SET007 Axioms: SET007+356.ax
%------------------------------------------------------------------------------
% File : SET007+356 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Cartesian 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 172 ( 9 unt; 0 def)
% Number of atoms : 1113 ( 198 equ)
% Maximal formula atoms : 34 ( 6 avg)
% Number of connectives : 1044 ( 103 ~; 6 |; 510 &)
% ( 9 <=>; 416 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-4 aty)
% Number of functors : 66 ( 66 usr; 1 con; 0-10 aty)
% Number of variables : 609 ( 587 !; 22 ?)
% 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_cat_4,axiom,
? [A] :
( l1_cat_4(A)
& v2_cat_4(A) ) ).
fof(rc2_cat_4,axiom,
? [A] :
( l1_cat_4(A)
& v2_cat_1(A)
& v2_cat_4(A) ) ).
fof(fc1_cat_4,axiom,
! [A,B] :
( v2_cat_1(k5_cat_4(A,B))
& v2_cat_4(k5_cat_4(A,B)) ) ).
fof(rc3_cat_4,axiom,
? [A] :
( l1_cat_4(A)
& v2_cat_1(A)
& v2_cat_4(A)
& v3_cat_4(A) ) ).
fof(rc4_cat_4,axiom,
? [A] :
( l2_cat_4(A)
& v5_cat_4(A) ) ).
fof(rc5_cat_4,axiom,
? [A] :
( l2_cat_4(A)
& v2_cat_1(A)
& v5_cat_4(A) ) ).
fof(fc2_cat_4,axiom,
! [A,B] :
( v2_cat_1(k23_cat_4(A,B))
& v5_cat_4(k23_cat_4(A,B)) ) ).
fof(rc6_cat_4,axiom,
? [A] :
( l2_cat_4(A)
& v2_cat_1(A)
& v5_cat_4(A)
& v6_cat_4(A) ) ).
fof(d1_cat_4,axiom,
$true ).
fof(d2_cat_4,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))
=> ( r1_cat_1(A,B,C)
<=> ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,B) != k1_xboole_0
& ? [D] :
( m1_cat_1(D,A,B,C)
& ? [E] :
( m1_cat_1(E,A,C,B)
& k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C)
& k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) ) ) ) ) ) ) ) ).
fof(d3_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v1_cat_4(A)
<=> ! [B] :
( v1_finset_1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_cat_1(A))
& m2_relset_1(C,B,u1_cat_1(A)) )
=> ? [D] :
( m1_subset_1(D,u1_cat_1(A))
& ? [E] :
( m1_cat_3(E,A,D,B)
& k4_cat_3(A,B,E) = C
& r1_cat_3(A,D,B,E) ) ) ) ) ) ) ).
fof(t1_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v1_cat_4(A)
<=> ( ? [B] :
( m1_subset_1(B,u1_cat_1(A))
& v6_cat_1(B,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))
& k2_cat_1(A,E) = D
& k2_cat_1(A,F) = D
& k3_cat_1(A,E) = B
& k3_cat_1(A,F) = C
& r2_cat_3(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(d4_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> k1_cat_4(A) = u1_cat_4(A) ) ).
fof(d5_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k2_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u2_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ).
fof(d6_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k3_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u3_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ).
fof(d7_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k4_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u4_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ).
fof(d8_cat_4,axiom,
! [A,B] : k5_cat_4(A,B) = g1_cat_4(k1_tarski(A),k1_tarski(B),k10_pboole(k1_tarski(B),A),k10_pboole(k1_tarski(B),A),k1_cat_1(B,B,B),k10_pboole(k1_tarski(A),B),k1_algstr_1(A),k9_funct_2(A,A,A),k9_funct_2(A,A,B),k9_funct_2(A,A,B)) ).
fof(t2_cat_4,axiom,
! [A,B] : g1_cat_1(u1_cat_1(k5_cat_4(A,B)),u2_cat_1(k5_cat_4(A,B)),u3_cat_1(k5_cat_4(A,B)),u4_cat_1(k5_cat_4(A,B)),u5_cat_1(k5_cat_4(A,B)),u6_cat_1(k5_cat_4(A,B))) = k8_cat_1(A,B) ).
fof(t3_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
=> C = A ) ).
fof(t4_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
=> C = D ) ) ).
fof(t5_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u2_cat_1(k5_cat_4(A,B)))
=> C = B ) ).
fof(t6_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u2_cat_1(k5_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k5_cat_4(A,B)))
=> C = D ) ) ).
fof(t7_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k5_cat_4(A,B)))
=> r2_hidden(E,k6_cat_1(k5_cat_4(A,B),C,D)) ) ) ) ).
fof(t8_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k5_cat_4(A,B)))
=> m1_cat_1(E,k5_cat_4(A,B),C,D) ) ) ) ).
fof(t9_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k5_cat_4(A,B)))
=> k6_cat_1(k5_cat_4(A,B),C,D) != k1_xboole_0 ) ) ).
fof(t10_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
=> v6_cat_1(C,k5_cat_4(A,B)) ) ).
fof(t11_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k5_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k5_cat_4(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k5_cat_4(A,B)))
=> r2_cat_3(k5_cat_4(A,B),C,D,E) ) ) ) ).
fof(d9_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_4(A) )
=> ( v3_cat_4(A)
<=> ( v6_cat_1(u1_cat_4(A),A)
& ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k3_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u3_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = B
& k3_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u4_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = C
& r2_cat_3(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u2_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u3_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u4_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) ) ) ) ) ) ) ).
