SET007 Axioms: SET007+418.ax
%------------------------------------------------------------------------------
% File : SET007+418 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Bounding Boxes for Compact Sets in E^2
% 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 : pscomp_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 262 ( 14 unt; 0 def)
% Number of atoms : 1224 ( 159 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1079 ( 117 ~; 2 |; 517 &)
% ( 44 <=>; 399 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 60 ( 58 usr; 1 prp; 0-3 aty)
% Number of functors : 90 ( 90 usr; 10 con; 0-4 aty)
% Number of variables : 435 ( 412 !; 23 ?)
% 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_pscomp_1,axiom,
( ~ v1_xboole_0(k1_numbers)
& v1_membered(k1_numbers)
& v2_membered(k1_numbers)
& ~ v1_setfam_1(k1_numbers) ) ).
fof(fc2_pscomp_1,axiom,
( ~ v1_xboole_0(k5_ordinal2)
& v1_ordinal1(k5_ordinal2)
& v2_ordinal1(k5_ordinal2)
& v3_ordinal1(k5_ordinal2)
& v1_membered(k5_ordinal2)
& v2_membered(k5_ordinal2)
& v3_membered(k5_ordinal2)
& v4_membered(k5_ordinal2)
& v5_membered(k5_ordinal2)
& ~ v1_setfam_1(k5_ordinal2) ) ).
fof(rc1_pscomp_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_setfam_1(A) ) ).
fof(rc2_pscomp_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& ~ v1_setfam_1(A) ) ).
fof(rc3_pscomp_1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& v1_setfam_1(A) ) ).
fof(rc4_pscomp_1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& ~ v1_setfam_1(A) ) ).
fof(cc1_pscomp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( ( ~ v1_xboole_0(B)
& v6_ordinal1(B)
& v1_setfam_1(B) )
=> v1_compts_1(B) ) ) ).
fof(fc3_pscomp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> ~ v1_xboole_0(k9_relat_1(C,A)) ) ).
fof(rc5_pscomp_1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& v3_seq_4(A)
& v2_rcomp_1(A) ) ).
fof(fc4_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( ~ v1_xboole_0(k5_pscomp_1(A))
& v1_membered(k5_pscomp_1(A))
& v2_membered(k5_pscomp_1(A)) ) ) ).
fof(fc5_pscomp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& m1_subset_1(B,k1_numbers) )
=> ( ~ v1_xboole_0(k8_measure6(A,B))
& v1_membered(k8_measure6(A,B))
& v2_membered(k8_measure6(A,B)) ) ) ).
fof(fc6_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( ~ v1_xboole_0(k6_pscomp_1(A))
& v1_membered(k6_pscomp_1(A))
& v2_membered(k6_pscomp_1(A))
& v1_setfam_1(k6_pscomp_1(A)) ) ) ).
fof(fc7_pscomp_1,axiom,
! [A] :
( ( v1_setfam_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( v1_membered(k6_pscomp_1(A))
& v2_membered(k6_pscomp_1(A))
& v1_setfam_1(k6_pscomp_1(A)) ) ) ).
fof(fc8_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v1_membered(k7_pscomp_1(A))
& v2_membered(k7_pscomp_1(A))
& v2_rcomp_1(k7_pscomp_1(A)) ) ) ).
fof(rc6_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),k1_numbers)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v1_seq_1(B)
& v1_seq_2(B)
& v2_seq_2(B)
& v3_seq_2(B)
& v1_partfun1(B,u1_struct_0(A),k1_numbers) ) ) ).
fof(rc7_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),k1_numbers)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v1_seq_1(B)
& v1_partfun1(B,u1_struct_0(A),k1_numbers)
& v9_pscomp_1(B,A) ) ) ).
fof(rc8_pscomp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(B),k1_numbers)
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& v1_seq_1(C)
& v1_partfun1(C,u1_struct_0(B),k1_numbers)
& v9_pscomp_1(C,B) ) ) ).
fof(rc9_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v6_compts_1(B,A) ) ) ).
fof(fc9_pscomp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v9_pscomp_1(B,A)
& m1_relset_1(B,u1_struct_0(A),k1_numbers)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_relat_1(k15_pscomp_1(A,C,B))
& v1_funct_1(k15_pscomp_1(A,C,B))
& v1_funct_2(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers)
& v1_seq_1(k15_pscomp_1(A,C,B))
& v1_partfun1(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers)
& v9_pscomp_1(k15_pscomp_1(A,C,B),k3_pre_topc(A,C)) ) ) ).
fof(fc10_pscomp_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v1_xboole_0(B)
& v6_compts_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k3_pre_topc(A,B))
& v1_pre_topc(k3_pre_topc(A,B))
& v2_pre_topc(k3_pre_topc(A,B))
& v2_compts_1(k3_pre_topc(A,B)) ) ) ).
fof(cc2_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_compts_1(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v10_pscomp_1(A) ) ) ) ).
fof(rc10_pscomp_1,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_compts_1(A)
& v10_pscomp_1(A) ) ).
fof(cc3_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v10_pscomp_1(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),k1_numbers)
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v9_pscomp_1(B,A) )
=> ( ~ v1_xboole_0(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v1_seq_1(B)
& v3_seq_2(B)
& v1_partfun1(B,u1_struct_0(A),k1_numbers)
& v7_pscomp_1(B,u1_struct_0(A))
& v8_pscomp_1(B,u1_struct_0(A)) ) ) ) ) ).
fof(fc11_pscomp_1,axiom,
( ~ v1_xboole_0(k16_pscomp_1)
& v1_relat_1(k16_pscomp_1)
& v1_funct_1(k16_pscomp_1)
& v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& v1_seq_1(k16_pscomp_1)
& v1_partfun1(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& v9_pscomp_1(k16_pscomp_1,k15_euclid(np__2)) ) ).
