_cat_1(A))
=> ( r2_hidden(H,k6_cat_1(A,E,B))
=> ( ! [I] :
( r2_hidden(I,C)
=> k4_cat_1(A,H,k4_finseq_4(C,u2_cat_1(A),D,I)) = k4_finseq_4(C,u2_cat_1(A),F,I) )
<=> G = H ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t53_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(B))
=> ! [E] :
( m1_cat_3(E,B,C,A)
=> ! [F] :
( m1_cat_3(F,B,D,A)
=> ( ( r1_cat_3(B,C,A,E)
& r1_cat_3(B,D,A,F)
& k4_cat_3(B,A,E) = k4_cat_3(B,A,F) )
=> r1_cat_1(B,C,D) ) ) ) ) ) ) ).
fof(t54_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_cat_3(D,B,C,A)
=> ( ( r1_cat_3(B,C,A,D)
& ! [E,F] :
~ ( r2_hidden(E,A)
& r2_hidden(F,A)
& k6_cat_1(B,k3_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),k3_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,F))) = k1_xboole_0 ) )
=> ! [E] :
( r2_hidden(E,A)
=> v1_cat_3(k4_finseq_4(A,u2_cat_1(B),D,E),B) ) ) ) ) ) ).
fof(t55_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
& m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
=> ( r1_cat_3(A,B,k1_xboole_0,C)
<=> v6_cat_1(B,A) ) ) ) ) ).
fof(t56_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(B))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(B))
=> ! [F] :
( m1_cat_3(F,B,C,A)
=> ( ( r1_cat_3(B,C,A,F)
& k2_cat_1(B,E) = D
& k3_cat_1(B,E) = C
& v5_cat_1(E,B) )
=> r1_cat_3(B,D,A,k7_cat_3(B,A,F,E)) ) ) ) ) ) ) ).
fof(t57_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> r1_cat_3(B,C,k1_tarski(A),k2_cat_3(u2_cat_1(B),A,k10_cat_1(B,C))) ) ) ).
fof(t58_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_cat_3(D,B,C,A)
=> ( ( r1_cat_3(B,C,A,D)
& ! [E] :
( r2_hidden(E,A)
=> v6_cat_1(k3_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),B) ) )
=> v6_cat_1(C,B) ) ) ) ) ).
fof(d16_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r2_cat_3(A,B,C,D)
<=> ( k2_cat_1(A,C) = B
& k2_cat_1(A,D) = B
& ! [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))
=> ~ ( r2_hidden(F,k6_cat_1(A,E,k3_cat_1(A,C)))
& r2_hidden(G,k6_cat_1(A,E,k3_cat_1(A,D)))
& ! [H] :
( m1_subset_1(H,u2_cat_1(A))
=> ~ ( r2_hidden(H,k6_cat_1(A,E,B))
& ! [I] :
( m1_subset_1(I,u2_cat_1(A))
=> ( r2_hidden(I,k6_cat_1(A,E,B))
=> ( ( k4_cat_1(A,I,C) = F
& k4_cat_1(A,I,D) = G )
<=> H = I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t59_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(C))
=> ( A != B
=> ( r2_cat_3(C,D,E,F)
<=> r1_cat_3(C,D,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,E,F)) ) ) ) ) ) ) ).
fof(t60_cat_3,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))
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,B,D) != k1_xboole_0
& ~ ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,B,D)
=> ( r2_cat_3(A,B,E,F)
<=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ~ ( k6_cat_1(A,G,C) != k1_xboole_0
& k6_cat_1(A,G,D) != k1_xboole_0
& ~ ( k6_cat_1(A,G,B) != k1_xboole_0
& ! [H] :
( m1_cat_1(H,A,G,C)
=> ! [I] :
( m1_cat_1(I,A,G,D)
=> ? [J] :
( m1_cat_1(J,A,G,B)
& ! [K] :
( m1_cat_1(K,A,G,B)
=> ( ( k9_cat_1(A,G,B,C,K,E) = H
& k9_cat_1(A,G,B,D,K,F) = I )
<=> J = K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t61_cat_3,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))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ( ( r2_cat_3(A,B,D,E)
& r2_cat_3(A,C,F,G)
& k3_cat_1(A,D) = k3_cat_1(A,F)
& k3_cat_1(A,E) = k3_cat_1(A,G) )
=> r1_cat_1(A,B,C) ) ) ) ) ) ) ) ) ).
