SET007 Axioms: SET007+532.ax
%------------------------------------------------------------------------------
% File : SET007+532 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Rectangular Finite Sequences of the Points of the Plane
% 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 : sprect_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 128 ( 1 unt; 0 def)
% Number of atoms : 685 ( 103 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 700 ( 143 ~; 0 |; 356 &)
% ( 9 <=>; 192 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 44 ( 42 usr; 1 prp; 0-3 aty)
% Number of functors : 76 ( 76 usr; 12 con; 0-4 aty)
% Number of variables : 188 ( 176 !; 12 ?)
% 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(cc1_sprect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v5_seqm_3(A) )
=> ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_realset1(A) ) ) ).
fof(cc2_sprect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_realset1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v5_seqm_3(A) ) ) ).
fof(fc1_sprect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v5_seqm_3(A) )
=> v1_realset1(k2_relat_1(A)) ) ).
fof(rc1_sprect_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v5_seqm_3(A) ) ).
fof(fc2_sprect_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& ~ v1_realset1(B)
& m1_finseq_1(B,u1_struct_0(k15_euclid(A))) )
=> ~ v1_xboole_0(k5_topreal1(A,B)) ) ).
fof(fc3_sprect_1,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ).
fof(fc4_sprect_1,axiom,
( ~ v1_xboole_0(k2_topreal1)
& ~ v1_sppol_1(k2_topreal1)
& ~ v2_sppol_1(k2_topreal1)
& v1_topreal4(k2_topreal1)
& ~ v1_realset1(k2_topreal1) ) ).
fof(rc2_sprect_1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& ~ v1_xboole_0(A)
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& v6_compts_1(A,k15_euclid(np__2)) ) ).
fof(fc5_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_sppol_1(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(k1_sprect_1(A))
& v1_relat_1(k1_sprect_1(A))
& v1_funct_1(k1_sprect_1(A))
& v1_finset_1(k1_sprect_1(A))
& v1_finseq_1(k1_sprect_1(A))
& ~ v1_realset1(k1_sprect_1(A))
& ~ v5_seqm_3(k1_sprect_1(A)) ) ) ).
fof(fc6_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_sppol_1(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(k1_sprect_1(A))
& v1_relat_1(k1_sprect_1(A))
& v1_funct_1(k1_sprect_1(A))
& v1_finset_1(k1_sprect_1(A))
& v1_finseq_1(k1_sprect_1(A))
& ~ v1_realset1(k1_sprect_1(A))
& ~ v5_seqm_3(k1_sprect_1(A)) ) ) ).
fof(fc7_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(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(k1_sprect_1(A))
& v1_relat_1(k1_sprect_1(A))
& v1_funct_1(k1_sprect_1(A))
& v1_finset_1(k1_sprect_1(A))
& v1_finseq_1(k1_sprect_1(A))
& ~ v1_realset1(k1_sprect_1(A))
& ~ v5_seqm_3(k1_sprect_1(A))
& v1_topreal1(k1_sprect_1(A))
& v2_topreal1(k1_sprect_1(A))
& v1_finseq_6(k1_sprect_1(A),u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(k1_sprect_1(A))
& v2_goboard5(k1_sprect_1(A)) ) ) ).
fof(rc3_sprect_1,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
& ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& v1_seq_4(A)
& v2_seq_4(A) ) ).
fof(fc8_sprect_1,axiom,
( v1_xboole_0(k1_subset_1(k1_numbers))
& v1_relat_1(k1_subset_1(k1_numbers))
& v1_membered(k1_subset_1(k1_numbers))
& v2_membered(k1_subset_1(k1_numbers))
& v3_membered(k1_subset_1(k1_numbers))
& v4_membered(k1_subset_1(k1_numbers))
& v5_membered(k1_subset_1(k1_numbers))
& v3_seq_4(k1_subset_1(k1_numbers))
& v1_realset1(k1_subset_1(k1_numbers)) ) ).
fof(fc9_sprect_1,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B) )
=> ( v1_membered(k1_rcomp_1(A,B))
& v2_membered(k1_rcomp_1(A,B))
& v3_seq_4(k1_rcomp_1(A,B)) ) ) ).
fof(cc3_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( v3_seq_4(A)
=> ( v1_membered(A)
& v2_membered(A)
& v1_seq_4(A)
& v2_seq_4(A) ) ) ) ).
