SET007 Axioms: SET007+570.ax
%------------------------------------------------------------------------------
% File : SET007+570 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of Special Polygonal Curves
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 82 ( 7 unt; 0 def)
% Number of atoms : 668 ( 60 equ)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 686 ( 100 ~; 15 |; 354 &)
% ( 5 <=>; 212 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-5 aty)
% Number of functors : 67 ( 67 usr; 7 con; 0-5 aty)
% Number of variables : 184 ( 178 !; 6 ?)
% 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_sprect_3,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(k5_topreal1(np__2,A))
& ~ v1_sppol_1(k5_topreal1(np__2,A))
& ~ v2_sppol_1(k5_topreal1(np__2,A))
& v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2))
& v1_topreal2(k5_topreal1(np__2,A)) ) ) ).
fof(fc2_sprect_3,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))
& v2_topreal4(k2_goboard9(A),k15_euclid(np__2)) ) ) ).
fof(fc3_sprect_3,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))
& v2_topreal4(k3_goboard9(A),k15_euclid(np__2)) ) ) ).
fof(rc1_sprect_3,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& ~ v1_realset1(A)
& v1_sprect_1(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) ) ).
fof(rc2_sprect_3,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_sprect_2(A)
& ~ v1_realset1(A)
& v1_sprect_1(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) ) ).
fof(cc1_sprect_3,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A) )
=> ( ~ v1_xboole_0(A)
& v1_sprect_2(A)
& v1_sprect_1(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) ) ) ) ).
fof(t1_sprect_3,axiom,
$true ).
fof(t2_sprect_3,axiom,
! [A,B,C,D] :
( ( r1_tarski(A,B)
& k3_xboole_0(B,C) = k1_tarski(D)
& r2_hidden(D,A) )
=> k3_xboole_0(A,C) = k1_tarski(D) ) ).
fof(t3_sprect_3,axiom,
$true ).
fof(t4_sprect_3,axiom,
$true ).
fof(t5_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k5_binarith(A,B),C)
=> r1_xreal_0(A,k1_nat_1(C,B)) ) ) ) ) ).
fof(t6_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(A,k1_nat_1(B,C))
=> r1_xreal_0(k5_binarith(A,C),B) ) ) ) ) ).
fof(t7_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(A,k5_binarith(B,C))
& r1_xreal_0(C,B) )
=> r1_xreal_0(k1_nat_1(A,C),B) ) ) ) ) ).
fof(t8_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k1_nat_1(A,B),C)
=> r1_xreal_0(B,k5_binarith(C,A)) ) ) ) ) ).
fof(t9_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(A,B)
& ~ r1_xreal_0(C,B)
& r1_xreal_0(k5_binarith(C,A),k5_binarith(B,A)) ) ) ) ) ).
fof(t10_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(B,C)
& r1_xreal_0(k5_binarith(B,C),k5_binarith(A,C)) ) ) ) ) ).
fof(t11_sprect_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> k4_finseq_4(k5_numbers,A,k8_finseq_1(A,C,B),k3_finseq_1(k8_finseq_1(A,C,B))) = k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B)) ) ) ) ).
fof(t12_sprect_3,axiom,
! [A,B,C,D] : k2_matrix_1(k3_matrix_2(A,B,C,D)) = k2_enumset1(k4_tarski(np__1,np__1),k4_tarski(np__1,np__2),k4_tarski(np__2,np__1),k4_tarski(np__2,np__2)) ).
fof(t13_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( B = k17_euclid(A,k18_euclid(k5_real_1(np__1,D),A,B),k18_euclid(D,A,C))
=> ( r1_xreal_0(D,np__0)
| B = C ) ) ) ) ) ) ).
fof(t14_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( B = k17_euclid(A,k18_euclid(k5_real_1(np__1,D),A,C),k18_euclid(D,A,B))
=> ( r1_xreal_0(np__1,D)
| B = C ) ) ) ) ) ) ).
fof(t15_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ( B = k18_euclid(k6_real_1(np__1,np__2),A,k17_euclid(A,B,C))
=> B = C ) ) ) ) ).
fof(t16_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ( ( r2_hidden(C,k3_topreal1(A,B,D))
& r2_hidden(D,k3_topreal1(A,B,C)) )
=> C = D ) ) ) ) ) ).
fof(t17_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( A = k9_metric_1(k14_euclid(np__2),B,C)
=> v2_connsp_1(A,k15_euclid(np__2)) ) ) ) ) ).
fof(t18_sprect_3,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))))
=> ( ( v3_pre_topc(A,k15_euclid(np__2))
& r4_connsp_1(k15_euclid(np__2),A,B) )
=> v3_pre_topc(B,k15_euclid(np__2)) ) ) ) ).
