SET007 Axioms: SET007+463.ax
%------------------------------------------------------------------------------
% File : SET007+463 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Functors for Alternative 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 : functor0 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 172 ( 5 unt; 0 def)
% Number of atoms : 1515 ( 116 equ)
% Maximal formula atoms : 19 ( 8 avg)
% Number of connectives : 1596 ( 253 ~; 1 |; 829 &)
% ( 40 <=>; 473 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 1 prp; 0-6 aty)
% Number of functors : 56 ( 56 usr; 6 con; 0-6 aty)
% Number of variables : 655 ( 618 !; 37 ?)
% 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(fc1_functor0,axiom,
! [A] :
( ( v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_xboole_0(k2_funct_4(A))
& v1_relat_1(k2_funct_4(A))
& v1_funct_1(k2_funct_4(A))
& v2_funct_1(k2_funct_4(A)) ) ) ).
fof(fc2_functor0,axiom,
! [A,B] :
( ( v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_xboole_0(k15_funct_3(A,B))
& v1_relat_1(k15_funct_3(A,B))
& v1_funct_1(k15_funct_3(A,B))
& v2_funct_1(k15_funct_3(A,B)) ) ) ).
fof(fc3_functor0,axiom,
! [A,B] :
( ( v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_xboole_0(k15_funct_3(B,A))
& v1_relat_1(k15_funct_3(B,A))
& v1_funct_1(k15_funct_3(B,A))
& v2_funct_1(k15_funct_3(B,A)) ) ) ).
fof(fc4_functor0,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ( v1_relat_1(k2_funct_4(A))
& v1_funct_1(k2_funct_4(A))
& v1_funcop_1(k2_funct_4(A)) ) ) ).
fof(rc1_functor0,axiom,
! [A,B] :
? [C] :
( m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
& v1_functor0(C,A,B)
& v2_functor0(C,A,B) ) ).
fof(cc1_functor0,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,A)
& m1_pboole(E,B) )
=> ! [F] :
( m1_functor0(F,A,B,C,D,E)
=> v1_funcop_1(F) ) ) ).
fof(rc2_functor0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ? [C] :
( l1_functor0(C,A,B)
& v3_functor0(C,A,B) ) ) ).
fof(rc3_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v9_functor0(C,A,B) ) ) ).
fof(rc4_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v10_functor0(C,A,B) ) ) ).
fof(rc5_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v11_functor0(C,A,B) ) ) ).
fof(fc5_functor0,axiom,
! [A,B,C,D,E] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& l2_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_relat_1(k4_functor0(A,B,C,D,E))
& v1_funct_1(k4_functor0(A,B,C,D,E)) ) ) ).
fof(fc6_functor0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_altcat_1(B,C,C)) )
=> ( v8_functor0(k9_functor0(A,B,C,D),A,B)
& v9_functor0(k9_functor0(A,B,C,D),A,B)
& v10_functor0(k9_functor0(A,B,C,D),A,B)
& v11_functor0(k9_functor0(A,B,C,D),A,B) ) ) ).
fof(rc6_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v8_functor0(C,A,B)
& v10_functor0(C,A,B)
& v11_functor0(C,A,B) ) ) ).
fof(fc7_functor0,axiom,
! [A,B,C] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> ( v1_relat_1(u2_functor0(A,B,C))
& v1_funct_1(u2_functor0(A,B,C))
& v1_funcop_1(u2_functor0(A,B,C)) ) ) ).
fof(rc7_functor0,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v1_altcat_2(A) ) ).
fof(cc2_functor0,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v12_altcat_1(A) )
=> ( ~ v3_struct_0(A)
& v1_altcat_2(A) ) ) ) ).
fof(fc8_functor0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( v8_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v9_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v10_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v11_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v12_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B) ) ) ).
fof(fc9_functor0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_altcat_1(B,C,C)) )
=> ( v6_functor0(k9_functor0(A,B,C,D),A,B)
& v8_functor0(k9_functor0(A,B,C,D),A,B)
& v9_functor0(k9_functor0(A,B,C,D),A,B)
& v10_functor0(k9_functor0(A,B,C,D),A,B)
& v11_functor0(k9_functor0(A,B,C,D),A,B) ) ) ).
fof(rc8_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v6_functor0(C,A,B)
& v8_functor0(C,A,B) ) ) ).
fof(rc9_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v9_functor0(C,A,B)
& v12_functor0(C,A,B) ) ) ).
fof(fc10_functor0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( v6_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v8_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v9_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v10_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v11_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v13_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
& v14_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B) ) ) ).
fof(fc11_functor0,axiom,
! [A,B] :
( ( l2_altcat_1(A)
& m1_altcat_2(B,A) )
=> ( v9_functor0(k10_functor0(A,B),B,A)
& v10_functor0(k10_functor0(A,B),B,A) ) ) ).