fof(fc12_pscomp_1,axiom,
( ~ v1_xboole_0(k17_pscomp_1)
& v1_relat_1(k17_pscomp_1)
& v1_funct_1(k17_pscomp_1)
& v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& v1_seq_1(k17_pscomp_1)
& v1_partfun1(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& v9_pscomp_1(k17_pscomp_1,k15_euclid(np__2)) ) ).
fof(fc13_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k26_pscomp_1(A))
& v6_compts_1(k26_pscomp_1(A),k15_euclid(np__2)) ) ) ).
fof(fc14_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k27_pscomp_1(A))
& v6_compts_1(k27_pscomp_1(A),k15_euclid(np__2)) ) ) ).
fof(fc15_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k28_pscomp_1(A))
& v6_compts_1(k28_pscomp_1(A),k15_euclid(np__2)) ) ) ).
fof(fc16_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k29_pscomp_1(A))
& v6_compts_1(k29_pscomp_1(A),k15_euclid(np__2)) ) ) ).
fof(d1_pscomp_1,axiom,
! [A] :
( v1_setfam_1(A)
<=> ~ r2_hidden(np__0,A) ) ).
fof(t1_pscomp_1,axiom,
! [A] :
( ( v1_setfam_1(A)
& v6_ordinal1(A) )
=> ( v1_xboole_0(A)
| v1_compts_1(A) ) ) ).
fof(d2_pscomp_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_pcomps_1(B),k1_pcomps_1(A))
& m2_relset_1(D,k1_pcomps_1(B),k1_pcomps_1(A)) )
=> ( D = k2_pscomp_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(B))
=> k8_funct_2(k1_zfmisc_1(B),k1_pcomps_1(A),D,E) = k3_funct_2(A,B,C,E) ) ) ) ) ).
fof(t2_pscomp_1,axiom,
! [A,B,C,D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( r2_hidden(C,k6_setfam_1(A,k2_funct_2(k1_pcomps_1(B),k1_pcomps_1(A),k2_pscomp_1(A,B,E),D)))
=> r2_hidden(k1_funct_1(E,C),k6_setfam_1(B,D)) ) ) ) ).
fof(t3_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( k3_real_1(k18_complex1(A),k18_complex1(B)) = np__0
=> A = np__0 ) ) ) ).
fof(t4_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(C,B)
& r1_xreal_0(k3_real_1(k18_complex1(A),k18_complex1(C)),k18_complex1(B)) ) ) ) ) ).
fof(t5_pscomp_1,axiom,
$true ).
fof(t6_pscomp_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ~ ( v4_seq_2(A)
& v2_relat_1(A)
& k2_seq_2(A) = np__0
& v3_seq_2(k18_seq_1(A)) ) ) ).
fof(t7_pscomp_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( v3_seq_4(k1_pscomp_1(k5_numbers,k1_numbers,A))
<=> v3_seq_2(A) ) ) ).
fof(d3_pscomp_1,axiom,
! [A] :
( v2_membered(A)
=> ( v1_pscomp_1(A)
<=> ( v1_seq_4(A)
& r2_hidden(k2_seq_4(A),A) ) ) ) ).
fof(d4_pscomp_1,axiom,
! [A] :
( v2_membered(A)
=> ( v2_pscomp_1(A)
<=> ( v2_seq_4(A)
& r2_hidden(k3_seq_4(A),A) ) ) ) ).
fof(d5_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
=> ( v3_pscomp_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(B,A)
=> v3_rcomp_1(B) ) ) ) ) ).
fof(d6_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
=> ( v4_pscomp_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(B,A)
=> v2_rcomp_1(B) ) ) ) ) ).
fof(t8_pscomp_1,axiom,
$true ).
fof(t9_pscomp_1,axiom,
$true ).
fof(t10_pscomp_1,axiom,
$true ).
fof(t11_pscomp_1,axiom,
$true ).
fof(t12_pscomp_1,axiom,
$true ).
fof(t13_pscomp_1,axiom,
$true ).
fof(t14_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(A,B)
<=> r2_hidden(k4_xcmplx_0(A),k5_pscomp_1(B)) ) ) ) ).
fof(t15_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v1_seq_4(A)
<=> v2_seq_4(k5_pscomp_1(A)) ) ) ).
fof(t16_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v2_seq_4(A)
<=> v1_seq_4(k5_pscomp_1(A)) ) ) ).
fof(t17_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( v2_seq_4(A)
=> k4_pscomp_1(A) = k1_real_1(k3_pscomp_1(k5_pscomp_1(A))) ) ) ).
fof(t18_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( v1_seq_4(A)
=> k3_pscomp_1(A) = k1_real_1(k4_pscomp_1(k5_pscomp_1(A))) ) ) ).
fof(t19_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v2_rcomp_1(A)
<=> v2_rcomp_1(k5_pscomp_1(A)) ) ) ).
fof(t20_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(A,B)
<=> r2_hidden(k2_xcmplx_0(C,A),k8_measure6(B,C)) ) ) ) ) ).
fof(t21_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> A = k8_measure6(A,np__0) ) ).
fof(t22_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k8_measure6(k8_measure6(A,C),B) = k8_measure6(A,k3_real_1(B,C)) ) ) ) ).
fof(t23_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( v1_seq_4(A)
<=> v1_seq_4(k8_measure6(A,B)) ) ) ) ).
fof(t24_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( v2_seq_4(A)
<=> v2_seq_4(k8_measure6(A,B)) ) ) ) ).
fof(t25_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( v2_seq_4(B)
=> k4_pscomp_1(k8_measure6(B,A)) = k3_real_1(A,k4_pscomp_1(B)) ) ) ) ).
fof(t26_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( v1_seq_4(B)
=> k3_pscomp_1(k8_measure6(B,A)) = k3_real_1(A,k3_pscomp_1(B)) ) ) ) ).
fof(t27_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( v2_rcomp_1(A)
<=> v2_rcomp_1(k8_measure6(A,B)) ) ) ) ).