fof(t12_cat_4,axiom,
! [A,B] : v3_cat_4(k5_cat_4(A,B)) ).
fof(t13_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> v6_cat_1(k1_cat_4(A),A) ) ).
fof(t14_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_cat_1(C,A,B,k1_cat_4(A))
=> ! [D] :
( m1_cat_1(D,A,B,k1_cat_4(A))
=> C = D ) ) ) ) ).
fof(t15_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k6_cat_1(A,B,k1_cat_4(A)) != k1_xboole_0 ) ) ).
fof(d10_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_cat_1(C,A,B,k1_cat_4(A))
=> C = k6_cat_4(A,B) ) ) ) ).
fof(t16_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k6_cat_4(A,B) = k10_cat_3(A,B,k1_cat_4(A)) ) ) ).
fof(t17_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( k2_cat_1(A,k6_cat_4(A,B)) = B
& k3_cat_1(A,k6_cat_4(A,B)) = k1_cat_4(A) ) ) ) ).
fof(t18_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k6_cat_1(A,B,k1_cat_4(A)) = k6_domain_1(u2_cat_1(A),k6_cat_4(A,B)) ) ) ).
fof(t19_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k2_cat_1(A,k3_cat_4(A,B,C)) = k2_cat_4(A,B,C)
& k3_cat_1(A,k3_cat_4(A,B,C)) = B ) ) ) ) ).
fof(t20_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k2_cat_1(A,k4_cat_4(A,B,C)) = k2_cat_4(A,B,C)
& k3_cat_1(A,k4_cat_4(A,B,C)) = C ) ) ) ) ).
fof(t21_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k6_cat_1(A,k2_cat_4(A,B,C),B) != k1_xboole_0
& k6_cat_1(A,k2_cat_4(A,B,C),C) != k1_xboole_0 ) ) ) ) ).
fof(t22_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> r2_cat_3(A,k2_cat_4(A,B,C),k7_cat_4(A,B,C),k8_cat_4(A,B,C)) ) ) ) ).
fof(t23_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> v1_cat_4(A) ) ).
fof(t24_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,B) != k1_xboole_0
& ~ ( v1_cat_3(k7_cat_4(A,B,C),A)
& v1_cat_3(k8_cat_4(A,B,C),A) ) ) ) ) ) ).
fof(d11_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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_cat_1(E,A,D,B)
=> ! [F] :
( m1_cat_1(F,A,D,C)
=> ~ ( k6_cat_1(A,D,B) != k1_xboole_0
& k6_cat_1(A,D,C) != k1_xboole_0
& ~ ! [G] :
( m1_cat_1(G,A,D,k2_cat_4(A,B,C))
=> ( G = k9_cat_4(A,B,C,D,E,F)
<=> ( k9_cat_1(A,D,k2_cat_4(A,B,C),B,G,k7_cat_4(A,B,C)) = E
& k9_cat_1(A,D,k2_cat_4(A,B,C),C,G,k8_cat_4(A,B,C)) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t25_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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
& k6_cat_1(A,B,k2_cat_4(A,C,D)) = k1_xboole_0 ) ) ) ) ) ).
fof(t26_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k9_cat_4(A,B,C,k2_cat_4(A,B,C),k7_cat_4(A,B,C),k8_cat_4(A,B,C)) = k10_cat_1(A,k2_cat_4(A,B,C)) ) ) ) ).
fof(t27_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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_cat_1(F,A,B,C)
=> ! [G] :
( m1_cat_1(G,A,B,D)
=> ! [H] :
( m1_cat_1(H,A,E,B)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,B,D) != k1_xboole_0
& k6_cat_1(A,E,B) != k1_xboole_0
& k9_cat_4(A,C,D,E,k9_cat_1(A,E,B,C,H,F),k9_cat_1(A,E,B,D,H,G)) != k9_cat_1(A,E,B,k2_cat_4(A,C,D),H,k9_cat_4(A,C,D,B,F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t28_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,B,C)
=> ! [G] :
( m1_cat_1(G,A,B,D)
=> ! [H] :
( m1_cat_1(H,A,B,D)
=> ( k9_cat_4(A,C,D,B,E,G) = k9_cat_4(A,C,D,B,F,H)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,B,D) = k1_xboole_0
| ( E = F
& G = H ) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,B,D)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,B,D) != k1_xboole_0
& ( v3_cat_1(E,A)
| v3_cat_1(F,A) )
& ~ v3_cat_1(k9_cat_4(A,C,D,B,E,F),A) ) ) ) ) ) ) ) ).
fof(t30_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( k6_cat_1(A,B,k2_cat_4(A,B,k1_cat_4(A))) != k1_xboole_0
& k6_cat_1(A,B,k2_cat_4(A,k1_cat_4(A),B)) != k1_xboole_0 ) ) ) ).
fof(d12_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k10_cat_4(A,B) = k8_cat_4(A,k1_cat_4(A),B) ) ) ).
fof(d13_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k11_cat_4(A,B) = k9_cat_4(A,k1_cat_4(A),B,B,k6_cat_4(A,B),k10_cat_1(A,B)) ) ) ).
fof(d14_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k12_cat_4(A,B) = k7_cat_4(A,B,k1_cat_4(A)) ) ) ).