fof(t19_sprect_3,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)))
=> ( ( v1_sppol_1(k3_topreal1(np__2,A,B))
& r2_hidden(C,k3_topreal1(np__2,A,B)) )
=> k22_euclid(A) = k22_euclid(C) ) ) ) ) ).
fof(t20_sprect_3,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)))
=> ( ( v2_sppol_1(k3_topreal1(np__2,A,B))
& r2_hidden(C,k3_topreal1(np__2,A,B)) )
=> k21_euclid(A) = k21_euclid(C) ) ) ) ) ).
fof(t21_sprect_3,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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_sppol_1(k3_topreal1(np__2,A,B))
& v1_sppol_1(k3_topreal1(np__2,C,D)) )
=> ( r2_subset_1(k3_topreal1(np__2,A,B),k3_topreal1(np__2,C,D))
| k22_euclid(A) = k22_euclid(C) ) ) ) ) ) ) ).
fof(t22_sprect_3,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)))
=> ( ( v2_sppol_1(k3_topreal1(np__2,A,B))
& v1_sppol_1(k3_topreal1(np__2,B,C)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k3_topreal1(np__2,B,C)) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) ).
fof(t23_sprect_3,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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( v1_sppol_1(k3_topreal1(np__2,A,B))
& v2_sppol_1(k3_topreal1(np__2,D,C))
& r2_hidden(C,k3_topreal1(np__2,A,B)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,A,B),k3_topreal1(np__2,D,C)) = k1_struct_0(k15_euclid(np__2),C) ) ) ) ) ) ).
fof(t24_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(B,k1_matrix_1(D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(D)) )
=> r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,A)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,B))) ) ) ) ) ) ).
fof(t25_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(D))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,C)
& r1_xreal_0(C,k3_finseq_1(D)) )
=> r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B,A)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,A))) ) ) ) ) ) ).
fof(t26_sprect_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> r1_tarski(k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A)),k5_topreal1(np__2,k1_sprect_1(A))) ) ).
fof(t27_sprect_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> r1_tarski(k27_pscomp_1(A),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) ).
fof(t28_sprect_3,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),k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) ).
fof(t29_sprect_3,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> v1_sppol_1(k3_topreal1(np__2,k23_pscomp_1(A),k24_pscomp_1(A))) ) ).
fof(t30_sprect_3,axiom,
$true ).
fof(t31_sprect_3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)),k5_topreal1(np__2,A)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = B
| ( k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) != k21_euclid(B)
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) != k22_euclid(B) )
| v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),k4_matrix_2(u1_struct_0(k15_euclid(np__2)),B),A)) ) ) ) ) ).
fof(t32_sprect_3,axiom,
$true ).
fof(t33_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(A,k3_finseq_1(B))
& r2_hidden(C,k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),B,np__1,A))) )
=> ( r1_xreal_0(A,np__1)
| r1_jordan5c(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),C,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ) ) ) ).
fof(t34_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(A,k4_finseq_1(C))
& r2_hidden(B,k4_finseq_1(C)) )
=> r1_tarski(k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)),k5_topreal1(np__2,C)) ) ) ) ) ).
fof(t35_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> ( r1_xreal_0(B,A)
| ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xreal_0(B,k3_finseq_1(C))
=> k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,C,A),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B))) ) ) ) ) ) ) ).
fof(t36_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(B,k3_finseq_1(C)) )
=> ( r1_xreal_0(B,A)
| k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,k5_binarith(B,np__1))),k4_topreal1(np__2,C,k5_binarith(B,np__1))) ) ) ) ) ) ).
fof(t37_sprect_3,axiom,
$true ).
fof(t38_sprect_3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v4_topreal1(A)
& v4_topreal1(B)
& r1_xboole_0(k5_topreal1(np__2,A),k5_topreal1(np__2,B))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)),k5_topreal1(np__2,A)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)))
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)),k5_topreal1(np__2,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
=> ( ( k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
| v4_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t39_sprect_3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k5_topreal1(np__2,A))
=> k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k4_jordan3(A,B),np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) ) ) ) ).
fof(t40_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,A)
& r2_hidden(C,k4_topreal1(np__2,B,A))
& r2_hidden(D,k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),C)) )
=> ( r1_xreal_0(k3_finseq_1(B),A)
| r1_jordan5c(k5_topreal1(np__2,B),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),D,C) ) ) ) ) ) ) ).
fof(t41_sprect_3,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)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( v3_pre_topc(k2_goboard9(A),k15_euclid(np__2))
& v3_pre_topc(k3_goboard9(A),k15_euclid(np__2)) ) ) ).
