SET007 Axioms: SET007+349.ax
%------------------------------------------------------------------------------
% File : SET007+349 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Go-Board - Part I
% 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 : goboard1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 75 ( 10 unt; 0 def)
% Number of atoms : 962 ( 100 equ)
% Maximal formula atoms : 51 ( 12 avg)
% Number of connectives : 995 ( 108 ~; 22 |; 524 &)
% ( 14 <=>; 327 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-3 aty)
% Number of functors : 38 ( 38 usr; 8 con; 0-4 aty)
% Number of variables : 282 ( 274 !; 8 ?)
% 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_goboard1,axiom,
? [A] :
( m1_finseq_1(A,k1_numbers)
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_goboard1(A) ) ).
fof(rc2_goboard1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_finseq_1(B,A)
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B) ) ) ).
fof(rc3_goboard1,axiom,
? [A] :
( m1_finseq_1(A,k1_numbers)
& v1_relat_1(A)
& v1_funct_1(A)
& v5_seqm_3(A)
& v1_finset_1(A)
& v1_finseq_1(A) ) ).
fof(rc4_goboard1,axiom,
? [A] :
( m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& v1_relat_1(A)
& ~ v3_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A) ) ).
fof(t1_goboard1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( k18_complex1(k5_real_1(A,B)) = np__1
<=> ( ( ~ r1_xreal_0(A,B)
& A = k3_real_1(B,np__1) )
| ( ~ r1_xreal_0(B,A)
& B = k3_real_1(A,np__1) ) ) ) ) ) ).
fof(t2_goboard1,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)
=> ( k3_real_1(k18_complex1(k5_real_1(A,B)),k18_complex1(k5_real_1(C,D))) = np__1
<=> ( ( k18_complex1(k5_real_1(A,B)) = np__1
& C = D )
| ( k18_complex1(k5_real_1(C,D)) = np__1
& A = B ) ) ) ) ) ) ) ).
fof(t3_goboard1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ~ ( ~ r1_xreal_0(A,np__1)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( A = k1_nat_1(B,np__1)
& ~ r1_xreal_0(B,np__0) ) ) )
& ~ ( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(B,np__1)
& ~ r1_xreal_0(B,np__0) )
& r1_xreal_0(A,np__1) ) ) ) ).
fof(t4_goboard1,axiom,
$true ).
fof(t5_goboard1,axiom,
$true ).
fof(t6_goboard1,axiom,
$true ).
fof(t7_goboard1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [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)
=> ~ ( k3_finseq_1(A) = k1_nat_1(C,np__1)
& r2_hidden(B,k4_finseq_1(A))
& r2_hidden(D,k2_finseq_1(C))
& k1_funct_1(k2_finseq_3(B,A),D) != k1_funct_1(A,D)
& k1_funct_1(k2_finseq_3(B,A),D) != k1_funct_1(A,k1_nat_1(D,np__1)) ) ) ) ) ) ).
fof(t8_goboard1,axiom,
$true ).
fof(t9_goboard1,axiom,
$true ).
fof(d1_goboard1,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(C,B)
& r1_xreal_0(k1_goboard1(A,C),k1_goboard1(A,B)) ) ) ) ) ) ).
fof(d2_goboard1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v5_seqm_3(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)) )
=> k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ) ) ).
fof(d3_goboard1,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,k1_numbers)
=> ( B = k2_goboard1(A)
<=> ( k3_finseq_1(B) = k3_finseq_1(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> k1_goboard1(B,C) = k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) ) ).
fof(d4_goboard1,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,k1_numbers)
=> ( B = k3_goboard1(A)
<=> ( k3_finseq_1(B) = k3_finseq_1(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(B))
=> k1_goboard1(B,C) = k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) ) ).
fof(t10_goboard1,axiom,
$true ).
fof(t11_goboard1,axiom,
$true ).
fof(t12_goboard1,axiom,
$true ).
fof(t13_goboard1,axiom,
$true ).