fof(d15_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k13_cat_4(A,B) = k9_cat_4(A,B,k1_cat_4(A),B,k10_cat_1(A,B),k6_cat_4(A,B)) ) ) ).
fof(t31_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( k9_cat_1(A,B,k2_cat_4(A,k1_cat_4(A),B),B,k11_cat_4(A,B),k10_cat_4(A,B)) = k10_cat_1(A,B)
& k9_cat_1(A,k2_cat_4(A,k1_cat_4(A),B),B,k2_cat_4(A,k1_cat_4(A),B),k10_cat_4(A,B),k11_cat_4(A,B)) = k10_cat_1(A,k2_cat_4(A,k1_cat_4(A),B))
& k9_cat_1(A,B,k2_cat_4(A,B,k1_cat_4(A)),B,k13_cat_4(A,B),k12_cat_4(A,B)) = k10_cat_1(A,B)
& k9_cat_1(A,k2_cat_4(A,B,k1_cat_4(A)),B,k2_cat_4(A,B,k1_cat_4(A)),k12_cat_4(A,B),k13_cat_4(A,B)) = k10_cat_1(A,k2_cat_4(A,B,k1_cat_4(A))) ) ) ) ).
fof(t32_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( r1_cat_1(A,B,k2_cat_4(A,B,k1_cat_4(A)))
& r1_cat_1(A,B,k2_cat_4(A,k1_cat_4(A),B)) ) ) ) ).
fof(d16_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k14_cat_4(A,B,C) = k9_cat_4(A,C,B,k2_cat_4(A,B,C),k8_cat_4(A,B,C),k7_cat_4(A,B,C)) ) ) ) ).
fof(t33_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k6_cat_1(A,k2_cat_4(A,B,C),k2_cat_4(A,C,B)) != k1_xboole_0 ) ) ) ).
fof(t34_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k9_cat_1(A,k2_cat_4(A,C,B),k2_cat_4(A,B,C),k2_cat_4(A,C,B),k14_cat_4(A,C,B),k14_cat_4(A,B,C)) = k10_cat_1(A,k2_cat_4(A,C,B)) ) ) ) ).
fof(t35_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> r1_cat_1(A,k2_cat_4(A,B,C),k2_cat_4(A,C,B)) ) ) ) ).
fof(d17_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k15_cat_4(A,B) = k9_cat_4(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) ) ) ).
fof(t36_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k6_cat_1(A,B,k2_cat_4(A,B,B)) != k1_xboole_0 ) ) ).
fof(t37_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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)
=> ( k6_cat_1(A,B,C) != k1_xboole_0
=> k9_cat_4(A,C,C,B,D,D) = k9_cat_1(A,B,C,k2_cat_4(A,C,C),D,k15_cat_4(A,C)) ) ) ) ) ) ).
fof(d18_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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))
=> k16_cat_4(A,B,C,D) = k9_cat_4(A,B,k2_cat_4(A,C,D),k2_cat_4(A,k2_cat_4(A,B,C),D),k9_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,C),B,k7_cat_4(A,k2_cat_4(A,B,C),D),k7_cat_4(A,B,C)),k9_cat_4(A,C,D,k2_cat_4(A,k2_cat_4(A,B,C),D),k9_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,C),C,k7_cat_4(A,k2_cat_4(A,B,C),D),k8_cat_4(A,B,C)),k8_cat_4(A,k2_cat_4(A,B,C),D))) ) ) ) ) ).
fof(d19_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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))
=> k17_cat_4(A,B,C,D) = k9_cat_4(A,k2_cat_4(A,B,C),D,k2_cat_4(A,B,k2_cat_4(A,C,D)),k9_cat_4(A,B,C,k2_cat_4(A,B,k2_cat_4(A,C,D)),k7_cat_4(A,B,k2_cat_4(A,C,D)),k9_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,C,D),C,k8_cat_4(A,B,k2_cat_4(A,C,D)),k7_cat_4(A,C,D))),k9_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,C,D),D,k8_cat_4(A,B,k2_cat_4(A,C,D)),k8_cat_4(A,C,D))) ) ) ) ) ).
fof(t38_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D))) != k1_xboole_0
& k6_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D)) != k1_xboole_0 ) ) ) ) ) ).
fof(t39_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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))
=> ( k9_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D)),k17_cat_4(A,B,C,D),k16_cat_4(A,B,C,D)) = k10_cat_1(A,k2_cat_4(A,B,k2_cat_4(A,C,D)))
& k9_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D),k16_cat_4(A,B,C,D),k17_cat_4(A,B,C,D)) = k10_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D)) ) ) ) ) ) ).
fof(t40_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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))
=> r1_cat_1(A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D))) ) ) ) ) ).
fof(d20_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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_cat_1(F,A,B,C)
=> ! [G] :
( m1_cat_1(G,A,D,E)
=> k18_cat_4(A,B,C,D,E,F,G) = k9_cat_4(A,C,E,k2_cat_4(A,B,D),k9_cat_1(A,k2_cat_4(A,B,D),B,C,k7_cat_4(A,B,D),F),k9_cat_1(A,k2_cat_4(A,B,D),D,E,k8_cat_4(A,B,D),G)) ) ) ) ) ) ) ) ).
fof(t41_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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))
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,E) != k1_xboole_0
& k6_cat_1(A,k2_cat_4(A,B,D),k2_cat_4(A,C,E)) = k1_xboole_0 ) ) ) ) ) ) ).
