SET007 Axioms: SET007+715.ax
%------------------------------------------------------------------------------
% File : SET007+715 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Remarks on Clockwise Oriented Sequences on Go-boards
% 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 : jordan1i [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 30 ( 0 unt; 0 def)
% Number of atoms : 500 ( 37 equ)
% Maximal formula atoms : 27 ( 16 avg)
% Number of connectives : 570 ( 100 ~; 1 |; 353 &)
% ( 3 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 14 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 27 ( 26 usr; 0 prp; 1-3 aty)
% Number of functors : 49 ( 49 usr; 6 con; 0-4 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% 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(t1_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( v1_jordan2c(B,A)
| v1_jordan2c(C,A) )
=> v1_jordan2c(k5_subset_1(u1_struct_0(k15_euclid(A)),B,C),A) ) ) ) ) ).
fof(t2_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( ~ v1_jordan2c(B,A)
& v1_jordan2c(C,A)
& v1_jordan2c(k6_subset_1(u1_struct_0(k15_euclid(A)),B,C),A) ) ) ) ) ).
fof(t3_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k5_finseq_4(k1_jordan9(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1) ) ) ).
fof(t4_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k5_finseq_4(k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1) ) ) ).
fof(t5_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k5_finseq_4(k1_jordan9(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1) ) ) ).
fof(t6_jordan1i,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] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k2_relat_1(A))
=> k5_goboard5(A,k5_finseq_4(A,B)) = k5_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,B),np__1) ) ) ) ).
fof(t7_jordan1i,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] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k2_relat_1(A))
=> k4_goboard5(A,k5_finseq_4(A,B)) = k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,B),np__1) ) ) ) ).
fof(t8_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k30_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1)) ) ) ).
fof(t9_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k34_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1)) ) ) ).
fof(t10_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k36_pscomp_1(B),k4_goboard5(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A)))),np__1)) ) ) ).
fof(t11_jordan1i,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)
& v1_sprect_2(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))
=> r2_hidden(B,k2_goboard9(A)) ) ) ) ).
fof(t12_jordan1i,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)
& v1_sprect_2(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(k21_euclid(B),k20_pscomp_1(k5_topreal1(np__2,A)))
=> r2_hidden(B,k2_goboard9(A)) ) ) ) ).
fof(t13_jordan1i,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)
& v1_sprect_2(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(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(B))
=> r2_hidden(B,k2_goboard9(A)) ) ) ) ).
fof(t14_jordan1i,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)
& v1_sprect_2(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(k22_euclid(B),k19_pscomp_1(k5_topreal1(np__2,A)))
=> r2_hidden(B,k2_goboard9(A)) ) ) ) ).
fof(t15_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& r1_xreal_0(k1_matrix_1(B),D) ) ) ) ) ) ) ) ).
fof(t16_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
& r1_xreal_0(k3_finseq_1(B),C) ) ) ) ) ) ) ) ).
fof(t17_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
& r1_xreal_0(D,np__1) ) ) ) ) ) ) ) ).
fof(t18_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& r1_xreal_0(C,np__1) ) ) ) ) ) ) ) ).
fof(t19_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k19_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t20_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
& k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k20_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t21_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),D)
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k21_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t22_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k3_finseq_1(A))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(B))
& r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,D)
& k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E)) = k18_pscomp_1(k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t23_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k30_pscomp_1(k5_topreal1(np__2,A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
& r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,k1_nat_1(E,np__1)) ) ) ) ) ) ) ) ).
fof(t24_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k32_pscomp_1(k5_topreal1(np__2,A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
& r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(D,np__1),E) ) ) ) ) ) ) ) ).
fof(t25_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k34_pscomp_1(k5_topreal1(np__2,A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,k1_nat_1(E,np__1)),k2_matrix_1(B))
& r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,k1_nat_1(E,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E) ) ) ) ) ) ) ) ).
fof(t26_jordan1i,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)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k36_pscomp_1(k5_topreal1(np__2,A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(k1_nat_1(D,np__1),E),k2_matrix_1(B))
& r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(D,np__1),E)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E) ) ) ) ) ) ) ) ).
fof(t27_jordan1i,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))) )
=> ( v1_sprect_2(A)
<=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,k30_pscomp_1(k5_topreal1(np__2,A))),np__2),k26_pscomp_1(k5_topreal1(np__2,A))) ) ) ).
fof(t28_jordan1i,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))) )
=> ( v1_sprect_2(A)
<=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,k34_pscomp_1(k5_topreal1(np__2,A))),np__2),k28_pscomp_1(k5_topreal1(np__2,A))) ) ) ).
fof(t29_jordan1i,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))) )
=> ( v1_sprect_2(A)
<=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),A,k36_pscomp_1(k5_topreal1(np__2,A))),np__2),k29_pscomp_1(k5_topreal1(np__2,A))) ) ) ).
fof(t30_jordan1i,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& v1_topreal2(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( k21_euclid(D) = k6_real_1(k3_real_1(k18_pscomp_1(C),k20_pscomp_1(C)),np__2)
& ~ r1_xreal_0(A,np__0)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(k1_jordan8(C,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),B),k8_jordan6(k5_topreal1(np__2,k1_jordan9(C,A))))
& k22_euclid(D) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,np__1),k1_jordan1a(k1_jordan8(C,np__1)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),B)),k9_jordan6(k5_topreal1(np__2,k1_jordan9(C,A))))))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(k1_jordan8(C,A)))
& D = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),E) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------