SET007 Axioms: SET007+709.ax
%------------------------------------------------------------------------------
% File : SET007+709 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : More on the Finite Sequences on the Plane
% 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 : topreal8 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 39 ( 0 unt; 0 def)
% Number of atoms : 285 ( 41 equ)
% Maximal formula atoms : 29 ( 7 avg)
% Number of connectives : 309 ( 63 ~; 8 |; 129 &)
% ( 0 <=>; 109 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 27 ( 26 usr; 0 prp; 1-3 aty)
% Number of functors : 39 ( 39 usr; 6 con; 0-4 aty)
% Number of variables : 96 ( 93 !; 3 ?)
% 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(rc1_topreal8,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_realset1(A)
& v5_seqm_3(A) ) ).
fof(rc2_topreal8,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& ~ v1_realset1(A)
& ~ v5_seqm_3(A) ) ).
fof(rc3_topreal8,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v3_topreal1(A) ) ).
fof(t1_topreal8,axiom,
! [A,B,C] :
( ( r1_tarski(A,k2_tarski(B,C))
& r2_hidden(B,A) )
=> ( r2_hidden(C,A)
| A = k1_tarski(B) ) ) ).
fof(t2_topreal8,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& ~ v1_realset1(A) )
=> ~ r1_xreal_0(k3_finseq_1(A),np__1) ) ).
fof(t3_topreal8,axiom,
! [A] :
( ~ v1_realset1(A)
=> ! [B] :
( ( ~ v5_seqm_3(B)
& v1_finseq_6(B,A)
& m2_finseq_1(B,A) )
=> ~ r1_xreal_0(k3_finseq_1(B),np__2) ) ) ).
fof(t4_topreal8,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
| k5_finseq_4(A,B) = np__0 ) ) ).
fof(t5_topreal8,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_finseq_1(C,B) )
=> ! [D] :
( m2_finseq_1(D,B)
=> ( k5_finseq_4(C,A) = k3_finseq_1(C)
=> k7_finseq_4(k8_finseq_1(B,C,D),A) = D ) ) ) ) ).
fof(t6_topreal8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v2_funct_1(B)
& m2_finseq_1(B,A) )
=> k5_finseq_4(B,k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))) = k3_finseq_1(B) ) ) ).
fof(t7_topreal8,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(k3_graph_2(A,B))) ) ) ).
fof(t8_topreal8,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( r2_hidden(C,k2_relat_1(A))
=> k5_finseq_4(A,C) = k5_finseq_4(k3_graph_2(A,B),C) ) ) ) ).
fof(t9_topreal8,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> r1_xreal_0(k3_finseq_1(B),k3_finseq_1(k3_graph_2(A,B))) ) ) ).
fof(t10_topreal8,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> r1_tarski(k2_relat_1(A),k2_relat_1(k3_graph_2(A,B))) ) ) ).
fof(t11_topreal8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> ! [C] :
( ( ~ v1_realset1(C)
& m2_finseq_1(C,A) )
=> ( k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,A,B,np__1)
=> v1_finseq_6(k4_graph_2(A,B,C),A) ) ) ) ) ).
fof(t12_topreal8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(A)) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m2_finseq_1(D,A) )
=> ( ( k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,A,D,np__1)
& r1_goboard1(A,C,B)
& r1_goboard1(A,D,B) )
=> r1_goboard1(A,k4_graph_2(A,C,D),B) ) ) ) ) ) ).
fof(t13_topreal8,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( m2_finseq_1(C,B)
=> ( r1_xreal_0(np__1,A)
=> k2_graph_2(B,C,k1_nat_1(A,np__1),k3_finseq_1(C)) = k1_rfinseq(B,C,A) ) ) ) ).
fof(t14_topreal8,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( m2_finseq_1(C,B)
=> ( r1_xreal_0(A,k3_finseq_1(C))
=> k2_graph_2(B,C,np__1,A) = k16_finseq_1(B,C,A) ) ) ) ).
fof(t15_topreal8,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_finseq_1(C,B) )
=> ! [D] :
( m2_finseq_1(D,B)
=> ( k5_finseq_4(C,A) = k3_finseq_1(C)
=> k6_finseq_4(k8_finseq_1(B,C,D),A) = k2_graph_2(B,C,np__1,k5_binarith(k3_finseq_1(C),np__1)) ) ) ) ) ).
fof(t16_topreal8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_finseq_1(C,A) )
=> ( k5_finseq_4(B,k4_finseq_4(k5_numbers,A,C,np__1)) = k3_finseq_1(B)
=> k2_finseq_5(A,k4_graph_2(A,B,C),k4_finseq_4(k5_numbers,A,C,np__1)) = C ) ) ) ) ).