fof(fc12_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& m1_altcat_2(B,A) )
=> ( v8_functor0(k10_functor0(A,B),B,A)
& v9_functor0(k10_functor0(A,B),B,A)
& v10_functor0(k10_functor0(A,B),B,A) ) ) ).
fof(rc10_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] :
( m2_functor0(C,A,B)
& v8_functor0(C,A,B)
& v9_functor0(C,A,B)
& v15_functor0(C,A,B)
& v16_functor0(C,A,B) ) ) ).
fof(fc13_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ( v8_functor0(k11_functor0(A),A,A)
& v9_functor0(k11_functor0(A),A,A)
& v10_functor0(k11_functor0(A),A,A) ) ) ).
fof(rc11_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ? [B] :
( l2_functor0(B,A,A)
& v8_functor0(B,A,A)
& v10_functor0(B,A,A) ) ) ).
fof(fc14_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v8_functor0(k11_functor0(A),A,A)
& v9_functor0(k11_functor0(A),A,A)
& v10_functor0(k11_functor0(A),A,A)
& v12_functor0(k11_functor0(A),A,A)
& v13_functor0(k11_functor0(A),A,A) ) ) ).
fof(fc15_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ( v9_functor0(k11_functor0(A),A,A)
& v21_functor0(k11_functor0(A),A,A) ) ) ).
fof(fc16_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& l2_functor0(D,A,B)
& v10_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v10_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc17_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& l2_functor0(D,A,B)
& v10_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v11_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc18_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& l2_functor0(D,A,B)
& v11_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v11_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc19_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& l2_functor0(D,A,B)
& v11_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v10_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc20_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& l2_functor0(D,A,B)
& v8_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v8_functor0(k13_functor0(A,B,C,D,E),A,C)
& v9_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc21_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v6_functor0(D,A,B)
& v8_functor0(D,A,B)
& v12_functor0(D,A,B)
& l2_functor0(D,A,B)
& v12_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v12_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(cc3_functor0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v10_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(cc4_functor0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v11_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(cc5_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v15_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(cc6_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v16_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(t1_functor0,axiom,
! [A] :
( v1_funct_1(k1_xboole_0)
& v1_funct_2(k1_xboole_0,A,k1_xboole_0)
& m2_relset_1(k1_xboole_0,A,k1_xboole_0) ) ).
fof(t2_functor0,axiom,
$true ).
fof(t3_functor0,axiom,
! [A,B] :
( m1_pboole(B,A)
=> k5_relat_1(k6_partfun1(A),B) = B ) ).
fof(t4_functor0,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> k9_relat_1(B,k6_partfun1(A)) = k9_relat_1(k2_funct_4(B),k6_partfun1(A)) ) ).
fof(t5_functor0,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_funct_2(C,A,B)
<=> v2_funct_2(k16_funct_3(A,A,B,B,C,C),k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) ) ) ).
fof(t6_functor0,axiom,
! [A,B,C] : k2_funct_4(k10_pboole(k2_zfmisc_1(A,B),C)) = k10_pboole(k2_zfmisc_1(B,A),C) ).
fof(t7_functor0,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) )
=> k2_funct_1(k15_funct_3(A,B)) = k15_funct_3(k2_funct_1(A),k2_funct_1(B)) ) ) ) ).
fof(t8_functor0,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v2_funct_1(k15_funct_3(A,A))
=> v2_funct_1(A) ) ) ).
fof(t9_functor0,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v2_funct_1(A)
=> v2_funct_1(k2_funct_4(A)) ) ) ).
fof(t10_functor0,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( v2_funct_1(k2_funct_4(k15_funct_3(A,B)))
=> v2_funct_1(k15_funct_3(B,A)) ) ) ) ).
fof(t11_functor0,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) )
=> k2_funct_1(k2_funct_4(k15_funct_3(A,B))) = k2_funct_4(k2_funct_1(k15_funct_3(B,A))) ) ) ) ).
fof(t12_functor0,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v2_funct_2(C,A,B)
=> r1_tarski(k6_partfun1(B),k2_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(A))) ) ) ).
fof(t13_functor0,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> k5_relat_1(C,k13_pboole(A,B)) = k13_pboole(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) ).
fof(t14_functor0,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m2_relset_1(D,k2_zfmisc_1(A,B),C) )
=> ( v2_funct_2(k1_functor0(A,B,C,D),k2_zfmisc_1(B,A),C)
=> v2_funct_2(D,k2_zfmisc_1(A,B),C) ) ) ).
fof(t15_functor0,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> r1_tarski(k2_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(A)),k6_partfun1(B)) ) ) ).
fof(d1_functor0,axiom,
$true ).
fof(d2_functor0,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
& m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
=> ( v1_functor0(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B)
& C = k16_funct_3(A,A,B,B,D,D) ) ) ) ).