fof(cc4_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ( ( v1_seq_4(A)
& v2_seq_4(A) )
=> ( v1_membered(A)
& v2_membered(A)
& v3_seq_4(A) ) ) ) ).
fof(fc10_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(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(k1_sprect_1(A))
& v1_relat_1(k1_sprect_1(A))
& v1_funct_1(k1_sprect_1(A))
& v1_finset_1(k1_sprect_1(A))
& v1_finseq_1(k1_sprect_1(A))
& ~ v1_realset1(k1_sprect_1(A))
& ~ v5_seqm_3(k1_sprect_1(A))
& v1_topreal1(k1_sprect_1(A))
& v2_topreal1(k1_sprect_1(A))
& v1_finseq_6(k1_sprect_1(A),u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(k1_sprect_1(A))
& v2_goboard5(k1_sprect_1(A))
& v1_sprect_1(k1_sprect_1(A)) ) ) ).
fof(rc4_sprect_1,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_sprect_1(A) ) ).
fof(cc5_sprect_1,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_sprect_1(A)
=> ~ v5_seqm_3(A) ) ) ).
fof(cc6_sprect_1,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ( ~ v1_xboole_0(A)
& v1_sprect_1(A) )
=> ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A) ) ) ) ).
fof(fc11_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k5_topreal1(np__2,A))
& v2_jordan1(k5_topreal1(np__2,A))
& v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ) ).
fof(fc12_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ v1_xboole_0(k2_goboard9(A)) ) ).
fof(fc13_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ v1_xboole_0(k3_goboard9(A)) ) ).
fof(t1_sprect_1,axiom,
! [A] :
( v1_realset1(A)
=> ! [B] :
( r1_tarski(B,A)
=> v1_realset1(B) ) ) ).
fof(t2_sprect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_realset1(k2_relat_1(A))
=> v5_seqm_3(A) ) ) ).
fof(t3_sprect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( v5_seqm_3(k7_finseq_1(A,B))
=> ( v5_seqm_3(A)
& v5_seqm_3(B) ) ) ) ) ).
fof(t4_sprect_1,axiom,
! [A,B] :
( v5_seqm_3(k10_finseq_1(A,B))
=> A = B ) ).
fof(t5_sprect_1,axiom,
! [A,B,C] :
( v5_seqm_3(k11_finseq_1(A,B,C))
=> ( A = B
& B = C
& C = A ) ) ).
fof(t6_sprect_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)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r4_connsp_1(A,C,B)
& B = k1_xboole_0 ) ) ) ) ).
fof(t7_sprect_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r4_connsp_1(A,C,B)
=> r1_tarski(B,C) ) ) ) ) ).
fof(t8_sprect_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] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r4_connsp_1(A,B,C)
& r4_connsp_1(A,B,D)
& r4_connsp_1(A,B,E)
& k4_subset_1(u1_struct_0(A),C,D) = B
& E != C
& E != D ) ) ) ) ) ) ).
fof(t9_sprect_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] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r4_connsp_1(A,B,C)
& r4_connsp_1(A,B,D)
& r4_connsp_1(A,B,E)
& r4_connsp_1(A,B,F)
& k4_subset_1(u1_struct_0(A),C,D) = B
& k4_subset_1(u1_struct_0(A),E,F) = B )
=> k2_tarski(C,D) = k2_tarski(E,F) ) ) ) ) ) ) ) ).
fof(t10_sprect_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> k5_topreal1(np__2,k3_finseq_4(u1_struct_0(k15_euclid(np__2)),A,B,C)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k3_topreal1(np__2,B,C)) ) ) ) ).
fof(t11_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r1_tarski(A,B)
& v1_sppol_1(B) )
=> v1_sppol_1(A) ) ) ) ).
fof(t12_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r1_tarski(A,B)
& v2_sppol_1(B) )
=> v2_sppol_1(A) ) ) ) ).
fof(t13_sprect_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),A)
& r2_hidden(k33_pscomp_1(A),A) ) ) ).
fof(t14_sprect_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),A)
& r2_hidden(k36_pscomp_1(A),A) ) ) ).
fof(t15_sprect_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),A)
& r2_hidden(k31_pscomp_1(A),A) ) ) ).