fof(t62_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r2_cat_3(A,B,C,D)
=> ( k6_cat_1(A,k3_cat_1(A,C),k3_cat_1(A,D)) = k1_xboole_0
| k6_cat_1(A,k3_cat_1(A,D),k3_cat_1(A,C)) = k1_xboole_0
| ( v1_cat_3(C,A)
& v1_cat_3(D,A) ) ) ) ) ) ) ) ).
fof(t63_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( ( r2_cat_3(A,B,C,D)
& r2_hidden(E,k6_cat_1(A,B,B))
& k4_cat_1(A,E,C) = C
& k4_cat_1(A,E,D) = D )
=> E = k10_cat_1(A,B) ) ) ) ) ) ) ).
fof(t64_cat_3,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))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ( ( r2_cat_3(A,B,D,E)
& k2_cat_1(A,F) = C
& k3_cat_1(A,F) = B
& v5_cat_1(F,A) )
=> r2_cat_3(A,C,k4_cat_1(A,F,D),k4_cat_1(A,F,E)) ) ) ) ) ) ) ) ).
fof(t65_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( r2_cat_3(A,B,C,D)
& v6_cat_1(k3_cat_1(A,D),A) )
=> r1_cat_1(A,B,k3_cat_1(A,C)) ) ) ) ) ) ).
fof(t66_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( r2_cat_3(A,B,C,D)
& v6_cat_1(k3_cat_1(A,C),A) )
=> r1_cat_1(A,B,k3_cat_1(A,D)) ) ) ) ) ) ).
fof(d17_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u2_cat_1(A))
& m2_relset_1(D,C,u2_cat_1(A)) )
=> ( m2_cat_3(D,A,B,C)
<=> k4_cat_3(A,C,D) = k1_cat_3(u1_cat_1(A),C,B) ) ) ) ) ).
fof(t67_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(C))
=> ! [E] :
( m2_cat_3(E,C,D,A)
=> ( r2_hidden(B,A)
=> k3_cat_1(C,k4_finseq_4(A,u2_cat_1(C),E,B)) = D ) ) ) ) ).
fof(t68_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_xboole_0,u2_cat_1(A))
& m2_relset_1(C,k1_xboole_0,u2_cat_1(A)) )
=> m2_cat_3(C,A,B,k1_xboole_0) ) ) ) ).
fof(t69_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(B))
=> ( k3_cat_1(B,D) = C
=> m2_cat_3(k2_cat_3(u2_cat_1(B),A,D),B,C,k1_tarski(A)) ) ) ) ) ).
fof(t70_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(C))
=> ( ( k3_cat_1(C,E) = D
& k3_cat_1(C,F) = D )
=> m2_cat_3(k5_funct_4(u2_cat_1(C),A,B,E,F),C,D,k2_tarski(A,B)) ) ) ) ) ) ).
fof(t71_cat_3,axiom,
$true ).
fof(t72_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(B))
=> ! [E] :
( m2_cat_3(E,B,C,A)
=> ( k2_cat_1(B,D) = C
=> m2_cat_3(k8_cat_3(B,A,E,D),B,k3_cat_1(B,D),A) ) ) ) ) ) ).
fof(t73_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m2_cat_3(D,B,C,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u2_cat_1(B))
& m2_relset_1(E,A,u2_cat_1(B)) )
=> ( k3_cat_3(B,A,D) = k4_cat_3(B,A,E)
=> m2_cat_3(k9_cat_3(B,A,D,E),B,C,A) ) ) ) ) ) ).
fof(t74_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> ( m1_cat_3(D,B,C,A)
<=> m2_cat_3(k5_cat_3(B,A,D),k2_oppcat_1(B),k3_oppcat_1(B,C),A) ) ) ) ) ).
fof(t75_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u2_cat_1(k2_oppcat_1(B)))
& m2_relset_1(C,A,u2_cat_1(k2_oppcat_1(B))) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k2_oppcat_1(B)))
=> ( m2_cat_3(C,k2_oppcat_1(B),D,A)
<=> m1_cat_3(k6_cat_3(B,A,C),B,k4_oppcat_1(B,D),A) ) ) ) ) ).
fof(t76_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(B))
=> ! [D] :
( m2_cat_3(D,B,k2_cat_1(B,C),A)
=> k7_cat_3(k2_oppcat_1(B),A,k5_cat_3(B,A,D),k5_oppcat_1(B,C)) = k5_cat_3(B,A,k8_cat_3(B,A,D,C)) ) ) ) ).