fof(d3_functor0,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
& m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
=> ( v2_functor0(C,A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B)
& C = k1_functor0(A,A,k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,D,D)) ) ) ) ).
fof(t16_functor0,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
& m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
=> ( D = k10_pboole(k2_zfmisc_1(A,A),k4_tarski(C,C))
=> ( v1_functor0(D,A,B)
& v2_functor0(D,A,B) ) ) ) ) ) ).
fof(t17_functor0,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
& v1_functor0(C,A,B)
& v2_functor0(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
=> ? [D] :
( m1_subset_1(D,B)
& C = k10_pboole(k2_zfmisc_1(A,A),k4_tarski(D,D)) ) ) ) ) ).
fof(d4_functor0,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,B)
=> ! [F] :
( m1_pboole(F,A)
=> ( ( B != k1_xboole_0
=> ( m1_functor0(F,A,B,C,D,E)
<=> ? [G] :
( ~ v1_xboole_0(G)
& ? [H] :
( m1_pboole(H,G)
& ? [I] :
( v1_funct_1(I)
& v1_funct_2(I,A,G)
& m2_relset_1(I,A,G)
& C = I
& E = H
& m3_pboole(F,A,D,k7_pboole(A,G,I,H)) ) ) ) ) )
& ( B = k1_xboole_0
=> ( m1_functor0(F,A,B,C,D,E)
<=> r6_pboole(A,F,k1_pboole(A)) ) ) ) ) ) ) ) ).
fof(d5_functor0,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m1_pboole(E,B)
=> ! [F] :
( m1_pboole(F,A)
=> ( m1_functor0(F,A,B,C,D,E)
<=> m3_pboole(F,A,D,k7_pboole(A,B,C,E)) ) ) ) ) ) ) ).
fof(t18_functor0,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ! [F] :
( m1_pboole(F,B)
=> ! [G] :
( m1_pboole(G,C)
=> ! [H] :
( m1_functor0(H,B,C,E,F,G)
=> m1_functor0(k7_pboole(A,B,D,H),A,C,k7_funct_2(A,B,C,D,E),k7_pboole(A,B,D,F),G) ) ) ) ) ) ) ) ).
fof(t20_functor0,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,C)
& m2_relset_1(E,B,C) )
=> ! [F] :
( m1_pboole(F,A)
=> ! [G] :
( m1_pboole(G,B)
=> ! [H] :
( m1_pboole(H,C)
=> ! [I] :
( m1_functor0(I,A,B,D,F,G)
=> ! [J] :
( m1_functor0(J,A,C,k7_funct_2(A,B,C,D,E),k7_pboole(A,B,D,G),H)
=> ( ! [K] :
~ ( r2_hidden(K,A)
& k1_funct_1(k7_pboole(A,B,D,G),K) = k1_xboole_0
& k1_funct_1(F,K) != k1_xboole_0
& k1_funct_1(k7_pboole(A,C,k7_funct_2(A,B,C,D,E),H),K) != k1_xboole_0 )
=> m1_functor0(k13_pboole(I,J),A,C,k7_funct_2(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_functor0(A,B,C,D) = k1_mcart_1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),D,D)) ) ) ) ) ).
fof(d7_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v4_functor0(C,A,B)
<=> v2_funct_1(u1_functor0(A,B,C)) ) ) ) ) ).
fof(d8_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v5_functor0(C,A,B)
<=> v2_funct_2(u1_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) ) ) ) ) ).
fof(d9_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v6_functor0(C,A,B)
<=> r1_tarski(k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),k6_partfun1(u1_struct_0(A))),k6_partfun1(u1_struct_0(B))) ) ) ) ) ).
fof(d10_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v7_functor0(C,A,B)
<=> r1_tarski(k6_partfun1(u1_struct_0(B)),k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),k6_partfun1(u1_struct_0(A)))) ) ) ) ) ).
fof(d11_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v6_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),D,D) = k4_tarski(k3_functor0(A,B,C,D),k3_functor0(A,B,C,D)) ) ) ) ) ) ).
fof(t21_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_altcat_2(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v7_functor0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& k3_functor0(A,B,C,E) = D ) ) ) ) ) ) ).
fof(d12_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v8_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_funct_1(u1_altcat_1(B),k2_binop_1(u1_struct_0(A),u1_struct_0(A),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),D,E)) = k1_xboole_0 ) ) ) ) ) ) ) ).
fof(d13_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v10_functor0(C,A,B)
<=> v1_functor0(u1_functor0(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(d14_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v11_functor0(C,A,B)
<=> v2_functor0(u1_functor0(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(d15_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( l1_altcat_1(B)
=> ! [C] :
( l2_functor0(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k4_functor0(A,B,C,D,E) = k1_binop_1(u2_functor0(A,B,C),D,E) ) ) ) ) ) ).