fof(t16_sprect_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),A)
& r2_hidden(k34_pscomp_1(A),A) ) ) ).
fof(t17_sprect_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)))) )
=> ( v2_sppol_1(A)
<=> k18_pscomp_1(A) = k20_pscomp_1(A) ) ) ).
fof(t18_sprect_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_sppol_1(A)
<=> k21_pscomp_1(A) = k19_pscomp_1(A) ) ) ).
fof(t19_sprect_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)))) )
=> ( k23_pscomp_1(A) = k24_pscomp_1(A)
=> v2_sppol_1(A) ) ) ).
fof(t20_sprect_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)))) )
=> ( k22_pscomp_1(A) = k25_pscomp_1(A)
=> v2_sppol_1(A) ) ) ).
fof(t21_sprect_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)))) )
=> ( k23_pscomp_1(A) = k22_pscomp_1(A)
=> v1_sppol_1(A) ) ) ).
fof(t22_sprect_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)))) )
=> ( k24_pscomp_1(A) = k25_pscomp_1(A)
=> v1_sppol_1(A) ) ) ).
fof(t23_sprect_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(k18_pscomp_1(A),k20_pscomp_1(A)) ) ).
fof(t24_sprect_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_pscomp_1(A),k19_pscomp_1(A)) ) ).
fof(t29_sprect_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),k23_pscomp_1(A)),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) = k1_struct_0(k15_euclid(np__2),k23_pscomp_1(A)) ) ).
fof(t30_sprect_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),k24_pscomp_1(A)),k3_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A))) = k1_struct_0(k15_euclid(np__2),k24_pscomp_1(A)) ) ).
fof(t31_sprect_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),k24_pscomp_1(A)),k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A))) = k1_struct_0(k15_euclid(np__2),k25_pscomp_1(A)) ) ).
fof(t32_sprect_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),k22_pscomp_1(A)),k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A))) = k1_struct_0(k15_euclid(np__2),k22_pscomp_1(A)) ) ).
fof(t33_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_sppol_1(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(k20_pscomp_1(A),k18_pscomp_1(A)) ) ).
fof(t34_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_sppol_1(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(k19_pscomp_1(A),k21_pscomp_1(A)) ) ).
fof(t35_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v2_sppol_1(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_subset_1(k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),k3_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A))) ) ).
fof(t36_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_sppol_1(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_subset_1(k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) ).
fof(d1_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k1_sprect_1(A) = k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k3_finseq_4(u1_struct_0(k15_euclid(np__2)),k23_pscomp_1(A),k24_pscomp_1(A),k25_pscomp_1(A)),k2_finseq_4(u1_struct_0(k15_euclid(np__2)),k22_pscomp_1(A),k23_pscomp_1(A))) ) ).
fof(t37_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__1) = k23_pscomp_1(A) ) ).
fof(t38_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__2) = k24_pscomp_1(A) ) ).
fof(t39_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__3) = k25_pscomp_1(A) ) ).
fof(t40_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__4) = k22_pscomp_1(A) ) ).
fof(t41_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__5) = k23_pscomp_1(A) ) ).
fof(t42_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k3_finseq_1(k1_sprect_1(A)) = np__5 ) ).
fof(t43_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k5_topreal1(np__2,k1_sprect_1(A)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A)),k3_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A))),k4_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)))) ) ).
fof(t44_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k5_topreal1(np__2,k1_sprect_1(A)) = k1_sppol_2(k18_pscomp_1(A),k20_pscomp_1(A),k21_pscomp_1(A),k19_pscomp_1(A)) ) ).
fof(t45_sprect_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) )
=> k1_pscomp_1(u1_struct_0(k3_pre_topc(A,B)),k1_numbers,k15_pscomp_1(A,B,C)) = k2_funct_2(u1_struct_0(A),k1_numbers,C,B) ) ) ) ).
fof(t46_sprect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,A)
& 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)
& v9_pscomp_1(C,A)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> v2_seq_4(k2_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ).
fof(t47_sprect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,A)
& 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)
& v9_pscomp_1(C,A)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> v1_seq_4(k2_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ).
fof(t48_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k18_pscomp_1(A) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) ) ).
fof(t49_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_pscomp_1(A) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) ) ).
fof(t50_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k19_pscomp_1(A) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) ) ).