fof(t42_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k18_cat_4(A,B,B,C,C,k10_cat_1(A,B),k10_cat_1(A,C)) = k10_cat_1(A,k2_cat_4(A,B,C)) ) ) ) ).
fof(t43_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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,u1_cat_1(A))
=> ! [G] :
( m1_cat_1(G,A,B,C)
=> ! [H] :
( m1_cat_1(H,A,D,E)
=> ! [I] :
( m1_cat_1(I,A,F,B)
=> ! [J] :
( m1_cat_1(J,A,F,D)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,E) != k1_xboole_0
& k6_cat_1(A,F,B) != k1_xboole_0
& k6_cat_1(A,F,D) != k1_xboole_0
& k9_cat_1(A,F,k2_cat_4(A,B,D),k2_cat_4(A,C,E),k9_cat_4(A,B,D,F,I,J),k18_cat_4(A,B,C,D,E,G,H)) != k9_cat_4(A,C,E,F,k9_cat_1(A,F,B,C,I,G),k9_cat_1(A,F,D,E,J,H)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,B,D)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,B,D) != k1_xboole_0
& k9_cat_4(A,C,D,B,E,F) != k9_cat_1(A,B,k2_cat_4(A,B,B),k2_cat_4(A,C,D),k15_cat_4(A,B),k18_cat_4(A,B,C,B,D,E,F)) ) ) ) ) ) ) ) ).
fof(t45_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(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,u1_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ! [H] :
( m1_cat_1(H,A,B,C)
=> ! [I] :
( m1_cat_1(I,A,D,E)
=> ! [J] :
( m1_cat_1(J,A,F,B)
=> ! [K] :
( m1_cat_1(K,A,G,D)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,E) != k1_xboole_0
& k6_cat_1(A,F,B) != k1_xboole_0
& k6_cat_1(A,G,D) != k1_xboole_0
& k9_cat_1(A,k2_cat_4(A,F,G),k2_cat_4(A,B,D),k2_cat_4(A,C,E),k18_cat_4(A,F,B,G,D,J,K),k18_cat_4(A,B,C,D,E,H,I)) != k18_cat_4(A,F,C,G,E,k9_cat_1(A,F,B,C,J,H),k9_cat_1(A,G,D,E,K,I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d21_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v4_cat_4(A)
<=> ! [B] :
( v1_finset_1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,u1_cat_1(A))
& m2_relset_1(C,B,u1_cat_1(A)) )
=> ? [D] :
( m1_subset_1(D,u1_cat_1(A))
& ? [E] :
( m2_cat_3(E,A,D,B)
& k3_cat_3(A,B,E) = C
& r3_cat_3(A,D,B,E) ) ) ) ) ) ) ).
fof(t46_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ( v4_cat_4(A)
<=> ( ? [B] :
( m1_subset_1(B,u1_cat_1(A))
& v7_cat_1(B,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))
& k2_cat_1(A,E) = B
& k2_cat_1(A,F) = C
& k3_cat_1(A,E) = D
& k3_cat_1(A,F) = D
& r4_cat_3(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(d22_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> k19_cat_4(A) = u5_cat_4(A) ) ).
fof(d23_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k20_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u6_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ).
fof(d24_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k21_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u7_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ).
fof(d25_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k22_cat_4(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u8_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)) ) ) ) ).
fof(d26_cat_4,axiom,
! [A,B] : k23_cat_4(A,B) = g2_cat_4(k1_tarski(A),k1_tarski(B),k10_pboole(k1_tarski(B),A),k10_pboole(k1_tarski(B),A),k1_cat_1(B,B,B),k10_pboole(k1_tarski(A),B),k1_algstr_1(A),k9_funct_2(A,A,A),k9_funct_2(A,A,B),k9_funct_2(A,A,B)) ).
fof(t47_cat_4,axiom,
! [A,B] : g1_cat_1(u1_cat_1(k23_cat_4(A,B)),u2_cat_1(k23_cat_4(A,B)),u3_cat_1(k23_cat_4(A,B)),u4_cat_1(k23_cat_4(A,B)),u5_cat_1(k23_cat_4(A,B)),u6_cat_1(k23_cat_4(A,B))) = k8_cat_1(A,B) ).
fof(t48_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
=> C = A ) ).
fof(t49_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
=> C = D ) ) ).
fof(t50_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u2_cat_1(k23_cat_4(A,B)))
=> C = B ) ).
fof(t51_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u2_cat_1(k23_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k23_cat_4(A,B)))
=> C = D ) ) ).
fof(t52_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k23_cat_4(A,B)))
=> r2_hidden(E,k6_cat_1(k23_cat_4(A,B),C,D)) ) ) ) ).
fof(t53_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k23_cat_4(A,B)))
=> m1_cat_1(E,k23_cat_4(A,B),C,D) ) ) ) ).
fof(t54_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k23_cat_4(A,B)))
=> k6_cat_1(k23_cat_4(A,B),C,D) != k1_xboole_0 ) ) ).
fof(t55_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
=> v7_cat_1(C,k23_cat_4(A,B)) ) ).
fof(t56_cat_4,axiom,
! [A,B,C] :
( m1_subset_1(C,u1_cat_1(k23_cat_4(A,B)))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k23_cat_4(A,B)))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(k23_cat_4(A,B)))
=> r4_cat_3(k23_cat_4(A,B),C,D,E) ) ) ) ).
