SET007 Axioms: SET007+674.ax
%------------------------------------------------------------------------------
% File : SET007+674 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of Cells and Gauges
% 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 : jordan1c [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 37 ( 1 unt; 0 def)
% Number of atoms : 220 ( 20 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 220 ( 37 ~; 2 |; 76 &)
% ( 0 <=>; 105 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 46 ( 46 usr; 7 con; 0-4 aty)
% Number of variables : 87 ( 87 !; 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(fc1_jordan1c,axiom,
! [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(k2_jordan2c(np__2,A))
& v3_pre_topc(k2_jordan2c(np__2,A),k15_euclid(np__2))
& v2_connsp_1(k2_jordan2c(np__2,A),k15_euclid(np__2)) ) ) ).
fof(t1_jordan1c,axiom,
$true ).
fof(t2_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [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)
=> ( ( r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,D)))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(k1_jordan8(A,D))) )
=> k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__2,np__1)) = k5_real_1(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),k1_nat_1(B,np__1),C)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),B,C))) ) ) ) ) ) ).
fof(t3_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [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)
=> ( ( r2_hidden(k4_tarski(B,C),k2_matrix_1(k1_jordan8(A,D)))
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(k1_jordan8(A,D))) )
=> k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),np__1,np__2)) = k5_real_1(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),B,k1_nat_1(C,np__1))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,D),B,C))) ) ) ) ) ) ).
fof(t4_jordan1c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_jordan2c(A,np__2)
=> v3_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A)) ) ) ).
fof(t5_jordan1c,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)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( C = k4_subset_1(u1_struct_0(k15_euclid(np__2)),A,B)
& v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B)) )
=> ( v1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B))
| k18_pscomp_1(C) = k3_square_1(k18_pscomp_1(A),k18_pscomp_1(B)) ) ) ) ) ) ).
fof(t6_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r2_hidden(A,B)
& v1_jordan2c(B,np__2) )
=> ( r1_xreal_0(k18_pscomp_1(B),k21_euclid(A))
& r1_xreal_0(k21_euclid(A),k20_pscomp_1(B))
& r1_xreal_0(k21_pscomp_1(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(A),k19_pscomp_1(B)) ) ) ) ) ).
fof(t7_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,k5_jordan1a(A))
& r2_hidden(A,k3_jordan1a(A))
& r2_hidden(A,k2_jordan1a(A))
& r2_hidden(A,k4_jordan1a(A)) ) ) ).
fof(t8_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_jordan2c(k5_jordan1a(A),np__2) ) ).
fof(t9_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_jordan2c(k3_jordan1a(A),np__2) ) ).
fof(t10_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_jordan2c(k2_jordan1a(A),np__2) ) ).
fof(t11_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ v1_jordan2c(k4_jordan1a(A),np__2) ) ).
fof(t12_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A),k2_jordan2c(np__2,A)) ) ).
fof(t13_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xboole_0(B,A)
=> ( v1_jordan2c(B,np__2)
| r1_tarski(B,k2_jordan2c(np__2,A)) ) ) ) ) ).
fof(t14_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xboole_0(k5_jordan1a(B),A)
=> r1_tarski(k5_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t15_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xboole_0(k3_jordan1a(B),A)
=> r1_tarski(k3_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t16_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xboole_0(k4_jordan1a(B),A)
=> r1_tarski(k4_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t17_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_xboole_0(k2_jordan1a(B),A)
=> r1_tarski(k2_jordan1a(B),k2_jordan2c(np__2,A)) ) ) ) ).
fof(t18_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k1_jordan2c(np__2,A) != k1_xboole_0
=> r1_xreal_0(k18_pscomp_1(A),k18_pscomp_1(k1_jordan2c(np__2,A))) ) ) ).
fof(t19_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k1_jordan2c(np__2,A) != k1_xboole_0
=> r1_xreal_0(k20_pscomp_1(k1_jordan2c(np__2,A)),k20_pscomp_1(A)) ) ) ).
fof(t20_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k1_jordan2c(np__2,A) != k1_xboole_0
=> r1_xreal_0(k21_pscomp_1(A),k21_pscomp_1(k1_jordan2c(np__2,A))) ) ) ).
fof(t21_jordan1c,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( k1_jordan2c(np__2,A) != k1_xboole_0
=> r1_xreal_0(k19_pscomp_1(k1_jordan2c(np__2,A)),k19_pscomp_1(A)) ) ) ).
fof(t22_jordan1c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( v1_int_1(D)
=> ~ ( r2_hidden(B,k1_jordan2c(np__2,C))
& D = k1_int_1(k3_real_1(k4_real_1(k6_real_1(k5_real_1(k21_euclid(B),k18_pscomp_1(C)),k5_real_1(k20_pscomp_1(C),k18_pscomp_1(C))),k1_card_4(np__2,A)),np__2))
& r1_xreal_0(D,np__1) ) ) ) ) ) ).
fof(t23_jordan1c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( v1_int_1(D)
=> ( ( r2_hidden(B,k1_jordan2c(np__2,C))
& D = k1_int_1(k3_real_1(k4_real_1(k6_real_1(k5_real_1(k21_euclid(B),k18_pscomp_1(C)),k5_real_1(k20_pscomp_1(C),k18_pscomp_1(C))),k1_card_4(np__2,A)),np__2)) )
=> r1_xreal_0(k2_xcmplx_0(D,np__1),k3_finseq_1(k1_jordan8(C,A))) ) ) ) ) ) ).