fof(t14_goboard1,axiom,
! [A] :
( m2_finseq_1(A,k1_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)
=> ( ( r1_tarski(k2_relat_1(A),k2_finseq_1(B))
& k1_goboard1(A,k3_finseq_1(A)) = B
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k5_real_1(k3_finseq_1(A),np__1)) )
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( F = k1_goboard1(A,E)
& G = k1_goboard1(A,k1_nat_1(E,np__1))
& k18_complex1(k5_real_1(F,G)) != np__1
& F != G ) ) ) ) )
& r2_hidden(C,k2_finseq_1(B))
& r2_hidden(k1_nat_1(C,np__1),k2_finseq_1(B))
& r2_hidden(D,k4_finseq_1(A))
& k1_goboard1(A,D) = C
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(A))
& k1_goboard1(A,E) = C )
=> r1_xreal_0(E,D) ) ) )
=> ( A = k1_xboole_0
| ( r2_hidden(k1_nat_1(D,np__1),k4_finseq_1(A))
& k1_goboard1(A,k1_nat_1(D,np__1)) = k1_nat_1(C,np__1) ) ) ) ) ) ) ) ).
fof(t15_goboard1,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_tarski(k2_relat_1(A),k2_finseq_1(B))
& k1_goboard1(A,np__1) = np__1
& k1_goboard1(A,k3_finseq_1(A)) = B
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k5_real_1(k3_finseq_1(A),np__1)) )
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( D = k1_goboard1(A,C)
& E = k1_goboard1(A,k1_nat_1(C,np__1))
& k18_complex1(k5_real_1(D,E)) != np__1
& D != E ) ) ) ) ) )
=> ( A = k1_xboole_0
| ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k2_finseq_1(B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(A))
& k1_goboard1(A,D) = C ) ) ) )
& ! [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)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( r2_hidden(C,k4_finseq_1(A))
& k1_goboard1(A,C) = E
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r2_hidden(G,k4_finseq_1(A))
& k1_goboard1(A,G) = E )
=> r1_xreal_0(G,C) ) )
& ~ r1_xreal_0(D,C)
& r2_hidden(D,k4_finseq_1(A))
& F = k1_goboard1(A,D)
& r1_xreal_0(F,E) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_goboard1,axiom,
! [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))
& r1_xreal_0(np__2,k3_finseq_1(A)) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k5_topreal1(np__2,A)) ) ) ) ).
fof(t17_goboard1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,k4_finseq_1(B))
& r2_hidden(C,k2_finseq_1(k1_matrix_1(B))) )
=> k1_funct_1(k8_matrix_1(A,B,C),D) = k1_funct_1(k7_matrix_1(A,B,D),C) ) ) ) ) ) ).
fof(d5_goboard1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(A)) )
=> ( v3_relat_1(B)
<=> ( np__0 = k3_finseq_1(B)
| np__0 = k1_matrix_1(B) ) ) ) ) ).
fof(d6_goboard1,axiom,
! [A] :
( ( v1_matrix_1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( v3_goboard1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k4_finseq_1(A))
=> v5_seqm_3(k2_goboard1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) ).
fof(d7_goboard1,axiom,
! [A] :
( ( v1_matrix_1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( v4_goboard1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_finseq_1(k1_matrix_1(A)))
=> v5_seqm_3(k3_goboard1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) ).
fof(d8_goboard1,axiom,
! [A] :
( ( v1_matrix_1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( v5_goboard1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k4_finseq_1(A))
=> v1_goboard1(k3_goboard1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) ).
fof(d9_goboard1,axiom,
! [A] :
( ( v1_matrix_1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( v6_goboard1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_finseq_1(k1_matrix_1(A)))
=> v1_goboard1(k2_goboard1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,B))) ) ) ) ) ).
fof(t18_goboard1,axiom,
$true ).
fof(t19_goboard1,axiom,
! [A] :
( ( v1_matrix_1(A)
& v3_goboard1(A)
& v6_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B,C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
& r2_hidden(B,k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
& r2_hidden(C,k4_finseq_1(A))
& r2_hidden(D,k4_finseq_1(A)) )
=> C = D ) ) ) ) ).