fof(d27_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& l2_cat_4(A) )
=> ( v6_cat_4(A)
<=> ( v7_cat_1(u5_cat_4(A),A)
& ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k2_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u7_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = B
& k2_cat_1(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u8_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) = C
& r4_cat_3(A,k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A),u6_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u7_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A),u8_cat_4(A),k1_domain_1(u1_cat_1(A),u1_cat_1(A),B,C))) ) ) ) ) ) ) ).
fof(t57_cat_4,axiom,
! [A,B] : v6_cat_4(k23_cat_4(A,B)) ).
fof(t58_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> v7_cat_1(k19_cat_4(A),A) ) ).
fof(t59_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_cat_1(C,A,k19_cat_4(A),B)
=> ! [D] :
( m1_cat_1(D,A,k19_cat_4(A),B)
=> C = D ) ) ) ) ).
fof(d28_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_cat_1(C,A,k19_cat_4(A),B)
=> C = k24_cat_4(A,B) ) ) ) ).
fof(t60_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k6_cat_1(A,k19_cat_4(A),B) != k1_xboole_0 ) ) ).
fof(t61_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k24_cat_4(A,B) = k11_cat_3(A,k19_cat_4(A),B) ) ) ).
fof(t62_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( k2_cat_1(A,k24_cat_4(A,B)) = k19_cat_4(A)
& k3_cat_1(A,k24_cat_4(A,B)) = B ) ) ) ).
fof(t63_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k6_cat_1(A,k19_cat_4(A),B) = k6_domain_1(u2_cat_1(A),k24_cat_4(A,B)) ) ) ).
fof(t64_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k2_cat_1(A,k21_cat_4(A,B,C)) = B
& k3_cat_1(A,k21_cat_4(A,B,C)) = k20_cat_4(A,B,C) ) ) ) ) ).
fof(t65_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k2_cat_1(A,k22_cat_4(A,B,C)) = C
& k3_cat_1(A,k22_cat_4(A,B,C)) = k20_cat_4(A,B,C) ) ) ) ) ).
fof(t66_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ( k6_cat_1(A,B,k20_cat_4(A,B,C)) != k1_xboole_0
& k6_cat_1(A,C,k20_cat_4(A,B,C)) != k1_xboole_0 ) ) ) ) ).
fof(t67_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> r4_cat_3(A,k20_cat_4(A,B,C),k21_cat_4(A,B,C),k22_cat_4(A,B,C)) ) ) ) ).
fof(t68_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> v4_cat_4(A) ) ).
fof(t69_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,C,B) != k1_xboole_0
& ~ ( v2_cat_3(k21_cat_4(A,B,C),A)
& v2_cat_3(k22_cat_4(A,B,C),A) ) ) ) ) ) ).
fof(d29_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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_cat_1(E,A,B,D)
=> ! [F] :
( m1_cat_1(F,A,C,D)
=> ~ ( k6_cat_1(A,B,D) != k1_xboole_0
& k6_cat_1(A,C,D) != k1_xboole_0
& ~ ! [G] :
( m1_cat_1(G,A,k20_cat_4(A,B,C),D)
=> ( G = k27_cat_4(A,B,C,D,E,F)
<=> ( k9_cat_1(A,B,k20_cat_4(A,B,C),D,k25_cat_4(A,B,C),G) = E
& k9_cat_1(A,C,k20_cat_4(A,B,C),D,k26_cat_4(A,B,C),G) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t70_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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
& k6_cat_1(A,k20_cat_4(A,B,D),C) = k1_xboole_0 ) ) ) ) ) ).
fof(t71_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k27_cat_4(A,B,C,k20_cat_4(A,B,C),k25_cat_4(A,B,C),k26_cat_4(A,B,C)) = k10_cat_1(A,k20_cat_4(A,B,C)) ) ) ) ).
fof(t72_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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_cat_1(F,A,B,C)
=> ! [G] :
( m1_cat_1(G,A,D,C)
=> ! [H] :
( m1_cat_1(H,A,C,E)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,C) != k1_xboole_0
& k6_cat_1(A,C,E) != k1_xboole_0
& k27_cat_4(A,B,D,E,k9_cat_1(A,B,C,E,F,H),k9_cat_1(A,D,C,E,G,H)) != k9_cat_1(A,k20_cat_4(A,B,D),C,E,k27_cat_4(A,B,D,C,F,G),H) ) ) ) ) ) ) ) ) ) ).
fof(t73_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,B,C)
=> ! [G] :
( m1_cat_1(G,A,D,C)
=> ! [H] :
( m1_cat_1(H,A,D,C)
=> ( k27_cat_4(A,B,D,C,E,G) = k27_cat_4(A,B,D,C,F,H)
=> ( k6_cat_1(A,B,C) = k1_xboole_0
| k6_cat_1(A,D,C) = k1_xboole_0
| ( E = F
& G = H ) ) ) ) ) ) ) ) ) ) ) ).
fof(t74_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,D,C)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,C) != k1_xboole_0
& ( v4_cat_1(E,A)
| v4_cat_1(F,A) )
& ~ v4_cat_1(k27_cat_4(A,B,D,C,E,F),A) ) ) ) ) ) ) ) ).
fof(t75_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ( r1_cat_1(A,B,k20_cat_4(A,B,k19_cat_4(A)))
& r1_cat_1(A,B,k20_cat_4(A,k19_cat_4(A),B)) ) ) ) ).