fof(t51_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k20_pscomp_1(A) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) ) ).
fof(t52_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_seq_4(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_seq_4(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> k4_pscomp_1(k4_subset_1(k1_numbers,A,B)) = k3_square_1(k4_pscomp_1(A),k4_pscomp_1(B)) ) ) ).
fof(t53_sprect_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_seq_4(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_seq_4(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> k3_pscomp_1(k4_subset_1(k1_numbers,A,B)) = k4_square_1(k3_pscomp_1(A),k3_pscomp_1(B)) ) ) ).
fof(t54_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
=> k18_pscomp_1(A) = k3_square_1(k18_pscomp_1(B),k18_pscomp_1(C)) ) ) ) ) ).
fof(t55_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
=> k21_pscomp_1(A) = k3_square_1(k21_pscomp_1(B),k21_pscomp_1(C)) ) ) ) ) ).
fof(t56_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
=> k19_pscomp_1(A) = k4_square_1(k19_pscomp_1(B),k19_pscomp_1(C)) ) ) ) ) ).
fof(t57_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
=> k20_pscomp_1(A) = k4_square_1(k20_pscomp_1(B),k20_pscomp_1(C)) ) ) ) ) ).
fof(t58_sprect_1,axiom,
$true ).
fof(t59_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(A,B)
=> ( r2_hidden(C,k1_rcomp_1(A,B))
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r1_xreal_0(np__0,D)
& r1_xreal_0(D,np__1)
& C = k3_real_1(k4_real_1(D,A),k4_real_1(k5_real_1(np__1,D),B)) ) ) ) ) ) ) ).
fof(t60_sprect_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k21_euclid(A),k21_euclid(B))
=> k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k3_topreal1(np__2,A,B)) = k1_rcomp_1(k21_euclid(A),k21_euclid(B)) ) ) ) ).
fof(t61_sprect_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k22_euclid(A),k22_euclid(B))
=> k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k3_topreal1(np__2,A,B)) = k1_rcomp_1(k22_euclid(A),k22_euclid(B)) ) ) ) ).
fof(t62_sprect_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k21_euclid(A),k21_euclid(B))
=> k18_pscomp_1(k3_topreal1(np__2,A,B)) = k21_euclid(A) ) ) ) ).
fof(t63_sprect_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k22_euclid(A),k22_euclid(B))
=> k21_pscomp_1(k3_topreal1(np__2,A,B)) = k22_euclid(A) ) ) ) ).
fof(t64_sprect_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k22_euclid(A),k22_euclid(B))
=> k19_pscomp_1(k3_topreal1(np__2,A,B)) = k22_euclid(B) ) ) ) ).
fof(t65_sprect_1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(k21_euclid(A),k21_euclid(B))
=> k20_pscomp_1(k3_topreal1(np__2,A,B)) = k21_euclid(B) ) ) ) ).
fof(t66_sprect_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)))) )
=> k18_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k18_pscomp_1(A) ) ).
fof(t67_sprect_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)))) )
=> k21_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k21_pscomp_1(A) ) ).
fof(t68_sprect_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)))) )
=> k19_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k19_pscomp_1(A) ) ).
fof(t69_sprect_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)))) )
=> k20_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k20_pscomp_1(A) ) ).
fof(t70_sprect_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)))) )
=> k23_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k23_pscomp_1(A) ) ).
fof(t71_sprect_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)))) )
=> k24_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k24_pscomp_1(A) ) ).
fof(t72_sprect_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)))) )
=> k22_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k22_pscomp_1(A) ) ).
fof(t73_sprect_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)))) )
=> k25_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k25_pscomp_1(A) ) ).
fof(t74_sprect_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)))) )
=> k26_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)) ) ).
fof(t75_sprect_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)))) )
=> k27_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A)) ) ).
fof(t76_sprect_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)))) )
=> k29_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)) ) ).
fof(t77_sprect_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)))) )
=> k28_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k3_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)) ) ).
fof(t78_sprect_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)))) )
=> k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A))) = k1_rcomp_1(k21_pscomp_1(A),k19_pscomp_1(A)) ) ).
fof(t79_sprect_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)))) )
=> k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) = k1_rcomp_1(k18_pscomp_1(A),k20_pscomp_1(A)) ) ).