fof(t20_goboard1,axiom,
! [A] :
( ( v1_matrix_1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B,C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
& r2_hidden(B,k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
& r2_hidden(C,k2_finseq_1(k1_matrix_1(A)))
& r2_hidden(D,k2_finseq_1(k1_matrix_1(A))) )
=> C = D ) ) ) ) ).
fof(t21_goboard1,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,F] :
( ( ~ v3_relat_1(F)
& v1_matrix_1(F)
& v3_goboard1(F)
& v4_goboard1(F)
& v5_goboard1(F)
& v6_goboard1(F)
& m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( E = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,A,B)
& E = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D)
& r2_hidden(k4_tarski(A,B),k2_matrix_1(F))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(F)) )
=> ( A = C
& B = D ) ) ) ) ) ) ) ).
fof(t22_goboard1,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [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)))) )
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1))) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1))) ) ) ) ) ).
fof(t23_goboard1,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [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)))) )
=> ( ( r2_hidden(B,k4_finseq_1(A))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_matrix_1(C)))) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k3_finseq_1(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_matrix_1(C)))) ) ) ) ) ).
fof(t24_goboard1,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)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( ~ v3_relat_1(F)
& v1_matrix_1(F)
& v3_goboard1(F)
& v4_goboard1(F)
& v5_goboard1(F)
& v6_goboard1(F)
& m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_xboole_0(k2_relat_1(A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),F,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)),F,D,E)
& r2_hidden(C,k4_finseq_1(A))
& r2_hidden(D,k4_finseq_1(F))
& B = E ) ) ) ) ) ) ) ).
fof(d10_goboard1,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)
=> ( r2_hidden(B,k2_finseq_1(k1_matrix_1(A)))
=> ( r1_xreal_0(k1_matrix_1(A),np__1)
| ! [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)))) )
=> ( C = k4_goboard1(A,B)
<=> ( k3_finseq_1(C) = k3_finseq_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(A))
=> k1_funct_1(C,D) = k2_finseq_3(B,k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)) ) ) ) ) ) ) ) ) ) ).
fof(t25_goboard1,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)))) )
=> ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(C)))
& r2_hidden(B,k4_finseq_1(C)) )
=> ( r1_xreal_0(k1_matrix_1(C),np__1)
| k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(C,A),B) = k2_finseq_3(A,k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)) ) ) ) ) ) ).
fof(t26_goboard1,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)))) )
=> ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(C)))
& k1_matrix_1(C) = k1_nat_1(B,np__1) )
=> ( r1_xreal_0(B,np__0)
| k1_matrix_1(k4_goboard1(C,A)) = B ) ) ) ) ) ).
fof(t27_goboard1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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)))) )
=> ( r2_hidden(A,k2_finseq_1(k1_matrix_1(B)))
=> ( r1_xreal_0(k1_matrix_1(B),np__1)
| k1_matrix_1(B) = k1_nat_1(k1_matrix_1(k4_goboard1(B,A)),np__1) ) ) ) ) ).
fof(t28_goboard1,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] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(D)))
& r2_hidden(B,k4_finseq_1(D))
& r2_hidden(C,k2_finseq_1(k1_matrix_1(k4_goboard1(D,A)))) )
=> ( r1_xreal_0(k1_matrix_1(D),np__1)
| k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,A),B,C) = k1_funct_1(k2_finseq_3(A,k7_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B)),C) ) ) ) ) ) ) ).
fof(t29_goboard1,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] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(D)))
& k1_matrix_1(D) = k1_nat_1(B,np__1)
& r1_xreal_0(np__1,C) )
=> ( r1_xreal_0(B,np__0)
| r1_xreal_0(A,C)
| ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,A),C) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C)
& r2_hidden(C,k2_finseq_1(k1_matrix_1(k4_goboard1(D,A))))
& r2_hidden(C,k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) ).
