SET007 Axioms: SET007+339.ax
%------------------------------------------------------------------------------
% File : SET007+339 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Isomorphisms Between Functor 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_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 83 ( 3 unt; 0 def)
% Number of atoms : 813 ( 44 equ)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 754 ( 24 ~; 0 |; 333 &)
% ( 8 <=>; 389 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 13 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-6 aty)
% Number of functors : 58 ( 58 usr; 1 con; 0-9 aty)
% Number of variables : 438 ( 432 !; 6 ?)
% 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_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m2_relset_1(D,A,k1_fraenkel(B,C)) )
=> r4_nattra_1(A,k1_fraenkel(B,C),A,k1_fraenkel(B,C),k2_cat_2(A,B,C,k1_isocat_2(A,B,C,D)),D) ) ) ) ) ).
fof(t2_isocat_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m2_relset_1(D,A,k1_fraenkel(B,C)) )
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> k1_funct_1(k1_isocat_2(A,B,C,D),k4_tarski(E,F)) = k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),D,E),F) ) ) ) ) ) ) ).
fof(t3_isocat_2,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_tarski(A),B)
& m2_relset_1(C,k1_tarski(A),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_tarski(A),B)
& m2_relset_1(D,k1_tarski(A),B) )
=> ( k1_funct_1(C,A) = k1_funct_1(D,A)
=> r4_nattra_1(k1_tarski(A),B,k1_tarski(A),B,C,D) ) ) ) ) ).
fof(t4_isocat_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> r2_hidden(k8_funct_2(A,B,D,C),k2_relat_1(D)) ) ) ) ) ).
fof(t5_isocat_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k2_zfmisc_1(B,C))
& m2_relset_1(D,A,k2_zfmisc_1(B,C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,k2_zfmisc_1(B,C))
& m2_relset_1(E,A,k2_zfmisc_1(B,C)) )
=> ( ( r4_nattra_1(A,B,A,B,k7_funct_2(A,k2_zfmisc_1(B,C),B,D,k9_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),B,E,k9_funct_3(B,C)))
& r4_nattra_1(A,C,A,C,k7_funct_2(A,k2_zfmisc_1(B,C),C,D,k10_funct_3(B,C)),k7_funct_2(A,k2_zfmisc_1(B,C),C,E,k10_funct_3(B,C))) )
=> r4_nattra_1(A,k2_zfmisc_1(B,C),A,k2_zfmisc_1(B,C),D,E) ) ) ) ) ) ) ).
fof(t6_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k4_cat_1(A,B,k10_cat_1(A,k3_cat_1(A,B))) = B ) ) ).
fof(t7_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> k4_cat_1(A,k10_cat_1(A,k2_cat_1(A,B)),B) = B ) ) ).
fof(t8_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(k12_nattra_1(A,B)))
<=> m2_cat_1(C,A,B) ) ) ) ).
fof(t9_isocat_2,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(k12_nattra_1(A,B)))
=> ? [D] :
( m2_cat_1(D,A,B)
& ? [E] :
( m2_cat_1(E,A,B)
& ? [F] :
( m2_nattra_1(F,A,B,D,E)
& r2_nattra_1(A,B,D,E)
& k2_cat_1(k12_nattra_1(A,B),C) = D
& k3_cat_1(k12_nattra_1(A,B),C) = E
& C = k4_tarski(k4_tarski(D,E),F) ) ) ) ) ) ) ).
fof(d1_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m2_cat_1(D,k12_nattra_1(A,B),B)
=> ( D = k2_isocat_2(A,B,C)
<=> ! [E] :
( m2_cat_1(E,A,B)
=> ! [F] :
( m2_cat_1(F,A,B)
=> ! [G] :
( m2_nattra_1(G,A,B,E,F)
=> ( r2_nattra_1(A,B,E,F)
=> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k5_nattra_1(A,B,E,F,G,C) ) ) ) ) ) ) ) ) ) ).
fof(t10_isocat_2,axiom,
$true ).
fof(t11_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B,C] : r1_isocat_1(k12_nattra_1(k8_cat_1(B,C),A),A) ) ).
