SET007 Axioms: SET007+435.ax
%------------------------------------------------------------------------------
% File : SET007+435 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Indexed Category
% 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 : index_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 113 ( 2 unt; 0 def)
% Number of atoms : 847 ( 76 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 779 ( 45 ~; 0 |; 384 &)
% ( 18 <=>; 332 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-7 aty)
% Number of functors : 62 ( 62 usr; 3 con; 0-6 aty)
% Number of variables : 449 ( 435 !; 14 ?)
% 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_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& ~ v3_relat_1(B)
& v1_funct_1(B) ) ) ).
fof(cc1_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ( v2_relat_1(B)
=> ~ v3_relat_1(B) ) ) ) ).
fof(rc2_index_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_index_1(A) ) ).
fof(rc3_index_1,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_index_1(B) ) ).
fof(fc1_index_1,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v1_index_1(k2_funcop_1(A,B)) ) ) ).
fof(cc2_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(fc2_index_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_index_1(A) )
=> v2_cat_5(k2_relat_1(A)) ) ).
fof(fc3_index_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_index_1(B) )
=> ( v1_relat_1(k5_relat_1(A,B))
& v1_funct_1(k5_relat_1(A,B))
& v1_index_1(k5_relat_1(A,B)) ) ) ).
fof(rc4_index_1,axiom,
! [A,B] :
? [C] :
( m1_index_1(C,A,B)
& v2_index_1(C,A,B)
& v3_index_1(C,A,B) ) ).
fof(fc4_index_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> v1_fraenkel(k2_relat_1(A)) ) ).
fof(rc5_index_1,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& m3_index_1(E,A,B,C,D) )
=> ? [F] :
( m4_index_1(F,A,B,C,D,E)
& v1_cat_1(F)
& v2_cat_1(F)
& v1_cat_5(F)
& v3_cat_5(F)
& v4_cat_5(F) ) ) ).
fof(fc5_index_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B)
& m2_cat_1(C,A,B) )
=> ( v1_relat_1(k12_cat_1(A,B,C))
& v1_funct_1(k12_cat_1(A,B,C))
& v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B))
& v1_index_1(k12_cat_1(A,B,C)) ) ) ).
fof(t1_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& v3_cat_5(A)
& l1_cat_1(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ( k2_cat_1(A,C) = k3_cat_1(A,B)
=> k4_cat_1(A,B,C) = k4_tarski(k12_cat_2(A,A,k2_cat_1(A,B),k3_cat_1(A,C)),k1_partfun1(u2_cat_1(k8_cat_5(A,B)),u2_cat_1(k9_cat_5(A,B)),u2_cat_1(k8_cat_5(A,C)),u2_cat_1(k9_cat_5(A,C)),k1_index_1(A,B),k1_index_1(A,C))) ) ) ) ) ).
fof(t2_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& v3_cat_5(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,C)
=> ( D = E
=> k12_cat_1(A,B,D) = k12_cat_1(A,C,E) ) ) ) ) ) ) ).
fof(d1_index_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_index_1(A)
<=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> ( v2_cat_1(k1_funct_1(A,B))
& l1_cat_1(k1_funct_1(A,B)) ) ) ) ) ).
fof(d2_index_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_index_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ( B = k3_index_1(A)
<=> ( k1_relat_1(B) = k1_relat_1(A)
& ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ( D = k1_funct_1(A,C)
=> k1_funct_1(B,C) = u1_cat_1(D) ) ) ) ) ) ) ) ).
fof(d3_index_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_index_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ( B = k4_index_1(A)
<=> ( k1_relat_1(B) = k1_relat_1(A)
& ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> ! [D] :
( ( v2_cat_1(D)
& l1_cat_1(D) )
=> ( D = k1_funct_1(A,C)
=> k1_funct_1(B,C) = u2_cat_1(D) ) ) ) ) ) ) ) ).
fof(t3_index_1,axiom,
! [A,B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( k3_index_1(k2_pre_circ(A,B)) = k2_pre_circ(A,u1_cat_1(B))
& k4_index_1(k2_pre_circ(A,B)) = k2_pre_circ(A,u2_cat_1(B)) ) ) ).
fof(d4_index_1,axiom,
! [A,B,C] :
( m1_index_1(C,A,B)
<=> ? [D] :
( m1_pboole(D,A)
& ? [E] :
( m1_pboole(E,B)
& C = k4_tarski(D,E) ) ) ) ).
