SET007 Axioms: SET007+322.ax
%------------------------------------------------------------------------------
% File : SET007+322 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Isomorphisms of 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 : isocat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 85 ( 6 unt; 0 def)
% Number of atoms : 787 ( 25 equ)
% Maximal formula atoms : 21 ( 9 avg)
% Number of connectives : 703 ( 1 ~; 0 |; 286 &)
% ( 5 <=>; 411 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 12 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-6 aty)
% Number of functors : 34 ( 34 usr; 1 con; 0-9 aty)
% Number of variables : 416 ( 406 !; 10 ?)
% 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(t1_isocat_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( v2_funct_1(A)
& v2_funct_1(B) )
=> v2_funct_1(k15_funct_3(A,B)) ) ) ) ).
fof(t2_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( k2_relat_1(k16_cat_2(A,B)) = u2_cat_1(A)
& k2_relat_1(k17_cat_2(B,A)) = u2_cat_1(A) ) ) ) ).
fof(t3_isocat_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,B,A)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(B))
=> ( v5_cat_1(D,B)
=> v5_cat_1(k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,D),A) ) ) ) ) ) ).
fof(t4_isocat_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] :
( m2_cat_1(D,B,A)
=> ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k14_cat_1(A,A,B,k15_cat_1(A),C),C)
& r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),k14_cat_1(B,A,A,D,k15_cat_1(A)),D) ) ) ) ) ) ).
fof(t5_isocat_1,axiom,
$true ).
fof(t6_isocat_1,axiom,
$true ).
fof(t7_isocat_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] :
( m2_cat_1(D,A,B)
=> ( r1_nattra_1(A,B,C,D)
=> ! [E] :
( m1_nattra_1(E,A,B,C,D)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> r2_hidden(k5_nattra_1(A,B,C,D,E,F),k6_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F))) ) ) ) ) ) ) ) ).
fof(t8_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(B,C,F,G) )
=> r1_nattra_1(A,C,k14_cat_1(A,B,C,D,F),k14_cat_1(A,B,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(t9_isocat_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] :
( m2_cat_1(D,A,B)
=> ( r1_nattra_1(A,B,C,D)
=> ! [E] :
( m1_nattra_1(E,A,B,C,D)
=> ( v1_nattra_1(E,A,B,C,D)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> r1_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)) ) ) ) ) ) ) ) ) ).
fof(d1_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u2_cat_1(A),u2_cat_1(B))
& m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) )
=> ( m2_cat_1(C,A,B)
<=> ( ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))
& k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) ) )
& ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ( k2_cat_1(A,E) = k3_cat_1(A,D)
=> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) ) ) ) ) ) ) ) ) ).
fof(t10_isocat_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,B,A)
=> ( v8_cat_1(C,B,A)
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u2_cat_1(B))
& k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,E) = D ) ) ) ) ) ) ).
fof(t11_isocat_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,B,A)
=> ( v8_cat_1(C,B,A)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(B))
& k13_cat_1(B,A,C,E) = D ) ) ) ) ) ) ).
fof(t12_isocat_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)
=> ( v2_funct_1(C)
=> v2_funct_1(k12_cat_1(A,B,C)) ) ) ) ) ).
fof(d2_isocat_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)
=> ( v8_cat_1(C,A,B)
=> k3_isocat_1(A,B,C) = k2_funct_1(C) ) ) ) ) ).
fof(d3_isocat_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)
=> ( v8_cat_1(C,A,B)
<=> ( v2_funct_1(C)
& k2_relat_1(C) = u2_cat_1(B) ) ) ) ) ) ).
fof(t13_isocat_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)
=> ( v8_cat_1(C,A,B)
=> v8_cat_1(k3_isocat_1(A,B,C),B,A) ) ) ) ) ).
fof(t14_isocat_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)
=> ( v8_cat_1(C,A,B)
=> k2_funct_1(k12_cat_1(A,B,C)) = k12_cat_1(B,A,k3_isocat_1(A,B,C)) ) ) ) ) ).