fof(d16_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> k6_functor0(A,B,C,D,E,F) = k1_funct_1(k5_functor0(A,B,C,D,E),F) ) ) ) ) ) ) ) ).
fof(d17_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) != k1_xboole_0
& ~ ! [F] :
( m1_subset_1(F,k1_altcat_1(A,D,E))
=> k8_functor0(A,B,C,D,E,F) = k1_funct_1(k7_functor0(A,B,C,D,E),F) ) ) ) ) ) ) ) ).
fof(t22_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k1_altcat_1(B,C,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(B,C,C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_functor0(A,B,k9_functor0(A,B,C,D),E) = C ) ) ) ) ) ) ).
fof(t23_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),D,E) = k4_tarski(k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) ).
fof(d19_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v8_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) = k1_xboole_0 ) ) ) ) ) ) ) ).
fof(t24_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),D,E) = k4_tarski(k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) ).
fof(d20_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v8_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) = k1_xboole_0 ) ) ) ) ) ) ) ).
fof(d21_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v12_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(k4_functor0(A,B,C,D,D),k8_altcat_1(A,D)) = k8_altcat_1(B,k3_functor0(A,B,C,D)) ) ) ) ) ) ).
fof(t25_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k1_altcat_1(B,C,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(B,C,C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,E,F))
=> ( k1_altcat_1(A,E,F) != k1_xboole_0
=> k1_funct_1(k4_functor0(A,B,k9_functor0(A,B,C,D),E,F),G) = D ) ) ) ) ) ) ) ) ) ).
fof(d22_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v13_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(A,E,F) != k1_xboole_0
& ? [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
& ? [H] :
( m1_subset_1(H,k1_altcat_1(A,E,F))
& ! [I] :
( m1_subset_1(I,k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)))
=> ! [J] :
( m1_subset_1(J,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F)))
=> ~ ( I = k1_funct_1(k4_functor0(A,B,C,D,E),G)
& J = k1_funct_1(k4_functor0(A,B,C,E,F),H)
& k1_funct_1(k4_functor0(A,B,C,D,F),k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d23_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v14_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(A,E,F) != k1_xboole_0
& ? [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
& ? [H] :
( m1_subset_1(H,k1_altcat_1(A,E,F))
& ! [I] :
( m1_subset_1(I,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)))
=> ! [J] :
( m1_subset_1(J,k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E)))
=> ~ ( I = k1_funct_1(k4_functor0(A,B,C,D,E),G)
& J = k1_funct_1(k4_functor0(A,B,C,E,F),H)
& k1_funct_1(k4_functor0(A,B,C,D,F),k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),k3_functor0(A,B,C,D),J,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d24_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& v10_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v13_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(A,E,F) != k1_xboole_0
& ~ ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,E,F))
=> k6_functor0(A,B,C,D,F,k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),k6_functor0(A,B,C,D,E,G),k6_functor0(A,B,C,E,F,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(d25_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& v11_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v14_functor0(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
& k1_altcat_1(A,E,F) != k1_xboole_0
& ~ ! [G] :
( m1_subset_1(G,k1_altcat_1(A,D,E))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,E,F))
=> k8_functor0(A,B,C,D,F,k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),k3_functor0(A,B,C,D),k8_functor0(A,B,C,E,F,H),k8_functor0(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(B,C,C))
=> ! [E] :
( ( v8_functor0(E,A,B)
& v10_functor0(E,A,B)
& l2_functor0(E,A,B) )
=> ( E = k9_functor0(A,B,C,D)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,k1_altcat_1(A,F,G))
=> ( k1_altcat_1(A,F,G) != k1_xboole_0
=> k6_functor0(A,B,E,F,G,H) = D ) ) ) ) ) ) ) ) ) ) ).
fof(t27_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(B,C,C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,k1_altcat_1(A,E,F))
=> ( k1_altcat_1(A,E,F) != k1_xboole_0
=> k8_functor0(A,B,k9_functor0(A,B,C,D),E,F,G) = D ) ) ) ) ) ) ) ) ).
fof(d26_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> ( m2_functor0(C,A,B)
<=> ( v8_functor0(C,A,B)
& v12_functor0(C,A,B)
& ( ( v10_functor0(C,A,B)
& v13_functor0(C,A,B) )
| ( v11_functor0(C,A,B)
& v14_functor0(C,A,B) ) ) ) ) ) ) ) ).
fof(d27_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v15_functor0(C,A,B)
<=> ( v10_functor0(C,A,B)
& v13_functor0(C,A,B) ) ) ) ) ) ).
fof(d28_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v16_functor0(C,A,B)
<=> ( v11_functor0(C,A,B)
& v14_functor0(C,A,B) ) ) ) ) ) ).