fof(d5_index_1,axiom,
! [A,B,C] :
( m1_index_1(C,A,B)
=> ( v2_index_1(C,A,B)
<=> v1_index_1(k8_index_1(A,B,C)) ) ) ).
fof(d6_index_1,axiom,
! [A,B,C] :
( m1_index_1(C,A,B)
=> ( v3_index_1(C,A,B)
<=> v1_funcop_1(k9_index_1(A,B,C)) ) ) ).
fof(d7_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_index_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_index_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v1_funcop_1(D)
& m1_pboole(D,A) )
=> ( m2_index_1(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> m2_cat_1(k1_funct_1(D,E),k2_index_1(A,B,E),k2_index_1(A,C,E)) ) ) ) ) ) ) ).
fof(d8_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( ( v2_index_1(E,A,B)
& m1_index_1(E,A,B) )
=> ( m3_index_1(E,A,B,C,D)
<=> m2_index_1(k9_index_1(A,B,E),B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E))) ) ) ) ) ) ) ).
fof(t4_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m3_index_1(E,A,B,C,D)
=> ! [F] :
( m1_subset_1(F,B)
=> m2_cat_1(k1_funct_1(k9_index_1(A,B,E),F),k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,C,F)),k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,D,F))) ) ) ) ) ) ) ).
fof(t5_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> m2_cat_1(k1_funct_1(k9_index_1(u1_cat_1(A),u2_cat_1(A),B),C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,C)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,C))) ) ) ) ).
fof(d9_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m3_index_1(E,A,B,C,D)
=> ! [F] :
( ( v2_cat_1(F)
& v3_cat_5(F)
& l1_cat_1(F) )
=> ( m4_index_1(F,A,B,C,D,E)
<=> ( ! [G] :
( m1_subset_1(G,A)
=> m1_subset_1(k2_index_1(A,k10_index_1(A,B,E),G),u1_cat_1(F)) )
& ! [G] :
( m1_subset_1(G,B)
=> m1_subset_1(k4_tarski(k4_tarski(k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,C,G)),k2_index_1(A,k10_index_1(A,B,E),k8_funct_2(B,A,D,G))),k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E)),k14_index_1(A,B,C,D,E),G)),u2_cat_1(F)) ) ) ) ) ) ) ) ) ) ).
fof(d10_index_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,A)
& m2_relset_1(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ? [G] :
( v2_cat_1(G)
& l1_cat_1(G)
& G = g1_cat_1(A,B,C,D,E,F) )
=> ! [G] :
( m3_index_1(G,A,B,C,D)
=> ( m5_index_1(G,A,B,C,D,E,F)
<=> ( ! [H] :
( m1_subset_1(H,A)
=> k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),k7_pboole(B,A,D,k10_index_1(A,B,G)),k14_index_1(A,B,C,D,G),k8_funct_2(A,B,F,H)) = k15_cat_1(k2_index_1(A,k10_index_1(A,B,G),H)) )
& ! [H] :
( m1_subset_1(H,B)
=> ! [I] :
( m1_subset_1(I,B)
=> ( k8_funct_2(B,A,C,I) = k8_funct_2(B,A,D,H)
=> k1_funct_1(k14_index_1(A,B,C,D,G),k1_funct_1(E,k4_tarski(I,H))) = k1_partfun1(u2_cat_1(k2_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),H)),u2_cat_1(k2_index_1(B,k7_pboole(B,A,D,k10_index_1(A,B,G)),H)),u2_cat_1(k2_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),I)),u2_cat_1(k2_index_1(B,k7_pboole(B,A,D,k10_index_1(A,B,G)),I)),k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),k7_pboole(B,A,D,k10_index_1(A,B,G)),k14_index_1(A,B,C,D,G),H),k13_index_1(B,k7_pboole(B,A,C,k10_index_1(A,B,G)),k7_pboole(B,A,D,k10_index_1(A,B,G)),k14_index_1(A,B,C,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A))
=> ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
<=> ( ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),k10_cat_1(A,C)) = k15_cat_1(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) )
& ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k2_cat_1(A,D) = k3_cat_1(A,C)
=> k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),k4_cat_1(A,C,D)) = k1_partfun1(u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),C),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),D)) ) ) ) ) ) ) ) ).
