SET007 Axioms: SET007+676.ax
%------------------------------------------------------------------------------
% File : SET007+676 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Gauges and Cages. Part II
% 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 : jordan1d [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 41 ( 0 unt; 0 def)
% Number of atoms : 383 ( 21 equ)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 430 ( 88 ~; 7 |; 239 &)
% ( 1 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 10 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 17 ( 16 usr; 0 prp; 1-3 aty)
% Number of functors : 48 ( 48 usr; 5 con; 0-5 aty)
% Number of variables : 124 ( 96 !; 28 ?)
% 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_jordan1d,axiom,
! [A] :
( ( v1_int_1(A)
& v1_abian(A) )
=> ( v1_xreal_0(k2_xcmplx_0(A,np__2))
& v1_int_1(k2_xcmplx_0(A,np__2))
& v1_xcmplx_0(k2_xcmplx_0(A,np__2))
& v1_abian(k2_xcmplx_0(A,np__2)) ) ) ).
fof(fc2_jordan1d,axiom,
! [A] :
( ( v1_int_1(A)
& ~ v1_abian(A) )
=> ( v1_xreal_0(k2_xcmplx_0(A,np__2))
& v1_int_1(k2_xcmplx_0(A,np__2))
& v1_xcmplx_0(k2_xcmplx_0(A,np__2))
& ~ v1_abian(k2_xcmplx_0(A,np__2)) ) ) ).
fof(fc3_jordan1d,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers) )
=> ( v4_ordinal2(k2_newton(np__2,A))
& v1_xreal_0(k2_newton(np__2,A))
& ~ v3_xreal_0(k2_newton(np__2,A))
& v1_int_1(k2_newton(np__2,A))
& v1_xcmplx_0(k2_newton(np__2,A))
& v1_abian(k2_newton(np__2,A)) ) ) ).
fof(fc4_jordan1d,axiom,
! [A,B] :
( ( v1_abian(A)
& m1_subset_1(A,k5_numbers)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k5_numbers) )
=> ( v4_ordinal2(k2_newton(A,B))
& v1_xreal_0(k2_newton(A,B))
& ~ v3_xreal_0(k2_newton(A,B))
& v1_int_1(k2_newton(A,B))
& v1_xcmplx_0(k2_newton(A,B))
& v1_abian(k2_newton(A,B)) ) ) ).
fof(t1_jordan1d,axiom,
! [A,B] :
( ! [C] :
~ ( r2_hidden(C,A)
& ! [D] :
~ ( r1_tarski(D,B)
& r1_tarski(C,k3_tarski(D)) ) )
=> r1_tarski(k3_tarski(A),k3_tarski(B)) ) ).
fof(t2_jordan1d,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_xreal_0(B)
=> ( B != np__0
=> k3_xcmplx_0(k7_xcmplx_0(np__1,B),k2_newton(B,k1_nat_1(A,np__1))) = k2_newton(B,A) ) ) ) ).
fof(t3_jordan1d,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ~ v1_int_1(k7_xcmplx_0(A,B))
=> k4_xcmplx_0(k1_int_1(k7_xcmplx_0(A,B))) = k2_xcmplx_0(k1_int_1(k7_xcmplx_0(k4_xcmplx_0(A),B)),np__1) ) ) ) ).
fof(t4_jordan1d,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( v1_int_1(k7_xcmplx_0(A,B))
=> k4_xcmplx_0(k1_int_1(k7_xcmplx_0(A,B))) = k1_int_1(k7_xcmplx_0(k4_xcmplx_0(A),B)) ) ) ) ).
fof(t5_jordan1d,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(A,np__0)
& k4_nat_1(B,A) != np__0
& k1_real_1(k3_nat_1(B,A)) != k2_xcmplx_0(k5_int_1(k1_real_1(B),A),np__1) ) ) ) ).
fof(t6_jordan1d,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k4_nat_1(B,A) = np__0
=> ( r1_xreal_0(A,np__0)
| k1_real_1(k3_nat_1(B,A)) = k5_int_1(k1_real_1(B),A) ) ) ) ) ).