fof(d18_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,C,u2_cat_1(A))
& m2_relset_1(D,C,u2_cat_1(A)) )
=> ( r3_cat_3(A,B,C,D)
<=> ( m2_cat_3(D,A,B,C)
& ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m2_cat_3(F,A,E,C)
=> ~ ( k3_cat_3(A,C,D) = k3_cat_3(A,C,F)
& ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ~ ( r2_hidden(G,k6_cat_1(A,B,E))
& ! [H] :
( m1_subset_1(H,u2_cat_1(A))
=> ( r2_hidden(H,k6_cat_1(A,B,E))
=> ( ! [I] :
( r2_hidden(I,C)
=> k4_cat_1(A,k4_finseq_4(C,u2_cat_1(A),D,I),H) = k4_finseq_4(C,u2_cat_1(A),F,I) )
<=> G = H ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t77_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u2_cat_1(B))
& m2_relset_1(D,A,u2_cat_1(B)) )
=> ( r1_cat_3(B,C,A,D)
<=> r3_cat_3(k2_oppcat_1(B),k3_oppcat_1(B,C),A,k5_cat_3(B,A,D)) ) ) ) ) ).
fof(t78_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(B))
=> ! [E] :
( m2_cat_3(E,B,C,A)
=> ! [F] :
( m2_cat_3(F,B,D,A)
=> ( ( r3_cat_3(B,C,A,E)
& r3_cat_3(B,D,A,F)
& k3_cat_3(B,A,E) = k3_cat_3(B,A,F) )
=> r1_cat_1(B,C,D) ) ) ) ) ) ) ).
fof(t79_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m2_cat_3(D,B,C,A)
=> ( ( r3_cat_3(B,C,A,D)
& ! [E,F] :
~ ( r2_hidden(E,A)
& r2_hidden(F,A)
& k6_cat_1(B,k2_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),k2_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,F))) = k1_xboole_0 ) )
=> ! [E] :
( r2_hidden(E,A)
=> v2_cat_3(k4_finseq_4(A,u2_cat_1(B),D,E),B) ) ) ) ) ) ).
fof(t80_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(B))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(B))
=> ! [F] :
( m2_cat_3(F,B,C,A)
=> ( ( r3_cat_3(B,C,A,F)
& k2_cat_1(B,E) = C
& k3_cat_1(B,E) = D
& v5_cat_1(E,B) )
=> r3_cat_3(B,D,A,k8_cat_3(B,A,F,E)) ) ) ) ) ) ) ).
fof(t81_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m2_cat_3(C,A,B,k1_xboole_0)
=> ( r3_cat_3(A,B,k1_xboole_0,C)
<=> v7_cat_1(B,A) ) ) ) ) ).
fof(t82_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> r3_cat_3(B,C,k1_tarski(A),k2_cat_3(u2_cat_1(B),A,k10_cat_1(B,C))) ) ) ).
fof(t83_cat_3,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(B))
=> ! [D] :
( m2_cat_3(D,B,C,A)
=> ( ( r3_cat_3(B,C,A,D)
& ! [E] :
( r2_hidden(E,A)
=> v7_cat_1(k2_cat_1(B,k4_finseq_4(A,u2_cat_1(B),D,E)),B) ) )
=> v7_cat_1(C,B) ) ) ) ) ).
fof(d19_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r4_cat_3(A,B,C,D)
<=> ( k3_cat_1(A,C) = B
& k3_cat_1(A,D) = B
& ! [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))
=> ~ ( r2_hidden(F,k6_cat_1(A,k2_cat_1(A,C),E))
& r2_hidden(G,k6_cat_1(A,k2_cat_1(A,D),E))
& ! [H] :
( m1_subset_1(H,u2_cat_1(A))
=> ~ ( r2_hidden(H,k6_cat_1(A,B,E))
& ! [I] :
( m1_subset_1(I,u2_cat_1(A))
=> ( r2_hidden(I,k6_cat_1(A,B,E))
=> ( ( k4_cat_1(A,C,I) = F
& k4_cat_1(A,D,I) = G )
<=> H = I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t84_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r2_cat_3(A,B,C,D)
<=> r4_cat_3(k2_oppcat_1(A),k3_oppcat_1(A,B),k5_oppcat_1(A,C),k5_oppcat_1(A,D)) ) ) ) ) ) ).
fof(t85_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_cat_1(C))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(C))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(C))
=> ( A != B
=> ( r4_cat_3(C,D,E,F)
<=> r3_cat_3(C,D,k2_tarski(A,B),k5_funct_4(u2_cat_1(C),A,B,E,F)) ) ) ) ) ) ) ).