fof(t12_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> k13_cat_1(B,C,k14_cat_2(A,B,C,D,E),F) = k13_cat_1(k11_cat_2(A,B),C,D,k12_cat_2(A,B,E,F)) ) ) ) ) ) ) ).
fof(t13_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [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(B))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> ( ( k6_cat_1(A,C,D) != k1_xboole_0
& k6_cat_1(B,E,F) != k1_xboole_0 )
<=> k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) != k1_xboole_0 ) ) ) ) ) ) ) ).
fof(t14_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [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(B))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> ( k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) != k1_xboole_0
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ! [H] :
( m1_subset_1(H,u2_cat_1(B))
=> ( m1_cat_1(k13_cat_2(A,B,G,H),k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F))
<=> ( m1_cat_1(G,A,C,D)
& m1_cat_1(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ( r2_nattra_1(B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G))
& m2_nattra_1(k1_funct_1(k3_funct_5(F),G),B,C,k14_cat_2(A,B,C,D,G),k14_cat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) ).
fof(d2_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> k3_isocat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E) ) ) ) ) ) ).
fof(t16_isocat_2,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [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(B))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> ! [G] :
( m1_subset_1(G,u2_cat_1(A))
=> ! [H] :
( m1_subset_1(H,u2_cat_1(B))
=> ( ( r2_hidden(G,k6_cat_1(A,C,D))
& r2_hidden(H,k6_cat_1(B,E,F)) )
=> r2_hidden(k13_cat_2(A,B,G,H),k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F))) ) ) ) ) ) ) ) ) ) ).
fof(t17_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> ( k6_cat_1(A,E,F) != k1_xboole_0
=> ! [G] :
( m1_cat_1(G,A,E,F)
=> ( r2_nattra_1(B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F))
& m2_nattra_1(k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,G)),B,C,k14_cat_2(A,B,C,D,E),k14_cat_2(A,B,C,D,F)) ) ) ) ) ) ) ) ) ) ).
fof(d3_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> k4_isocat_2(A,B,C,D,E) = k7_funct_2(u1_cat_1(B),u2_cat_1(B),u2_cat_1(C),u6_cat_1(B),k3_isocat_2(A,B,C,D,E)) ) ) ) ) ) ).
fof(t18_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> r2_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) ) ) ) ) ).
fof(t19_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u1_cat_1(B))
=> k5_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),k4_isocat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,E,k10_cat_1(B,F))) ) ) ) ) ) ) ).
fof(t20_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k7_nattra_1(B,C,k14_cat_2(A,B,C,D,E)),k4_isocat_2(A,B,C,D,k10_cat_1(A,E))) ) ) ) ) ) ).
fof(t21_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> ( k2_cat_1(A,E) = k3_cat_1(A,F)
=> ! [G] :
( m2_nattra_1(G,B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E)))
=> ( r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),G,k4_isocat_2(A,B,C,D,F))
=> r4_nattra_1(u1_cat_1(B),u2_cat_1(C),u1_cat_1(B),u2_cat_1(C),k4_isocat_2(A,B,C,D,k4_cat_1(A,F,E)),k8_nattra_1(B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E)),G,k4_isocat_2(A,B,C,D,E))) ) ) ) ) ) ) ) ) ) ).
fof(d4_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,A,k12_nattra_1(B,C))
=> ( E = k5_isocat_2(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),E,F) = k4_tarski(k4_tarski(k14_cat_2(A,B,C,D,k2_cat_1(A,F)),k14_cat_2(A,B,C,D,k3_cat_1(A,F))),k4_isocat_2(A,B,C,D,F)) ) ) ) ) ) ) ) ).
fof(t22_isocat_2,axiom,
$true ).
fof(t23_isocat_2,axiom,
$true ).
fof(t24_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E) = k14_cat_2(A,B,C,D,E) ) ) ) ) ) ).
fof(t25_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m1_subset_1(E,u1_cat_1(A))
=> m2_cat_1(k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),E),B,C) ) ) ) ) ) ).
fof(t26_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> r4_nattra_1(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,E) ) ) ) ) ) ) ).