fof(t30_goboard1,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] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(D)))
& k1_matrix_1(D) = k1_nat_1(B,np__1)
& r1_xreal_0(A,C)
& r1_xreal_0(C,B) )
=> ( r1_xreal_0(B,np__0)
| ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,A),C) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(C,np__1))
& r2_hidden(C,k2_finseq_1(k1_matrix_1(k4_goboard1(D,A))))
& r2_hidden(k1_nat_1(C,np__1),k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) ).
fof(t31_goboard1,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)))) )
=> ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(E)))
& k1_matrix_1(E) = k1_nat_1(B,np__1)
& r2_hidden(C,k4_finseq_1(E))
& r1_xreal_0(np__1,D) )
=> ( r1_xreal_0(B,np__0)
| r1_xreal_0(A,D)
| ( k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(E,A),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,D)
& r2_hidden(D,k2_finseq_1(k1_matrix_1(E))) ) ) ) ) ) ) ) ) ).
fof(t32_goboard1,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)))) )
=> ( ( r2_hidden(A,k2_finseq_1(k1_matrix_1(E)))
& k1_matrix_1(E) = k1_nat_1(B,np__1)
& r2_hidden(C,k4_finseq_1(E))
& r1_xreal_0(A,D)
& r1_xreal_0(D,B) )
=> ( r1_xreal_0(B,np__0)
| ( k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(E,A),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,k1_nat_1(D,np__1))
& r2_hidden(k1_nat_1(D,np__1),k2_finseq_1(k1_matrix_1(E))) ) ) ) ) ) ) ) ) ).
fof(t33_goboard1,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)))) )
=> ( ( k1_matrix_1(C) = k1_nat_1(A,np__1)
& r2_hidden(B,k2_finseq_1(A)) )
=> ( r1_xreal_0(A,np__0)
| ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(C,np__1),B) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1))
& r2_hidden(B,k2_finseq_1(k1_matrix_1(k4_goboard1(C,np__1))))
& r2_hidden(k1_nat_1(B,np__1),k2_finseq_1(k1_matrix_1(C))) ) ) ) ) ) ) ).
fof(t34_goboard1,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] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( k1_matrix_1(D) = k1_nat_1(A,np__1)
& r2_hidden(B,k2_finseq_1(A))
& r2_hidden(C,k4_finseq_1(D)) )
=> ( r1_xreal_0(A,np__0)
| ( k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,np__1),C,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,k1_nat_1(B,np__1))
& r2_hidden(np__1,k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) ).
fof(t35_goboard1,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)))) )
=> ( ( k1_matrix_1(C) = k1_nat_1(A,np__1)
& r2_hidden(B,k2_finseq_1(A)) )
=> ( r1_xreal_0(A,np__0)
| ( k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(C,k1_matrix_1(C)),B) = k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)
& r2_hidden(B,k2_finseq_1(k1_matrix_1(k4_goboard1(C,k1_matrix_1(C))))) ) ) ) ) ) ) ).
fof(t36_goboard1,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] :
( ( ~ v3_relat_1(D)
& v1_matrix_1(D)
& v3_goboard1(D)
& v4_goboard1(D)
& v5_goboard1(D)
& v6_goboard1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( k1_matrix_1(D) = k1_nat_1(A,np__1)
& r2_hidden(B,k2_finseq_1(A))
& r2_hidden(C,k4_finseq_1(D)) )
=> ( r1_xreal_0(A,np__0)
| ( r2_hidden(B,k2_finseq_1(k1_matrix_1(D)))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(D,k1_matrix_1(D)),C,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,B)
& r2_hidden(k1_matrix_1(D),k2_finseq_1(k1_matrix_1(D))) ) ) ) ) ) ) ) ).
fof(t37_goboard1,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)
=> ! [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_xboole_0(k2_relat_1(A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),E,D)))
& r2_hidden(C,k4_finseq_1(A))
& r2_hidden(B,k2_finseq_1(k1_matrix_1(E)))
& r2_hidden(D,k4_finseq_1(E)) )
=> ( r1_xreal_0(k1_matrix_1(E),np__1)
| r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(E,B),D))) ) ) ) ) ) ) ) ).
