SET007 Axioms: SET007+444.ax
%------------------------------------------------------------------------------
% File : SET007+444 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : More on Segments on a Go-Board
% 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 : goboard8 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 38 ( 0 unt; 0 def)
% Number of atoms : 632 ( 100 equ)
% Maximal formula atoms : 23 ( 16 avg)
% Number of connectives : 714 ( 120 ~; 20 |; 420 &)
% ( 0 <=>; 154 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 13 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 14 ( 13 usr; 0 prp; 1-3 aty)
% Number of functors : 28 ( 28 usr; 5 con; 0-4 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,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)),k3_goboard2(A),C,k1_nat_1(D,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t2_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,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)),k3_goboard2(A),C,k1_nat_1(D,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t3_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),D) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),D) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,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)),k3_goboard2(A),C,k1_nat_1(D,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t4_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__2)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__2)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,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)),k3_goboard2(A),C,k1_nat_1(D,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t5_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__2)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),k1_nat_1(C,np__1),D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,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)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t6_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),D) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),D) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),k1_nat_1(C,np__1),D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,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)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t7_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__1) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__2) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__2) ) )
| r1_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),C,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__1))),k23_euclid(np__0,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)),k3_goboard2(A),C,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__2)))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t8_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__1) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__2) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),np__2) ) )
| r1_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),k1_nat_1(C,np__1),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),np__1))),k23_euclid(np__0,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)),k3_goboard2(A),k1_nat_1(C,np__1),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),np__2)))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t9_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_matrix_1(k3_goboard2(A))) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),C,k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_matrix_1(k3_goboard2(A))))),k17_euclid(np__2,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(A),C,k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__0,np__1))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t10_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_matrix_1(k3_goboard2(A))) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),k1_nat_1(C,np__1),k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A))))),k17_euclid(np__2,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(A),k1_nat_1(C,np__1),k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__0,np__1))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t11_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__1),k1_matrix_1(k3_goboard2(A)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,k1_nat_1(D,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__1),k1_nat_1(D,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)),k3_goboard2(A),k1_nat_1(C,np__1),D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(C,np__2),k1_nat_1(D,np__1))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t12_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,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)),k3_goboard2(A),k1_nat_1(D,np__1),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__1))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t13_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,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)),k3_goboard2(A),k1_nat_1(D,np__1),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__1))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t14_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k1_matrix_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),C) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),C) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),C) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),D,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,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)),k3_goboard2(A),k1_nat_1(D,np__1),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__1))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t15_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),D,k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__2)))),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(A),k1_nat_1(D,np__1),k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t16_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& r1_xreal_0(np__1,D)
& r1_xreal_0(k1_nat_1(D,np__2),k3_finseq_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),D,k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__1),k1_nat_1(C,np__2)))),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(A),k1_nat_1(D,np__1),k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(D,np__2),k1_nat_1(C,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ) ).
fof(t17_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),np__1,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(C,np__1)))),k23_euclid(np__1,np__0)),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(A),np__1,C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,k1_nat_1(C,np__1))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t18_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),np__1,k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(C,np__2)))),k23_euclid(np__1,np__0)),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(A),np__1,k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,k1_nat_1(C,np__2))))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t19_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__2))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__1)))),k17_euclid(np__2,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(A),k3_finseq_1(k3_goboard2(A)),C),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__1)))),k23_euclid(np__1,np__0))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t20_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__2),k1_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__1)) )
=> ( ( ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),k1_nat_1(C,np__1)) )
& ~ ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__2)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),k1_nat_1(C,np__1)) ) )
| r1_xboole_0(k3_topreal1(np__2,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(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__2)))),k17_euclid(np__2,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(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(C,np__2)))),k23_euclid(np__1,np__0))),k5_topreal1(np__2,A)) ) ) ) ) ) ) ).
fof(t21_goboard8,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,np__1)),k21_euclid(C)) ) )
=> r1_xboole_0(B,k5_topreal1(np__2,A)) ) ) ) ).
fof(t22_goboard8,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r1_xreal_0(k21_euclid(C),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),np__1))) ) )
=> r1_xboole_0(B,k5_topreal1(np__2,A)) ) ) ) ).
fof(t23_goboard8,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,np__1)),k22_euclid(C)) ) )
=> r1_xboole_0(B,k5_topreal1(np__2,A)) ) ) ) ).
fof(t24_goboard8,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r1_xreal_0(k22_euclid(C),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_matrix_1(k3_goboard2(A))))) ) )
=> r1_xboole_0(B,k5_topreal1(np__2,A)) ) ) ) ).