fof(t27_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ( r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
& ? [G] :
( m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C))
& m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) )
=> ( r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H)
=> ! [I] :
( m1_subset_1(I,u1_cat_1(A))
=> k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I) = k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ! [G] :
( m2_nattra_1(G,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> ( G = k6_isocat_2(A,B,C,D,E,F)
<=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C))
& m2_relset_1(H,k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C)) )
=> ( r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),u2_cat_1(C),F,H)
=> ! [I] :
( m1_subset_1(I,u1_cat_1(A))
=> k5_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),G,I) = k4_tarski(k12_cat_2(k12_nattra_1(B,C),k12_nattra_1(B,C),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),I),k13_cat_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,E),I)),k1_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k1_fraenkel(u1_cat_1(B),u2_cat_1(C)),k2_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),H),I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_isocat_2,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,k11_cat_2(A,B),C)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k7_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D)),k6_isocat_2(A,B,C,D,D,k7_nattra_1(k11_cat_2(A,B),C,D))) ) ) ) ) ).
fof(t29_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ! [F] :
( m2_cat_1(F,k11_cat_2(A,B),C)
=> ( ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
& r2_nattra_1(k11_cat_2(A,B),C,E,F) )
=> ! [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
=> ! [H] :
( m2_nattra_1(H,k11_cat_2(A,B),C,E,F)
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,F,k8_nattra_1(k11_cat_2(A,B),C,D,E,F,G,H)),k8_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F),k6_isocat_2(A,B,C,D,E,G),k6_isocat_2(A,B,C,E,F,H))) ) ) ) ) ) ) ) ) ) ).
fof(t30_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
=> ! [F] :
( m2_nattra_1(F,k11_cat_2(A,B),C,D,E)
=> ! [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
=> ( r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),k6_isocat_2(A,B,C,D,E,F),k6_isocat_2(A,B,C,D,E,G))
=> r4_nattra_1(u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),u1_cat_1(k11_cat_2(A,B)),u2_cat_1(C),F,G) ) ) ) ) ) ) ) ) ) ).
fof(t31_isocat_2,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,k12_nattra_1(B,C))
=> ? [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
& r4_nattra_1(u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u2_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),D,k5_isocat_2(A,B,C,E)) ) ) ) ) ) ).
fof(t32_isocat_2,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,k11_cat_2(A,B),C)
=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ( r2_nattra_1(A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> ! [F] :
( m2_nattra_1(F,A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E))
=> ( r2_nattra_1(k11_cat_2(A,B),C,D,E)
& ? [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,D,E)
& r4_nattra_1(u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),u1_cat_1(A),u2_cat_1(k12_nattra_1(B,C)),F,k6_isocat_2(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) ).
fof(d6_isocat_2,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,k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C)))
=> ( D = k7_isocat_2(A,B,C)
<=> ! [E] :
( m2_cat_1(E,k11_cat_2(A,B),C)
=> ! [F] :
( m2_cat_1(F,k11_cat_2(A,B),C)
=> ( r2_nattra_1(k11_cat_2(A,B),C,E,F)
=> ! [G] :
( m2_nattra_1(G,k11_cat_2(A,B),C,E,F)
=> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k4_tarski(k4_tarski(k5_isocat_2(A,B,C,E),k5_isocat_2(A,B,C,F)),k6_isocat_2(A,B,C,E,F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t33_isocat_2,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) )
=> v8_cat_1(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ) ) ).
fof(t34_isocat_2,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(k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ) ) ).
fof(t35_isocat_2,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)
=> ( r2_nattra_1(A,B,D,E)
=> ! [G] :
( m2_nattra_1(G,A,B,D,E)
=> k6_isocat_1(A,B,C,D,E,G,F) = k5_relat_1(G,F) ) ) ) ) ) ) ) ) ).
fof(d7_isocat_2,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,k11_cat_2(B,C))
=> k11_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),B,D,k8_isocat_2(B,C)) ) ) ) ) ).
fof(d8_isocat_2,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,k11_cat_2(B,C))
=> k12_isocat_2(A,B,C,D) = k2_isocat_1(A,k11_cat_2(B,C),C,D,k9_isocat_2(B,C)) ) ) ) ) ).
fof(t36_isocat_2,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,C)
=> ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),D)
& r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,E)),E) ) ) ) ) ) ) ).