fof(t42_sprect_3,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)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_subset_1(k3_goboard9(A),k5_topreal1(np__2,A)) ) ).
fof(t43_sprect_3,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)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> r1_subset_1(k2_goboard9(A),k5_topreal1(np__2,A)) ) ).
fof(t44_sprect_3,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)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k8_jordan5d(A),k7_jordan5d(A)) ) ).
fof(t45_sprect_3,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)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(k3_goboard2(A)),B)
& k32_pscomp_1(k5_topreal1(np__2,A)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),B,k1_matrix_1(k3_goboard2(A))) ) ) ).
fof(t46_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_sprect_2(B)
& ~ v5_seqm_3(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r2_hidden(A,k4_finseq_1(k3_goboard2(B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),A,k1_matrix_1(k3_goboard2(B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k32_pscomp_1(k5_topreal1(np__2,B)) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),k1_nat_1(A,np__1),k1_matrix_1(k3_goboard2(B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k5_binarith(k3_finseq_1(B),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),A,k5_binarith(k1_matrix_1(k3_goboard2(B)),np__1)) ) ) ) ) ).
fof(t47_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& ~ r1_xreal_0(B,A)
& r1_xreal_0(B,k3_finseq_1(C))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),C,A,B)))
& A != np__1
& B != k3_finseq_1(C) ) ) ) ) ).
fof(t48_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_2(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)
& 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))
=> r1_tarski(k3_topreal1(np__2,k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2)),k5_topreal1(np__2,k1_sprect_1(k5_topreal1(np__2,A)))) ) ) ).
fof(t49_sprect_3,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k5_topreal1(np__2,A))
& k21_euclid(B) != k18_pscomp_1(k5_topreal1(np__2,A))
& k21_euclid(B) != k20_pscomp_1(k5_topreal1(np__2,A))
& k22_euclid(B) != k21_pscomp_1(k5_topreal1(np__2,A))
& k22_euclid(B) != k19_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ).
fof(t50_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A))
& r2_subset_1(k5_topreal1(np__2,A),k5_topreal1(np__2,B)) ) ) ) ).
fof(t51_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k1_sprect_1(k5_topreal1(np__2,A)) = A ) ).
fof(t53_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k3_goboard2(A) = k6_matrix_2(u1_struct_0(k15_euclid(np__2)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__4),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__3),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2)) ) ).
fof(t55_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A))
& k2_jordan5c(k5_topreal1(np__2,B),k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) = k23_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ).
fof(t56_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A))
& k2_jordan5c(k5_topreal1(np__2,B),k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))) = k25_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ).
fof(t57_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ~ ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,A)),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),k20_pscomp_1(k5_topreal1(np__2,A)))
& r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),k19_pscomp_1(k5_topreal1(np__2,A))) )
=> r2_hidden(B,k2_goboard9(A)) ) ) ) ).
fof(t58_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_2(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)
& 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))
=> r1_tarski(k2_goboard9(k1_sprect_1(k5_topreal1(np__2,A))),k2_goboard9(A)) ) ) ).
fof(t59_sprect_3,axiom,
! [A] :
( m2_finseq_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)))
=> ( r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C))
<=> ( r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),B))
& r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C)) ) ) ) ) ) ).
fof(t60_sprect_3,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),B))
=> ( ( k21_euclid(B) != k18_pscomp_1(k5_topreal1(np__2,A))
& k21_euclid(B) != k20_pscomp_1(k5_topreal1(np__2,A))
& k22_euclid(B) != k21_pscomp_1(k5_topreal1(np__2,A))
& k22_euclid(B) != k19_pscomp_1(k5_topreal1(np__2,A)) )
| r2_hidden(B,k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t61_sprect_3,axiom,
! [A] :
( m2_finseq_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)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( r1_xreal_0(np__0,D)
& r1_xreal_0(D,np__1)
& r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C)) )
=> r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k17_euclid(np__2,k18_euclid(k5_real_1(np__1,D),np__2,B),k18_euclid(D,np__2,C)))) ) ) ) ) ) ).
fof(t62_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sprect_2(B,C)
& r2_hidden(A,k4_finseq_1(C)) )
=> r1_sprect_2(B,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A))) ) ) ) ) ).
fof(t63_sprect_3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sprect_2(A,B)
& r2_hidden(C,k5_topreal1(np__2,B)) )
=> r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C)) ) ) ) ) ).
fof(t64_sprect_3,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_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)))
=> ( r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C))
=> ( r2_hidden(C,k5_topreal1(np__2,A))
| r1_tarski(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,C),k5_topreal1(np__2,A)),k1_struct_0(k15_euclid(np__2),B)) ) ) ) ) ) ).