fof(t7_jordan1d,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__2,A)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(k1_jordan8(E,k1_nat_1(B,np__1)))) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan8(E,B)),A)
| k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),A,C)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__2),D)) ) ) ) ) ) ) ) ).
fof(t8_jordan1d,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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__2,A)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(k1_jordan8(E,k1_nat_1(B,np__1)))) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan8(E,B)),A)
| k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,A)) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,k1_nat_1(B,np__1)),D,k5_binarith(k2_nat_1(np__2,A),np__2))) ) ) ) ) ) ) ) ).
fof(t9_jordan1d,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] :
( ( v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__2,A)
& r1_xreal_0(np__2,C) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(A,np__1))
| r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(C,np__1))
| k3_goboard5(k1_jordan8(D,B),A,C) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__2),k5_binarith(k2_nat_1(np__2,C),np__2)),k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__1),k5_binarith(k2_nat_1(np__2,C),np__2))),k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__2),k5_binarith(k2_nat_1(np__2,C),np__1))),k3_goboard5(k1_jordan8(D,k1_nat_1(B,np__1)),k5_binarith(k2_nat_1(np__2,A),np__1),k5_binarith(k2_nat_1(np__2,C),np__1))) ) ) ) ) ) ) ).
fof(t11_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k33_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) ).
fof(t12_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k33_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) ).
fof(t13_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k35_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) ).
fof(t14_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k35_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) ).
fof(t15_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k34_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) ).
fof(t16_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k34_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) ).
fof(t17_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k37_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) ).
fof(t18_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k37_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) ).
fof(t19_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k36_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) ).
fof(t20_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k36_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) ).
fof(t21_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k30_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) ).
fof(t22_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k30_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) ).
fof(t23_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k31_pscomp_1(B),k3_gobrd13(k1_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) ).
fof(t24_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r2_hidden(k31_pscomp_1(B),k4_goboard5(k1_jordan9(B,A),C)) ) ) ) ).
fof(t25_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& k32_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))) ) ) ) ).
fof(t26_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& k33_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))) ) ) ) ).
fof(t27_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,k1_matrix_1(k1_jordan8(B,A))),k2_relat_1(k1_jordan9(B,A))) ) ) ) ).
fof(t28_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& k35_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C) ) ) ) ).
fof(t29_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C) ) ) ) ).
fof(t30_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C),k2_relat_1(k1_jordan9(B,A))) ) ) ) ).
fof(t31_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& k37_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1) ) ) ) ).
fof(t32_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1) ) ) ) ).
fof(t33_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),C,np__1),k2_relat_1(k1_jordan9(B,A))) ) ) ) ).
fof(t34_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__1,C) ) ) ) ).
fof(t35_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& k31_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__1,C) ) ) ) ).
fof(t36_jordan1d,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)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(B,A)))
& r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__1,C),k2_relat_1(k1_jordan9(B,A))) ) ) ) ).
fof(t10_jordan1d,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] :
( ( v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__2,A)
& r1_xreal_0(np__2,C) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(A,np__1))
| r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(C,np__1))
| k3_goboard5(k1_jordan8(D,B),A,C) = k3_tarski(a_5_0_jordan1d(A,B,C,D,E)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_5_0_jordan1d,axiom,
! [A,B,C,D,E,F] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers)
& m2_subset_1(D,k1_numbers,k5_numbers)
& v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m2_subset_1(F,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_5_0_jordan1d(B,C,D,E,F))
<=> ? [G,H] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& m2_subset_1(H,k1_numbers,k5_numbers)
& A = k3_goboard5(k1_jordan8(E,k1_nat_1(C,F)),G,H)
& r1_xreal_0(k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),B),k3_newton(np__2,k1_nat_1(F,np__1))),np__2),G)
& r1_xreal_0(G,k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),B),k3_newton(np__2,F)),np__1))
& r1_xreal_0(k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),D),k3_newton(np__2,k1_nat_1(F,np__1))),np__2),H)
& r1_xreal_0(H,k3_real_1(k5_real_1(k4_real_1(k3_newton(np__2,F),D),k3_newton(np__2,F)),np__1)) ) ) ) ).
%------------------------------------------------------------------------------