fof(t15_isocat_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)
=> ( v8_cat_1(C,A,B)
=> r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k3_isocat_1(B,A,k3_isocat_1(A,B,C)),C) ) ) ) ) ).
fof(t16_isocat_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,B,A)
=> ( v8_cat_1(C,B,A)
=> ( r4_nattra_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),k2_isocat_1(A,B,A,k3_isocat_1(B,A,C),C),k1_isocat_1(A))
& r4_nattra_1(u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),k2_isocat_1(B,A,B,C,k3_isocat_1(B,A,C)),k1_isocat_1(B)) ) ) ) ) ) ).
fof(t17_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ( ( v8_cat_1(D,A,B)
& v8_cat_1(E,B,C) )
=> v8_cat_1(k2_isocat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) ).
fof(d4_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( r1_isocat_1(A,B)
<=> ? [C] :
( m2_cat_1(C,A,B)
& v8_cat_1(C,A,B) ) ) ) ) ).
fof(t18_isocat_1,axiom,
$true ).
fof(t19_isocat_1,axiom,
$true ).
fof(t20_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ( ( r1_isocat_1(A,B)
& r1_isocat_1(B,C) )
=> r1_isocat_1(A,C) ) ) ) ) ).
fof(t21_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] : r1_isocat_1(k11_cat_2(k8_cat_1(B,C),A),A) ) ).
fof(t22_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> r1_isocat_1(k11_cat_2(A,B),k11_cat_2(B,A)) ) ) ).
fof(t23_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> r1_isocat_1(k11_cat_2(k11_cat_2(A,B),C),k11_cat_2(A,k11_cat_2(B,C))) ) ) ) ).
fof(t24_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ( ( r1_isocat_1(A,B)
& r1_isocat_1(C,D) )
=> r1_isocat_1(k11_cat_2(A,C),k11_cat_2(B,D)) ) ) ) ) ) ).
fof(d5_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ( r1_nattra_1(A,B,D,E)
=> ! [F] :
( m1_nattra_1(F,A,B,D,E)
=> ! [G] :
( m2_cat_1(G,B,C)
=> k4_isocat_1(A,B,C,D,E,F,G) = k7_funct_2(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),F,G) ) ) ) ) ) ) ) ) ).
fof(d6_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,B,C)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ( r1_nattra_1(B,C,D,E)
=> ! [F] :
( m2_cat_1(F,A,B)
=> ! [G] :
( m1_nattra_1(G,B,C,D,E)
=> k5_isocat_1(A,B,C,D,E,F,G) = k7_funct_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k12_cat_1(A,B,F),G) ) ) ) ) ) ) ) ) ).
fof(t25_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ( r1_nattra_1(A,B,D,E)
=> ! [F] :
( m2_cat_1(F,C,A)
=> ! [G] :
( m1_nattra_1(G,A,B,D,E)
=> ! [H] :
( m1_subset_1(H,u1_cat_1(C))
=> k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k5_isocat_1(C,A,B,D,E,F,G),H) = k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t26_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ( r1_nattra_1(A,B,D,E)
=> ! [F] :
( m1_nattra_1(F,A,B,D,E)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m1_subset_1(H,u1_cat_1(A))
=> k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k4_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t27_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ( ( r2_nattra_1(A,B,D,E)
& r2_nattra_1(B,C,F,G) )
=> r2_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(d7_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ( r2_nattra_1(A,B,D,E)
=> ! [F] :
( m2_nattra_1(F,A,B,D,E)
=> ! [G] :
( m2_cat_1(G,B,C)
=> k6_isocat_1(A,B,C,D,E,F,G) = k4_isocat_1(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t28_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ( r2_nattra_1(A,B,D,E)
=> ! [F] :
( m2_nattra_1(F,A,B,D,E)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m1_subset_1(H,u1_cat_1(A))
=> k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(d8_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,B,C)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ( r2_nattra_1(B,C,D,E)
=> ! [F] :
( m2_cat_1(F,A,B)
=> ! [G] :
( m2_nattra_1(G,B,C,D,E)
=> k7_isocat_1(A,B,C,D,E,F,G) = k5_isocat_1(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t29_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ( r2_nattra_1(A,B,D,E)
=> ! [F] :
( m2_cat_1(F,C,A)
=> ! [G] :
( m2_nattra_1(G,A,B,D,E)
=> ! [H] :
( m1_subset_1(H,u1_cat_1(C))
=> k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k7_isocat_1(C,A,B,D,E,F,G),H) = k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t30_isocat_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,B,A)
=> ! [D] :
( m2_cat_1(D,B,A)
=> ( r2_nattra_1(B,A,C,D)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(B))
=> k6_cat_1(A,k13_cat_1(B,A,C,E),k13_cat_1(B,A,D,E)) != k1_xboole_0 ) ) ) ) ) ) ).