fof(t28_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_setfam_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( r2_hidden(A,B)
<=> r2_hidden(k7_xcmplx_0(np__1,A),k6_pscomp_1(B)) ) ) ) ).
fof(t29_pscomp_1,axiom,
! [A] :
( ( v1_setfam_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> k6_pscomp_1(k6_pscomp_1(A)) = A ) ).
fof(t30_pscomp_1,axiom,
! [A] :
( ( v1_setfam_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( ( v2_rcomp_1(A)
& v3_seq_4(A) )
=> v2_rcomp_1(k6_pscomp_1(A)) ) ) ).
fof(t31_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
=> ( v4_pscomp_1(A)
=> v2_rcomp_1(k6_setfam_1(k1_numbers,A)) ) ) ).
fof(t32_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( ( v2_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( r1_tarski(A,B)
=> r1_tarski(k7_pscomp_1(A),B) ) ) ) ).
fof(t33_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> r1_tarski(A,k7_pscomp_1(A)) ) ).
fof(t34_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v2_rcomp_1(A)
<=> A = k7_pscomp_1(A) ) ) ).
fof(t35_pscomp_1,axiom,
k7_pscomp_1(k1_subset_1(k1_numbers)) = k1_xboole_0 ).
fof(t36_pscomp_1,axiom,
k7_pscomp_1(k2_subset_1(k1_numbers)) = k1_numbers ).
fof(t37_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( r1_tarski(A,B)
=> r1_tarski(k7_pscomp_1(A),k7_pscomp_1(B)) ) ) ) ).
fof(t38_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(B,k7_pscomp_1(A))
<=> ! [C] :
( ( v3_rcomp_1(C)
& m1_subset_1(C,k1_zfmisc_1(k1_numbers)) )
=> ~ ( r2_hidden(B,C)
& v1_xboole_0(k5_subset_1(k1_numbers,C,A)) ) ) ) ) ) ).
fof(t39_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( r2_hidden(B,k7_pscomp_1(A))
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ~ ( r1_tarski(k1_pscomp_1(k5_numbers,k1_numbers,C),A)
& v4_seq_2(C)
& k2_seq_2(C) = B ) ) ) ) ) ).
fof(d11_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ( v2_seq_2(B)
<=> v2_seq_4(k2_funct_2(A,k1_numbers,B,A)) ) ) ).
fof(d12_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ( v1_seq_2(B)
<=> v1_seq_4(k2_funct_2(A,k1_numbers,B,A)) ) ) ).
fof(d13_pscomp_1,axiom,
$true ).
fof(d14_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ( v7_pscomp_1(B,A)
<=> v1_pscomp_1(k2_funct_2(A,k1_numbers,B,A)) ) ) ).
fof(d15_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ( v8_pscomp_1(B,A)
<=> v2_pscomp_1(k2_funct_2(A,k1_numbers,B,A)) ) ) ).
fof(d16_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ( C = k8_pscomp_1(A,B)
<=> ! [D] :
( r2_hidden(D,A)
=> k2_seq_1(A,k1_numbers,C,D) = k1_real_1(k2_seq_1(A,k1_numbers,B,D)) ) ) ) ) ).
fof(t40_pscomp_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> k2_funct_2(A,k1_numbers,k8_pscomp_1(A,C),B) = k5_pscomp_1(k2_funct_2(A,k1_numbers,C,B)) ) ).
fof(t41_pscomp_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ( v8_pscomp_1(B,A)
<=> v7_pscomp_1(k8_pscomp_1(A,B),A) ) ) ) ).
fof(t42_pscomp_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ( v7_pscomp_1(B,A)
<=> v8_pscomp_1(k8_pscomp_1(A,B),A) ) ) ) ).
fof(t43_pscomp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> k3_funct_2(A,k1_numbers,k8_pscomp_1(A,C),B) = k3_funct_2(A,k1_numbers,C,k5_pscomp_1(B)) ) ) ).
fof(d17_pscomp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,k1_numbers)
& m2_relset_1(D,A,k1_numbers) )
=> ( D = k9_pscomp_1(A,B,C)
<=> ! [E] :
( r2_hidden(E,A)
=> k2_seq_1(A,k1_numbers,D,E) = k3_real_1(B,k2_seq_1(A,k1_numbers,C,E)) ) ) ) ) ) ).
fof(t44_pscomp_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k2_funct_2(A,k1_numbers,k9_pscomp_1(A,D,C),B) = k8_measure6(k2_funct_2(A,k1_numbers,C,B),D) ) ) ).
fof(t45_pscomp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k3_funct_2(A,k1_numbers,k9_pscomp_1(A,D,C),B) = k3_funct_2(A,k1_numbers,C,k8_measure6(B,k1_real_1(D))) ) ) ) ).
fof(d18_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m2_relset_1(B,A,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> ( C = k10_pscomp_1(A,B)
<=> ! [D] :
( r2_hidden(D,A)
=> k2_seq_1(A,k1_numbers,C,D) = k6_real_1(np__1,k2_seq_1(A,k1_numbers,B,D)) ) ) ) ) ).
fof(t46_pscomp_1,axiom,
! [A,B] :
( ( v1_setfam_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m2_relset_1(C,A,k1_numbers) )
=> k3_funct_2(A,k1_numbers,k10_pscomp_1(A,C),B) = k3_funct_2(A,k1_numbers,C,k6_pscomp_1(B)) ) ) ).
fof(d19_pscomp_1,axiom,
$true ).
fof(d20_pscomp_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> k12_pscomp_1(A,B) = k4_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) ).
fof(d21_pscomp_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> k13_pscomp_1(A,B) = k3_pscomp_1(k2_funct_2(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) ).
fof(t47_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v2_seq_2(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k12_pscomp_1(A,B),k2_seq_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ).
fof(t48_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v2_seq_2(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(C,k2_seq_1(u1_struct_0(A),k1_numbers,B,D)) )
=> r1_xreal_0(C,k12_pscomp_1(A,B)) ) ) ) ) ).