fof(t17_topreal8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_finseq_1(C,A) )
=> ( k5_finseq_4(B,k4_finseq_4(k5_numbers,A,C,np__1)) = k3_finseq_1(B)
=> k1_finseq_5(A,k4_graph_2(A,B,C),k4_finseq_4(k5_numbers,A,C,np__1)) = B ) ) ) ) ).
fof(t18_topreal8,axiom,
! [A] :
( ~ v1_realset1(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,A) )
=> ! [C] :
( ( ~ v1_realset1(C)
& m2_finseq_1(C,A) )
=> ( ( k4_finseq_4(k5_numbers,A,C,np__1) = k4_finseq_4(k5_numbers,A,B,k3_finseq_1(B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& ~ r1_xreal_0(k3_finseq_1(B),D)
& k4_finseq_4(k5_numbers,A,B,D) = k4_finseq_4(k5_numbers,A,C,np__1) ) ) )
=> k1_finseq_6(A,k4_graph_2(A,B,C),k4_finseq_4(k5_numbers,A,C,np__1)) = k4_graph_2(A,C,B) ) ) ) ) ).
fof(t19_topreal8,axiom,
! [A] :
( ( ~ v1_realset1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k4_topreal1(np__2,A,np__1) = k5_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,np__2)) ) ).
fof(t20_topreal8,axiom,
! [A] :
( ( v1_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(A),B)
=> v3_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t21_topreal8,axiom,
! [A] :
( ( v1_goboard5(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)
=> v3_topreal1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t22_topreal8,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))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(k3_finseq_1(A),B)
& ~ r1_xreal_0(k3_finseq_1(A),np__4)
& ~ v2_funct_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t23_topreal8,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(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(t24_topreal8,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))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k3_finseq_1(A),np__4)
| v2_funct_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t25_topreal8,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)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> v1_topreal1(k2_graph_2(u1_struct_0(k15_euclid(np__2)),C,A,B)) ) ) ) ).
fof(t26_topreal8,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v1_realset1(B)
& v1_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
=> v1_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t27_topreal8,axiom,
! [A] :
( ( v2_topreal1(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)
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,np__1),k5_topreal1(np__2,k1_rfinseq(u1_struct_0(k15_euclid(np__2)),A,np__1))) = k2_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__2)) ) ) ).
fof(t28_topreal8,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ~ r1_xreal_0(k3_finseq_1(B),A)
=> k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),A) = k4_topreal1(np__2,B,A) ) ) ) ) ).
fof(t29_topreal8,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( r1_xreal_0(np__1,A)
=> ( r1_xreal_0(k3_finseq_1(C),k1_nat_1(A,np__1))
| k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),k1_nat_1(k3_finseq_1(B),A)) = k4_topreal1(np__2,C,k1_nat_1(A,np__1)) ) ) ) ) ) ).
fof(t30_topreal8,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( ~ v1_realset1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
=> k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B),k3_finseq_1(A)) = k4_topreal1(np__2,B,np__1) ) ) ) ).
fof(t31_topreal8,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ! [C] :
( ( ~ v1_realset1(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)
=> ( r1_xreal_0(k3_finseq_1(C),k1_nat_1(A,np__1))
| k4_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),B,C),k1_nat_1(k3_finseq_1(B),A)) = k4_topreal1(np__2,C,k1_nat_1(A,np__1)) ) ) ) ) ) ).
fof(t32_topreal8,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_topreal1(A)
& v3_topreal1(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(k3_finseq_1(A),B)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,B),k5_relset_1(k5_numbers,u1_struct_0(k15_euclid(np__2)),A)) = k2_struct_0(k15_euclid(np__2),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,k1_nat_1(B,np__1))) ) ) ) ) ).
fof(t33_topreal8,axiom,
! [A] :
( ( v2_funct_1(A)
& ~ v1_realset1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( ( v2_funct_1(B)
& ~ v1_realset1(B)
& v2_topreal1(B)
& v3_topreal1(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ( k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) = k2_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) )
=> v1_goboard5(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t34_topreal8,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( v2_topreal1(A)
& v2_topreal1(B)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_topreal1(np__2,A,k5_binarith(k3_finseq_1(A),np__1)),k4_topreal1(np__2,B,np__1)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) )
=> v2_topreal1(k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t35_topreal8,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)
=> ( v1_xboole_0(A)
| v1_realset1(B)
| k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,A),k5_topreal1(np__2,B)) ) ) ) ) ).
fof(t36_topreal8,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_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k4_finseq_1(B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D,E) ) ) ) ) )
& ~ v5_seqm_3(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v2_topreal1(B)
& v1_goboard5(B)
& v1_topreal1(B)
& ~ r1_xreal_0(k3_finseq_1(B),np__4)
& ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,A)
& v2_topreal1(C)
& v1_goboard5(C)
& v1_topreal1(C)
& k5_topreal1(np__2,B) = k5_topreal1(np__2,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))
& r1_xreal_0(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) ) ).
%------------------------------------------------------------------------------