SET007 Axioms: SET007+311.ax
%------------------------------------------------------------------------------
% File : SET007+311 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Categories of Groups
% 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 : grcat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 185 ( 14 unt; 0 def)
% Number of atoms : 1405 ( 135 equ)
% Maximal formula atoms : 33 ( 7 avg)
% Number of connectives : 1447 ( 227 ~; 0 |; 850 &)
% ( 31 <=>; 339 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-4 aty)
% Number of functors : 93 ( 93 usr; 11 con; 0-6 aty)
% Number of variables : 436 ( 395 !; 41 ?)
% 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_grcat_1,axiom,
( ~ v3_struct_0(k2_algstr_1)
& v1_rlvect_1(k2_algstr_1)
& v3_rlvect_1(k2_algstr_1)
& v4_rlvect_1(k2_algstr_1)
& v5_rlvect_1(k2_algstr_1)
& v6_rlvect_1(k2_algstr_1)
& v13_vectsp_1(k2_algstr_1)
& v1_midsp_2(k2_algstr_1)
& v1_algstr_1(k2_algstr_1)
& v2_algstr_1(k2_algstr_1)
& v3_algstr_1(k2_algstr_1)
& v4_algstr_1(k2_algstr_1)
& v5_algstr_1(k2_algstr_1)
& v6_algstr_1(k2_algstr_1) ) ).
fof(fc2_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> ~ v1_xboole_0(k1_grcat_1(A,B)) ) ).
fof(fc3_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> ( v1_cat_1(k6_grcat_1(A,B))
& v2_cat_1(k6_grcat_1(A,B)) ) ) ).
fof(rc1_grcat_1,axiom,
? [A] :
( l1_grcat_1(A)
& v2_grcat_1(A) ) ).
fof(fc4_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> v2_grcat_1(k12_grcat_1(A,B)) ) ).
fof(rc2_grcat_1,axiom,
? [A] :
( l1_grcat_1(A)
& v2_grcat_1(A)
& v3_grcat_1(A) ) ).
fof(fc5_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ( v2_grcat_1(k12_grcat_1(A,B))
& v3_grcat_1(k12_grcat_1(A,B)) ) ) ).
fof(rc3_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ? [C] :
( m1_grcat_1(C,A,B)
& v2_grcat_1(C)
& v3_grcat_1(C) ) ) ).
fof(fc6_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ( v2_grcat_1(k13_grcat_1(A))
& v3_grcat_1(k13_grcat_1(A)) ) ) ).
fof(rc4_grcat_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v4_grcat_1(A) ) ).
fof(rc5_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ? [B] :
( m1_subset_1(B,A)
& ~ v3_struct_0(B)
& v1_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v1_algstr_1(B)
& v2_algstr_1(B)
& v3_algstr_1(B)
& v4_algstr_1(B)
& v5_algstr_1(B)
& v6_algstr_1(B) ) ) ).
fof(rc6_grcat_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v5_grcat_1(A) ) ).
fof(rc7_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v5_grcat_1(A) )
=> ? [B] :
( m1_subset_1(B,A)
& v2_grcat_1(B)
& v3_grcat_1(B) ) ) ).
fof(fc7_grcat_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ~ v1_xboole_0(k17_grcat_1(A,B)) ) ).
fof(rc8_grcat_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ? [C] :
( m5_grcat_1(C,A,B)
& ~ v1_xboole_0(C) ) ) ).
fof(rc9_grcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& m4_grcat_1(C,A,B) )
=> ? [D] :
( m1_subset_1(D,C)
& v2_grcat_1(D)
& v3_grcat_1(D) ) ) ).
fof(fc8_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ~ v1_xboole_0(k19_grcat_1(A)) ) ).
fof(fc9_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ( ~ v1_xboole_0(k19_grcat_1(A))
& v4_grcat_1(k19_grcat_1(A)) ) ) ).
fof(fc10_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> v1_cat_1(k28_grcat_1(A)) ) ).
fof(fc11_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ( v1_cat_1(k28_grcat_1(A))
& v2_cat_1(k28_grcat_1(A)) ) ) ).
fof(fc12_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ~ v1_xboole_0(k29_grcat_1(A)) ) ).
fof(fc13_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ( v1_cat_1(k30_grcat_1(A))
& v2_cat_1(k30_grcat_1(A)) ) ) ).
fof(fc14_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ~ v1_xboole_0(k31_grcat_1(A)) ) ).
fof(fc15_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ( v1_cat_1(k32_grcat_1(A))
& v2_cat_1(k32_grcat_1(A)) ) ) ).
fof(t1_grcat_1,axiom,
$true ).
fof(t2_grcat_1,axiom,
! [A,B,C,D] :
~ ( r2_hidden(D,C)
& r1_tarski(C,k2_zfmisc_1(A,B))
& ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,B)
=> D != k4_tarski(E,F) ) ) ) ).
fof(t3_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( m1_subset_1(k3_mcart_1(B,C,D),A)
& m1_subset_1(k4_mcart_1(B,C,D,E),A) ) ) ) ) ) ) ).
fof(t4_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B,C] :
( ( r2_hidden(B,C)
& r2_hidden(C,A) )
=> r2_hidden(B,A) ) ) ).