fof(t31_isocat_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,B,A)
=> ! [D] :
( m2_cat_1(D,B,A)
=> ( r2_nattra_1(B,A,C,D)
=> ! [E] :
( m2_nattra_1(E,B,A,C,D)
=> ! [F] :
( m2_nattra_1(F,B,A,C,D)
=> ( ! [G] :
( m1_subset_1(G,u1_cat_1(B))
=> k5_nattra_1(B,A,C,D,E,G) = k5_nattra_1(B,A,C,D,F,G) )
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),E,F) ) ) ) ) ) ) ) ) ).
fof(t32_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,B,C)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_cat_1(G,C,A)
=> ! [H] :
( m2_nattra_1(H,B,C,D,E)
=> ! [I] :
( m2_nattra_1(I,B,C,E,F)
=> ( ( r2_nattra_1(B,C,D,E)
& r2_nattra_1(B,C,E,F) )
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,F,k8_nattra_1(B,C,D,E,F,H,I),G),k8_nattra_1(B,A,k2_isocat_1(B,C,A,D,G),k2_isocat_1(B,C,A,E,G),k2_isocat_1(B,C,A,F,G),k6_isocat_1(B,C,A,D,E,H,G),k6_isocat_1(B,C,A,E,F,I,G))) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m2_nattra_1(H,B,C,E,F)
=> ! [I] :
( m2_nattra_1(I,B,C,F,G)
=> ( ( r2_nattra_1(B,C,E,F)
& r2_nattra_1(B,C,F,G) )
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,G,D,k8_nattra_1(B,C,E,F,G,H,I)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,E),k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k7_isocat_1(A,B,C,E,F,D,H),k7_isocat_1(A,B,C,F,G,D,I))) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_cat_1(G,C,D)
=> ! [H] :
( m2_cat_1(H,C,D)
=> ! [I] :
( m2_nattra_1(I,C,D,G,H)
=> ( r2_nattra_1(C,D,G,H)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k7_isocat_1(A,B,D,k2_isocat_1(B,C,D,F,G),k2_isocat_1(B,C,D,F,H),E,k7_isocat_1(B,C,D,G,H,F,I)),k7_isocat_1(A,C,D,G,H,k2_isocat_1(A,B,C,E,F),I)) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,A,C)
=> ! [F] :
( m2_cat_1(F,C,D)
=> ! [G] :
( m2_cat_1(G,C,D)
=> ! [H] :
( m2_cat_1(H,D,B)
=> ! [I] :
( m2_nattra_1(I,C,D,F,G)
=> ( r2_nattra_1(C,D,F,G)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_isocat_1(A,C,B,k2_isocat_1(C,D,B,F,H),k2_isocat_1(C,D,B,G,H),E,k6_isocat_1(C,D,B,F,G,I,H)),k6_isocat_1(A,D,B,k2_isocat_1(A,C,D,E,F),k2_isocat_1(A,C,D,E,G),k7_isocat_1(A,C,D,F,G,E,I),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,C,D)
=> ! [F] :
( m2_cat_1(F,C,D)
=> ! [G] :
( m2_cat_1(G,D,A)
=> ! [H] :
( m2_cat_1(H,A,B)
=> ! [I] :
( m2_nattra_1(I,C,D,E,F)
=> ( r2_nattra_1(C,D,E,F)
=> r4_nattra_1(u1_cat_1(C),u2_cat_1(B),u1_cat_1(C),u2_cat_1(B),k6_isocat_1(C,D,B,E,F,I,k2_isocat_1(D,A,B,G,H)),k6_isocat_1(C,A,B,k2_isocat_1(C,D,A,E,G),k2_isocat_1(C,D,A,F,G),k6_isocat_1(C,D,A,E,F,I,G),H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,E,D,k7_nattra_1(B,C,E)),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))) ) ) ) ) ) ).
