SET007 Axioms: SET007+350.ax
%------------------------------------------------------------------------------
% File : SET007+350 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Go-Board - Part II
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : goboard2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 41 ( 1 unt; 0 def)
% Number of atoms : 320 ( 50 equ)
% Maximal formula atoms : 25 ( 7 avg)
% Number of connectives : 326 ( 47 ~; 5 |; 150 &)
% ( 2 <=>; 122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-3 aty)
% Number of functors : 45 ( 45 usr; 8 con; 0-4 aty)
% Number of variables : 95 ( 93 !; 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(fc1_goboard2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k2_goboard1(A))
& v1_relat_1(k2_goboard1(A))
& v1_funct_1(k2_goboard1(A))
& v1_finset_1(k2_goboard1(A))
& v1_finseq_1(k2_goboard1(A)) ) ) ).
fof(fc2_goboard2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k3_goboard1(A))
& v1_relat_1(k3_goboard1(A))
& v1_funct_1(k3_goboard1(A))
& v1_finset_1(k3_goboard1(A))
& v1_finseq_1(k3_goboard1(A)) ) ) ).
fof(fc3_goboard2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_goboard1(A)
& m1_finseq_1(A,k1_numbers)
& ~ v1_xboole_0(B)
& v1_goboard1(B)
& m1_finseq_1(B,k1_numbers) )
=> ( v1_relat_1(k1_goboard2(A,B))
& ~ v3_relat_1(k1_goboard2(A,B))
& v1_funct_1(k1_goboard2(A,B))
& v1_finset_1(k1_goboard2(A,B))
& v1_finseq_1(k1_goboard2(A,B))
& v1_matrix_1(k1_goboard2(A,B))
& v3_goboard1(k1_goboard2(A,B))
& v4_goboard1(k1_goboard2(A,B))
& v5_goboard1(k1_goboard2(A,B))
& v6_goboard1(k1_goboard2(A,B)) ) ) ).
fof(fc4_goboard2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,k1_numbers) )
=> ( ~ v1_xboole_0(k2_goboard2(A))
& v1_relat_1(k2_goboard2(A))
& v1_funct_1(k2_goboard2(A))
& v1_finset_1(k2_goboard2(A))
& v1_finseq_1(k2_goboard2(A))
& v1_goboard1(k2_goboard2(A)) ) ) ).
fof(fc5_goboard2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_relat_1(k3_goboard2(A))
& ~ v3_relat_1(k3_goboard2(A))
& v1_funct_1(k3_goboard2(A))
& v1_finset_1(k3_goboard2(A))
& v1_finseq_1(k3_goboard2(A))
& v1_matrix_1(k3_goboard2(A))
& v3_goboard1(k3_goboard2(A))
& v4_goboard1(k3_goboard2(A))
& v5_goboard1(k3_goboard2(A))
& v6_goboard1(k3_goboard2(A)) ) ) ).
fof(t1_goboard2,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( A != k1_xboole_0
=> ( v1_seq_4(A)
& r2_hidden(k4_seq_4(A),A)
& v2_seq_4(A)
& r2_hidden(k5_seq_4(A),A) ) ) ) ).
fof(t2_goboard2,axiom,
$true ).
fof(t3_goboard2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) )
=> ( r2_hidden(A,k4_finseq_1(B))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B)) ) )
& ( ( r2_hidden(A,k4_finseq_1(B))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B)) )
=> ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) ) ) ) ) ) ).
fof(t4_goboard2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(B)) )
=> ( r2_hidden(A,k4_finseq_1(B))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B))
& r2_hidden(k1_nat_1(A,np__2),k4_finseq_1(B)) ) )
& ( ( r2_hidden(A,k4_finseq_1(B))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(B))
& r2_hidden(k1_nat_1(A,np__2),k4_finseq_1(B)) )
=> ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(B)) ) ) ) ) ) ).
fof(t5_goboard2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(C)) )
=> k4_finseq_4(k5_numbers,A,k8_finseq_1(A,B,C),k1_nat_1(D,k3_finseq_1(B))) = k4_finseq_4(k5_numbers,A,C,D) ) ) ) ) ) ).