fof(t5_grcat_1,axiom,
( k1_binop_1(k2_midsp_1,k1_xboole_0,k1_xboole_0) = k1_xboole_0
& k1_funct_1(k7_vectsp_2,k1_xboole_0) = k1_xboole_0
& k8_vectsp_2 = k1_xboole_0 ) ).
fof(t6_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ( r2_hidden(k1_tarski(k1_xboole_0),A)
& r2_hidden(k4_tarski(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A)
& r2_hidden(k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A)
& r2_hidden(k2_midsp_1,A)
& r2_hidden(k7_vectsp_2,A) ) ) ).
fof(t7_grcat_1,axiom,
v1_midsp_2(g1_rlvect_1(k1_tarski(k1_xboole_0),k2_midsp_1,k1_algstr_1(k1_xboole_0))) ).
fof(t8_grcat_1,axiom,
( ! [A] :
( m1_subset_1(A,u1_struct_0(k2_algstr_1))
=> A = k1_xboole_0 )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k2_algstr_1))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_algstr_1))
=> k4_rlvect_1(k2_algstr_1,A,B) = k1_xboole_0 ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k2_algstr_1))
=> k5_rlvect_1(k2_algstr_1,A) = k1_xboole_0 )
& k1_rlvect_1(k2_algstr_1) = k1_xboole_0 ) ).
fof(d1_grcat_1,axiom,
$true ).
fof(d2_grcat_1,axiom,
$true ).
fof(d3_grcat_1,axiom,
$true ).
fof(d4_grcat_1,axiom,
$true ).
fof(d6_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> k2_grcat_1(A,B) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k1_grcat_1(A,B)) ) ) ).
fof(d7_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> k3_grcat_1(A,B) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k1_grcat_1(A,B)) ) ) ).
fof(d8_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> k4_grcat_1(A,B) = k1_realset1(u5_cat_1(A),k1_grcat_1(A,B)) ) ) ).
fof(d9_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> k5_grcat_1(A,B) = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) ) ) ).
fof(t9_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> r1_cat_2(g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)),A) ) ) ).
fof(d10_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> k6_grcat_1(A,B) = g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)) ) ) ).
fof(t10_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> u1_cat_1(k6_grcat_1(A,B)) = B ) ) ).
fof(d11_grcat_1,axiom,
! [A] :
( l1_struct_0(A)
=> k7_grcat_1(A) = k6_partfun1(u1_struct_0(A)) ) ).
fof(t11_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B ) ) ).
fof(t12_grcat_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C) = C
& k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)) = C ) ) ) ) ).
fof(d12_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> k8_grcat_1(A,B) = k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)) ) ) ).
fof(d13_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_grcat_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ).
fof(t13_grcat_1,axiom,
k7_vectsp_1(k2_algstr_1) = k7_vectsp_2 ).
fof(t14_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v1_grcat_1(D,A,B)
& v1_grcat_1(E,B,C) )
=> v1_grcat_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t15_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),k8_grcat_1(A,B),C) = k1_rlvect_1(B) ) ) ) ).
fof(t16_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l1_rlvect_1(B) )
=> v1_grcat_1(k8_grcat_1(A,B),A,B) ) ) ).
fof(d14_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> k9_grcat_1(A) = u1_grcat_1(A) ) ).
fof(d15_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> k10_grcat_1(A) = u2_grcat_1(A) ) ).
fof(d16_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> k11_grcat_1(A) = u3_grcat_1(A) ) ).
fof(t17_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( A = g1_grcat_1(B,C,D)
=> ( k9_grcat_1(A) = B
& k10_grcat_1(A) = C
& k11_grcat_1(A) = D ) ) ) ) ) ) ).
fof(d17_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> k12_grcat_1(A,B) = g1_grcat_1(A,B,k8_grcat_1(A,B)) ) ) ).
fof(d18_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( v3_grcat_1(A)
<=> v1_grcat_1(k11_grcat_1(A),k9_grcat_1(A),k10_grcat_1(A)) ) ) ).
fof(t18_grcat_1,axiom,
! [A] :
( ( v3_grcat_1(A)
& l1_grcat_1(A) )
=> v1_grcat_1(u3_grcat_1(A),u1_grcat_1(A),u2_grcat_1(A)) ) ).
fof(d19_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v3_grcat_1(C)
& l1_grcat_1(C) )
=> ( m1_grcat_1(C,A,B)
<=> ( k9_grcat_1(C) = A
& k10_grcat_1(C) = B ) ) ) ) ) ).
fof(t19_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v2_grcat_1(C)
& l1_grcat_1(C) )
=> ( ( k9_grcat_1(C) = A
& k10_grcat_1(C) = B
& v1_grcat_1(k11_grcat_1(C),k9_grcat_1(C),k10_grcat_1(C)) )
=> ( v2_grcat_1(C)
& m1_grcat_1(C,A,B) ) ) ) ) ) ).
fof(t20_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_grcat_1(C,A,B)
=> ( v2_grcat_1(g1_grcat_1(A,B,C))
& m1_grcat_1(g1_grcat_1(A,B,C),A,B) ) ) ) ) ) ).
fof(t21_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> v1_grcat_1(k7_grcat_1(A),A,A) ) ).
fof(d20_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> k13_grcat_1(A) = g1_grcat_1(A,A,k7_grcat_1(A)) ) ).