fof(d29_functor0,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( m1_altcat_2(B,A)
=> ! [C] :
( ( v9_functor0(C,B,A)
& l2_functor0(C,B,A) )
=> ( C = k10_functor0(A,B)
<=> ( u1_functor0(B,A,C) = k6_partfun1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& r6_pboole(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u2_functor0(B,A,C),k2_msualg_3(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_altcat_1(B))) ) ) ) ) ) ).
fof(d30_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( ( v9_functor0(B,A,A)
& l2_functor0(B,A,A) )
=> ( B = k11_functor0(A)
<=> ( u1_functor0(A,A,B) = k6_partfun1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u2_functor0(A,A,B),k2_msualg_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A))) ) ) ) ) ).
fof(t28_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_functor0(B,A,k10_functor0(A,B),C) = C ) ) ) ).
fof(t29_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_altcat_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> r1_tarski(k1_altcat_1(B,C,D),k1_altcat_1(A,k3_functor0(B,A,k10_functor0(A,B),C),k3_functor0(B,A,k10_functor0(A,B),D))) ) ) ) ) ).
fof(d31_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( l1_altcat_1(B)
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v17_functor0(C,A,B)
<=> v1_msualg_3(u2_functor0(A,B,C)) ) ) ) ) ).
fof(d32_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( l1_altcat_1(B)
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v18_functor0(C,A,B)
<=> ? [D] :
( m1_pboole(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
& ? [E] :
( m3_pboole(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),D)
& D = k5_relat_1(u1_functor0(A,B,C),u1_altcat_1(B))
& r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),E,u2_functor0(A,B,C))
& v2_msualg_3(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),D) ) ) ) ) ) ) ).
fof(d33_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v18_functor0(C,A,B)
<=> ? [D] :
( m3_pboole(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),u1_altcat_1(B)))
& r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),D,u2_functor0(A,B,C))
& v2_msualg_3(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),u1_altcat_1(B))) ) ) ) ) ) ).
fof(d34_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( l1_altcat_1(B)
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v19_functor0(C,A,B)
<=> ( v4_functor0(C,A,B)
& v17_functor0(C,A,B) ) ) ) ) ) ).
fof(d35_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( l1_altcat_1(B)
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v20_functor0(C,A,B)
<=> ( v18_functor0(C,A,B)
& v5_functor0(C,A,B) ) ) ) ) ) ).
fof(d36_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( l1_altcat_1(B)
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v21_functor0(C,A,B)
<=> ( v19_functor0(C,A,B)
& v20_functor0(C,A,B) ) ) ) ) ) ).
fof(t30_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_functor0(A,A,k11_functor0(A),B) = B ) ) ).
fof(t31_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(A,B,C))
=> k1_funct_1(k4_functor0(A,A,k11_functor0(A),B,C),D) = D ) ) ) ) ) ).
fof(t32_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_altcat_1(A,B,C) != k1_xboole_0
=> ! [D] :
( ( v8_functor0(D,A,A)
& v10_functor0(D,A,A)
& l2_functor0(D,A,A) )
=> ( D = k11_functor0(A)
=> ! [E] :
( m1_subset_1(E,k1_altcat_1(A,B,C))
=> k6_functor0(A,A,D,B,C,E) = E ) ) ) ) ) ) ) ).
fof(d37_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C) )
=> ! [D] :
( ( v8_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( l2_functor0(E,B,C)
=> ! [F] :
( ( v9_functor0(F,A,C)
& l2_functor0(F,A,C) )
=> ( F = k13_functor0(A,B,C,D,E)
<=> ( u1_functor0(A,C,F) = k7_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_functor0(A,B,D),u1_functor0(B,C,E))
& r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u2_functor0(A,C,F),k3_altcat_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u2_functor0(A,B,D),k7_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,D),u2_functor0(B,C,E)))) ) ) ) ) ) ) ) ) ).
fof(t33_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_altcat_2(D)
& l1_altcat_1(D) )
=> ! [E] :
( ( v8_functor0(E,A,B)
& l2_functor0(E,A,B) )
=> ! [F] :
( ( v8_functor0(F,B,C)
& l2_functor0(F,B,C) )
=> ! [G] :
( l2_functor0(G,C,D)
=> k13_functor0(A,B,D,E,k13_functor0(B,C,D,F,G)) = k13_functor0(A,C,D,k13_functor0(A,B,C,E,F),G) ) ) ) ) ) ) ) ).
fof(t34_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l2_altcat_1(C) )
=> ! [D] :
( ( v6_functor0(D,A,B)
& v8_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( l2_functor0(E,B,C)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k3_functor0(A,C,k13_functor0(A,B,C,D,E),F) = k3_functor0(B,C,E,k3_functor0(A,B,D,F)) ) ) ) ) ) ) ).
fof(t35_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C) )
=> ! [D] :
( ( v6_functor0(D,A,B)
& v8_functor0(D,A,B)
& l2_functor0(D,A,B) )
=> ! [E] :
( l2_functor0(E,B,C)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k4_functor0(A,C,k13_functor0(A,B,C,D,E),F,F) = k5_relat_1(k4_functor0(A,B,D,F,F),k4_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,F))) ) ) ) ) ) ) ).