fof(t49_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> r1_xreal_0(A,k2_seq_1(u1_struct_0(B),k1_numbers,C,D)) )
& ! [D] :
( v1_xreal_0(D)
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r1_xreal_0(D,k2_seq_1(u1_struct_0(B),k1_numbers,C,E)) )
=> r1_xreal_0(D,A) ) ) )
=> A = k12_pscomp_1(B,C) ) ) ) ) ).
fof(t50_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v1_seq_2(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k2_seq_1(u1_struct_0(A),k1_numbers,B,C),k13_pscomp_1(A,B)) ) ) ) ).
fof(t51_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v1_seq_2(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( v1_xreal_0(C)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k2_seq_1(u1_struct_0(A),k1_numbers,B,D),C) )
=> r1_xreal_0(k13_pscomp_1(A,B),C) ) ) ) ) ).
fof(t52_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( ( ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> r1_xreal_0(k2_seq_1(u1_struct_0(B),k1_numbers,C,D),A) )
& ! [D] :
( v1_xreal_0(D)
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r1_xreal_0(k2_seq_1(u1_struct_0(B),k1_numbers,C,E),D) )
=> r1_xreal_0(A,D) ) ) )
=> A = k13_pscomp_1(B,C) ) ) ) ) ).
fof(t53_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v3_seq_2(B)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> r1_xreal_0(k12_pscomp_1(A,B),k13_pscomp_1(A,B)) ) ) ).
fof(d22_pscomp_1,axiom,
$true ).
fof(d23_pscomp_1,axiom,
$true ).
fof(d24_pscomp_1,axiom,
$true ).
fof(d25_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( v2_rcomp_1(C)
=> v4_pre_topc(k11_pscomp_1(A,B,C),A) ) ) ) ) ) ).
fof(t54_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
=> ( v3_rcomp_1(C)
=> v3_pre_topc(k11_pscomp_1(A,B,C),A) ) ) ) ) ) ).
fof(t55_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
=> v9_pscomp_1(k8_pscomp_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t56_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( v9_pscomp_1(C,B)
=> v9_pscomp_1(k9_pscomp_1(u1_struct_0(B),A,C),B) ) ) ) ) ).
fof(t57_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
=> ( r2_hidden(np__0,k1_pscomp_1(u1_struct_0(A),k1_numbers,B))
| v9_pscomp_1(k10_pscomp_1(u1_struct_0(A),B),A) ) ) ) ) ).
fof(t58_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
=> ( ( v9_pscomp_1(B,A)
& v3_pscomp_1(C) )
=> v1_tops_2(k14_pscomp_1(k1_numbers,u1_struct_0(A),k2_pscomp_1(u1_struct_0(A),k1_numbers,B),C),A) ) ) ) ) ).
fof(t59_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k1_numbers)))
=> ( ( v9_pscomp_1(B,A)
& v4_pscomp_1(C) )
=> v2_tops_2(k14_pscomp_1(k1_numbers,u1_struct_0(A),k2_pscomp_1(u1_struct_0(A),k1_numbers,B),C),A) ) ) ) ) ).
fof(d26_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_numbers)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> k15_pscomp_1(A,B,C) = k7_relat_1(C,B) ) ) ) ).
fof(t60_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
=> v7_pscomp_1(B,u1_struct_0(A)) ) )
<=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
=> v8_pscomp_1(B,u1_struct_0(A)) ) ) ) ) ).
fof(t61_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
=> v3_seq_2(B) ) )
<=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
=> v7_pscomp_1(B,u1_struct_0(A)) ) ) ) ) ).
fof(d27_pscomp_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v10_pscomp_1(A)
<=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v9_pscomp_1(B,A)
=> v3_seq_2(B) ) ) ) ) ).
fof(t62_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v6_compts_1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),k1_numbers)
& v9_pscomp_1(D,A)
& m2_relset_1(D,u1_struct_0(A),k1_numbers) )
=> ( r1_tarski(B,C)
=> r1_xreal_0(k12_pscomp_1(k3_pre_topc(A,C),k15_pscomp_1(A,C,D)),k12_pscomp_1(k3_pre_topc(A,B),k15_pscomp_1(A,B,D))) ) ) ) ) ) ).
fof(t63_pscomp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v6_compts_1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),k1_numbers)
& v9_pscomp_1(D,A)
& m2_relset_1(D,u1_struct_0(A),k1_numbers) )
=> ( r1_tarski(B,C)
=> r1_xreal_0(k13_pscomp_1(k3_pre_topc(A,B),k15_pscomp_1(A,B,D)),k13_pscomp_1(k3_pre_topc(A,C),k15_pscomp_1(A,C,D))) ) ) ) ) ) ).
fof(t64_pscomp_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(A))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> v6_compts_1(k5_subset_1(u1_struct_0(k15_euclid(A)),B,C),k15_euclid(A)) ) ) ) ).
fof(d28_pscomp_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),k1_numbers) )
=> ( A = k16_pscomp_1
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> k2_seq_1(u1_struct_0(k15_euclid(np__2)),k1_numbers,A,B) = k21_euclid(B) ) ) ) ).
fof(d29_pscomp_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),k1_numbers) )
=> ( A = k17_pscomp_1
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> k2_seq_1(u1_struct_0(k15_euclid(np__2)),k1_numbers,A,B) = k22_euclid(B) ) ) ) ).
fof(t69_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,A)
=> k2_seq_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),k1_numbers,k15_pscomp_1(k15_euclid(np__2),A,k16_pscomp_1),B) = k21_euclid(B) ) ) ) ).
fof(t70_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,A)
=> k2_seq_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),A)),k1_numbers,k15_pscomp_1(k15_euclid(np__2),A,k17_pscomp_1),B) = k22_euclid(B) ) ) ) ).
fof(d30_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k18_pscomp_1(A) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k16_pscomp_1)) ) ).