fof(t65_sprect_3,axiom,
! [A] :
( ( v1_sprect_1(A)
& m2_finseq_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)))
=> ( ( r2_hidden(B,k5_topreal1(np__2,A))
& r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C)) )
=> ( r2_hidden(C,k5_topreal1(np__2,A))
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,B,C),k5_topreal1(np__2,A)) = k1_struct_0(k15_euclid(np__2),B) ) ) ) ) ) ).
fof(t66_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k3_goboard2(C)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(k3_goboard2(C))) )
=> r1_sprect_2(C,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B))) ) ) ) ) ).
fof(t67_sprect_3,axiom,
! [A] :
( m2_finseq_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)))
=> ( r1_sprect_2(A,k2_finseq_4(u1_struct_0(k15_euclid(np__2)),B,C))
=> r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,B,C)))) ) ) ) ) ).
fof(t68_sprect_3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(A,B)
=> r1_sprect_2(A,k4_finseq_5(u1_struct_0(k15_euclid(np__2)),B)) ) ) ) ).
fof(t69_sprect_3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sprect_2(A,B)
& r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C))
& v4_topreal1(B)
& r2_hidden(C,k5_topreal1(np__2,B)) )
=> r1_sprect_2(A,k4_jordan3(B,C)) ) ) ) ) ).
fof(t70_sprect_3,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)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(A,B)
<=> r1_sprect_2(k1_sprect_1(k5_topreal1(np__2,A)),B) ) ) ) ).
fof(t71_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v4_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_goboard9(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k3_goboard9(A)) )
=> r1_sprect_2(A,k3_jordan3(B,k2_jordan5c(k5_topreal1(np__2,B),k5_topreal1(np__2,A),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))))) ) ) ) ).
fof(t72_sprect_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B) )
=> ( r1_xreal_0(k3_finseq_1(k3_goboard2(C)),A)
| r1_xreal_0(k1_matrix_1(k3_goboard2(C)),B)
| r1_xboole_0(k1_tops_1(k15_euclid(np__2),k3_goboard5(k3_goboard2(C),A,B)),k5_topreal1(np__2,k1_sprect_1(k5_topreal1(np__2,C)))) ) ) ) ) ) ).
fof(t73_sprect_3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_sprect_2(A,B)
& r1_sprect_2(A,k4_matrix_2(u1_struct_0(k15_euclid(np__2)),C))
& v4_topreal1(B)
& r2_hidden(C,k5_topreal1(np__2,B)) )
=> r1_sprect_2(A,k3_jordan3(B,C)) ) ) ) ) ).
fof(t52_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k5_topreal1(np__2,A) = a_1_0_sprect_3(A) ) ).
fof(t54_sprect_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_sprect_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k2_goboard9(A) = a_1_1_sprect_3(A)
& k3_goboard9(A) = a_1_2_sprect_3(A) ) ) ).
fof(fraenkel_a_1_0_sprect_3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_sprect_1(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_1_0_sprect_3(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& ~ ( ~ ( k21_euclid(C) = k18_pscomp_1(k5_topreal1(np__2,B))
& r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(np__2,B)))
& r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C)) )
& ~ ( r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(np__2,B)))
& r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
& k22_euclid(C) = k19_pscomp_1(k5_topreal1(np__2,B)) )
& ~ ( r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(np__2,B)))
& r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
& k22_euclid(C) = k21_pscomp_1(k5_topreal1(np__2,B)) )
& ~ ( k21_euclid(C) = k20_pscomp_1(k5_topreal1(np__2,B))
& r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(np__2,B)))
& r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C)) ) ) ) ) ) ).
fof(fraenkel_a_1_1_sprect_3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_sprect_1(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_1_1_sprect_3(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& ~ ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
& r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(np__2,B)))
& r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C))
& r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(np__2,B))) ) ) ) ) ).
fof(fraenkel_a_1_2_sprect_3,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_sprect_1(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r2_hidden(A,a_1_2_sprect_3(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& ~ r1_xreal_0(k21_euclid(C),k18_pscomp_1(k5_topreal1(np__2,B)))
& ~ r1_xreal_0(k20_pscomp_1(k5_topreal1(np__2,B)),k21_euclid(C))
& ~ r1_xreal_0(k22_euclid(C),k21_pscomp_1(k5_topreal1(np__2,B)))
& ~ r1_xreal_0(k19_pscomp_1(k5_topreal1(np__2,B)),k22_euclid(C)) ) ) ) ).
%------------------------------------------------------------------------------