fof(t22_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( m1_grcat_1(C,A,B)
=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& g1_grcat_1(u1_grcat_1(C),u2_grcat_1(C),u3_grcat_1(C)) = g1_grcat_1(A,B,D)
& v1_grcat_1(D,A,B) ) ) ) ) ).
fof(t23_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v2_grcat_1(C)
& m1_grcat_1(C,A,B) )
=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& C = g1_grcat_1(A,B,D) ) ) ) ) ).
fof(t24_grcat_1,axiom,
! [A] :
( ( v3_grcat_1(A)
& l1_grcat_1(A) )
=> ? [B] :
( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& ? [C] :
( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& m1_grcat_1(A,B,C) ) ) ) ).
fof(t25_grcat_1,axiom,
! [A] :
( ( v2_grcat_1(A)
& v3_grcat_1(A)
& l1_grcat_1(A) )
=> ? [B] :
( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& ? [C] :
( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_grcat_1(A,B,C)
& A = g1_grcat_1(B,C,D)
& v1_grcat_1(D,B,C) ) ) ) ) ).
fof(t26_grcat_1,axiom,
! [A] :
( ( v3_grcat_1(A)
& l1_grcat_1(A) )
=> ! [B] :
( ( v3_grcat_1(B)
& l1_grcat_1(B) )
=> ~ ( k9_grcat_1(A) = k10_grcat_1(B)
& ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& l1_rlvect_1(E) )
=> ~ ( m1_grcat_1(A,D,E)
& m1_grcat_1(B,C,D) ) ) ) ) ) ) ) ).
fof(d21_grcat_1,axiom,
! [A] :
( ( v3_grcat_1(A)
& l1_grcat_1(A) )
=> ! [B] :
( ( v3_grcat_1(B)
& l1_grcat_1(B) )
=> ( k9_grcat_1(A) = k10_grcat_1(B)
=> ! [C] :
( ( v2_grcat_1(C)
& v3_grcat_1(C)
& l1_grcat_1(C) )
=> ( C = k15_grcat_1(A,B)
<=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& l1_rlvect_1(E) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v4_rlvect_1(F)
& v5_rlvect_1(F)
& v6_rlvect_1(F)
& l1_rlvect_1(F) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(E),u1_struct_0(F))
& m2_relset_1(G,u1_struct_0(E),u1_struct_0(F)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(H,u1_struct_0(D),u1_struct_0(E)) )
=> ( ( g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) = g1_grcat_1(E,F,G)
& g1_grcat_1(u1_grcat_1(B),u2_grcat_1(B),u3_grcat_1(B)) = g1_grcat_1(D,E,H) )
=> C = g1_grcat_1(D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),H,G)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_grcat_1,axiom,
$true ).
fof(t28_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( m1_grcat_1(D,B,C)
=> ! [E] :
( m1_grcat_1(E,A,B)
=> m1_grcat_1(k15_grcat_1(D,E),A,C) ) ) ) ) ) ).
fof(t29_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( m1_grcat_1(D,B,C)
=> ! [E] :
( m1_grcat_1(E,A,B)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(G,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( D = g1_grcat_1(B,C,F)
& E = g1_grcat_1(A,B,G) )
=> k16_grcat_1(A,B,C,D,E) = g1_grcat_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),G,F)) ) ) ) ) ) ) ) ) ).
fof(t30_grcat_1,axiom,
! [A] :
( ( v2_grcat_1(A)
& v3_grcat_1(A)
& l1_grcat_1(A) )
=> ! [B] :
( ( v2_grcat_1(B)
& v3_grcat_1(B)
& l1_grcat_1(B) )
=> ~ ( k9_grcat_1(B) = k10_grcat_1(A)
& ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& l1_rlvect_1(E) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
=> ~ ( A = g1_grcat_1(C,D,F)
& B = g1_grcat_1(D,E,G)
& k15_grcat_1(B,A) = g1_grcat_1(C,E,k7_funct_2(u1_struct_0(C),u1_struct_0(D),u1_struct_0(E),F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t31_grcat_1,axiom,
! [A] :
( ( v2_grcat_1(A)
& v3_grcat_1(A)
& l1_grcat_1(A) )
=> ! [B] :
( ( v2_grcat_1(B)
& v3_grcat_1(B)
& l1_grcat_1(B) )
=> ( k9_grcat_1(B) = k10_grcat_1(A)
=> ( k9_grcat_1(k15_grcat_1(B,A)) = k9_grcat_1(A)
& k10_grcat_1(k15_grcat_1(B,A)) = k10_grcat_1(B) ) ) ) ) ).
fof(t32_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D) )
=> ! [E] :
( ( v2_grcat_1(E)
& m1_grcat_1(E,A,B) )
=> ! [F] :
( ( v2_grcat_1(F)
& m1_grcat_1(F,B,C) )
=> ! [G] :
( ( v2_grcat_1(G)
& m1_grcat_1(G,C,D) )
=> k16_grcat_1(A,C,D,G,k16_grcat_1(A,B,C,F,E)) = k16_grcat_1(A,B,D,k16_grcat_1(B,C,D,G,F),E) ) ) ) ) ) ) ) ).