fof(d31_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k19_pscomp_1(A) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k17_pscomp_1)) ) ).
fof(d32_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k20_pscomp_1(A) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k16_pscomp_1)) ) ).
fof(d33_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_pscomp_1(A) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),A),k15_pscomp_1(k15_euclid(np__2),A,k17_pscomp_1)) ) ).
fof(t71_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,B)
=> ( r1_xreal_0(k18_pscomp_1(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k20_pscomp_1(B))
& r1_xreal_0(k21_pscomp_1(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k19_pscomp_1(B)) ) ) ) ) ).
fof(d34_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k21_pscomp_1(A)) ) ).
fof(d35_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k23_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k19_pscomp_1(A)) ) ).
fof(d36_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k24_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k19_pscomp_1(A)) ) ).
fof(d37_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k25_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k21_pscomp_1(A)) ) ).
fof(t72_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k22_pscomp_1(A)) = k18_pscomp_1(A) ) ).
fof(t73_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k22_pscomp_1(A)) = k21_pscomp_1(A) ) ).
fof(t74_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k23_pscomp_1(A)) = k18_pscomp_1(A) ) ).
fof(t75_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k23_pscomp_1(A)) = k19_pscomp_1(A) ) ).
fof(t76_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k24_pscomp_1(A)) = k20_pscomp_1(A) ) ).
fof(t77_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k24_pscomp_1(A)) = k19_pscomp_1(A) ) ).
fof(t78_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k25_pscomp_1(A)) = k20_pscomp_1(A) ) ).
fof(t79_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k25_pscomp_1(A)) = k21_pscomp_1(A) ) ).
fof(t80_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k22_pscomp_1(A)) = k21_euclid(k23_pscomp_1(A)) ) ).
fof(t81_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k25_pscomp_1(A)) = k21_euclid(k24_pscomp_1(A)) ) ).
fof(t82_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k23_pscomp_1(A)) = k22_euclid(k24_pscomp_1(A)) ) ).
fof(t83_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k22_pscomp_1(A)) = k22_euclid(k25_pscomp_1(A)) ) ).
fof(d38_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k26_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),A) ) ).
fof(d39_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k27_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A)),A) ) ).
fof(d40_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k28_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),A) ) ).
fof(d41_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k29_pscomp_1(A) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),A) ) ).
fof(d42_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k30_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1))) ) ).
fof(d43_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k31_pscomp_1(A) = k23_euclid(k18_pscomp_1(A),k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1))) ) ).
fof(d44_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k32_pscomp_1(A) = k23_euclid(k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1)),k19_pscomp_1(A)) ) ).
fof(d45_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k33_pscomp_1(A) = k23_euclid(k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1)),k19_pscomp_1(A)) ) ).
fof(d46_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k34_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1))) ) ).
fof(d47_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k35_pscomp_1(A) = k23_euclid(k20_pscomp_1(A),k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1))) ) ).
fof(d48_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k36_pscomp_1(A) = k23_euclid(k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1)),k21_pscomp_1(A)) ) ).
fof(d49_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k37_pscomp_1(A) = k23_euclid(k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1)),k21_pscomp_1(A)) ) ).
fof(t84_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k21_euclid(k30_pscomp_1(A)) = k18_pscomp_1(A)
& k21_euclid(k31_pscomp_1(A)) = k18_pscomp_1(A) ) ) ).
fof(t85_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k21_euclid(k22_pscomp_1(A)) = k21_euclid(k30_pscomp_1(A))
& k21_euclid(k22_pscomp_1(A)) = k21_euclid(k31_pscomp_1(A))
& k21_euclid(k30_pscomp_1(A)) = k21_euclid(k31_pscomp_1(A))
& k21_euclid(k30_pscomp_1(A)) = k21_euclid(k23_pscomp_1(A))
& k21_euclid(k31_pscomp_1(A)) = k21_euclid(k23_pscomp_1(A)) ) ) ).
fof(t86_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k22_euclid(k30_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1))
& k22_euclid(k31_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k26_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k26_pscomp_1(A),k17_pscomp_1)) ) ) ).
fof(t87_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k22_euclid(k22_pscomp_1(A)),k22_euclid(k30_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k22_pscomp_1(A)),k22_euclid(k31_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k22_pscomp_1(A)),k22_euclid(k23_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k30_pscomp_1(A)),k22_euclid(k31_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k30_pscomp_1(A)),k22_euclid(k23_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k31_pscomp_1(A)),k22_euclid(k23_pscomp_1(A))) ) ) ).
fof(t88_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k26_pscomp_1(B))
=> ( k21_euclid(A) = k21_euclid(k30_pscomp_1(B))
& ( v6_compts_1(B,k15_euclid(np__2))
=> ( r1_xreal_0(k22_euclid(k30_pscomp_1(B)),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k22_euclid(k31_pscomp_1(B))) ) ) ) ) ) ) ).
fof(t89_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k26_pscomp_1(A),k3_topreal1(np__2,k30_pscomp_1(A),k31_pscomp_1(A))) ) ).
fof(t90_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k3_topreal1(np__2,k30_pscomp_1(A),k31_pscomp_1(A)),k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A))) ) ).
fof(t91_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(k30_pscomp_1(A),k26_pscomp_1(A))
& r2_hidden(k31_pscomp_1(A),k26_pscomp_1(A)) ) ) ).
fof(t92_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k30_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k30_pscomp_1(A))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k31_pscomp_1(A),k23_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k31_pscomp_1(A)) ) ) ).
fof(t93_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k30_pscomp_1(A) = k31_pscomp_1(A)
=> k26_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k30_pscomp_1(A)) ) ) ).
fof(t94_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k22_euclid(k32_pscomp_1(A)) = k19_pscomp_1(A)
& k22_euclid(k33_pscomp_1(A)) = k19_pscomp_1(A) ) ) ).