fof(t86_cat_3,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))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ( ( r4_cat_3(A,B,D,E)
& r4_cat_3(A,C,F,G)
& k2_cat_1(A,D) = k2_cat_1(A,F)
& k2_cat_1(A,E) = k2_cat_1(A,G) )
=> r1_cat_1(A,B,C) ) ) ) ) ) ) ) ) ).
fof(t87_cat_3,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))
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,C) != k1_xboole_0
& ~ ! [E] :
( m1_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,D,C)
=> ( r4_cat_3(A,C,E,F)
<=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ~ ( k6_cat_1(A,B,G) != k1_xboole_0
& k6_cat_1(A,D,G) != k1_xboole_0
& ~ ( k6_cat_1(A,C,G) != k1_xboole_0
& ! [H] :
( m1_cat_1(H,A,B,G)
=> ! [I] :
( m1_cat_1(I,A,D,G)
=> ? [J] :
( m1_cat_1(J,A,C,G)
& ! [K] :
( m1_cat_1(K,A,C,G)
=> ( ( k9_cat_1(A,B,C,G,E,K) = H
& k9_cat_1(A,D,C,G,F,K) = I )
<=> J = K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t88_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( r4_cat_3(A,B,C,D)
=> ( k6_cat_1(A,k2_cat_1(A,C),k2_cat_1(A,D)) = k1_xboole_0
| k6_cat_1(A,k2_cat_1(A,D),k2_cat_1(A,C)) = k1_xboole_0
| ( v2_cat_3(C,A)
& v2_cat_3(D,A) ) ) ) ) ) ) ) ).
fof(t89_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( ( r4_cat_3(A,B,C,D)
& r2_hidden(E,k6_cat_1(A,B,B))
& k4_cat_1(A,C,E) = C
& k4_cat_1(A,D,E) = D )
=> E = k10_cat_1(A,B) ) ) ) ) ) ) ).
fof(t90_cat_3,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))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ( ( r4_cat_3(A,B,D,E)
& k2_cat_1(A,F) = B
& k3_cat_1(A,F) = C
& v5_cat_1(F,A) )
=> r4_cat_3(A,C,k4_cat_1(A,D,F),k4_cat_1(A,E,F)) ) ) ) ) ) ) ) ).
fof(t91_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( r4_cat_3(A,B,C,D)
& v7_cat_1(k2_cat_1(A,D),A) )
=> r1_cat_1(A,k2_cat_1(A,C),B) ) ) ) ) ) ).
fof(t92_cat_3,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( ( r4_cat_3(A,B,C,D)
& v7_cat_1(k2_cat_1(A,C),A) )
=> r1_cat_1(A,k2_cat_1(A,D),B) ) ) ) ) ) ).
fof(s1_cat_3,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s1_cat_3,f2_s1_cat_3)
& m2_relset_1(A,f1_s1_cat_3,f2_s1_cat_3)
& ! [B] :
( r2_hidden(B,f1_s1_cat_3)
=> k4_finseq_4(f1_s1_cat_3,f2_s1_cat_3,A,B) = f3_s1_cat_3(B) ) ) ).
fof(s2_cat_3,axiom,
( ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s2_cat_3,f2_s2_cat_3)
& m2_relset_1(A,f1_s2_cat_3,f2_s2_cat_3)
& ! [B] :
( r2_hidden(B,f1_s2_cat_3)
=> k4_finseq_4(f1_s2_cat_3,f2_s2_cat_3,A,B) = f3_s2_cat_3(B) ) )
& ! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,f1_s2_cat_3,f2_s2_cat_3)
& m2_relset_1(A,f1_s2_cat_3,f2_s2_cat_3) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,f1_s2_cat_3,f2_s2_cat_3)
& m2_relset_1(B,f1_s2_cat_3,f2_s2_cat_3) )
=> ( ( ! [C] :
( r2_hidden(C,f1_s2_cat_3)
=> k4_finseq_4(f1_s2_cat_3,f2_s2_cat_3,A,C) = f3_s2_cat_3(C) )
& ! [C] :
( r2_hidden(C,f1_s2_cat_3)
=> k4_finseq_4(f1_s2_cat_3,f2_s2_cat_3,B,C) = f3_s2_cat_3(C) ) )
=> A = B ) ) ) ) ).
fof(dt_m1_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> ! [D] :
( m1_cat_3(D,A,B,C)
=> ( v1_funct_1(D)
& v1_funct_2(D,C,u2_cat_1(A))
& m2_relset_1(D,C,u2_cat_1(A)) ) ) ) ).
fof(existence_m1_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> ? [D] : m1_cat_3(D,A,B,C) ) ).