fof(t76_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> r1_cat_1(A,k20_cat_4(A,B,C),k20_cat_4(A,C,B)) ) ) ) ).
fof(t77_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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))
=> r1_cat_1(A,k20_cat_4(A,k20_cat_4(A,B,C),D),k20_cat_4(A,B,k20_cat_4(A,C,D))) ) ) ) ) ).
fof(d30_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> k28_cat_4(A,B) = k27_cat_4(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) ) ) ).
fof(d31_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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_cat_1(F,A,B,D)
=> ! [G] :
( m1_cat_1(G,A,C,E)
=> k29_cat_4(A,B,C,D,E,F,G) = k27_cat_4(A,B,C,k20_cat_4(A,D,E),k9_cat_1(A,B,D,k20_cat_4(A,D,E),F,k25_cat_4(A,D,E)),k9_cat_1(A,C,E,k20_cat_4(A,D,E),G,k26_cat_4(A,D,E))) ) ) ) ) ) ) ) ).
fof(t78_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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))
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,E) != k1_xboole_0
& k6_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,E)) = k1_xboole_0 ) ) ) ) ) ) ).
fof(t79_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k29_cat_4(A,B,C,B,C,k10_cat_1(A,B),k10_cat_1(A,C)) = k10_cat_1(A,k20_cat_4(A,B,C)) ) ) ) ).
fof(t80_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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,u1_cat_1(A))
=> ! [G] :
( m1_cat_1(G,A,B,C)
=> ! [H] :
( m1_cat_1(H,A,D,E)
=> ! [I] :
( m1_cat_1(I,A,C,F)
=> ! [J] :
( m1_cat_1(J,A,E,F)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,E) != k1_xboole_0
& k6_cat_1(A,C,F) != k1_xboole_0
& k6_cat_1(A,E,F) != k1_xboole_0
& k9_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,E),F,k29_cat_4(A,B,D,C,E,G,H),k27_cat_4(A,C,E,F,I,J)) != k27_cat_4(A,B,D,F,k9_cat_1(A,B,C,F,G,I),k9_cat_1(A,D,E,F,H,J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t81_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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_cat_1(E,A,B,C)
=> ! [F] :
( m1_cat_1(F,A,D,C)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,C) != k1_xboole_0
& k9_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,C),C,k29_cat_4(A,B,D,C,C,E,F),k28_cat_4(A,C)) != k27_cat_4(A,B,D,C,E,F) ) ) ) ) ) ) ) ).
fof(t82_cat_4,axiom,
! [A] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(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,u1_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ! [H] :
( m1_cat_1(H,A,B,C)
=> ! [I] :
( m1_cat_1(I,A,D,E)
=> ! [J] :
( m1_cat_1(J,A,C,F)
=> ! [K] :
( m1_cat_1(K,A,E,G)
=> ~ ( k6_cat_1(A,B,C) != k1_xboole_0
& k6_cat_1(A,D,E) != k1_xboole_0
& k6_cat_1(A,C,F) != k1_xboole_0
& k6_cat_1(A,E,G) != k1_xboole_0
& k9_cat_1(A,k20_cat_4(A,B,D),k20_cat_4(A,C,E),k20_cat_4(A,F,G),k29_cat_4(A,B,D,C,E,H,I),k29_cat_4(A,C,E,F,G,J,K)) != k29_cat_4(A,B,D,F,G,k9_cat_1(A,B,C,F,H,J),k9_cat_1(A,D,E,G,I,K)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_l1_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> l1_cat_1(A) ) ).
fof(existence_l1_cat_4,axiom,
? [A] : l1_cat_4(A) ).
fof(dt_l2_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> l1_cat_1(A) ) ).
fof(existence_l2_cat_4,axiom,
? [A] : l2_cat_4(A) ).
fof(abstractness_v2_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> ( v2_cat_4(A)
=> A = g1_cat_4(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A),u1_cat_4(A),u2_cat_4(A),u3_cat_4(A),u4_cat_4(A)) ) ) ).
fof(abstractness_v5_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> ( v5_cat_4(A)
=> A = g2_cat_4(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A),u5_cat_4(A),u6_cat_4(A),u7_cat_4(A),u8_cat_4(A)) ) ) ).
fof(dt_k1_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> m1_subset_1(k1_cat_4(A),u1_cat_1(A)) ) ).
fof(dt_k2_cat_4,axiom,
! [A,B,C] :
( ( l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_subset_1(k2_cat_4(A,B,C),u1_cat_1(A)) ) ).
fof(dt_k3_cat_4,axiom,
! [A,B,C] :
( ( l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_subset_1(k3_cat_4(A,B,C),u2_cat_1(A)) ) ).
fof(dt_k4_cat_4,axiom,
! [A,B,C] :
( ( l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_subset_1(k4_cat_4(A,B,C),u2_cat_1(A)) ) ).
fof(dt_k5_cat_4,axiom,
! [A,B] :
( v2_cat_4(k5_cat_4(A,B))
& l1_cat_4(k5_cat_4(A,B)) ) ).
fof(dt_k6_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k6_cat_4(A,B),A,B,k1_cat_4(A)) ) ).
fof(dt_k7_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_cat_1(k7_cat_4(A,B,C),A,k2_cat_4(A,B,C),B) ) ).
fof(redefinition_k7_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> k7_cat_4(A,B,C) = k3_cat_4(A,B,C) ) ).