fof(d38_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_altcat_2(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_altcat_2(C,A) )
=> ! [D] :
( l2_functor0(D,A,B)
=> k14_functor0(A,B,C,D) = k13_functor0(C,A,B,k10_functor0(A,C),D) ) ) ) ) ).
fof(d39_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( v9_functor0(D,B,A)
& l2_functor0(D,B,A) )
=> ( D = k15_functor0(A,B,C)
<=> ( u1_functor0(B,A,D) = k2_funct_1(u1_functor0(A,B,C))
& ? [E] :
( m3_pboole(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),u1_altcat_1(B)))
& r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),E,u2_functor0(A,B,C))
& u2_functor0(B,A,D) = k5_relat_1(k2_funct_1(u1_functor0(A,B,C)),k4_msualg_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),u1_altcat_1(B)),E)) ) ) ) ) ) ) ) ) ).
fof(t36_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v21_functor0(C,A,B)
=> ( v21_functor0(k15_functor0(A,B,C),B,A)
& v8_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ) ).
fof(t37_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v7_functor0(C,A,B) )
=> v6_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ).
fof(t38_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v12_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v7_functor0(C,A,B) )
=> v12_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ).
fof(t39_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v10_functor0(C,A,B) )
=> v10_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ).
fof(t40_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v11_functor0(C,A,B) )
=> v11_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ).
fof(t41_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v7_functor0(C,A,B)
& v10_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(B,D,E))
=> ( k1_altcat_1(B,D,E) != k1_xboole_0
=> k1_funct_1(k4_functor0(A,B,C,k3_functor0(B,A,k15_functor0(A,B,C),D),k3_functor0(B,A,k15_functor0(A,B,C),E)),k1_funct_1(k4_functor0(B,A,k15_functor0(A,B,C),D,E),F)) = F ) ) ) ) ) ) ) ) ).
fof(t42_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v7_functor0(C,A,B)
& v11_functor0(C,A,B) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,k1_altcat_1(B,D,E))
=> ( k1_altcat_1(B,D,E) != k1_xboole_0
=> k1_funct_1(k4_functor0(A,B,C,k3_functor0(B,A,k15_functor0(A,B,C),E),k3_functor0(B,A,k15_functor0(A,B,C),D)),k1_funct_1(k4_functor0(B,A,k15_functor0(A,B,C),D,E),F)) = F ) ) ) ) ) ) ) ) ).
fof(t43_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v13_functor0(C,A,B)
& v10_functor0(C,A,B)
& v7_functor0(C,A,B) )
=> v13_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ).
fof(t44_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( ( v21_functor0(C,A,B)
& v14_functor0(C,A,B)
& v11_functor0(C,A,B)
& v7_functor0(C,A,B) )
=> v14_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ).
fof(t45_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( ( v10_functor0(C,A,B)
& v5_functor0(C,A,B) )
=> v7_functor0(C,A,B) ) ) ) ) ).
fof(t46_functor0,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( l1_functor0(C,A,B)
=> ( ( v11_functor0(C,A,B)
& v5_functor0(C,A,B) )
=> v7_functor0(C,A,B) ) ) ) ) ).
fof(t47_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( ( v15_functor0(C,A,B)
& v5_functor0(C,A,B) )
=> v7_functor0(C,A,B) ) ) ) ) ).
fof(t48_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( ( v16_functor0(C,A,B)
& v5_functor0(C,A,B) )
=> v7_functor0(C,A,B) ) ) ) ) ).
fof(t49_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v15_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ~ ( v21_functor0(C,A,B)
& ! [D] :
( m2_functor0(D,B,A)
=> ~ ( D = k15_functor0(A,B,C)
& v21_functor0(D,B,A)
& v15_functor0(D,B,A) ) ) ) ) ) ) ).
fof(t50_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v16_functor0(C,A,B)
& m2_functor0(C,A,B) )
=> ~ ( v21_functor0(C,A,B)
& ! [D] :
( m2_functor0(D,B,A)
=> ~ ( D = k15_functor0(A,B,C)
& v21_functor0(D,B,A)
& v16_functor0(D,B,A) ) ) ) ) ) ) ).
fof(d40_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ( r1_functor0(A,B)
<=> ? [C] :
( m2_functor0(C,A,B)
& v21_functor0(C,A,B)
& v15_functor0(C,A,B) ) ) ) ) ).
fof(d41_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ( r2_functor0(A,B)
<=> ? [C] :
( m2_functor0(C,A,B)
& v21_functor0(C,A,B)
& v16_functor0(C,A,B) ) ) ) ) ).