fof(t24_jordan1c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( v1_int_1(D)
=> ( ( r2_hidden(B,k1_jordan2c(np__2,C))
& D = k1_int_1(k3_real_1(k4_real_1(k6_real_1(k5_real_1(k22_euclid(B),k21_pscomp_1(C)),k5_real_1(k19_pscomp_1(C),k21_pscomp_1(C))),k1_card_4(np__2,A)),np__2)) )
=> ( ~ r1_xreal_0(D,np__1)
& r1_xreal_0(k2_xcmplx_0(D,np__1),k1_matrix_1(k1_jordan8(C,A))) ) ) ) ) ) ) ).
fof(t25_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( v1_int_1(D)
=> ( D = k1_int_1(k3_real_1(k4_real_1(k6_real_1(k5_real_1(k21_euclid(C),k18_pscomp_1(A)),k5_real_1(k20_pscomp_1(A),k18_pscomp_1(A))),k1_card_4(np__2,B)),np__2))
=> r1_xreal_0(k2_xcmplx_0(k18_pscomp_1(A),k3_xcmplx_0(k6_real_1(k5_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),k1_card_4(np__2,B)),k6_xcmplx_0(D,np__2))),k21_euclid(C)) ) ) ) ) ) ).
fof(t26_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( v1_int_1(D)
=> ~ ( D = k1_int_1(k3_real_1(k4_real_1(k6_real_1(k5_real_1(k21_euclid(C),k18_pscomp_1(A)),k5_real_1(k20_pscomp_1(A),k18_pscomp_1(A))),k1_card_4(np__2,B)),np__2))
& r1_xreal_0(k2_xcmplx_0(k18_pscomp_1(A),k3_xcmplx_0(k6_real_1(k5_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),k1_card_4(np__2,B)),k6_xcmplx_0(D,np__1))),k21_euclid(C)) ) ) ) ) ) ).
fof(t27_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( v1_int_1(D)
=> ( D = k1_int_1(k3_real_1(k4_real_1(k6_real_1(k5_real_1(k22_euclid(C),k21_pscomp_1(A)),k5_real_1(k19_pscomp_1(A),k21_pscomp_1(A))),k1_card_4(np__2,B)),np__2))
=> r1_xreal_0(k2_xcmplx_0(k21_pscomp_1(A),k3_xcmplx_0(k6_real_1(k5_real_1(k19_pscomp_1(A),k21_pscomp_1(A)),k1_card_4(np__2,B)),k6_xcmplx_0(D,np__2))),k22_euclid(C)) ) ) ) ) ) ).
fof(t28_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( v1_int_1(D)
=> ~ ( D = k1_int_1(k3_real_1(k4_real_1(k6_real_1(k5_real_1(k22_euclid(C),k21_pscomp_1(A)),k5_real_1(k19_pscomp_1(A),k21_pscomp_1(A))),k1_card_4(np__2,B)),np__2))
& r1_xreal_0(k2_xcmplx_0(k21_pscomp_1(A),k3_xcmplx_0(k6_real_1(k5_real_1(k19_pscomp_1(A),k21_pscomp_1(A)),k1_card_4(np__2,B)),k6_xcmplx_0(D,np__1))),k22_euclid(C)) ) ) ) ) ) ).
fof(t29_jordan1c,axiom,
! [A] :
( ( v4_pre_topc(A,k15_euclid(np__2))
& 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)))
=> ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& r1_tarski(k9_metric_1(k14_euclid(np__2),B,C),k1_jordan2c(np__2,A)) ) ) ) ) ) ).
fof(t30_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [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] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ! [G] :
( v1_xreal_0(G)
=> ~ ( ~ r1_xreal_0(G,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),np__1,np__2)))
& ~ r1_xreal_0(G,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),np__2,np__1)))
& r2_hidden(E,k3_goboard5(k1_jordan8(A,B),C,D))
& r2_hidden(F,k3_goboard5(k1_jordan8(A,B),C,D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan8(A,B)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k1_matrix_1(k1_jordan8(A,B)))
& r1_xreal_0(k3_xcmplx_0(np__2,G),k1_gobrd14(np__2,E,F)) ) ) ) ) ) ) ) ) ).
fof(t31_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [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,k1_jordan2c(np__2,B))
& k22_euclid(A) = k19_pscomp_1(k1_jordan2c(np__2,B)) ) ) ) ).
fof(t32_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [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,k1_jordan2c(np__2,B))
& k21_euclid(A) = k20_pscomp_1(k1_jordan2c(np__2,B)) ) ) ) ).
fof(t33_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [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,k1_jordan2c(np__2,B))
& k22_euclid(A) = k21_pscomp_1(k1_jordan2c(np__2,B)) ) ) ) ).
fof(t34_jordan1c,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [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,k1_jordan2c(np__2,B))
& k21_euclid(A) = k18_pscomp_1(k1_jordan2c(np__2,B)) ) ) ) ).
fof(t35_jordan1c,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k1_jordan2c(np__2,A))
& ! [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(D,np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(A,C)),D)
& ~ r1_xreal_0(E,np__1)
& ~ r1_xreal_0(k1_matrix_1(k1_jordan8(A,C)),E)
& k21_euclid(B) != k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,C),D,E))
& r2_hidden(B,k3_goboard5(k1_jordan8(A,C),D,E))
& r1_tarski(k3_goboard5(k1_jordan8(A,C),D,E),k1_jordan2c(np__2,A)) ) ) ) ) ) ) ) ).
fof(t36_jordan1c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( v1_jordan2c(A,np__2)
& v1_xboole_0(k2_jordan2c(np__2,A)) ) ) ).
%------------------------------------------------------------------------------