fof(t33_grcat_1,axiom,
! [A] :
( ( v2_grcat_1(A)
& v3_grcat_1(A)
& l1_grcat_1(A) )
=> ! [B] :
( ( v2_grcat_1(B)
& v3_grcat_1(B)
& l1_grcat_1(B) )
=> ! [C] :
( ( v2_grcat_1(C)
& v3_grcat_1(C)
& l1_grcat_1(C) )
=> ( ( k9_grcat_1(C) = k10_grcat_1(B)
& k9_grcat_1(B) = k10_grcat_1(A) )
=> k15_grcat_1(C,k15_grcat_1(B,A)) = k15_grcat_1(k15_grcat_1(C,B),A) ) ) ) ) ).
fof(t34_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ( k9_grcat_1(k13_grcat_1(A)) = A
& k10_grcat_1(k13_grcat_1(A)) = A
& ! [B] :
( ( v2_grcat_1(B)
& v3_grcat_1(B)
& l1_grcat_1(B) )
=> ( k10_grcat_1(B) = A
=> k15_grcat_1(k13_grcat_1(A),B) = B ) )
& ! [B] :
( ( v2_grcat_1(B)
& v3_grcat_1(B)
& l1_grcat_1(B) )
=> ( k9_grcat_1(B) = A
=> k15_grcat_1(B,k13_grcat_1(A)) = B ) ) ) ) ).
fof(d22_grcat_1,axiom,
! [A] :
( v4_grcat_1(A)
<=> ! [B] :
( r2_hidden(B,A)
=> ( ~ v3_struct_0(B)
& v1_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) ) ) ) ).
fof(d23_grcat_1,axiom,
! [A] :
( v5_grcat_1(A)
<=> ! [B] :
( r2_hidden(B,A)
=> ( v2_grcat_1(B)
& v3_grcat_1(B)
& l1_grcat_1(B) ) ) ) ).
fof(t35_grcat_1,axiom,
$true ).
fof(t36_grcat_1,axiom,
$true ).
fof(t37_grcat_1,axiom,
! [A] :
( ( v2_grcat_1(A)
& v3_grcat_1(A)
& l1_grcat_1(A) )
=> ( ~ v1_xboole_0(k1_tarski(A))
& v5_grcat_1(k1_tarski(A)) ) ) ).
fof(d24_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v5_grcat_1(C) )
=> ( m4_grcat_1(C,A,B)
<=> ! [D] :
( m3_grcat_1(D,C)
=> ( v2_grcat_1(D)
& m1_grcat_1(D,A,B) ) ) ) ) ) ) ).
fof(t38_grcat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ( m4_grcat_1(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ( v2_grcat_1(D)
& m1_grcat_1(D,B,C) ) ) ) ) ) ) ).
fof(t39_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v2_grcat_1(C)
& m1_grcat_1(C,A,B) )
=> m4_grcat_1(k1_tarski(C),A,B) ) ) ) ).
fof(d25_grcat_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( m5_grcat_1(C,A,B)
<=> ! [D] :
( r2_hidden(D,C)
=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ).
fof(d26_grcat_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> k17_grcat_1(A,B) = k1_funct_2(u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(d27_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( m4_grcat_1(C,A,B)
=> ( C = k18_grcat_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( v2_grcat_1(D)
& m1_grcat_1(D,A,B) ) ) ) ) ) ) ).
fof(d28_grcat_1,axiom,
! [A,B] :
( r1_grcat_1(A,B)
<=> ? [C,D,E,F] :
( A = k4_mcart_1(C,D,E,F)
& ? [G] :
( ~ v3_struct_0(G)
& v1_rlvect_1(G)
& v4_rlvect_1(G)
& v5_rlvect_1(G)
& v6_rlvect_1(G)
& l1_rlvect_1(G)
& B = G
& C = u1_struct_0(G)
& D = u1_rlvect_1(G)
& E = k7_vectsp_1(G)
& F = u2_struct_0(G) ) ) ) ).
fof(t40_grcat_1,axiom,
! [A,B,C] :
( ( r1_grcat_1(A,B)
& r1_grcat_1(A,C) )
=> B = C ) ).
fof(t41_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ? [B] :
( r2_hidden(B,A)
& r1_grcat_1(B,k2_algstr_1) ) ) ).
fof(d29_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( B = k19_grcat_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( r2_hidden(D,A)
& r1_grcat_1(D,C) ) ) ) ) ).
fof(t42_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> r2_hidden(k2_algstr_1,k19_grcat_1(A)) ) ).
fof(t43_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,k19_grcat_1(A))
=> ( ~ v3_struct_0(B)
& v1_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) ) ) ) ).
fof(d30_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v5_grcat_1(B) )
=> ( B = k20_grcat_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( v1_rlvect_1(D)
& m2_grcat_1(D,A)
& ? [E] :
( v1_rlvect_1(E)
& m2_grcat_1(E,A)
& v2_grcat_1(C)
& m1_grcat_1(C,D,E) ) ) ) ) ) ) ).
fof(d31_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( m2_grcat_1(B,A)
=> k23_grcat_1(A,B) = k13_grcat_1(B) ) ) ).