fof(dt_m1_functor0,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,A)
& m1_pboole(E,B) )
=> ! [F] :
( m1_functor0(F,A,B,C,D,E)
=> m1_pboole(F,A) ) ) ).
fof(existence_m1_functor0,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,A)
& m1_pboole(E,B) )
=> ? [F] : m1_functor0(F,A,B,C,D,E) ) ).
fof(dt_m2_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> l2_functor0(C,A,B) ) ) ).
fof(existence_m2_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] : m2_functor0(C,A,B) ) ).
fof(dt_l1_functor0,axiom,
$true ).
fof(existence_l1_functor0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ? [C] : l1_functor0(C,A,B) ) ).
fof(dt_l2_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> l1_functor0(C,A,B) ) ) ).
fof(existence_l2_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] : l2_functor0(C,A,B) ) ).
fof(abstractness_v3_functor0,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& l1_functor0(C,A,B) )
=> ( v3_functor0(C,A,B)
=> C = g1_functor0(A,B,u1_functor0(A,B,C)) ) ) ).
fof(abstractness_v9_functor0,axiom,
! [A,B,C] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> ( v9_functor0(C,A,B)
=> C = g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) ) ) ).
fof(symmetry_r1_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ( r1_functor0(A,B)
=> r1_functor0(B,A) ) ) ).
fof(reflexivity_r1_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> r1_functor0(A,A) ) ).
fof(symmetry_r2_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ( r2_functor0(A,B)
=> r2_functor0(B,A) ) ) ).
fof(dt_k1_functor0,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C) )
=> ( v1_funct_1(k1_functor0(A,B,C,D))
& v1_funct_2(k1_functor0(A,B,C,D),k2_zfmisc_1(B,A),C)
& m2_relset_1(k1_functor0(A,B,C,D),k2_zfmisc_1(B,A),C) ) ) ).
fof(redefinition_k1_functor0,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C) )
=> k1_functor0(A,B,C,D) = k2_funct_4(D) ) ).
fof(dt_k2_functor0,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,k2_zfmisc_1(A,A))
& m1_pboole(E,k2_zfmisc_1(B,B))
& m1_functor0(F,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),D,E) )
=> m1_functor0(k2_functor0(A,B,C,D,E,F),k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k1_altcat_2(A,D),k1_altcat_2(B,E)) ) ).
fof(redefinition_k2_functor0,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,k2_zfmisc_1(A,A))
& m1_pboole(E,k2_zfmisc_1(B,B))
& m1_functor0(F,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),D,E) )
=> k2_functor0(A,B,C,D,E,F) = k2_funct_4(F) ) ).
fof(dt_k3_functor0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& l1_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k3_functor0(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k4_functor0,axiom,
$true ).
fof(dt_k5_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& v10_functor0(C,A,B)
& l2_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_funct_1(k5_functor0(A,B,C,D,E))
& v1_funct_2(k5_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)))
& m2_relset_1(k5_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E))) ) ) ).
fof(redefinition_k5_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& v10_functor0(C,A,B)
& l2_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> k5_functor0(A,B,C,D,E) = k4_functor0(A,B,C,D,E) ) ).
fof(dt_k6_functor0,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& v10_functor0(C,A,B)
& l2_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A))
& m1_subset_1(F,k1_altcat_1(A,D,E)) )
=> m1_subset_1(k6_functor0(A,B,C,D,E,F),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E))) ) ).
fof(dt_k7_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& v11_functor0(C,A,B)
& l2_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_funct_1(k7_functor0(A,B,C,D,E))
& v1_funct_2(k7_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)))
& m2_relset_1(k7_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D))) ) ) ).
fof(redefinition_k7_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& v11_functor0(C,A,B)
& l2_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> k7_functor0(A,B,C,D,E) = k4_functor0(A,B,C,D,E) ) ).
fof(dt_k8_functor0,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& v11_functor0(C,A,B)
& l2_functor0(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A))
& m1_subset_1(F,k1_altcat_1(A,D,E)) )
=> m1_subset_1(k8_functor0(A,B,C,D,E,F),k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D))) ) ).
fof(dt_k9_functor0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_altcat_1(B,C,C)) )
=> ( v9_functor0(k9_functor0(A,B,C,D),A,B)
& l2_functor0(k9_functor0(A,B,C,D),A,B) ) ) ).
fof(dt_k10_functor0,axiom,
! [A,B] :
( ( l2_altcat_1(A)
& m1_altcat_2(B,A) )
=> ( v9_functor0(k10_functor0(A,B),B,A)
& l2_functor0(k10_functor0(A,B),B,A) ) ) ).
fof(dt_k11_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ( v9_functor0(k11_functor0(A),A,A)
& l2_functor0(k11_functor0(A),A,A) ) ) ).
fof(dt_k12_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v9_functor0(k12_functor0(A),A,A)
& v15_functor0(k12_functor0(A),A,A)
& m2_functor0(k12_functor0(A),A,A) ) ) ).