fof(dt_k8_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_cat_1(k8_cat_4(A,B,C),A,k2_cat_4(A,B,C),C) ) ).
fof(redefinition_k8_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> k8_cat_4(A,B,C) = k4_cat_4(A,B,C) ) ).
fof(dt_k9_cat_4,axiom,
! [A,B,C,D,E,F] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_subset_1(D,u1_cat_1(A))
& m1_cat_1(E,A,D,B)
& m1_cat_1(F,A,D,C) )
=> m1_cat_1(k9_cat_4(A,B,C,D,E,F),A,D,k2_cat_4(A,B,C)) ) ).
fof(dt_k10_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k10_cat_4(A,B),A,k2_cat_4(A,k1_cat_4(A),B),B) ) ).
fof(dt_k11_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k11_cat_4(A,B),A,B,k2_cat_4(A,k1_cat_4(A),B)) ) ).
fof(dt_k12_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k12_cat_4(A,B),A,k2_cat_4(A,B,k1_cat_4(A)),B) ) ).
fof(dt_k13_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k13_cat_4(A,B),A,B,k2_cat_4(A,B,k1_cat_4(A))) ) ).
fof(dt_k14_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_cat_1(k14_cat_4(A,B,C),A,k2_cat_4(A,B,C),k2_cat_4(A,C,B)) ) ).
fof(dt_k15_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k15_cat_4(A,B),A,B,k2_cat_4(A,B,B)) ) ).
fof(dt_k16_cat_4,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_subset_1(D,u1_cat_1(A)) )
=> m1_cat_1(k16_cat_4(A,B,C,D),A,k2_cat_4(A,k2_cat_4(A,B,C),D),k2_cat_4(A,B,k2_cat_4(A,C,D))) ) ).
fof(dt_k17_cat_4,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_subset_1(D,u1_cat_1(A)) )
=> m1_cat_1(k17_cat_4(A,B,C,D),A,k2_cat_4(A,B,k2_cat_4(A,C,D)),k2_cat_4(A,k2_cat_4(A,B,C),D)) ) ).
fof(dt_k18_cat_4,axiom,
! [A,B,C,D,E,F,G] :
( ( v2_cat_1(A)
& v3_cat_4(A)
& l1_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_subset_1(D,u1_cat_1(A))
& m1_subset_1(E,u1_cat_1(A))
& m1_cat_1(F,A,B,C)
& m1_cat_1(G,A,D,E) )
=> m1_cat_1(k18_cat_4(A,B,C,D,E,F,G),A,k2_cat_4(A,B,D),k2_cat_4(A,C,E)) ) ).
fof(dt_k19_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> m1_subset_1(k19_cat_4(A),u1_cat_1(A)) ) ).
fof(dt_k20_cat_4,axiom,
! [A,B,C] :
( ( l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_subset_1(k20_cat_4(A,B,C),u1_cat_1(A)) ) ).
fof(dt_k21_cat_4,axiom,
! [A,B,C] :
( ( l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_subset_1(k21_cat_4(A,B,C),u2_cat_1(A)) ) ).
fof(dt_k22_cat_4,axiom,
! [A,B,C] :
( ( l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_subset_1(k22_cat_4(A,B,C),u2_cat_1(A)) ) ).
fof(dt_k23_cat_4,axiom,
! [A,B] :
( v5_cat_4(k23_cat_4(A,B))
& l2_cat_4(k23_cat_4(A,B)) ) ).
fof(dt_k24_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k24_cat_4(A,B),A,k19_cat_4(A),B) ) ).
fof(dt_k25_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_cat_1(k25_cat_4(A,B,C),A,B,k20_cat_4(A,B,C)) ) ).
fof(redefinition_k25_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> k25_cat_4(A,B,C) = k21_cat_4(A,B,C) ) ).
fof(dt_k26_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> m1_cat_1(k26_cat_4(A,B,C),A,C,k20_cat_4(A,B,C)) ) ).
fof(redefinition_k26_cat_4,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A)) )
=> k26_cat_4(A,B,C) = k22_cat_4(A,B,C) ) ).
fof(dt_k27_cat_4,axiom,
! [A,B,C,D,E,F] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_subset_1(D,u1_cat_1(A))
& m1_cat_1(E,A,B,D)
& m1_cat_1(F,A,C,D) )
=> m1_cat_1(k27_cat_4(A,B,C,D,E,F),A,k20_cat_4(A,B,C),D) ) ).
fof(dt_k28_cat_4,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A)) )
=> m1_cat_1(k28_cat_4(A,B),A,k20_cat_4(A,B,B),B) ) ).
fof(dt_k29_cat_4,axiom,
! [A,B,C,D,E,F,G] :
( ( v2_cat_1(A)
& v6_cat_4(A)
& l2_cat_4(A)
& m1_subset_1(B,u1_cat_1(A))
& m1_subset_1(C,u1_cat_1(A))
& m1_subset_1(D,u1_cat_1(A))
& m1_subset_1(E,u1_cat_1(A))
& m1_cat_1(F,A,B,D)
& m1_cat_1(G,A,C,E) )
=> m1_cat_1(k29_cat_4(A,B,C,D,E,F,G),A,k20_cat_4(A,B,C),k20_cat_4(A,D,E)) ) ).
fof(dt_u1_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> m1_subset_1(u1_cat_4(A),u1_cat_1(A)) ) ).