fof(dt_m2_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> ! [D] :
( m2_cat_3(D,A,B,C)
=> ( v1_funct_1(D)
& v1_funct_2(D,C,u2_cat_1(A))
& m2_relset_1(D,C,u2_cat_1(A)) ) ) ) ).
fof(existence_m2_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> ? [D] : m2_cat_3(D,A,B,C) ) ).
fof(dt_k1_cat_3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(C,A) )
=> ( v1_funct_1(k1_cat_3(A,B,C))
& v1_funct_2(k1_cat_3(A,B,C),B,A)
& m2_relset_1(k1_cat_3(A,B,C),B,A) ) ) ).
fof(redefinition_k1_cat_3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(C,A) )
=> k1_cat_3(A,B,C) = k2_funcop_1(B,C) ) ).
fof(dt_k2_cat_3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(C,A) )
=> ( v1_funct_1(k2_cat_3(A,B,C))
& v1_funct_2(k2_cat_3(A,B,C),k1_tarski(B),A)
& m2_relset_1(k2_cat_3(A,B,C),k1_tarski(B),A) ) ) ).
fof(redefinition_k2_cat_3,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(C,A) )
=> k2_cat_3(A,B,C) = k3_cqc_lang(B,C) ) ).
fof(dt_k3_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m1_relset_1(C,B,u2_cat_1(A)) )
=> ( v1_funct_1(k3_cat_3(A,B,C))
& v1_funct_2(k3_cat_3(A,B,C),B,u1_cat_1(A))
& m2_relset_1(k3_cat_3(A,B,C),B,u1_cat_1(A)) ) ) ).
fof(dt_k4_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m1_relset_1(C,B,u2_cat_1(A)) )
=> ( v1_funct_1(k4_cat_3(A,B,C))
& v1_funct_2(k4_cat_3(A,B,C),B,u1_cat_1(A))
& m2_relset_1(k4_cat_3(A,B,C),B,u1_cat_1(A)) ) ) ).
fof(dt_k5_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m1_relset_1(C,B,u2_cat_1(A)) )
=> ( v1_funct_1(k5_cat_3(A,B,C))
& v1_funct_2(k5_cat_3(A,B,C),B,u2_cat_1(k2_oppcat_1(A)))
& m2_relset_1(k5_cat_3(A,B,C),B,u2_cat_1(k2_oppcat_1(A))) ) ) ).
fof(dt_k6_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(k2_oppcat_1(A)))
& m1_relset_1(C,B,u2_cat_1(k2_oppcat_1(A))) )
=> ( v1_funct_1(k6_cat_3(A,B,C))
& v1_funct_2(k6_cat_3(A,B,C),B,u2_cat_1(A))
& m2_relset_1(k6_cat_3(A,B,C),B,u2_cat_1(A)) ) ) ).
fof(dt_k7_cat_3,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m1_relset_1(C,B,u2_cat_1(A))
& m1_subset_1(D,u2_cat_1(A)) )
=> ( v1_funct_1(k7_cat_3(A,B,C,D))
& v1_funct_2(k7_cat_3(A,B,C,D),B,u2_cat_1(A))
& m2_relset_1(k7_cat_3(A,B,C,D),B,u2_cat_1(A)) ) ) ).
fof(dt_k8_cat_3,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m1_relset_1(C,B,u2_cat_1(A))
& m1_subset_1(D,u2_cat_1(A)) )
=> ( v1_funct_1(k8_cat_3(A,B,C,D))
& v1_funct_2(k8_cat_3(A,B,C,D),B,u2_cat_1(A))
& m2_relset_1(k8_cat_3(A,B,C,D),B,u2_cat_1(A)) ) ) ).
fof(dt_k9_cat_3,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v1_funct_1(C)
& v1_funct_2(C,B,u2_cat_1(A))
& m1_relset_1(C,B,u2_cat_1(A))
& v1_funct_1(D)
& v1_funct_2(D,B,u2_cat_1(A))
& m1_relset_1(D,B,u2_cat_1(A)) )
=> ( v1_funct_1(k9_cat_3(A,B,C,D))
& v1_funct_2(k9_cat_3(A,B,C,D),B,u2_cat_1(A))
& m2_relset_1(k9_cat_3(A,B,C,D),B,u2_cat_1(A)) ) ) ).
fof(dt_k10_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_cat_1(k10_cat_3(A,B,C),A,B,C) ) ).
fof(dt_k11_cat_3,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_cat_1(k11_cat_3(A,B,C),A,B,C) ) ).
%------------------------------------------------------------------------------