fof(d32_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k20_grcat_1(A),A)
& m2_relset_1(B,k20_grcat_1(A),A) )
=> ( B = k24_grcat_1(A)
<=> ! [C] :
( m3_grcat_1(C,k20_grcat_1(A))
=> k8_funct_2(k20_grcat_1(A),A,B,C) = k21_grcat_1(A,C) ) ) ) ) ).
fof(d33_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k20_grcat_1(A),A)
& m2_relset_1(B,k20_grcat_1(A),A) )
=> ( B = k25_grcat_1(A)
<=> ! [C] :
( m3_grcat_1(C,k20_grcat_1(A))
=> k8_funct_2(k20_grcat_1(A),A,B,C) = k22_grcat_1(A,C) ) ) ) ) ).
fof(d34_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k20_grcat_1(A))
& m2_relset_1(B,A,k20_grcat_1(A)) )
=> ( B = k26_grcat_1(A)
<=> ! [C] :
( m2_grcat_1(C,A)
=> k8_funct_2(A,k20_grcat_1(A),B,C) = k23_grcat_1(A,C) ) ) ) ) ).
fof(t44_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( m3_grcat_1(B,k20_grcat_1(A))
=> ! [C] :
( m3_grcat_1(C,k20_grcat_1(A))
=> ~ ( k21_grcat_1(A,B) = k22_grcat_1(A,C)
& ! [D] :
( ( v1_rlvect_1(D)
& m2_grcat_1(D,A) )
=> ! [E] :
( ( v1_rlvect_1(E)
& m2_grcat_1(E,A) )
=> ! [F] :
( ( v1_rlvect_1(F)
& m2_grcat_1(F,A) )
=> ~ ( m1_grcat_1(B,E,F)
& m1_grcat_1(C,D,E) ) ) ) ) ) ) ) ) ).
fof(t45_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( m3_grcat_1(B,k20_grcat_1(A))
=> ! [C] :
( m3_grcat_1(C,k20_grcat_1(A))
=> ( k21_grcat_1(A,B) = k22_grcat_1(A,C)
=> r2_hidden(k15_grcat_1(B,C),k20_grcat_1(A)) ) ) ) ) ).
fof(d35_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) )
=> ( B = k27_grcat_1(A)
<=> ( ! [C] :
( m3_grcat_1(C,k20_grcat_1(A))
=> ! [D] :
( m3_grcat_1(D,k20_grcat_1(A))
=> ( r2_hidden(k4_tarski(C,D),k1_relat_1(B))
<=> k21_grcat_1(A,C) = k22_grcat_1(A,D) ) ) )
& ! [C] :
( m3_grcat_1(C,k20_grcat_1(A))
=> ! [D] :
( m3_grcat_1(D,k20_grcat_1(A))
=> ( r2_hidden(k4_tarski(C,D),k1_relat_1(B))
=> k1_funct_1(B,k4_tarski(C,D)) = k15_grcat_1(C,D) ) ) ) ) ) ) ) ).
fof(d36_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> k28_grcat_1(A) = g1_cat_1(k19_grcat_1(A),k20_grcat_1(k19_grcat_1(A)),k24_grcat_1(k19_grcat_1(A)),k25_grcat_1(k19_grcat_1(A)),k27_grcat_1(k19_grcat_1(A)),k26_grcat_1(k19_grcat_1(A))) ) ).
fof(t46_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
=> ( r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(k28_grcat_1(A))))
<=> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) ) ) ) ) ).
fof(t47_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
=> ! [C] :
( m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_cat_1(k28_grcat_1(A)))
=> ! [E] :
( m2_grcat_1(E,k19_grcat_1(A))
=> ( v2_grcat_1(B)
& m3_grcat_1(B,k20_grcat_1(k19_grcat_1(A)))
& m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
& v1_rlvect_1(D)
& m2_grcat_1(D,k19_grcat_1(A))
& m1_subset_1(E,u1_cat_1(k28_grcat_1(A))) ) ) ) ) ) ) ).
fof(t48_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,u1_cat_1(k28_grcat_1(A)))
=> ! [C] :
( m2_grcat_1(C,k19_grcat_1(A))
=> ( B = C
=> k5_cat_1(k28_grcat_1(A),B) = k23_grcat_1(k19_grcat_1(A),C) ) ) ) ) ).
fof(t49_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
=> ! [C] :
( m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A)))
=> ( B = C
=> ( k2_cat_1(k28_grcat_1(A),B) = k21_grcat_1(k19_grcat_1(A),C)
& k3_cat_1(k28_grcat_1(A),B) = k22_grcat_1(k19_grcat_1(A),C) ) ) ) ) ) ).
fof(t50_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,u2_cat_1(k28_grcat_1(A)))
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k28_grcat_1(A)))
=> ! [D] :
( m3_grcat_1(D,k20_grcat_1(k19_grcat_1(A)))
=> ! [E] :
( m3_grcat_1(E,k20_grcat_1(k19_grcat_1(A)))
=> ( ( B = D
& C = E )
=> ( ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
=> k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D) )
& ( k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)
=> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) )
& ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
=> r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A)))) )
& ( r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A))))
=> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) )
& ( k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)
=> k4_cat_1(k28_grcat_1(A),B,C) = k15_grcat_1(E,D) )
& ( k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)
=> k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E) )
& ( k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E)
=> k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) )
& ( k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C)
=> k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E) )
& ( k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E)
=> k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C) ) ) ) ) ) ) ) ) ).