fof(t7_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m3_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A))
=> ( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
<=> ( ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),k10_cat_1(A,C)) = k15_cat_1(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) )
& ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(A))
=> ( k2_cat_1(A,D) = k3_cat_1(A,C)
=> k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),k4_cat_1(A,C,D)) = k1_partfun1(u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),D)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),u2_cat_1(k2_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),C)),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),D),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),C)) ) ) ) ) ) ) ) ).
fof(t8_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
<=> m5_index_1(B,u1_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(A)),u3_cat_1(k2_oppcat_1(A)),u4_cat_1(k2_oppcat_1(A)),u5_cat_1(k2_oppcat_1(A)),u6_cat_1(k2_oppcat_1(A))) ) ) ).
fof(t9_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ( ~ v1_xboole_0(k6_cat_1(A,C,D))
=> ! [E] :
( m1_cat_1(E,A,C,D)
=> m2_cat_1(k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),E),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),D)) ) ) ) ) ) ) ).
fof(t10_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u1_cat_1(A))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> ( ~ v1_xboole_0(k6_cat_1(A,C,D))
=> ! [E] :
( m1_cat_1(E,A,C,D)
=> m2_cat_1(k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),E),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),D),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),C)) ) ) ) ) ) ) ).
fof(d11_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( m2_cat_1(D,A,C)
=> ( D = k15_index_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u2_cat_1(A))
=> k8_funct_2(u2_cat_1(A),u2_cat_1(C),D,E) = k4_tarski(k4_tarski(k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,E)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,E))),k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),E)) ) ) ) ) ) ) ).
fof(t11_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ( k15_index_1(A,B,C) = k15_index_1(A,B,D)
& k12_cat_1(A,C,k15_index_1(A,B,C)) = k12_cat_1(A,D,k15_index_1(A,B,D)) ) ) ) ) ) ).
fof(t12_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> k12_cat_1(A,C,k15_index_1(A,B,C)) = k10_index_1(u1_cat_1(A),u2_cat_1(A),B) ) ) ) ).
fof(t13_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( m1_subset_1(D,u1_cat_1(A))
=> k13_cat_1(A,C,k15_index_1(A,B,C),D) = k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),D) ) ) ) ) ).
fof(d12_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( ( v1_cat_1(C)
& m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) )
=> ( C = k16_index_1(A,B)
<=> ! [D] :
( m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> C = k7_cat_5(A,D,k15_index_1(A,B,D)) ) ) ) ) ) ).
fof(t14_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( ( v2_cat_1(C)
& v3_cat_5(C)
& l1_cat_1(C) )
=> ( m3_cat_2(k16_index_1(A,B),C)
<=> m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) ) ) ) ) ).
fof(d13_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> k17_index_1(A,B,C) = k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B),C) ) ) ) ).
fof(d14_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(A))
=> k18_index_1(A,B,C) = k13_index_1(u2_cat_1(A),k7_pboole(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k7_pboole(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B)),k14_index_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),B),C) ) ) ) ).
fof(t15_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ( m5_index_1(k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
& m5_index_1(k12_index_1(u1_cat_1(A),u2_cat_1(A),k2_pre_circ(u1_cat_1(A),B),k2_pre_circ(u2_cat_1(A),k15_cat_1(B))),u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)) ) ) ) ).
fof(t16_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> m5_index_1(k4_tarski(k12_cat_1(A,B,C),k16_mcart_1(C)),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ) ) ).
fof(d15_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> k19_index_1(A,B,C) = k4_tarski(k12_cat_1(A,B,C),k16_mcart_1(C)) ) ) ) ).
fof(t17_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> m4_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k19_index_1(A,B,C)) ) ) ) ).
fof(t18_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( m2_cat_1(C,A,B)
=> ! [D] :
( m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k19_index_1(A,B,C))
=> C = k15_index_1(A,k19_index_1(A,B,C),D) ) ) ) ) ).
fof(t19_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( ( v2_cat_1(C)
& v3_cat_5(C)
& l1_cat_1(C) )
=> ! [D] :
( m2_cat_1(D,A,B)
=> ! [E] :
( m2_cat_1(E,A,C)
=> ( D = E
=> k19_index_1(A,B,D) = k19_index_1(A,C,E) ) ) ) ) ) ) ).
fof(t20_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> k16_mcart_1(k15_index_1(A,B,C)) = k14_index_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) ) ) ) ).
fof(t21_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> k19_index_1(A,C,k15_index_1(A,B,C)) = B ) ) ) ).