fof(t6_goboard2,axiom,
! [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)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) )
=> ( r1_xreal_0(C,k1_nat_1(B,np__1))
| r1_xboole_0(k4_topreal1(np__2,A,B),k4_topreal1(np__2,A,C)) ) ) ) )
=> v3_topreal1(A) ) ) ).
fof(t7_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( v2_topreal1(A)
& v3_topreal1(A)
& v2_funct_1(A)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)),k4_topreal1(np__2,A,B))
& r2_hidden(B,k4_finseq_1(A))
& r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) )
=> k1_nat_1(B,np__1) = k3_finseq_1(A) ) ) ) ).
fof(t8_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k3_finseq_1(A) = k1_nat_1(B,np__1)
=> ( B = np__0
| k5_topreal1(np__2,A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)),k4_topreal1(np__2,A,B)) ) ) ) ) ).
fof(t9_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( k3_finseq_1(A) = k1_nat_1(B,np__1)
& v2_topreal1(A)
& v3_topreal1(A) )
=> ( r1_xreal_0(B,np__1)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)),k4_topreal1(np__2,A,B)) = k1_struct_0(k15_euclid(np__2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t10_goboard2,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)))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)))
& k1_nat_1(D,k3_finseq_1(A)) = C )
=> ( r1_xreal_0(C,k3_finseq_1(A))
| k4_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),C) = k4_topreal1(np__2,B,D) ) ) ) ) ) ) ).
fof(t11_goboard2,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)))
=> r1_tarski(k5_topreal1(np__2,A),k5_topreal1(np__2,k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ).
fof(t12_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( v3_topreal1(A)
=> v3_topreal1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ).
fof(t13_goboard2,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)))
=> ( ( v1_topreal1(A)
& v1_topreal1(B) )
=> ( ( k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) != k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1))
& k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))) != k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1)) )
| v1_topreal1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)) ) ) ) ) ).
fof(t14_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ ( A != k1_xboole_0
& k2_goboard1(A) = k1_xboole_0 ) ) ).
fof(t15_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ~ ( A != k1_xboole_0
& k3_goboard1(A) = k1_xboole_0 ) ) ).
fof(t16_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( v1_topreal1(A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k4_finseq_1(A))
& r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
& r2_hidden(k4_tarski(F,G),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,F,G)
& D != F
& G != E ) ) ) ) ) ) ) ) ) ) ).
fof(t17_goboard2,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k4_finseq_1(A))
& ! [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(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E) ) ) ) ) )
& v1_topreal1(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k4_finseq_1(A))
& r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(C,np__1)) ) )
& ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& k5_topreal1(np__2,A) = k5_topreal1(np__2,C)
& 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)),A,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))
& r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) ) ) ) ) ) ).
fof(t18_goboard2,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ( v1_goboard1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& r1_xreal_0(B,C) )
=> r1_xreal_0(k1_goboard1(A,B),k1_goboard1(A,C)) ) ) ) ) ) ).
fof(t19_goboard2,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ( v1_goboard1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(C,k4_finseq_1(A))
& B != C
& k1_goboard1(A,B) = k1_goboard1(A,C) ) ) ) ) ) ).
fof(t20_goboard2,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( m2_finseq_1(B,k1_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( v1_goboard1(A)
& B = k7_relat_1(A,k2_finseq_1(C)) )
=> v1_goboard1(B) ) ) ) ) ).
fof(t21_goboard2,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ? [B] :
( m2_finseq_1(B,k1_numbers)
& k2_relat_1(B) = k2_relat_1(A)
& k3_finseq_1(B) = k4_card_1(k2_relat_1(A))
& v1_goboard1(B) ) ) ).
fof(t22_goboard2,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( m2_finseq_1(B,k1_numbers)
=> ( ( k3_finseq_1(A) = k3_finseq_1(B)
& k2_relat_1(A) = k2_relat_1(B)
& v1_goboard1(A)
& v1_goboard1(B) )
=> A = B ) ) ) ).