fof(t51_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> r2_hidden(k2_algstr_1,k29_grcat_1(A)) ) ).
fof(d38_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> k30_grcat_1(A) = k6_grcat_1(k28_grcat_1(A),k29_grcat_1(A)) ) ).
fof(t52_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> u1_cat_1(k30_grcat_1(A)) = k29_grcat_1(A) ) ).
fof(d40_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> k32_grcat_1(A) = k6_grcat_1(k30_grcat_1(A),k31_grcat_1(A)) ) ).
fof(t53_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> u1_cat_1(k32_grcat_1(A)) = k31_grcat_1(A) ) ).
fof(t54_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> r2_hidden(k2_algstr_1,k31_grcat_1(A)) ) ).
fof(s1_grcat_1,axiom,
( ! [A,B] :
( ( r2_hidden(A,f1_s1_grcat_1)
& r2_hidden(B,f2_s1_grcat_1)
& p1_s1_grcat_1(A,B) )
=> r2_hidden(f4_s1_grcat_1(A,B),f3_s1_grcat_1) )
=> ? [A] :
( v1_funct_1(A)
& m2_relset_1(A,k2_zfmisc_1(f1_s1_grcat_1,f2_s1_grcat_1),f3_s1_grcat_1)
& ! [B,C] :
( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
<=> ( r2_hidden(B,f1_s1_grcat_1)
& r2_hidden(C,f2_s1_grcat_1)
& p1_s1_grcat_1(B,C) ) )
& ! [B,C] :
( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
=> k1_funct_1(A,k4_tarski(B,C)) = f4_s1_grcat_1(B,C) ) ) ) ).
fof(s2_grcat_1,axiom,
( ! [A] :
( m1_subset_1(A,f1_s2_grcat_1)
=> ! [B] :
( m1_subset_1(B,f2_s2_grcat_1)
=> ( p1_s2_grcat_1(A,B)
=> r2_hidden(f4_s2_grcat_1(A,B),f3_s2_grcat_1) ) ) )
=> ? [A] :
( v1_funct_1(A)
& m2_relset_1(A,k2_zfmisc_1(f1_s2_grcat_1,f2_s2_grcat_1),f3_s2_grcat_1)
& ! [B] :
( m1_subset_1(B,f1_s2_grcat_1)
=> ! [C] :
( m1_subset_1(C,f2_s2_grcat_1)
=> ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
<=> p1_s2_grcat_1(B,C) ) ) )
& ! [B] :
( m1_subset_1(B,f1_s2_grcat_1)
=> ! [C] :
( m1_subset_1(C,f2_s2_grcat_1)
=> ( r2_hidden(k4_tarski(B,C),k1_relat_1(A))
=> k1_funct_1(A,k4_tarski(B,C)) = f4_s2_grcat_1(B,C) ) ) ) ) ) ).
fof(dt_m1_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( m1_grcat_1(C,A,B)
=> ( v3_grcat_1(C)
& l1_grcat_1(C) ) ) ) ).
fof(existence_m1_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ? [C] : m1_grcat_1(C,A,B) ) ).
fof(dt_m2_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( m2_grcat_1(B,A)
=> ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) ) ) ) ).
fof(existence_m2_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ? [B] : m2_grcat_1(B,A) ) ).
fof(redefinition_m2_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ! [B] :
( m2_grcat_1(B,A)
<=> m1_subset_1(B,A) ) ) ).
fof(dt_m3_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v5_grcat_1(A) )
=> ! [B] :
( m3_grcat_1(B,A)
=> ( v3_grcat_1(B)
& l1_grcat_1(B) ) ) ) ).
fof(existence_m3_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v5_grcat_1(A) )
=> ? [B] : m3_grcat_1(B,A) ) ).
fof(redefinition_m3_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v5_grcat_1(A) )
=> ! [B] :
( m3_grcat_1(B,A)
<=> m1_subset_1(B,A) ) ) ).
fof(dt_m4_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( m4_grcat_1(C,A,B)
=> ( ~ v1_xboole_0(C)
& v5_grcat_1(C) ) ) ) ).
fof(existence_m4_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ? [C] : m4_grcat_1(C,A,B) ) ).
fof(dt_m5_grcat_1,axiom,
$true ).
fof(existence_m5_grcat_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ? [C] : m5_grcat_1(C,A,B) ) ).
fof(dt_m6_grcat_1,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& ~ v1_xboole_0(C)
& m5_grcat_1(C,A,B) )
=> ! [D] :
( m6_grcat_1(D,A,B,C)
=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) ).
fof(existence_m6_grcat_1,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& ~ v1_xboole_0(C)
& m5_grcat_1(C,A,B) )
=> ? [D] : m6_grcat_1(D,A,B,C) ) ).
fof(redefinition_m6_grcat_1,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& ~ v1_xboole_0(C)
& m5_grcat_1(C,A,B) )
=> ! [D] :
( m6_grcat_1(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_m7_grcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& m4_grcat_1(C,A,B) )
=> ! [D] :
( m7_grcat_1(D,A,B,C)
=> m1_grcat_1(D,A,B) ) ) ).