fof(d16_index_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] :
( m5_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
=> ( m3_cat_2(k7_cat_5(A,B,D),C)
=> ! [F] :
( m5_index_1(F,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ( F = k20_index_1(A,B,C,D,E)
<=> ! [G] :
( m2_cat_1(G,A,C)
=> ( G = D
=> F = k19_index_1(A,k16_index_1(C,E),k14_cat_1(A,C,k16_index_1(C,E),G,k15_index_1(C,E,k16_index_1(C,E)))) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_index_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] :
( m5_index_1(E,u1_cat_1(D),u2_cat_1(D),u3_cat_1(D),u4_cat_1(D),u5_cat_1(D),u6_cat_1(D))
=> ! [F] :
( m2_cat_1(F,A,B)
=> ! [G] :
( m2_cat_1(G,A,C)
=> ( ( m3_cat_2(k7_cat_5(A,B,F),D)
& m3_cat_2(k7_cat_5(A,C,G),D)
& F = G )
=> k20_index_1(A,B,D,F,E) = k20_index_1(A,C,D,G,E) ) ) ) ) ) ) ) ) ).
fof(t23_index_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] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> ! [E] :
( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
=> k20_index_1(A,B,B,C,D) = k19_index_1(A,E,k14_cat_1(A,B,E,C,k15_index_1(B,D,E))) ) ) ) ) ) ).
fof(t24_index_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] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> ! [E] :
( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
=> m4_index_1(E,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k20_index_1(A,B,B,C,D)) ) ) ) ) ) ).
fof(t25_index_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] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> ! [E] :
( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
=> m3_cat_2(k16_index_1(A,k20_index_1(A,B,B,C,D)),E) ) ) ) ) ) ).
fof(t26_index_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] :
( m5_index_1(F,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
=> k20_index_1(A,B,B,D,k20_index_1(B,C,C,E,F)) = k20_index_1(A,C,C,k14_cat_1(A,B,C,D,E),F) ) ) ) ) ) ) ).
fof(d17_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( ( v2_cat_1(C)
& v3_cat_5(C)
& l1_cat_1(C) )
=> ( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( ( v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,C,D)
=> ! [F] :
( m5_index_1(F,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ( F = k21_index_1(A,B,C,D,E)
<=> ! [G] :
( m4_index_1(G,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [H] :
( m2_cat_1(H,G,D)
=> ( ( G = C
& H = E )
=> F = k19_index_1(A,D,k14_cat_1(A,G,D,k15_index_1(A,B,G),H)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( ( v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D) )
=> ! [E] :
( ( v2_cat_1(E)
& v3_cat_5(E)
& l1_cat_1(E) )
=> ! [F] :
( m2_cat_1(F,C,D)
=> ! [G] :
( m2_cat_1(G,C,E)
=> ( F = G
=> k21_index_1(A,B,C,D,F) = k21_index_1(A,B,C,E,G) ) ) ) ) ) ) ) ) ).
fof(t28_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( ( v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,C,D)
=> m4_index_1(k7_cat_5(C,D,E),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k21_index_1(A,B,C,D,E)) ) ) ) ) ) ).
fof(t29_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( ( v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,C,D)
=> m4_index_1(D,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),k21_index_1(A,B,C,D,E)) ) ) ) ) ) ).
fof(t30_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( ( v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,C,D)
=> m3_cat_2(k16_index_1(A,k21_index_1(A,B,C,D,E)),k7_cat_5(C,D,E)) ) ) ) ) ) ).
fof(t31_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( ( v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D) )
=> ! [E] :
( ( v2_cat_1(E)
& v3_cat_5(E)
& l1_cat_1(E) )
=> ! [F] :
( m2_cat_1(F,C,D)
=> ! [G] :
( m2_cat_1(G,D,E)
=> k21_index_1(A,B,C,E,k14_cat_1(C,D,E,F,G)) = k21_index_1(A,k21_index_1(A,B,C,D,F),D,E,G) ) ) ) ) ) ) ) ).
fof(d18_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& l1_cat_1(B) )
=> ! [C] :
( m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [D] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> k22_index_1(A,B,C,D) = k20_index_1(A,k16_index_1(A,C),B,k15_index_1(A,C,k16_index_1(A,C)),D) ) ) ) ) ).
fof(t32_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [D] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> ! [E] :
( m4_index_1(E,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),C)
=> ( m4_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),C)
=> k22_index_1(A,B,C,D) = k20_index_1(A,E,B,k15_index_1(A,C,E),D) ) ) ) ) ) ) ).