fof(t25_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(k3_goboard2(A))) )
=> r1_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),B,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(B,np__1),np__1))),k23_euclid(np__0,np__1)),k20_euclid(np__2,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(A),k1_nat_1(B,np__1),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(B,np__2),np__1))),k23_euclid(np__0,np__1))),k5_topreal1(np__2,A)) ) ) ) ).
fof(t26_goboard8,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_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,np__1),k23_euclid(np__1,np__1)),k20_euclid(np__2,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(A),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,np__1))),k23_euclid(np__0,np__1))),k5_topreal1(np__2,A)) ) ).
fof(t27_goboard8,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_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),np__1))),k23_euclid(np__0,np__1)),k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),np__1),k23_euclid(np__1,k1_real_1(np__1)))),k5_topreal1(np__2,A)) ) ).
fof(t28_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k3_finseq_1(k3_goboard2(A))) )
=> r1_xboole_0(k3_topreal1(np__2,k17_euclid(np__2,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(A),B,k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__0,np__1)),k17_euclid(np__2,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(A),k1_nat_1(B,np__1),k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k1_nat_1(B,np__2),k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__0,np__1))),k5_topreal1(np__2,A)) ) ) ) ).
fof(t29_goboard8,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_xboole_0(k3_topreal1(np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_matrix_1(k3_goboard2(A))),k23_euclid(k1_real_1(np__1),np__1)),k17_euclid(np__2,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(A),np__1,k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__2,k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__0,np__1))),k5_topreal1(np__2,A)) ) ).
fof(t30_goboard8,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_xboole_0(k3_topreal1(np__2,k17_euclid(np__2,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(A),k5_binarith(k3_finseq_1(k3_goboard2(A)),np__1),k1_matrix_1(k3_goboard2(A))),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__0,np__1)),k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))),k23_euclid(np__1,np__1))),k5_topreal1(np__2,A)) ) ).
fof(t31_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k1_matrix_1(k3_goboard2(A))) )
=> r1_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),np__1,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(B,np__1)))),k23_euclid(np__1,np__0)),k20_euclid(np__2,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(A),np__1,k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_nat_1(B,np__2)))),k23_euclid(np__1,np__0))),k5_topreal1(np__2,A)) ) ) ) ).
fof(t32_goboard8,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_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,np__1),k23_euclid(np__1,np__1)),k20_euclid(np__2,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(A),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,np__2))),k23_euclid(np__1,np__0))),k5_topreal1(np__2,A)) ) ).
fof(t33_goboard8,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_xboole_0(k3_topreal1(np__2,k20_euclid(np__2,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(A),np__1,k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__1,np__0)),k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),np__1,k1_matrix_1(k3_goboard2(A))),k23_euclid(k1_real_1(np__1),np__1))),k5_topreal1(np__2,A)) ) ).
fof(t34_goboard8,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(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__2),k1_matrix_1(k3_goboard2(A))) )
=> r1_xboole_0(k3_topreal1(np__2,k17_euclid(np__2,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(A),k3_finseq_1(k3_goboard2(A)),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(B,np__1)))),k23_euclid(np__1,np__0)),k17_euclid(np__2,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(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(B,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_nat_1(B,np__2)))),k23_euclid(np__1,np__0))),k5_topreal1(np__2,A)) ) ) ) ).
fof(t35_goboard8,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_xboole_0(k3_topreal1(np__2,k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),np__1),k23_euclid(np__1,k1_real_1(np__1))),k17_euclid(np__2,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(A),k3_finseq_1(k3_goboard2(A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),np__2))),k23_euclid(np__1,np__0))),k5_topreal1(np__2,A)) ) ).
fof(t36_goboard8,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_xboole_0(k3_topreal1(np__2,k17_euclid(np__2,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(A),k3_finseq_1(k3_goboard2(A)),k5_binarith(k1_matrix_1(k3_goboard2(A)),np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))))),k23_euclid(np__1,np__0)),k17_euclid(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),k3_finseq_1(k3_goboard2(A)),k1_matrix_1(k3_goboard2(A))),k23_euclid(np__1,np__1))),k5_topreal1(np__2,A)) ) ).
fof(t37_goboard8,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& ~ v5_seqm_3(B)
& m2_finseq_1(B,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(B)) )
=> r1_xboole_0(k1_tops_1(k15_euclid(np__2),k5_goboard5(B,A)),k5_topreal1(np__2,B)) ) ) ) ).
fof(t38_goboard8,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& ~ v5_seqm_3(B)
& m2_finseq_1(B,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(B)) )
=> r1_xboole_0(k1_tops_1(k15_euclid(np__2),k4_goboard5(B,A)),k5_topreal1(np__2,B)) ) ) ) ).
%------------------------------------------------------------------------------