fof(t38_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k6_isocat_1(A,B,C,D,D,k7_nattra_1(A,B,D),E),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))) ) ) ) ) ) ).
fof(t39_isocat_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,B,A)
=> ! [D] :
( m2_cat_1(D,B,A)
=> ! [E] :
( m2_nattra_1(E,B,A,C,D)
=> ( r2_nattra_1(B,A,C,D)
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k7_isocat_1(B,B,A,C,D,k1_isocat_1(B),E),E) ) ) ) ) ) ) ).
fof(t40_isocat_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] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_nattra_1(E,A,B,C,D)
=> ( r2_nattra_1(A,B,C,D)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k6_isocat_1(A,B,B,C,D,E,k1_isocat_1(B)),E) ) ) ) ) ) ) ).
fof(d9_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m2_nattra_1(H,A,B,D,E)
=> ! [I] :
( m2_nattra_1(I,B,C,F,G)
=> k8_isocat_1(A,B,C,D,E,F,G,H,I) = k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,F),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,H,F),k7_isocat_1(A,B,C,F,G,E,I)) ) ) ) ) ) ) ) ) ) ).
fof(t41_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m2_nattra_1(H,A,B,D,E)
=> ! [I] :
( m2_nattra_1(I,B,C,F,G)
=> ( ( r2_nattra_1(A,B,D,E)
& r2_nattra_1(B,C,F,G) )
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,E,F,G,H,I),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k7_isocat_1(A,B,C,F,G,D,I),k6_isocat_1(A,B,C,D,E,H,G))) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_isocat_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] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_nattra_1(E,A,B,C,D)
=> ( r2_nattra_1(A,B,C,D)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k8_isocat_1(A,B,B,C,D,k1_isocat_1(B),k1_isocat_1(B),E,k7_nattra_1(B,B,k1_isocat_1(B))),E) ) ) ) ) ) ) ).
fof(t43_isocat_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,B,A)
=> ! [D] :
( m2_cat_1(D,B,A)
=> ! [E] :
( m2_nattra_1(E,B,A,C,D)
=> ( r2_nattra_1(B,A,C,D)
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k8_isocat_1(B,B,A,k1_isocat_1(B),k1_isocat_1(B),C,D,k7_nattra_1(B,B,k1_isocat_1(B)),E),E) ) ) ) ) ) ) ).
fof(t44_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,B)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m2_cat_1(H,B,C)
=> ! [I] :
( m2_cat_1(I,C,D)
=> ! [J] :
( m2_cat_1(J,C,D)
=> ! [K] :
( m2_nattra_1(K,A,B,E,F)
=> ! [L] :
( m2_nattra_1(L,B,C,G,H)
=> ! [M] :
( m2_nattra_1(M,C,D,I,J)
=> ( ( r2_nattra_1(A,B,E,F)
& r2_nattra_1(B,C,G,H)
& r2_nattra_1(C,D,I,J) )
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k8_isocat_1(A,C,D,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,F,H),I,J,k8_isocat_1(A,B,C,E,F,G,H,K,L),M),k8_isocat_1(A,B,D,E,F,k2_isocat_1(B,C,D,G,I),k2_isocat_1(B,C,D,H,J),K,k8_isocat_1(B,C,D,G,H,I,J,L,M))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ! [F] :
( m2_cat_1(F,B,C)
=> ! [G] :
( m2_nattra_1(G,B,C,E,F)
=> ( r2_nattra_1(B,C,E,F)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,F,D,G),k8_isocat_1(A,B,C,D,D,E,F,k7_nattra_1(A,B,D),G)) ) ) ) ) ) ) ) ) ).