fof(t33_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B) )
=> ! [C] :
( m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [D] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> ! [E] :
( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
=> ( m4_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),C)
=> k22_index_1(A,B,C,D) = k21_index_1(A,C,B,E,k15_index_1(B,D,E)) ) ) ) ) ) ) ).
fof(t34_index_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] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> ! [E] :
( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
=> ! [F] :
( ( v2_cat_1(F)
& v3_cat_5(F)
& l1_cat_1(F) )
=> ! [G] :
( m2_cat_1(G,E,F)
=> k20_index_1(A,B,B,C,k21_index_1(B,D,E,F,G)) = k21_index_1(A,k20_index_1(A,B,B,C,D),E,F,G) ) ) ) ) ) ) ) ).
fof(t35_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( ( v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D) )
=> ! [E] :
( m2_cat_1(E,C,D)
=> ! [F] :
( m5_index_1(F,u1_cat_1(D),u2_cat_1(D),u3_cat_1(D),u4_cat_1(D),u5_cat_1(D),u6_cat_1(D))
=> k22_index_1(A,C,B,k20_index_1(C,D,D,E,F)) = k22_index_1(A,D,k21_index_1(A,B,C,D,E),F) ) ) ) ) ) ) ).
fof(t36_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( m5_index_1(D,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
=> ! [E] :
( m4_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),D)
=> ! [F] :
( ( v2_cat_1(F)
& v3_cat_5(F)
& l1_cat_1(F) )
=> ! [G] :
( m2_cat_1(G,E,F)
=> k22_index_1(A,C,B,k21_index_1(C,D,E,F,G)) = k21_index_1(A,k22_index_1(A,C,B,D),E,F,G) ) ) ) ) ) ) ) ).
fof(t37_index_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] :
( m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B))
=> ! [E] :
( m4_index_1(E,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),D)
=> ! [F] :
( m5_index_1(F,u1_cat_1(E),u2_cat_1(E),u3_cat_1(E),u4_cat_1(E),u5_cat_1(E),u6_cat_1(E))
=> k20_index_1(A,B,B,C,k22_index_1(B,E,D,F)) = k22_index_1(A,E,k20_index_1(A,B,B,C,D),F) ) ) ) ) ) ) ).
fof(t38_index_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
=> ! [C] :
( m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B)
=> ! [D] :
( m5_index_1(D,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C))
=> ! [E] :
( m4_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),D)
=> ! [F] :
( m5_index_1(F,u1_cat_1(E),u2_cat_1(E),u3_cat_1(E),u4_cat_1(E),u5_cat_1(E),u6_cat_1(E))
=> k22_index_1(A,C,B,k22_index_1(C,E,D,F)) = k22_index_1(A,E,k22_index_1(A,C,B,D),F) ) ) ) ) ) ) ).
fof(s1_index_1,axiom,
( ! [A] :
( m1_subset_1(A,f1_s1_index_1)
=> m2_cat_1(f4_s1_index_1(A),k2_index_1(f1_s1_index_1,f2_s1_index_1,A),k2_index_1(f1_s1_index_1,f3_s1_index_1,A)) )
=> ? [A] :
( m2_index_1(A,f1_s1_index_1,f2_s1_index_1,f3_s1_index_1)
& ! [B] :
( m1_subset_1(B,f1_s1_index_1)
=> k1_funct_1(A,B) = f4_s1_index_1(B) ) ) ) ).
fof(dt_m1_index_1,axiom,
$true ).
fof(existence_m1_index_1,axiom,
! [A,B] :
? [C] : m1_index_1(C,A,B) ).
fof(dt_m2_index_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A)
& v1_index_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( m2_index_1(D,A,B,C)
=> ( v1_funcop_1(D)
& m1_pboole(D,A) ) ) ) ).
fof(existence_m2_index_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A)
& v1_index_1(C)
& m1_pboole(C,A) )
=> ? [D] : m2_index_1(D,A,B,C) ) ).
fof(dt_m3_index_1,axiom,
! [A,B,C,D] :
( ( ~ 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) )
=> ! [E] :
( m3_index_1(E,A,B,C,D)
=> ( v2_index_1(E,A,B)
& m1_index_1(E,A,B) ) ) ) ).
fof(existence_m3_index_1,axiom,
! [A,B,C,D] :
( ( ~ 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) )
=> ? [E] : m3_index_1(E,A,B,C,D) ) ).