fof(d1_goboard2,axiom,
! [A] :
( ( v1_goboard1(A)
& m2_finseq_1(A,k1_numbers) )
=> ! [B] :
( ( v1_goboard1(B)
& m2_finseq_1(B,k1_numbers) )
=> ~ ( A != k1_xboole_0
& B != k1_xboole_0
& ~ ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( C = k1_goboard2(A,B)
<=> ( k3_finseq_1(C) = k3_finseq_1(A)
& k1_matrix_1(C) = k3_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(C))
=> k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,D,E) = k23_euclid(k1_goboard1(A,D),k1_goboard1(B,E)) ) ) ) ) ) ) ) ) ) ).
fof(d2_goboard2,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( ( v1_goboard1(B)
& m2_finseq_1(B,k1_numbers) )
=> ( B = k2_goboard2(A)
<=> ( k2_relat_1(B) = k2_relat_1(A)
& k3_finseq_1(B) = k4_card_1(k2_relat_1(A)) ) ) ) ) ).
fof(d3_goboard2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> k3_goboard2(A) = k1_goboard2(k2_goboard2(k2_goboard1(A)),k2_goboard2(k3_goboard1(A))) ) ).
fof(t23_goboard2,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ~ ( A != k1_xboole_0
& k2_goboard2(A) = k1_xboole_0 ) ) ).
fof(t24_goboard2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( k3_finseq_1(k3_goboard2(A)) = k4_card_1(k2_relat_1(k2_goboard1(A)))
& k1_matrix_1(k3_goboard2(A)) = k4_card_1(k2_relat_1(k3_goboard1(A))) ) ) ).
fof(t25_goboard2,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)
=> ~ ( r2_hidden(B,k4_finseq_1(A))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(C,D),k2_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,D) ) ) ) ) ) ) ).
fof(t26_goboard2,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))) )
=> ( ( r2_hidden(A,k4_finseq_1(B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> r1_xreal_0(k1_goboard1(k2_goboard1(B),A),k1_goboard1(k2_goboard1(B),C)) ) ) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),np__1))) ) ) ) ).
fof(t27_goboard2,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))) )
=> ( ( r2_hidden(A,k4_finseq_1(B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> r1_xreal_0(k1_goboard1(k2_goboard1(B),C),k1_goboard1(k2_goboard1(B),A)) ) ) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),k3_finseq_1(k3_goboard2(B))))) ) ) ) ).
fof(t28_goboard2,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))) )
=> ( ( r2_hidden(A,k4_finseq_1(B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> r1_xreal_0(k1_goboard1(k3_goboard1(B),A),k1_goboard1(k3_goboard1(B),C)) ) ) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),np__1))) ) ) ) ).
fof(t29_goboard2,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))) )
=> ( ( r2_hidden(A,k4_finseq_1(B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> r1_xreal_0(k1_goboard1(k3_goboard1(B),C),k1_goboard1(k3_goboard1(B),A)) ) ) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(B),k1_matrix_1(k3_goboard2(B))))) ) ) ) ).
fof(s1_goboard2,axiom,
? [A] :
( m2_finseq_1(A,f1_s1_goboard2)
& k3_finseq_1(A) = f2_s1_goboard2
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k4_finseq_1(A))
=> k4_finseq_4(k5_numbers,f1_s1_goboard2,A,B) = f3_s1_goboard2(B) ) ) ) ).
fof(dt_k1_goboard2,axiom,
! [A,B] :
( ( v1_goboard1(A)
& m1_finseq_1(A,k1_numbers)
& v1_goboard1(B)
& m1_finseq_1(B,k1_numbers) )
=> ( v1_matrix_1(k1_goboard2(A,B))
& m2_finseq_1(k1_goboard2(A,B),k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) ) ) ).
fof(dt_k2_goboard2,axiom,
! [A] :
( m1_finseq_1(A,k1_numbers)
=> ( v1_goboard1(k2_goboard2(A))
& m2_finseq_1(k2_goboard2(A),k1_numbers) ) ) ).
fof(dt_k3_goboard2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( v1_matrix_1(k3_goboard2(A))
& m2_finseq_1(k3_goboard2(A),k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) ) ) ).
%------------------------------------------------------------------------------