SET007 Axioms: SET007+417.ax
%------------------------------------------------------------------------------
% File : SET007+417 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Go-Board of a Standard Special Circular Sequence
% 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 : goboard7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 64 ( 0 unt; 0 def)
% Number of atoms : 1069 ( 179 equ)
% Maximal formula atoms : 29 ( 16 avg)
% Number of connectives : 1171 ( 166 ~; 34 |; 708 &)
% ( 1 <=>; 262 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 15 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 23 ( 22 usr; 0 prp; 1-3 aty)
% Number of functors : 35 ( 35 usr; 6 con; 0-4 aty)
% Number of variables : 226 ( 224 !; 2 ?)
% 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_goboard7,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(k18_complex1(k5_real_1(A,B)),C)
& r1_xreal_0(B,k3_real_1(A,C))
& r1_xreal_0(A,k3_real_1(B,C)) ) ) ) ) ).
fof(t2_goboard7,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( k18_complex1(k5_real_1(A,B)) = np__0
<=> A = B ) ) ) ).
fof(t3_goboard7,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)))
=> ( k17_euclid(A,B,C) = k17_euclid(A,D,C)
=> B = D ) ) ) ) ) ).
fof(t4_goboard7,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)))
=> ( k17_euclid(A,C,B) = k17_euclid(A,C,D)
=> B = D ) ) ) ) ) ).
fof(t5_goboard7,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)))
=> ( ( r2_hidden(A,k3_topreal1(np__2,B,C))
& k21_euclid(B) = k21_euclid(C) )
=> k21_euclid(A) = k21_euclid(C) ) ) ) ) ).
fof(t6_goboard7,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)))
=> ( ( r2_hidden(A,k3_topreal1(np__2,B,C))
& k22_euclid(B) = k22_euclid(C) )
=> k22_euclid(A) = k22_euclid(C) ) ) ) ) ).
fof(t7_goboard7,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)))
=> r2_hidden(k18_euclid(k6_real_1(np__1,np__2),A,k17_euclid(A,B,C)),k3_topreal1(A,B,C)) ) ) ) ).
fof(t8_goboard7,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)))
=> ( ( k21_euclid(A) = k21_euclid(B)
& k21_euclid(B) = k21_euclid(C)
& r1_xreal_0(k22_euclid(A),k22_euclid(B))
& r1_xreal_0(k22_euclid(B),k22_euclid(C)) )
=> r2_hidden(B,k3_topreal1(np__2,A,C)) ) ) ) ) ).
fof(t9_goboard7,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)))
=> ( ( r1_xreal_0(k21_euclid(A),k21_euclid(B))
& r1_xreal_0(k21_euclid(B),k21_euclid(C))
& k22_euclid(A) = k22_euclid(B)
& k22_euclid(B) = k22_euclid(C) )
=> r2_hidden(B,k3_topreal1(np__2,A,C)) ) ) ) ) ).
fof(t10_goboard7,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(A)) )
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(D)) )
=> r2_hidden(k4_tarski(B,C),k2_matrix_1(D)) ) ) ) ) ) ).
fof(t11_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
=> k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1)))) = k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B))) ) ) ) ) ).
fof(t12_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( v1_sppol_1(k4_topreal1(np__2,A,B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k3_goboard2(A)))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,k4_topreal1(np__2,A,B))
=> k22_euclid(D) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,C)) ) ) ) ) ) ) ) ).
fof(t13_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( v2_sppol_1(k4_topreal1(np__2,A,B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k3_goboard2(A)))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(D,k4_topreal1(np__2,A,B))
=> k21_euclid(D) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,np__1)) ) ) ) ) ) ) ) ).
fof(t14_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,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)
=> ( ( v1_topreal1(A)
& r1_xreal_0(B,k3_finseq_1(k3_goboard2(A)))
& r1_xreal_0(C,k1_matrix_1(k3_goboard2(A))) )
=> r1_xboole_0(k1_tops_1(k15_euclid(np__2),k3_goboard5(k3_goboard2(A),B,C)),k5_topreal1(np__2,A)) ) ) ) ) ).
fof(t15_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k1_matrix_1(C)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__2)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))) ) ) ) ) ).
fof(t16_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(C)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__2),B))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B)) ) ) ) ) ).
fof(t17_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))) ) ) ) ) ).
fof(t18_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))) ) ) ) ) ).
fof(t19_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B)) ) ) ) ) ).
fof(t20_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B)) ) ) ) ) ).