fof(t95_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k22_euclid(k23_pscomp_1(A)) = k22_euclid(k32_pscomp_1(A))
& k22_euclid(k23_pscomp_1(A)) = k22_euclid(k33_pscomp_1(A))
& k22_euclid(k32_pscomp_1(A)) = k22_euclid(k33_pscomp_1(A))
& k22_euclid(k32_pscomp_1(A)) = k22_euclid(k24_pscomp_1(A))
& k22_euclid(k33_pscomp_1(A)) = k22_euclid(k24_pscomp_1(A)) ) ) ).
fof(t96_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k21_euclid(k32_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1))
& k21_euclid(k33_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k27_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k27_pscomp_1(A),k16_pscomp_1)) ) ) ).
fof(t97_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k21_euclid(k23_pscomp_1(A)),k21_euclid(k32_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k23_pscomp_1(A)),k21_euclid(k33_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k23_pscomp_1(A)),k21_euclid(k24_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k32_pscomp_1(A)),k21_euclid(k33_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k32_pscomp_1(A)),k21_euclid(k24_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k33_pscomp_1(A)),k21_euclid(k24_pscomp_1(A))) ) ) ).
fof(t98_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k27_pscomp_1(B))
=> ( k22_euclid(A) = k22_euclid(k32_pscomp_1(B))
& ( v6_compts_1(B,k15_euclid(np__2))
=> ( r1_xreal_0(k21_euclid(k32_pscomp_1(B)),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k21_euclid(k33_pscomp_1(B))) ) ) ) ) ) ) ).
fof(t99_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k27_pscomp_1(A),k3_topreal1(np__2,k32_pscomp_1(A),k33_pscomp_1(A))) ) ).
fof(t100_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k3_topreal1(np__2,k32_pscomp_1(A),k33_pscomp_1(A)),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) ).
fof(t101_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(k32_pscomp_1(A),k27_pscomp_1(A))
& r2_hidden(k33_pscomp_1(A),k27_pscomp_1(A)) ) ) ).
fof(t102_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_pscomp_1(A),k32_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k32_pscomp_1(A))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k33_pscomp_1(A),k24_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k33_pscomp_1(A)) ) ) ).
fof(t103_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k32_pscomp_1(A) = k33_pscomp_1(A)
=> k27_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k32_pscomp_1(A)) ) ) ).
fof(t104_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k21_euclid(k35_pscomp_1(A)) = k20_pscomp_1(A)
& k21_euclid(k34_pscomp_1(A)) = k20_pscomp_1(A) ) ) ).
fof(t105_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k21_euclid(k25_pscomp_1(A)) = k21_euclid(k35_pscomp_1(A))
& k21_euclid(k25_pscomp_1(A)) = k21_euclid(k34_pscomp_1(A))
& k21_euclid(k35_pscomp_1(A)) = k21_euclid(k34_pscomp_1(A))
& k21_euclid(k35_pscomp_1(A)) = k21_euclid(k24_pscomp_1(A))
& k21_euclid(k34_pscomp_1(A)) = k21_euclid(k24_pscomp_1(A)) ) ) ).
fof(t106_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k22_euclid(k35_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1))
& k22_euclid(k34_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k28_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k28_pscomp_1(A),k17_pscomp_1)) ) ) ).
fof(t107_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k22_euclid(k25_pscomp_1(A)),k22_euclid(k35_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k25_pscomp_1(A)),k22_euclid(k34_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k25_pscomp_1(A)),k22_euclid(k24_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k35_pscomp_1(A)),k22_euclid(k34_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k35_pscomp_1(A)),k22_euclid(k24_pscomp_1(A)))
& r1_xreal_0(k22_euclid(k34_pscomp_1(A)),k22_euclid(k24_pscomp_1(A))) ) ) ).
fof(t108_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k28_pscomp_1(B))
=> ( k21_euclid(A) = k21_euclid(k35_pscomp_1(B))
& ( v6_compts_1(B,k15_euclid(np__2))
=> ( r1_xreal_0(k22_euclid(k35_pscomp_1(B)),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k22_euclid(k34_pscomp_1(B))) ) ) ) ) ) ) ).
fof(t109_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k28_pscomp_1(A),k3_topreal1(np__2,k35_pscomp_1(A),k34_pscomp_1(A))) ) ).
fof(t110_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k3_topreal1(np__2,k35_pscomp_1(A),k34_pscomp_1(A)),k3_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A))) ) ).
fof(t111_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(k35_pscomp_1(A),k28_pscomp_1(A))
& r2_hidden(k34_pscomp_1(A),k28_pscomp_1(A)) ) ) ).
fof(t112_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k25_pscomp_1(A),k35_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k35_pscomp_1(A))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k34_pscomp_1(A),k24_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k34_pscomp_1(A)) ) ) ).
fof(t113_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k35_pscomp_1(A) = k34_pscomp_1(A)
=> k28_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k35_pscomp_1(A)) ) ) ).
fof(t114_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k22_euclid(k37_pscomp_1(A)) = k21_pscomp_1(A)
& k22_euclid(k36_pscomp_1(A)) = k21_pscomp_1(A) ) ) ).
fof(t115_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k22_euclid(k22_pscomp_1(A)) = k22_euclid(k37_pscomp_1(A))
& k22_euclid(k22_pscomp_1(A)) = k22_euclid(k36_pscomp_1(A))
& k22_euclid(k37_pscomp_1(A)) = k22_euclid(k36_pscomp_1(A))
& k22_euclid(k37_pscomp_1(A)) = k22_euclid(k25_pscomp_1(A))
& k22_euclid(k36_pscomp_1(A)) = k22_euclid(k25_pscomp_1(A)) ) ) ).
fof(t116_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k21_euclid(k37_pscomp_1(A)) = k12_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1))
& k21_euclid(k36_pscomp_1(A)) = k13_pscomp_1(k3_pre_topc(k15_euclid(np__2),k29_pscomp_1(A)),k15_pscomp_1(k15_euclid(np__2),k29_pscomp_1(A),k16_pscomp_1)) ) ) ).