fof(t37_isocat_2,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,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ( ( r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E))
& r4_nattra_1(u2_cat_1(A),u2_cat_1(C),u2_cat_1(A),u2_cat_1(C),k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) )
=> r4_nattra_1(u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u2_cat_1(A),u2_cat_1(k11_cat_2(B,C)),D,E) ) ) ) ) ) ) ).
fof(d9_isocat_2,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,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_nattra_1(F,A,k11_cat_2(B,C),D,E)
=> k13_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),B,D,E,F,k8_isocat_2(B,C)) ) ) ) ) ) ) ).
fof(d10_isocat_2,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,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_nattra_1(F,A,k11_cat_2(B,C),D,E)
=> k14_isocat_2(A,B,C,D,E,F) = k6_isocat_1(A,k11_cat_2(B,C),C,D,E,F,k9_isocat_2(B,C)) ) ) ) ) ) ) ).
fof(t38_isocat_2,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,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
=> ( r2_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E))
& r2_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) ) ) ) ) ) ) ) ).
fof(t39_isocat_2,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,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_cat_1(F,A,k11_cat_2(B,C))
=> ! [G] :
( m2_cat_1(G,A,k11_cat_2(B,C))
=> ( ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
& r2_nattra_1(A,k11_cat_2(B,C),F,G) )
=> ! [H] :
( m2_nattra_1(H,A,k11_cat_2(B,C),D,E)
=> ! [I] :
( m2_nattra_1(I,A,k11_cat_2(B,C),F,G)
=> ( ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,E,H),k13_isocat_2(A,B,C,F,G,I))
& r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,E,H),k14_isocat_2(A,B,C,F,G,I)) )
=> r4_nattra_1(u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),u1_cat_1(A),u2_cat_1(k11_cat_2(B,C)),H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_isocat_2,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,k11_cat_2(B,C))
=> ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_nattra_1(A,B,k11_isocat_2(A,B,C,D)),k13_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D)))
& r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_nattra_1(A,C,k12_isocat_2(A,B,C,D)),k14_isocat_2(A,B,C,D,D,k7_nattra_1(A,k11_cat_2(B,C),D))) ) ) ) ) ) ).
fof(t41_isocat_2,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,k11_cat_2(B,C))
=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_cat_1(F,A,k11_cat_2(B,C))
=> ( ( r2_nattra_1(A,k11_cat_2(B,C),D,E)
& r2_nattra_1(A,k11_cat_2(B,C),E,F) )
=> ! [G] :
( m2_nattra_1(G,A,k11_cat_2(B,C),D,E)
=> ! [H] :
( m2_nattra_1(H,A,k11_cat_2(B,C),E,F)
=> ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E),k11_isocat_2(A,B,C,F),k13_isocat_2(A,B,C,D,E,G),k13_isocat_2(A,B,C,E,F,H)))
& r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,D,F,k8_nattra_1(A,k11_cat_2(B,C),D,E,F,G,H)),k8_nattra_1(A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E),k12_isocat_2(A,B,C,F),k14_isocat_2(A,B,C,D,E,G),k14_isocat_2(A,B,C,E,F,H))) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_isocat_2,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,C)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> ! [G] :
( m1_subset_1(G,u1_cat_1(A))
=> ( k6_cat_1(A,F,G) != k1_xboole_0
=> ! [H] :
( m1_cat_1(H,A,F,G)
=> k3_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F,G,H) = k13_cat_2(B,C,k3_nattra_1(A,B,D,F,G,H),k3_nattra_1(A,C,E,F,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t43_isocat_2,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,C)
=> ! [F] :
( m1_subset_1(F,u1_cat_1(A))
=> k13_cat_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,E),F) = k12_cat_2(B,C,k13_cat_1(A,B,D,F),k13_cat_1(A,C,E,F)) ) ) ) ) ) ) ).