fof(t21_goboard7,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k1_matrix_1(A)) )
=> ( r1_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,k1_nat_1(E,np__1))))
| ( B = D
& r1_xreal_0(k1_int_2(k5_real_1(C,E)),np__1) ) ) ) ) ) ) ) ) ).
fof(t22_goboard7,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(A)) )
=> ( r1_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1),C)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E)))
| ( C = E
& r1_xreal_0(k1_int_2(k5_real_1(B,D)),np__1) ) ) ) ) ) ) ) ) ).
fof(t23_goboard7,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(A)) )
=> ( r1_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E)))
| ( ( B = D
| B = k1_nat_1(D,np__1) )
& ( C = E
| k1_nat_1(C,np__1) = E ) ) ) ) ) ) ) ) ) ).
fof(t24_goboard7,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k1_matrix_1(A))
& ~ r1_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,k1_nat_1(E,np__1))))
& ~ ( C = E
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))) = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,k1_nat_1(E,np__1))) )
& ~ ( C = k1_nat_1(E,np__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)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,k1_nat_1(E,np__1)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C)) )
& ~ ( k1_nat_1(C,np__1) = E
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,k1_nat_1(E,np__1)))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E)) ) ) ) ) ) ) ) ).
fof(t25_goboard7,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(A))
& ~ r1_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1),C)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E)))
& ~ ( B = D
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1),C)) = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E)) )
& ~ ( B = k1_nat_1(D,np__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)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1),C)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C)) )
& ~ ( k1_nat_1(B,np__1) = D
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1),C)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E)) ) ) ) ) ) ) ) ).
fof(t26_goboard7,axiom,
! [A] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(A))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(A))
& ~ r1_xboole_0(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E)))
& ~ ( C = E
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C)) )
& ~ ( k1_nat_1(C,np__1) = E
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(D,np__1),E))) = k1_struct_0(k15_euclid(np__2),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B,k1_nat_1(C,np__1))) ) ) ) ) ) ) ) ).
fof(t27_goboard7,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] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(E))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(E))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(E))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k1_matrix_1(E))
& r2_hidden(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,k1_nat_1(B,np__1)))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,k1_nat_1(D,np__1)))) )
=> ( A = C
& B = D ) ) ) ) ) ) ) ).
fof(t28_goboard7,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] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(E))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(E))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(E))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(E))
& r2_hidden(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(A,np__1),B))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(C,np__1),D))) )
=> ( A = C
& B = D ) ) ) ) ) ) ) ).
fof(t29_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(C)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(C))
& r1_xreal_0(np__1,E)
& r1_xreal_0(k1_nat_1(E,np__1),k1_matrix_1(C))
& r2_hidden(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,D,k1_nat_1(E,np__1)))) ) ) ) ) ) ) ) ).
fof(t30_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(C))
& r1_xreal_0(np__1,E)
& r1_xreal_0(E,k1_matrix_1(C))
& r2_hidden(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1)))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,D,E),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1),E))) ) ) ) ) ) ) ) ).
fof(t31_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r2_hidden(A,k4_finseq_1(B))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(A,np__1)) ) ) ) ).
fof(t32_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& r2_hidden(B,k4_finseq_1(A))
& k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) ) ) ).
fof(t33_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& r2_hidden(B,k4_finseq_1(A))
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1)) ) ) ).
fof(t34_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k3_finseq_1(k3_goboard2(A)),np__1) ) ).
fof(t35_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k1_matrix_1(k3_goboard2(A)),np__1) ) ).
fof(t36_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ~ r1_xreal_0(k3_finseq_1(A),np__4) ) ).
fof(t37_goboard7,axiom,
! [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))) )
=> ( ~ r1_xreal_0(k3_finseq_1(A),np__4)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(C,B)
& ~ r1_xreal_0(k3_finseq_1(A),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) ) ) ) ) ) ).
fof(t38_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,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)
=> ~ ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(C,B)
& ~ r1_xreal_0(k3_finseq_1(A),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) ) ) ) ) ).
fof(t39_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,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)
=> ~ ( ~ r1_xreal_0(B,np__1)
& ~ r1_xreal_0(C,B)
& r1_xreal_0(C,k3_finseq_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) ) ) ) ) ).
fof(t40_goboard7,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& ~ v5_seqm_3(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(B,k3_finseq_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) )
=> ( r1_xreal_0(B,np__1)
| B = k3_finseq_1(A) ) ) ) ) ).
fof(t41_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(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(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(C)))
& r2_hidden(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)))),k5_topreal1(np__2,C))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(C))
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))) = k4_topreal1(np__2,C,D) ) ) ) ) ) ) ).