fof(t46_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,B,C)
=> ! [E] :
( m2_cat_1(E,B,C)
=> ! [F] :
( m2_cat_1(F,C,A)
=> ! [G] :
( m2_nattra_1(G,B,C,D,E)
=> ( r2_nattra_1(B,C,D,E)
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,E,G,F),k8_isocat_1(B,C,A,D,E,F,F,G,k7_nattra_1(C,A,F))) ) ) ) ) ) ) ) ) ).
fof(t47_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,B)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m2_cat_1(H,B,C)
=> ! [I] :
( m2_cat_1(I,B,C)
=> ! [J] :
( m2_nattra_1(J,A,B,D,E)
=> ! [K] :
( m2_nattra_1(K,A,B,E,F)
=> ! [L] :
( m2_nattra_1(L,B,C,G,H)
=> ! [M] :
( m2_nattra_1(M,B,C,H,I)
=> ( ( r2_nattra_1(A,B,D,E)
& r2_nattra_1(A,B,E,F)
& r2_nattra_1(B,C,G,H)
& r2_nattra_1(B,C,H,I) )
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,F,G,I,k8_nattra_1(A,B,D,E,F,J,K),k8_nattra_1(B,C,G,H,I,L,M)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,H),k2_isocat_1(A,B,C,F,I),k8_isocat_1(A,B,C,D,E,G,H,J,L),k8_isocat_1(A,B,C,E,F,H,I,K,M))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t48_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,C,D)
=> ! [G] :
( m2_cat_1(G,B,C)
=> ! [H] :
( m2_cat_1(H,B,C)
=> ( r3_nattra_1(B,C,G,H)
=> ( r3_nattra_1(B,D,k2_isocat_1(B,C,D,G,F),k2_isocat_1(B,C,D,H,F))
& r3_nattra_1(A,C,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,E,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_isocat_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] :
( m2_cat_1(D,B,A)
=> ! [E] :
( m2_cat_1(E,A,A)
=> ( r3_nattra_1(A,A,E,k1_isocat_1(A))
=> ( r3_nattra_1(A,B,k2_isocat_1(A,A,B,E,C),C)
& r3_nattra_1(B,A,k2_isocat_1(B,A,A,D,E),D) ) ) ) ) ) ) ) ).
fof(d10_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( r2_isocat_1(A,B)
<=> ? [C] :
( m2_cat_1(C,A,B)
& ? [D] :
( m2_cat_1(D,B,A)
& r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
& r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) ) ) ) ) ) ).
fof(t50_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( r1_isocat_1(A,B)
=> r2_isocat_1(A,B) ) ) ) ).
fof(t51_isocat_1,axiom,
$true ).
fof(t52_isocat_1,axiom,
$true ).
fof(t53_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ( ( r2_isocat_1(A,B)
& r2_isocat_1(B,C) )
=> r2_isocat_1(A,C) ) ) ) ) ).
fof(d11_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( r2_isocat_1(A,B)
=> ! [C] :
( m2_cat_1(C,A,B)
=> ( m1_isocat_1(C,A,B)
<=> ? [D] :
( m2_cat_1(D,B,A)
& r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
& r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) ) ) ) ) ) ) ).
fof(t54_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> m1_isocat_1(k1_isocat_1(A),A,A) ) ).
fof(t55_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& l1_cat_1(C) )
=> ( ( r2_isocat_1(A,B)
& r2_isocat_1(B,C) )
=> ! [D] :
( m1_isocat_1(D,A,B)
=> ! [E] :
( m1_isocat_1(E,B,C)
=> m1_isocat_1(k2_isocat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) ).