fof(t44_isocat_2,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,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> r1_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(d11_isocat_2,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,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> ! [H] :
( m1_nattra_1(H,A,B,D,E)
=> ! [I] :
( m1_nattra_1(I,A,C,F,G)
=> k15_isocat_2(A,B,C,D,E,F,G,H,I) = k14_funct_3(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),H,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_isocat_2,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,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r1_nattra_1(A,B,D,E)
& r1_nattra_1(A,C,F,G) )
=> ! [H] :
( m1_nattra_1(H,A,B,D,E)
=> ! [I] :
( m1_nattra_1(I,A,C,F,G)
=> ! [J] :
( m1_subset_1(J,u1_cat_1(A))
=> k5_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k15_isocat_2(A,B,C,D,E,F,G,H,I),J) = k13_cat_2(B,C,k5_nattra_1(A,B,D,E,H,J),k5_nattra_1(A,C,F,G,I,J)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_isocat_2,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,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r2_nattra_1(A,B,D,E)
& r2_nattra_1(A,C,F,G) )
=> r2_nattra_1(A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(d12_isocat_2,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,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r2_nattra_1(A,B,D,E)
& r2_nattra_1(A,C,F,G) )
=> ! [H] :
( m2_nattra_1(H,A,B,D,E)
=> ! [I] :
( m2_nattra_1(I,A,C,F,G)
=> k16_isocat_2(A,B,C,D,E,F,G,H,I) = k15_isocat_2(A,B,C,D,E,F,G,H,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t47_isocat_2,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,C)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( r2_nattra_1(A,B,D,E)
& r2_nattra_1(A,C,F,G) )
=> ! [H] :
( m2_nattra_1(H,A,B,D,E)
=> ! [I] :
( m2_nattra_1(I,A,C,F,G)
=> ( r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k13_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k16_isocat_2(A,B,C,D,E,F,G,H,I)),H)
& r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k14_isocat_2(A,B,C,k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G),k16_isocat_2(A,B,C,D,E,F,G,H,I)),I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d13_isocat_2,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,k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C)))
=> ( D = k17_isocat_2(A,B,C)
<=> ! [E] :
( m2_cat_1(E,A,k11_cat_2(B,C))
=> ! [F] :
( m2_cat_1(F,A,k11_cat_2(B,C))
=> ( r2_nattra_1(A,k11_cat_2(B,C),E,F)
=> ! [G] :
( m2_nattra_1(G,A,k11_cat_2(B,C),E,F)
=> k1_funct_1(D,k4_tarski(k4_tarski(E,F),G)) = k4_tarski(k4_tarski(k4_tarski(k11_isocat_2(A,B,C,E),k11_isocat_2(A,B,C,F)),k13_isocat_2(A,B,C,E,F,G)),k4_tarski(k4_tarski(k12_isocat_2(A,B,C,E),k12_isocat_2(A,B,C,F)),k14_isocat_2(A,B,C,E,F,G))) ) ) ) ) ) ) ) ) ) ).
fof(t48_isocat_2,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) )
=> v8_cat_1(k17_isocat_2(A,B,C),k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) ) ) ) ).
fof(t49_isocat_2,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(k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) ) ) ) ).
fof(dt_k1_isocat_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m1_relset_1(D,A,k1_fraenkel(B,C)) )
=> ( v1_funct_1(k1_isocat_2(A,B,C,D))
& v1_funct_2(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C)
& m2_relset_1(k1_isocat_2(A,B,C,D),k2_zfmisc_1(A,B),C) ) ) ).
fof(redefinition_k1_isocat_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,k1_fraenkel(B,C))
& m1_relset_1(D,A,k1_fraenkel(B,C)) )
=> k1_isocat_2(A,B,C,D) = k4_funct_5(D) ) ).
fof(dt_k2_isocat_2,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m1_subset_1(C,u1_cat_1(A)) )
=> m2_cat_1(k2_isocat_2(A,B,C),k12_nattra_1(A,B),B) ) ).
fof(dt_k3_isocat_2,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,k11_cat_2(A,B),C)
& m1_subset_1(E,u2_cat_1(A)) )
=> ( v1_funct_1(k3_isocat_2(A,B,C,D,E))
& v1_funct_2(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C))
& m2_relset_1(k3_isocat_2(A,B,C,D,E),u2_cat_1(B),u2_cat_1(C)) ) ) ).
fof(dt_k4_isocat_2,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,k11_cat_2(A,B),C)
& m1_subset_1(E,u2_cat_1(A)) )
=> m2_nattra_1(k4_isocat_2(A,B,C,D,E),B,C,k14_cat_2(A,B,C,D,k2_cat_1(A,E)),k14_cat_2(A,B,C,D,k3_cat_1(A,E))) ) ).