fof(existence_m7_grcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& m4_grcat_1(C,A,B) )
=> ? [D] : m7_grcat_1(D,A,B,C) ) ).
fof(redefinition_m7_grcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& m4_grcat_1(C,A,B) )
=> ! [D] :
( m7_grcat_1(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_l1_grcat_1,axiom,
$true ).
fof(existence_l1_grcat_1,axiom,
? [A] : l1_grcat_1(A) ).
fof(abstractness_v2_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( v2_grcat_1(A)
=> A = g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) ) ) ).
fof(dt_k1_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> m1_subset_1(k1_grcat_1(A,B),k1_zfmisc_1(u2_cat_1(A))) ) ).
fof(dt_k2_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> ( v1_funct_1(k2_grcat_1(A,B))
& v1_funct_2(k2_grcat_1(A,B),k1_grcat_1(A,B),B)
& m2_relset_1(k2_grcat_1(A,B),k1_grcat_1(A,B),B) ) ) ).
fof(dt_k3_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> ( v1_funct_1(k3_grcat_1(A,B))
& v1_funct_2(k3_grcat_1(A,B),k1_grcat_1(A,B),B)
& m2_relset_1(k3_grcat_1(A,B),k1_grcat_1(A,B),B) ) ) ).
fof(dt_k4_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> ( v1_funct_1(k4_grcat_1(A,B))
& m2_relset_1(k4_grcat_1(A,B),k12_mcart_1(u2_cat_1(A),u2_cat_1(A),k1_grcat_1(A,B),k1_grcat_1(A,B)),k1_grcat_1(A,B)) ) ) ).
fof(dt_k5_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> ( v1_funct_1(k5_grcat_1(A,B))
& v1_funct_2(k5_grcat_1(A,B),B,k1_grcat_1(A,B))
& m2_relset_1(k5_grcat_1(A,B),B,k1_grcat_1(A,B)) ) ) ).
fof(dt_k6_grcat_1,axiom,
! [A,B] :
( ( v2_cat_1(A)
& l1_cat_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> m3_cat_2(k6_grcat_1(A,B),A) ) ).
fof(dt_k7_grcat_1,axiom,
! [A] :
( l1_struct_0(A)
=> ( v1_funct_1(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k8_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ( v1_funct_1(k8_grcat_1(A,B))
& v1_funct_2(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(dt_k9_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( ~ v3_struct_0(k9_grcat_1(A))
& v4_rlvect_1(k9_grcat_1(A))
& v5_rlvect_1(k9_grcat_1(A))
& v6_rlvect_1(k9_grcat_1(A))
& l1_rlvect_1(k9_grcat_1(A)) ) ) ).
fof(dt_k10_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( ~ v3_struct_0(k10_grcat_1(A))
& v4_rlvect_1(k10_grcat_1(A))
& v5_rlvect_1(k10_grcat_1(A))
& v6_rlvect_1(k10_grcat_1(A))
& l1_rlvect_1(k10_grcat_1(A)) ) ) ).
fof(dt_k11_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( v1_funct_1(k11_grcat_1(A))
& v1_funct_2(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A)))
& m2_relset_1(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) ) ) ).
fof(dt_k12_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> l1_grcat_1(k12_grcat_1(A,B)) ) ).
fof(dt_k13_grcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> m1_grcat_1(k13_grcat_1(A),A,A) ) ).
fof(dt_k14_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ( v2_grcat_1(k14_grcat_1(A,B))
& m1_grcat_1(k14_grcat_1(A,B),A,B) ) ) ).
fof(redefinition_k14_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> k14_grcat_1(A,B) = k12_grcat_1(A,B) ) ).
fof(dt_k15_grcat_1,axiom,
! [A,B] :
( ( v3_grcat_1(A)
& l1_grcat_1(A)
& v3_grcat_1(B)
& l1_grcat_1(B) )
=> ( v2_grcat_1(k15_grcat_1(A,B))
& v3_grcat_1(k15_grcat_1(A,B))
& l1_grcat_1(k15_grcat_1(A,B)) ) ) ).
fof(dt_k16_grcat_1,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& m1_grcat_1(D,B,C)
& m1_grcat_1(E,A,B) )
=> ( v2_grcat_1(k16_grcat_1(A,B,C,D,E))
& m1_grcat_1(k16_grcat_1(A,B,C,D,E),A,C) ) ) ).
fof(redefinition_k16_grcat_1,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& m1_grcat_1(D,B,C)
& m1_grcat_1(E,A,B) )
=> k16_grcat_1(A,B,C,D,E) = k15_grcat_1(D,E) ) ).
fof(dt_k17_grcat_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> m5_grcat_1(k17_grcat_1(A,B),A,B) ) ).
fof(dt_k18_grcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> m4_grcat_1(k18_grcat_1(A,B),A,B) ) ).
fof(dt_k19_grcat_1,axiom,
$true ).
fof(dt_k20_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ( ~ v1_xboole_0(k20_grcat_1(A))
& v5_grcat_1(k20_grcat_1(A)) ) ) ).
fof(dt_k21_grcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A)
& m1_subset_1(B,k20_grcat_1(A)) )
=> ( v1_rlvect_1(k21_grcat_1(A,B))
& m2_grcat_1(k21_grcat_1(A,B),A) ) ) ).