fof(t117_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(k21_euclid(k22_pscomp_1(A)),k21_euclid(k37_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k22_pscomp_1(A)),k21_euclid(k36_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k22_pscomp_1(A)),k21_euclid(k25_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k37_pscomp_1(A)),k21_euclid(k36_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k37_pscomp_1(A)),k21_euclid(k25_pscomp_1(A)))
& r1_xreal_0(k21_euclid(k36_pscomp_1(A)),k21_euclid(k25_pscomp_1(A))) ) ) ).
fof(t118_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k29_pscomp_1(B))
=> ( k22_euclid(A) = k22_euclid(k37_pscomp_1(B))
& ( v6_compts_1(B,k15_euclid(np__2))
=> ( r1_xreal_0(k21_euclid(k37_pscomp_1(B)),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k21_euclid(k36_pscomp_1(B))) ) ) ) ) ) ) ).
fof(t119_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k29_pscomp_1(A),k3_topreal1(np__2,k37_pscomp_1(A),k36_pscomp_1(A))) ) ).
fof(t120_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k3_topreal1(np__2,k37_pscomp_1(A),k36_pscomp_1(A)),k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A))) ) ).
fof(t121_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(k37_pscomp_1(A),k29_pscomp_1(A))
& r2_hidden(k36_pscomp_1(A),k29_pscomp_1(A)) ) ) ).
fof(t122_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k22_pscomp_1(A),k37_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k37_pscomp_1(A))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k36_pscomp_1(A),k25_pscomp_1(A)),A) = k1_struct_0(k15_euclid(np__2),k36_pscomp_1(A)) ) ) ).
fof(t123_pscomp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k37_pscomp_1(A) = k36_pscomp_1(A)
=> k29_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k37_pscomp_1(A)) ) ) ).
fof(t124_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k31_pscomp_1(A) = k32_pscomp_1(A)
=> k31_pscomp_1(A) = k23_pscomp_1(A) ) ) ).
fof(t125_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k33_pscomp_1(A) = k34_pscomp_1(A)
=> k33_pscomp_1(A) = k24_pscomp_1(A) ) ) ).
fof(t126_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k35_pscomp_1(A) = k36_pscomp_1(A)
=> k35_pscomp_1(A) = k25_pscomp_1(A) ) ) ).
fof(t127_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k37_pscomp_1(A) = k30_pscomp_1(A)
=> k37_pscomp_1(A) = k22_pscomp_1(A) ) ) ).
fof(s1_pscomp_1,axiom,
( ! [A] :
~ ( r2_hidden(A,u1_struct_0(f1_s1_pscomp_1))
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ p1_s1_pscomp_1(A,B) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(f1_s1_pscomp_1),k1_numbers)
& m2_relset_1(A,u1_struct_0(f1_s1_pscomp_1),k1_numbers)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_pscomp_1))
=> p1_s1_pscomp_1(B,k2_seq_1(u1_struct_0(f1_s1_pscomp_1),k1_numbers,A,B)) ) ) ) ).
fof(redefinition_v5_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m1_relset_1(B,A,k1_numbers) )
=> ( v5_pscomp_1(B,A)
<=> v2_seq_2(B) ) ) ).
fof(redefinition_v6_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m1_relset_1(B,A,k1_numbers) )
=> ( v6_pscomp_1(B,A)
<=> v1_seq_2(B) ) ) ).
fof(dt_k1_pscomp_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k1_pscomp_1(A,B,C),k1_zfmisc_1(B)) ) ).
fof(redefinition_k1_pscomp_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k1_pscomp_1(A,B,C) = k2_relat_1(C) ) ).
fof(dt_k2_pscomp_1,axiom,
! [A,B,C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> ( v1_funct_1(k2_pscomp_1(A,B,C))
& v1_funct_2(k2_pscomp_1(A,B,C),k1_pcomps_1(B),k1_pcomps_1(A))
& m2_relset_1(k2_pscomp_1(A,B,C),k1_pcomps_1(B),k1_pcomps_1(A)) ) ) ).
fof(dt_k3_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> m1_subset_1(k3_pscomp_1(A),k1_numbers) ) ).
fof(redefinition_k3_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k3_pscomp_1(A) = k2_seq_4(A) ) ).
fof(dt_k4_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> m1_subset_1(k4_pscomp_1(A),k1_numbers) ) ).
fof(redefinition_k4_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k4_pscomp_1(A) = k3_seq_4(A) ) ).
fof(dt_k5_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> m1_subset_1(k5_pscomp_1(A),k1_zfmisc_1(k1_numbers)) ) ).
fof(involutiveness_k5_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k5_pscomp_1(k5_pscomp_1(A)) = A ) ).
fof(dt_k6_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> m1_subset_1(k6_pscomp_1(A),k1_zfmisc_1(k1_numbers)) ) ).
fof(dt_k7_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> m1_subset_1(k7_pscomp_1(A),k1_zfmisc_1(k1_numbers)) ) ).
fof(projectivity_k7_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k7_pscomp_1(k7_pscomp_1(A)) = k7_pscomp_1(A) ) ).
fof(dt_k8_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m1_relset_1(B,A,k1_numbers) )
=> ( v1_funct_1(k8_pscomp_1(A,B))
& v1_funct_2(k8_pscomp_1(A,B),A,k1_numbers)
& m2_relset_1(k8_pscomp_1(A,B),A,k1_numbers) ) ) ).
fof(involutiveness_k8_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m1_relset_1(B,A,k1_numbers) )
=> k8_pscomp_1(A,k8_pscomp_1(A,B)) = B ) ).
fof(dt_k9_pscomp_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,A,k1_numbers)
& m1_relset_1(C,A,k1_numbers) )
=> ( v1_funct_1(k9_pscomp_1(A,B,C))
& v1_funct_2(k9_pscomp_1(A,B,C),A,k1_numbers)
& m2_relset_1(k9_pscomp_1(A,B,C),A,k1_numbers) ) ) ).