fof(t80_sprect_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)))) )
=> k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k3_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A))) = k1_rcomp_1(k21_pscomp_1(A),k19_pscomp_1(A)) ) ).
fof(t81_sprect_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)))) )
=> k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k3_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A))) = k1_rcomp_1(k18_pscomp_1(A),k20_pscomp_1(A)) ) ).
fof(t82_sprect_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(k5_topreal1(np__2,k1_sprect_1(A))) = k22_pscomp_1(A) ) ).
fof(t83_sprect_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)))) )
=> k31_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k23_pscomp_1(A) ) ).
fof(t84_sprect_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(k5_topreal1(np__2,k1_sprect_1(A))) = k23_pscomp_1(A) ) ).
fof(t85_sprect_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)))) )
=> k33_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k24_pscomp_1(A) ) ).
fof(t86_sprect_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(k5_topreal1(np__2,k1_sprect_1(A))) = k25_pscomp_1(A) ) ).
fof(t87_sprect_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)))) )
=> k34_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k24_pscomp_1(A) ) ).
fof(t88_sprect_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(k5_topreal1(np__2,k1_sprect_1(A))) = k22_pscomp_1(A) ) ).
fof(t89_sprect_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)))) )
=> k36_pscomp_1(k5_topreal1(np__2,k1_sprect_1(A))) = k25_pscomp_1(A) ) ).
fof(d2_sprect_1,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_sprect_1(A)
<=> ? [B] :
( ~ v1_xboole_0(B)
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& A = k1_sprect_1(B) ) ) ) ).
fof(t90_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k3_finseq_1(A) = np__5 ) ).
fof(t91_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k31_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t92_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2) = k33_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2) = k34_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t93_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__3) = k36_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__3) = k35_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t94_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__4) = k37_pscomp_1(k5_topreal1(np__2,A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__4) = k30_pscomp_1(k5_topreal1(np__2,A)) ) ) ).
fof(t95_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& ~ v2_jordan1(k1_sppol_2(A,B,C,D)) ) ) ) ) ) ).
fof(d3_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v2_jordan1(A)
<=> ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) != k1_xboole_0
& ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
& r1_xboole_0(B,C)
& k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),B),B) = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),C),C)
& r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A),B)
& r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A),C) ) ) ) ) ) ).
fof(t96_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_xboole_0(k2_goboard9(A),k3_goboard9(A)) ) ).
fof(t97_sprect_1,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k2_goboard9(A) != k3_goboard9(A) ) ).
fof(dt_k1_sprect_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m2_finseq_1(k1_sprect_1(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(t25_sprect_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)))) )
=> k3_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)) = a_1_0_sprect_1(A) ) ).
fof(t26_sprect_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)))) )
=> k3_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)) = a_1_1_sprect_1(A) ) ).
fof(t27_sprect_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)))) )
=> k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A)) = a_1_2_sprect_1(A) ) ).
fof(t28_sprect_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)))) )
=> k3_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)) = a_1_3_sprect_1(A) ) ).
fof(fraenkel_a_1_0_sprect_1,axiom,
! [A,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,a_1_0_sprect_1(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& k21_euclid(C) = k20_pscomp_1(B)
& r1_xreal_0(k22_euclid(C),k19_pscomp_1(B))
& r1_xreal_0(k21_pscomp_1(B),k22_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_1_sprect_1,axiom,
! [A,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,a_1_1_sprect_1(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k21_euclid(C),k20_pscomp_1(B))
& r1_xreal_0(k18_pscomp_1(B),k21_euclid(C))
& k22_euclid(C) = k21_pscomp_1(B) ) ) ) ).
fof(fraenkel_a_1_2_sprect_1,axiom,
! [A,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,a_1_2_sprect_1(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k21_euclid(C),k20_pscomp_1(B))
& r1_xreal_0(k18_pscomp_1(B),k21_euclid(C))
& k22_euclid(C) = k19_pscomp_1(B) ) ) ) ).
fof(fraenkel_a_1_3_sprect_1,axiom,
! [A,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,a_1_3_sprect_1(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& k21_euclid(C) = k18_pscomp_1(B)
& r1_xreal_0(k22_euclid(C),k19_pscomp_1(B))
& r1_xreal_0(k21_pscomp_1(B),k22_euclid(C)) ) ) ) ).
%------------------------------------------------------------------------------