fof(dt_m4_index_1,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& m3_index_1(E,A,B,C,D) )
=> ! [F] :
( m4_index_1(F,A,B,C,D,E)
=> ( v2_cat_1(F)
& v3_cat_5(F)
& l1_cat_1(F) ) ) ) ).
fof(existence_m4_index_1,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& m3_index_1(E,A,B,C,D) )
=> ? [F] : m4_index_1(F,A,B,C,D,E) ) ).
fof(dt_m5_index_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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) )
=> ! [G] :
( m5_index_1(G,A,B,C,D,E,F)
=> m3_index_1(G,A,B,C,D) ) ) ).
fof(existence_m5_index_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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) )
=> ? [G] : m5_index_1(G,A,B,C,D,E,F) ) ).
fof(dt_k1_index_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_5(A)
& l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(A)) )
=> m2_cat_1(k1_index_1(A,B),k8_cat_5(A,B),k9_cat_5(A,B)) ) ).
fof(redefinition_k1_index_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& v3_cat_5(A)
& l1_cat_1(A)
& m1_subset_1(B,u2_cat_1(A)) )
=> k1_index_1(A,B) = k2_mcart_1(B) ) ).
fof(dt_k2_index_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ( v2_cat_1(k2_index_1(A,B,C))
& l1_cat_1(k2_index_1(A,B,C)) ) ) ).
fof(redefinition_k2_index_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> k2_index_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k3_index_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_index_1(A) )
=> ( v1_relat_1(k3_index_1(A))
& v2_relat_1(k3_index_1(A))
& v1_funct_1(k3_index_1(A)) ) ) ).
fof(dt_k4_index_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_index_1(A) )
=> ( v1_relat_1(k4_index_1(A))
& v2_relat_1(k4_index_1(A))
& v1_funct_1(k4_index_1(A)) ) ) ).
fof(dt_k5_index_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A) )
=> ( v2_relat_1(k5_index_1(A,B))
& m1_pboole(k5_index_1(A,B),A) ) ) ).
fof(redefinition_k5_index_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A) )
=> k5_index_1(A,B) = k3_index_1(B) ) ).
fof(dt_k6_index_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A) )
=> ( v2_relat_1(k6_index_1(A,B))
& m1_pboole(k6_index_1(A,B),A) ) ) ).
fof(redefinition_k6_index_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A) )
=> k6_index_1(A,B) = k4_index_1(B) ) ).
fof(dt_k7_index_1,axiom,
! [A,B,C,D] :
( ( m1_pboole(C,A)
& m1_pboole(D,B) )
=> m1_index_1(k7_index_1(A,B,C,D),A,B) ) ).
fof(redefinition_k7_index_1,axiom,
! [A,B,C,D] :
( ( m1_pboole(C,A)
& m1_pboole(D,B) )
=> k7_index_1(A,B,C,D) = k4_tarski(C,D) ) ).
fof(dt_k8_index_1,axiom,
! [A,B,C] :
( m1_index_1(C,A,B)
=> m1_pboole(k8_index_1(A,B,C),A) ) ).
fof(redefinition_k8_index_1,axiom,
! [A,B,C] :
( m1_index_1(C,A,B)
=> k8_index_1(A,B,C) = k1_mcart_1(C) ) ).
fof(dt_k9_index_1,axiom,
! [A,B,C] :
( m1_index_1(C,A,B)
=> m1_pboole(k9_index_1(A,B,C),B) ) ).
fof(redefinition_k9_index_1,axiom,
! [A,B,C] :
( m1_index_1(C,A,B)
=> k9_index_1(A,B,C) = k2_mcart_1(C) ) ).
fof(dt_k10_index_1,axiom,
! [A,B,C] :
( ( v2_index_1(C,A,B)
& m1_index_1(C,A,B) )
=> ( v1_index_1(k10_index_1(A,B,C))
& m1_pboole(k10_index_1(A,B,C),A) ) ) ).
fof(redefinition_k10_index_1,axiom,
! [A,B,C] :
( ( v2_index_1(C,A,B)
& m1_index_1(C,A,B) )
=> k10_index_1(A,B,C) = k1_mcart_1(C) ) ).
fof(dt_k11_index_1,axiom,
! [A,B,C] :
( ( v3_index_1(C,A,B)
& m1_index_1(C,A,B) )
=> ( v1_funcop_1(k11_index_1(A,B,C))
& m1_pboole(k11_index_1(A,B,C),B) ) ) ).