fof(dt_k5_isocat_2,axiom,
! [A,B,C,D] :
( ( 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,k11_cat_2(A,B),C) )
=> m2_cat_1(k5_isocat_2(A,B,C,D),A,k12_nattra_1(B,C)) ) ).
fof(dt_k6_isocat_2,axiom,
! [A,B,C,D,E,F] :
( ( 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,k11_cat_2(A,B),C)
& m2_cat_1(E,k11_cat_2(A,B),C)
& m2_nattra_1(F,k11_cat_2(A,B),C,D,E) )
=> m2_nattra_1(k6_isocat_2(A,B,C,D,E,F),A,k12_nattra_1(B,C),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) ) ).
fof(dt_k7_isocat_2,axiom,
! [A,B,C] :
( ( 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(k7_isocat_2(A,B,C),k12_nattra_1(k11_cat_2(A,B),C),k12_nattra_1(A,k12_nattra_1(B,C))) ) ).
fof(dt_k8_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> m2_cat_1(k8_isocat_2(A,B),k11_cat_2(A,B),A) ) ).
fof(redefinition_k8_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> k8_isocat_2(A,B) = k16_cat_2(A,B) ) ).
fof(dt_k9_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> m2_cat_1(k9_isocat_2(A,B),k11_cat_2(A,B),B) ) ).
fof(redefinition_k9_isocat_2,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B) )
=> k9_isocat_2(A,B) = k17_cat_2(A,B) ) ).
fof(dt_k10_isocat_2,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,A,C) )
=> m2_cat_1(k10_isocat_2(A,B,C,D,E),A,k11_cat_2(B,C)) ) ).
fof(redefinition_k10_isocat_2,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,A,C) )
=> k10_isocat_2(A,B,C,D,E) = k13_funct_3(D,E) ) ).
fof(dt_k11_isocat_2,axiom,
! [A,B,C,D] :
( ( 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,k11_cat_2(B,C)) )
=> m2_cat_1(k11_isocat_2(A,B,C,D),A,B) ) ).
fof(dt_k12_isocat_2,axiom,
! [A,B,C,D] :
( ( 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,k11_cat_2(B,C)) )
=> m2_cat_1(k12_isocat_2(A,B,C,D),A,C) ) ).
fof(dt_k13_isocat_2,axiom,
! [A,B,C,D,E,F] :
( ( 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,k11_cat_2(B,C))
& m2_cat_1(E,A,k11_cat_2(B,C))
& m2_nattra_1(F,A,k11_cat_2(B,C),D,E) )
=> m2_nattra_1(k13_isocat_2(A,B,C,D,E,F),A,B,k11_isocat_2(A,B,C,D),k11_isocat_2(A,B,C,E)) ) ).
fof(dt_k14_isocat_2,axiom,
! [A,B,C,D,E,F] :
( ( 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,k11_cat_2(B,C))
& m2_cat_1(E,A,k11_cat_2(B,C))
& m2_nattra_1(F,A,k11_cat_2(B,C),D,E) )
=> m2_nattra_1(k14_isocat_2(A,B,C,D,E,F),A,C,k12_isocat_2(A,B,C,D),k12_isocat_2(A,B,C,E)) ) ).
fof(dt_k15_isocat_2,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,A,C)
& m2_cat_1(G,A,C)
& m1_nattra_1(H,A,B,D,E)
& m1_nattra_1(I,A,C,F,G) )
=> m1_nattra_1(k15_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ).
fof(dt_k16_isocat_2,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,A,C)
& m2_cat_1(G,A,C)
& m2_nattra_1(H,A,B,D,E)
& m2_nattra_1(I,A,C,F,G) )
=> m2_nattra_1(k16_isocat_2(A,B,C,D,E,F,G,H,I),A,k11_cat_2(B,C),k10_isocat_2(A,B,C,D,F),k10_isocat_2(A,B,C,E,G)) ) ).
fof(dt_k17_isocat_2,axiom,
! [A,B,C] :
( ( 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(k17_isocat_2(A,B,C),k12_nattra_1(A,k11_cat_2(B,C)),k11_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,C))) ) ).
%------------------------------------------------------------------------------