fof(redefinition_k12_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k12_functor0(A) = k11_functor0(A) ) ).
fof(dt_k13_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& l2_functor0(D,A,B)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& l2_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(dt_k14_functor0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v1_altcat_2(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& m1_altcat_2(C,A)
& l2_functor0(D,A,B) )
=> l2_functor0(k14_functor0(A,B,C,D),C,B) ) ).
fof(dt_k15_functor0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> ( v9_functor0(k15_functor0(A,B,C),B,A)
& l2_functor0(k15_functor0(A,B,C),B,A) ) ) ).
fof(dt_u1_functor0,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& l1_functor0(C,A,B) )
=> ( v1_funct_1(u1_functor0(A,B,C))
& v1_funct_2(u1_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m2_relset_1(u1_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) ) ) ).
fof(dt_u2_functor0,axiom,
! [A,B,C] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> m1_functor0(u2_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),u1_altcat_1(A),u1_altcat_1(B)) ) ).
fof(dt_g1_functor0,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) )
=> ( v3_functor0(g1_functor0(A,B,C),A,B)
& l1_functor0(g1_functor0(A,B,C),A,B) ) ) ).
fof(free_g1_functor0,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) )
=> ! [D,E,F] :
( g1_functor0(A,B,C) = g1_functor0(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(dt_g2_functor0,axiom,
! [A,B,C,D] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_functor0(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),C,u1_altcat_1(A),u1_altcat_1(B)) )
=> ( v9_functor0(g2_functor0(A,B,C,D),A,B)
& l2_functor0(g2_functor0(A,B,C,D),A,B) ) ) ).
fof(free_g2_functor0,axiom,
! [A,B,C,D] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_functor0(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),C,u1_altcat_1(A),u1_altcat_1(B)) )
=> ! [E,F,G,H] :
( g2_functor0(A,B,C,D) = g2_functor0(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(t19_functor0,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_pboole(C,A)
=> ! [D] :
( m1_pboole(D,B)
=> ! [E] :
( m1_subset_1(E,B)
=> ( k1_funct_1(D,E) != k1_xboole_0
=> ! [F] :
( m1_subset_1(F,k1_funct_1(D,E))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,B)
& m2_relset_1(G,A,B) )
=> ( G = k10_pboole(A,E)
=> m1_functor0(a_6_0_functor0(A,B,C,D,E,F),A,B,G,C,D) ) ) ) ) ) ) ) ) ) ).
fof(d18_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( k1_altcat_1(B,C,C) != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,k1_altcat_1(B,C,C))
=> ! [E] :
( ( v9_functor0(E,A,B)
& l2_functor0(E,A,B) )
=> ( E = k9_functor0(A,B,C,D)
<=> ( u1_functor0(A,B,E) = k10_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k4_tarski(C,C))
& u2_functor0(A,B,E) = a_4_0_functor0(A,B,C,D) ) ) ) ) ) ) ) ) ).
fof(s1_functor0,axiom,
( ( f2_s1_functor0 = a_0_0_functor0
& p1_s1_functor0(f3_s1_functor0,f4_s1_functor0) )
=> k1_binop_1(f2_s1_functor0,f3_s1_functor0,f4_s1_functor0) = f5_s1_functor0(f3_s1_functor0,f4_s1_functor0) ) ).
fof(fraenkel_a_6_0_functor0,axiom,
! [A,B,C,D,E,F,G] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_pboole(D,B)
& m1_pboole(E,C)
& m1_subset_1(F,C)
& m1_subset_1(G,k1_funct_1(E,F)) )
=> ( r2_hidden(A,a_6_0_functor0(B,C,D,E,F,G))
<=> ? [H] :
( m1_subset_1(H,B)
& A = k4_tarski(H,k10_pboole(k1_funct_1(D,H),G)) ) ) ) ).
fof(fraenkel_a_4_0_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& l1_altcat_1(C)
& m1_subset_1(D,u1_struct_0(C))
& m1_subset_1(E,k1_altcat_1(C,D,D)) )
=> ( r2_hidden(A,a_4_0_functor0(B,C,D,E))
<=> ? [F,G] :
( m1_subset_1(F,u1_struct_0(B))
& m1_subset_1(G,u1_struct_0(B))
& A = k4_tarski(k4_tarski(F,G),k10_pboole(k1_altcat_1(B,F,G),E)) ) ) ) ).
fof(fraenkel_a_0_0_functor0,axiom,
! [A] :
( r2_hidden(A,a_0_0_functor0)
<=> ? [B,C] :
( m1_subset_1(B,f1_s1_functor0)
& m1_subset_1(C,f1_s1_functor0)
& A = k4_tarski(k4_tarski(B,C),f5_s1_functor0(B,C))
& p1_s1_functor0(B,C) ) ) ).
%------------------------------------------------------------------------------