fof(dt_u2_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> ( v1_funct_1(u2_cat_4(A))
& v1_funct_2(u2_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A))
& m2_relset_1(u2_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A)) ) ) ).
fof(dt_u3_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> ( v1_funct_1(u3_cat_4(A))
& v1_funct_2(u3_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
& m2_relset_1(u3_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ).
fof(dt_u4_cat_4,axiom,
! [A] :
( l1_cat_4(A)
=> ( v1_funct_1(u4_cat_4(A))
& v1_funct_2(u4_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
& m2_relset_1(u4_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ).
fof(dt_u5_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> m1_subset_1(u5_cat_4(A),u1_cat_1(A)) ) ).
fof(dt_u6_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> ( v1_funct_1(u6_cat_4(A))
& v1_funct_2(u6_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A))
& m2_relset_1(u6_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u1_cat_1(A)) ) ) ).
fof(dt_u7_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> ( v1_funct_1(u7_cat_4(A))
& v1_funct_2(u7_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
& m2_relset_1(u7_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ).
fof(dt_u8_cat_4,axiom,
! [A] :
( l2_cat_4(A)
=> ( v1_funct_1(u8_cat_4(A))
& v1_funct_2(u8_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A))
& m2_relset_1(u8_cat_4(A),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(A)),u2_cat_1(A)) ) ) ).
fof(dt_g1_cat_4,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,A)
& m1_relset_1(C,B,A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(F)
& v1_funct_2(F,A,B)
& m1_relset_1(F,A,B)
& m1_subset_1(G,A)
& v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,A),A)
& m1_relset_1(H,k2_zfmisc_1(A,A),A)
& v1_funct_1(I)
& v1_funct_2(I,k2_zfmisc_1(A,A),B)
& m1_relset_1(I,k2_zfmisc_1(A,A),B)
& v1_funct_1(J)
& v1_funct_2(J,k2_zfmisc_1(A,A),B)
& m1_relset_1(J,k2_zfmisc_1(A,A),B) )
=> ( v2_cat_4(g1_cat_4(A,B,C,D,E,F,G,H,I,J))
& l1_cat_4(g1_cat_4(A,B,C,D,E,F,G,H,I,J)) ) ) ).
fof(free_g1_cat_4,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,A)
& m1_relset_1(C,B,A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(F)
& v1_funct_2(F,A,B)
& m1_relset_1(F,A,B)
& m1_subset_1(G,A)
& v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,A),A)
& m1_relset_1(H,k2_zfmisc_1(A,A),A)
& v1_funct_1(I)
& v1_funct_2(I,k2_zfmisc_1(A,A),B)
& m1_relset_1(I,k2_zfmisc_1(A,A),B)
& v1_funct_1(J)
& v1_funct_2(J,k2_zfmisc_1(A,A),B)
& m1_relset_1(J,k2_zfmisc_1(A,A),B) )
=> ! [K,L,M,N,O,P,Q,R,S,T] :
( g1_cat_4(A,B,C,D,E,F,G,H,I,J) = g1_cat_4(K,L,M,N,O,P,Q,R,S,T)
=> ( A = K
& B = L
& C = M
& D = N
& E = O
& F = P
& G = Q
& H = R
& I = S
& J = T ) ) ) ).
fof(dt_g2_cat_4,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,A)
& m1_relset_1(C,B,A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(F)
& v1_funct_2(F,A,B)
& m1_relset_1(F,A,B)
& m1_subset_1(G,A)
& v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,A),A)
& m1_relset_1(H,k2_zfmisc_1(A,A),A)
& v1_funct_1(I)
& v1_funct_2(I,k2_zfmisc_1(A,A),B)
& m1_relset_1(I,k2_zfmisc_1(A,A),B)
& v1_funct_1(J)
& v1_funct_2(J,k2_zfmisc_1(A,A),B)
& m1_relset_1(J,k2_zfmisc_1(A,A),B) )
=> ( v5_cat_4(g2_cat_4(A,B,C,D,E,F,G,H,I,J))
& l2_cat_4(g2_cat_4(A,B,C,D,E,F,G,H,I,J)) ) ) ).
fof(free_g2_cat_4,axiom,
! [A,B,C,D,E,F,G,H,I,J] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,B,A)
& m1_relset_1(C,B,A)
& v1_funct_1(D)
& v1_funct_2(D,B,A)
& m1_relset_1(D,B,A)
& v1_funct_1(E)
& m1_relset_1(E,k2_zfmisc_1(B,B),B)
& v1_funct_1(F)
& v1_funct_2(F,A,B)
& m1_relset_1(F,A,B)
& m1_subset_1(G,A)
& v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(A,A),A)
& m1_relset_1(H,k2_zfmisc_1(A,A),A)
& v1_funct_1(I)
& v1_funct_2(I,k2_zfmisc_1(A,A),B)
& m1_relset_1(I,k2_zfmisc_1(A,A),B)
& v1_funct_1(J)
& v1_funct_2(J,k2_zfmisc_1(A,A),B)
& m1_relset_1(J,k2_zfmisc_1(A,A),B) )
=> ! [K,L,M,N,O,P,Q,R,S,T] :
( g2_cat_4(A,B,C,D,E,F,G,H,I,J) = g2_cat_4(K,L,M,N,O,P,Q,R,S,T)
=> ( A = K
& B = L
& C = M
& D = N
& E = O
& F = P
& G = Q
& H = R
& I = S
& J = T ) ) ) ).
%------------------------------------------------------------------------------