fof(redefinition_k11_index_1,axiom,
! [A,B,C] :
( ( v3_index_1(C,A,B)
& m1_index_1(C,A,B) )
=> k11_index_1(A,B,C) = k2_mcart_1(C) ) ).
fof(dt_k12_index_1,axiom,
! [A,B,C,D] :
( ( v1_index_1(C)
& m1_pboole(C,A)
& v1_funcop_1(D)
& m1_pboole(D,B) )
=> ( v2_index_1(k12_index_1(A,B,C,D),A,B)
& v3_index_1(k12_index_1(A,B,C,D),A,B)
& m1_index_1(k12_index_1(A,B,C,D),A,B) ) ) ).
fof(redefinition_k12_index_1,axiom,
! [A,B,C,D] :
( ( v1_index_1(C)
& m1_pboole(C,A)
& v1_funcop_1(D)
& m1_pboole(D,B) )
=> k12_index_1(A,B,C,D) = k4_tarski(C,D) ) ).
fof(dt_k13_index_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A)
& v1_index_1(C)
& m1_pboole(C,A)
& m2_index_1(D,A,B,C)
& m1_subset_1(E,A) )
=> m2_cat_1(k13_index_1(A,B,C,D,E),k2_index_1(A,B,E),k2_index_1(A,C,E)) ) ).
fof(redefinition_k13_index_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_index_1(B)
& m1_pboole(B,A)
& v1_index_1(C)
& m1_pboole(C,A)
& m2_index_1(D,A,B,C)
& m1_subset_1(E,A) )
=> k13_index_1(A,B,C,D,E) = k1_funct_1(D,E) ) ).
fof(dt_k14_index_1,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& m3_index_1(E,A,B,C,D) )
=> m2_index_1(k14_index_1(A,B,C,D,E),B,k7_pboole(B,A,C,k10_index_1(A,B,E)),k7_pboole(B,A,D,k10_index_1(A,B,E))) ) ).
fof(redefinition_k14_index_1,axiom,
! [A,B,C,D,E] :
( ( ~ 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)
& m3_index_1(E,A,B,C,D) )
=> k14_index_1(A,B,C,D,E) = k2_mcart_1(E) ) ).
fof(dt_k15_index_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
& m4_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) )
=> m2_cat_1(k15_index_1(A,B,C),A,C) ) ).
fof(dt_k16_index_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) )
=> ( v1_cat_1(k16_index_1(A,B))
& m4_index_1(k16_index_1(A,B),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),B) ) ) ).
fof(dt_k17_index_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
& m1_subset_1(C,u2_cat_1(A)) )
=> m2_cat_1(k17_index_1(A,B,C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,C)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,C))) ) ).
fof(dt_k18_index_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))
& m1_subset_1(C,u2_cat_1(A)) )
=> m2_cat_1(k18_index_1(A,B,C),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k3_cat_1(A,C)),k2_index_1(u1_cat_1(A),k10_index_1(u1_cat_1(A),u2_cat_1(A),B),k2_cat_1(A,C))) ) ).
fof(dt_k19_index_1,axiom,
! [A,B,C] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& v3_cat_5(B)
& l1_cat_1(B)
& m2_cat_1(C,A,B) )
=> m5_index_1(k19_index_1(A,B,C),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ).
fof(dt_k20_index_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)
& m5_index_1(E,u1_cat_1(C),u2_cat_1(C),u3_cat_1(C),u4_cat_1(C),u5_cat_1(C),u6_cat_1(C)) )
=> m5_index_1(k20_index_1(A,B,C,D,E),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ).
fof(dt_k21_index_1,axiom,
! [A,B,C,D,E] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& m5_index_1(B,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
& v2_cat_1(C)
& v3_cat_5(C)
& l1_cat_1(C)
& v2_cat_1(D)
& v3_cat_5(D)
& l1_cat_1(D)
& m2_cat_1(E,C,D) )
=> m5_index_1(k21_index_1(A,B,C,D,E),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ).
fof(dt_k22_index_1,axiom,
! [A,B,C,D] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& v2_cat_1(B)
& l1_cat_1(B)
& m5_index_1(C,u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))
& m5_index_1(D,u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) )
=> m5_index_1(k22_index_1(A,B,C,D),u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) ) ).
%------------------------------------------------------------------------------