fof(t42_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(C)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(k3_goboard2(C)))
& r2_hidden(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B))),k5_topreal1(np__2,C))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k3_finseq_1(C))
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)) = k4_topreal1(np__2,C,D) ) ) ) ) ) ) ).
fof(t43_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B) ) ) ) ) ) ) ) ).
fof(t44_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__2))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k1_matrix_1(k3_goboard2(D)),k1_nat_1(B,np__1))
| r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B) ) ) ) ) ) ) ) ).
fof(t45_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B) ) ) ) ) ) ) ) ).
fof(t46_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)) ) ) ) ) ) ) ) ).
fof(t47_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__2),B)) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(k3_goboard2(D)),k1_nat_1(A,np__1))
| r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__2),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B) ) ) ) ) ) ) ) ).
fof(t48_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B) ) ) ) ) ) ) ) ).
fof(t49_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)) ) ) ) ) ) ) ) ).
fof(t50_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__2))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k1_matrix_1(k3_goboard2(D)),k1_nat_1(B,np__1))
| r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__2)) ) ) ) ) ) ) ) ).
fof(t51_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1)) ) ) ) ) ) ) ) ).
fof(t52_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B) ) ) ) ) ) ) ) ).
fof(t53_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__2),B)) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(k3_goboard2(D)),k1_nat_1(A,np__1))
| r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__2),B) ) ) ) ) ) ) ) ).
fof(t54_goboard7,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& ~ v5_seqm_3(D)
& m2_finseq_1(D,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(D)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(D)))
& r1_xreal_0(np__1,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)) = k4_topreal1(np__2,D,C)
& k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1))) = k4_topreal1(np__2,D,k1_nat_1(C,np__1)) )
=> ( r1_xreal_0(k3_finseq_1(D),k1_nat_1(C,np__1))
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(A,np__1),k1_nat_1(B,np__1)) ) ) ) ) ) ) ) ).
fof(t55_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(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(k1_matrix_1(k3_goboard2(C)),k1_nat_1(B,np__1))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__2))),k5_topreal1(np__2,C))
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__2)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& ~ r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__2)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) ) ) ) ) ) ) ).
fof(t56_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(C)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(C)))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& ~ r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) ) ) ) ) ) ) ).
fof(t57_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(C)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(C)))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)),k5_topreal1(np__2,C))
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)) ) ) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& ~ r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)) ) ) ) ) ) ) ) ) ).
fof(t58_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k3_finseq_1(k3_goboard2(C)),k1_nat_1(A,np__1))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(k3_goboard2(C)))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__2),B)),k5_topreal1(np__2,C))
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__2),B) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__2),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& ~ r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__2),B) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__2),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) ) ) ) ) ) ) ).
fof(t59_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(C)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(C)))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& ~ r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B) ) ) ) ) ) ) ) ) ).
fof(t60_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k3_goboard2(C)))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(C)))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k5_binarith(k3_finseq_1(C),np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B) ) ) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& ~ r1_xreal_0(k3_finseq_1(C),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))
& ( ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)) )
| ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(D,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B) ) ) ) ) ) ) ) ) ).
fof(t61_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k3_finseq_1(k3_goboard2(C)),A)
& r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k1_matrix_1(k3_goboard2(C)),k1_nat_1(B,np__1))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__2))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k5_topreal1(np__2,C)) ) ) ) ) ).
fof(t62_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k3_finseq_1(k3_goboard2(C)),A)
& r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k1_matrix_1(k3_goboard2(C)),k1_nat_1(B,np__1))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__2))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),A,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k5_topreal1(np__2,C)) ) ) ) ) ).
fof(t63_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k1_matrix_1(k3_goboard2(C)),A)
& r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(k3_goboard2(C)),k1_nat_1(B,np__1))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),B,A),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),A)),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),A),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__2),A)),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),A),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),k1_nat_1(A,np__1))),k5_topreal1(np__2,C)) ) ) ) ) ).
fof(t64_goboard7,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& ~ v5_seqm_3(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ~ ( r1_xreal_0(np__1,A)
& ~ r1_xreal_0(k1_matrix_1(k3_goboard2(C)),A)
& r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(k3_goboard2(C)),k1_nat_1(B,np__1))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),B,k1_nat_1(A,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),k1_nat_1(A,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),k1_nat_1(A,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__2),k1_nat_1(A,np__1))),k5_topreal1(np__2,C))
& r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),A),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(C),k1_nat_1(B,np__1),k1_nat_1(A,np__1))),k5_topreal1(np__2,C)) ) ) ) ) ).
%------------------------------------------------------------------------------