fof(dt_k10_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m1_relset_1(B,A,k1_numbers) )
=> ( v1_funct_1(k10_pscomp_1(A,B))
& v1_funct_2(k10_pscomp_1(A,B),A,k1_numbers)
& m2_relset_1(k10_pscomp_1(A,B),A,k1_numbers) ) ) ).
fof(involutiveness_k10_pscomp_1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k1_numbers)
& m1_relset_1(B,A,k1_numbers) )
=> k10_pscomp_1(A,k10_pscomp_1(A,B)) = B ) ).
fof(dt_k11_pscomp_1,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> m1_subset_1(k11_pscomp_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(redefinition_k11_pscomp_1,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> k11_pscomp_1(A,B,C) = k10_relat_1(B,C) ) ).
fof(dt_k12_pscomp_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> m1_subset_1(k12_pscomp_1(A,B),k1_numbers) ) ).
fof(dt_k13_pscomp_1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> m1_subset_1(k13_pscomp_1(A,B),k1_numbers) ) ).
fof(dt_k14_pscomp_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B))
& m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B))
& m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> m1_subset_1(k14_pscomp_1(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))) ) ).
fof(redefinition_k14_pscomp_1,axiom,
! [A,B,C,D] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B))
& m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B))
& m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> k14_pscomp_1(A,B,C,D) = k9_relat_1(C,D) ) ).
fof(dt_k15_pscomp_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_numbers)
& m1_relset_1(C,u1_struct_0(A),k1_numbers) )
=> ( v1_funct_1(k15_pscomp_1(A,B,C))
& v1_funct_2(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers)
& m2_relset_1(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers) ) ) ).
fof(dt_k16_pscomp_1,axiom,
( v1_funct_1(k16_pscomp_1)
& v1_funct_2(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& m2_relset_1(k16_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers) ) ).
fof(dt_k17_pscomp_1,axiom,
( v1_funct_1(k17_pscomp_1)
& v1_funct_2(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)
& m2_relset_1(k17_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers) ) ).
fof(dt_k18_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k18_pscomp_1(A),k1_numbers) ) ).
fof(dt_k19_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k19_pscomp_1(A),k1_numbers) ) ).
fof(dt_k20_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k20_pscomp_1(A),k1_numbers) ) ).
fof(dt_k21_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k21_pscomp_1(A),k1_numbers) ) ).
fof(dt_k22_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k22_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k23_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k23_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k24_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k24_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k25_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k25_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k26_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k26_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k27_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k27_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k28_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k28_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k29_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k29_pscomp_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k30_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k30_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k31_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k31_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k32_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k32_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k33_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k33_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k34_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k34_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k35_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k35_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k36_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k36_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k37_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k37_pscomp_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(d7_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k5_pscomp_1(A) = a_1_0_pscomp_1(A) ) ).
fof(d8_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> k8_measure6(A,B) = a_2_0_pscomp_1(A,B) ) ) ).
fof(d9_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k6_pscomp_1(A) = a_1_1_pscomp_1(A) ) ).
fof(d10_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> k7_pscomp_1(A) = k1_setfam_1(a_1_2_pscomp_1(A)) ) ).
fof(t65_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k11_pscomp_1(k15_euclid(np__2),k16_pscomp_1,k2_rcomp_1(A,B)) = a_2_1_pscomp_1(A,B) ) ) ).
fof(t66_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( A = a_2_2_pscomp_1(B,C)
=> v3_pre_topc(A,k15_euclid(np__2)) ) ) ) ) ).
fof(t67_pscomp_1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k11_pscomp_1(k15_euclid(np__2),k17_pscomp_1,k2_rcomp_1(A,B)) = a_2_3_pscomp_1(A,B) ) ) ).
fof(t68_pscomp_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( A = a_2_4_pscomp_1(B,C)
=> v3_pre_topc(A,k15_euclid(np__2)) ) ) ) ) ).
fof(fraenkel_a_1_0_pscomp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(A,a_1_0_pscomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& A = k1_real_1(C)
& r2_hidden(C,B) ) ) ) ).
fof(fraenkel_a_2_0_pscomp_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
& m1_subset_1(C,k1_numbers) )
=> ( r2_hidden(A,a_2_0_pscomp_1(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& A = k3_real_1(C,D)
& r2_hidden(D,B) ) ) ) ).
fof(fraenkel_a_1_1_pscomp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(A,a_1_1_pscomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& A = k6_real_1(np__1,C)
& r2_hidden(C,B) ) ) ) ).
fof(fraenkel_a_1_2_pscomp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ( r2_hidden(A,a_1_2_pscomp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_numbers))
& A = C
& r1_tarski(B,C)
& v2_rcomp_1(C) ) ) ) ).
fof(fraenkel_a_2_1_pscomp_1,axiom,
! [A,B,C] :
( ( v1_xreal_0(B)
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_1_pscomp_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& ~ r1_xreal_0(D,B)
& ~ r1_xreal_0(C,D) ) ) ) ).
fof(fraenkel_a_2_2_pscomp_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_numbers)
& m1_subset_1(C,k1_numbers) )
=> ( r2_hidden(A,a_2_2_pscomp_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& ~ r1_xreal_0(D,B)
& ~ r1_xreal_0(C,D) ) ) ) ).
fof(fraenkel_a_2_3_pscomp_1,axiom,
! [A,B,C] :
( ( v1_xreal_0(B)
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_3_pscomp_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& ~ r1_xreal_0(E,B)
& ~ r1_xreal_0(C,E) ) ) ) ).
fof(fraenkel_a_2_4_pscomp_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_numbers)
& m1_subset_1(C,k1_numbers) )
=> ( r2_hidden(A,a_2_4_pscomp_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& ~ r1_xreal_0(E,B)
& ~ r1_xreal_0(C,E) ) ) ) ).
%------------------------------------------------------------------------------