fof(t56_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( r2_isocat_1(A,B)
=> ! [C] :
( m1_isocat_1(C,A,B)
=> ? [D] :
( m1_isocat_1(D,B,A)
& r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
& r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) ) ) ) ) ) ).
fof(t57_isocat_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] :
( m2_cat_1(D,B,A)
=> ( r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))
=> v10_cat_1(C,A,B) ) ) ) ) ) ).
fof(t58_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( r2_isocat_1(A,B)
=> ! [C] :
( m1_isocat_1(C,A,B)
=> ( v9_cat_1(C,A,B)
& v10_cat_1(C,A,B)
& ! [D] :
( m1_subset_1(D,u1_cat_1(B))
=> ? [E] :
( m1_subset_1(E,u1_cat_1(A))
& r1_cat_1(B,D,k13_cat_1(A,B,C,E)) ) ) ) ) ) ) ) ).
fof(dt_m1_isocat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_isocat_1(C,A,B)
=> m2_cat_1(C,A,B) ) ) ).
fof(existence_m1_isocat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ? [C] : m1_isocat_1(C,A,B) ) ).
fof(symmetry_r1_isocat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ( r1_isocat_1(A,B)
=> r1_isocat_1(B,A) ) ) ).
fof(reflexivity_r1_isocat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> r1_isocat_1(A,A) ) ).
fof(symmetry_r2_isocat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> ( r2_isocat_1(A,B)
=> r2_isocat_1(B,A) ) ) ).
fof(reflexivity_r2_isocat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> r2_isocat_1(A,A) ) ).
fof(dt_k1_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> m2_cat_1(k1_isocat_1(A),A,A) ) ).
fof(redefinition_k1_isocat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> k1_isocat_1(A) = k15_cat_1(A) ) ).
fof(dt_k2_isocat_1,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,B,C) )
=> m2_cat_1(k2_isocat_1(A,B,C,D,E),A,C) ) ).
fof(redefinition_k2_isocat_1,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,B,C) )
=> k2_isocat_1(A,B,C,D,E) = k5_relat_1(D,E) ) ).
fof(dt_k3_isocat_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) )
=> m2_cat_1(k3_isocat_1(A,B,C),B,A) ) ).
fof(dt_k4_isocat_1,axiom,
! [A,B,C,D,E,F,G] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,A,B)
& m1_nattra_1(F,A,B,D,E)
& m2_cat_1(G,B,C) )
=> m1_nattra_1(k4_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)) ) ).
fof(dt_k5_isocat_1,axiom,
! [A,B,C,D,E,F,G] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,B,C)
& m2_cat_1(E,B,C)
& m2_cat_1(F,A,B)
& m1_nattra_1(G,B,C,D,E) )
=> m1_nattra_1(k5_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)) ) ).
fof(dt_k6_isocat_1,axiom,
! [A,B,C,D,E,F,G] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,A,B)
& m2_nattra_1(F,A,B,D,E)
& m2_cat_1(G,B,C) )
=> m2_nattra_1(k6_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)) ) ).
fof(dt_k7_isocat_1,axiom,
! [A,B,C,D,E,F,G] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,B,C)
& m2_cat_1(E,B,C)
& m2_cat_1(F,A,B)
& m2_nattra_1(G,B,C,D,E) )
=> m2_nattra_1(k7_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)) ) ).
fof(dt_k8_isocat_1,axiom,
! [A,B,C,D,E,F,G,H,I] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& v2_cat_1(C)
& l1_cat_1(C)
& m2_cat_1(D,A,B)
& m2_cat_1(E,A,B)
& m2_cat_1(F,B,C)
& m2_cat_1(G,B,C)
& m2_nattra_1(H,A,B,D,E)
& m2_nattra_1(I,B,C,F,G) )
=> m2_nattra_1(k8_isocat_1(A,B,C,D,E,F,G,H,I),A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G)) ) ).
%------------------------------------------------------------------------------