fof(redefinition_k21_grcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A)
& m1_subset_1(B,k20_grcat_1(A)) )
=> k21_grcat_1(A,B) = k9_grcat_1(B) ) ).
fof(dt_k22_grcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A)
& m1_subset_1(B,k20_grcat_1(A)) )
=> ( v1_rlvect_1(k22_grcat_1(A,B))
& m2_grcat_1(k22_grcat_1(A,B),A) ) ) ).
fof(redefinition_k22_grcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A)
& m1_subset_1(B,k20_grcat_1(A)) )
=> k22_grcat_1(A,B) = k10_grcat_1(B) ) ).
fof(dt_k23_grcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A)
& m1_subset_1(B,A) )
=> ( v2_grcat_1(k23_grcat_1(A,B))
& m3_grcat_1(k23_grcat_1(A,B),k20_grcat_1(A)) ) ) ).
fof(dt_k24_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ( v1_funct_1(k24_grcat_1(A))
& v1_funct_2(k24_grcat_1(A),k20_grcat_1(A),A)
& m2_relset_1(k24_grcat_1(A),k20_grcat_1(A),A) ) ) ).
fof(dt_k25_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ( v1_funct_1(k25_grcat_1(A))
& v1_funct_2(k25_grcat_1(A),k20_grcat_1(A),A)
& m2_relset_1(k25_grcat_1(A),k20_grcat_1(A),A) ) ) ).
fof(dt_k26_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ( v1_funct_1(k26_grcat_1(A))
& v1_funct_2(k26_grcat_1(A),A,k20_grcat_1(A))
& m2_relset_1(k26_grcat_1(A),A,k20_grcat_1(A)) ) ) ).
fof(dt_k27_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v4_grcat_1(A) )
=> ( v1_funct_1(k27_grcat_1(A))
& m2_relset_1(k27_grcat_1(A),k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) ) ) ).
fof(dt_k28_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> l1_cat_1(k28_grcat_1(A)) ) ).
fof(dt_k29_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> m1_subset_1(k29_grcat_1(A),k1_zfmisc_1(u1_cat_1(k28_grcat_1(A)))) ) ).
fof(dt_k30_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> m3_cat_2(k30_grcat_1(A),k28_grcat_1(A)) ) ).
fof(dt_k31_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> m1_subset_1(k31_grcat_1(A),k1_zfmisc_1(u1_cat_1(k30_grcat_1(A)))) ) ).
fof(dt_k32_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> m3_cat_2(k32_grcat_1(A),k30_grcat_1(A)) ) ).
fof(dt_u1_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( ~ v3_struct_0(u1_grcat_1(A))
& v4_rlvect_1(u1_grcat_1(A))
& v5_rlvect_1(u1_grcat_1(A))
& v6_rlvect_1(u1_grcat_1(A))
& l1_rlvect_1(u1_grcat_1(A)) ) ) ).
fof(dt_u2_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( ~ v3_struct_0(u2_grcat_1(A))
& v4_rlvect_1(u2_grcat_1(A))
& v5_rlvect_1(u2_grcat_1(A))
& v6_rlvect_1(u2_grcat_1(A))
& l1_rlvect_1(u2_grcat_1(A)) ) ) ).
fof(dt_u3_grcat_1,axiom,
! [A] :
( l1_grcat_1(A)
=> ( v1_funct_1(u3_grcat_1(A))
& v1_funct_2(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A)))
& m2_relset_1(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))) ) ) ).
fof(dt_g1_grcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v2_grcat_1(g1_grcat_1(A,B,C))
& l1_grcat_1(g1_grcat_1(A,B,C)) ) ) ).
fof(free_g1_grcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D,E,F] :
( g1_grcat_1(A,B,C) = g1_grcat_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(d5_grcat_1,axiom,
! [A] :
( ( v2_cat_1(A)
& l1_cat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) )
=> k1_grcat_1(A,B) = k3_tarski(a_2_0_grcat_1(A,B)) ) ) ).
fof(d37_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> k29_grcat_1(A) = a_1_0_grcat_1(A) ) ).
fof(d39_grcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> k31_grcat_1(A) = a_1_1_grcat_1(A) ) ).
fof(fraenkel_a_2_0_grcat_1,axiom,
! [A,B,C] :
( ( v2_cat_1(B)
& l1_cat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) )
=> ( r2_hidden(A,a_2_0_grcat_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,u1_cat_1(B))
& m1_subset_1(E,u1_cat_1(B))
& A = k6_cat_1(B,D,E)
& r2_hidden(D,C)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_1_0_grcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_classes2(B) )
=> ( r2_hidden(A,a_1_0_grcat_1(B))
<=> ? [C] :
( m1_subset_1(C,u1_cat_1(k28_grcat_1(B)))
& A = C
& ? [D] :
( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& l1_rlvect_1(D)
& C = D ) ) ) ) ).
fof(fraenkel_a_1_1_grcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_classes2(B) )
=> ( r2_hidden(A,a_1_1_grcat_1(B))
<=> ? [C] :
( m1_subset_1(C,u1_cat_1(k30_grcat_1(B)))
& A = C
& ? [D] :
( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v1_midsp_2(D)
& l1_rlvect_1(D)
& C = D ) ) ) ) ).
%------------------------------------------------------------------------------