fof(d11_goboard1,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(A)) )
=> ( r1_goboard1(A,B,C)
<=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(B))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F) ) ) ) ) )
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,k4_finseq_1(B))
& r2_hidden(k1_nat_1(D,np__1),k4_finseq_1(B)) )
=> ! [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)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(E,F),k2_matrix_1(C))
& r2_hidden(k4_tarski(G,H),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,D) = k3_matrix_1(A,C,E,F)
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__1)) = k3_matrix_1(A,C,G,H) )
=> k3_real_1(k18_complex1(k5_real_1(E,G)),k18_complex1(k5_real_1(F,H))) = np__1 ) ) ) ) ) ) ) ) ) ) ) ).
fof(t38_goboard1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( m2_finseq_1(C,B)
=> ! [D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(B)) )
=> ( ( r2_hidden(A,k4_finseq_1(C))
=> r1_xreal_0(np__1,k3_finseq_1(k16_finseq_1(B,C,A))) )
& ( r1_goboard1(B,C,D)
=> r1_goboard1(B,k16_finseq_1(B,C,A),D) ) ) ) ) ) ).
fof(t39_goboard1,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,D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(C)) )
=> ( ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(A))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(C,D,F,G) ) ) ) ) )
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(B))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E) = k3_matrix_1(C,D,F,G) ) ) ) ) ) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),E) = k3_matrix_1(C,D,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t40_goboard1,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,D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(C)) )
=> ( ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(A))
& r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(A)) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
& r2_hidden(k4_tarski(H,I),k2_matrix_1(D))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,E) = k3_matrix_1(C,D,F,G)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(E,np__1)) = k3_matrix_1(C,D,H,I) )
=> k3_real_1(k18_complex1(k5_real_1(F,H)),k18_complex1(k5_real_1(G,I))) = np__1 ) ) ) ) ) ) )
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(B))
& r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(B)) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
& r2_hidden(k4_tarski(H,I),k2_matrix_1(D))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E) = k3_matrix_1(C,D,F,G)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(E,np__1)) = k3_matrix_1(C,D,H,I) )
=> k3_real_1(k18_complex1(k5_real_1(F,H)),k18_complex1(k5_real_1(G,I))) = np__1 ) ) ) ) ) ) )
& ! [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)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(E,F),k2_matrix_1(D))
& r2_hidden(k4_tarski(G,H),k2_matrix_1(D))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k3_matrix_1(C,D,E,F)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1) = k3_matrix_1(C,D,G,H)
& r2_hidden(k3_finseq_1(A),k4_finseq_1(A))
& r2_hidden(np__1,k4_finseq_1(B)) )
=> k3_real_1(k18_complex1(k5_real_1(E,G)),k18_complex1(k5_real_1(F,H))) = np__1 ) ) ) ) ) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B)))
& r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B))) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k4_tarski(F,G),k2_matrix_1(D))
& r2_hidden(k4_tarski(H,I),k2_matrix_1(D))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),E) = k3_matrix_1(C,D,F,G)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k8_finseq_1(u1_struct_0(k15_euclid(np__2)),A,B),k1_nat_1(E,np__1)) = k3_matrix_1(C,D,H,I) )
=> k3_real_1(k18_complex1(k5_real_1(F,H)),k18_complex1(k5_real_1(G,I))) = np__1 ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_goboard1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& r2_hidden(A,k2_finseq_1(k1_matrix_1(B)))
& r1_xboole_0(k2_relat_1(C),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),B,A))) )
=> ( r1_xreal_0(k1_matrix_1(B),np__1)
| r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k4_goboard1(B,A)) ) ) ) ) ) ).
fof(t42_goboard1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& r2_hidden(A,k4_finseq_1(C))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D))) ) ) ) ) ) ) ).
fof(t43_goboard1,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)))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
& r2_hidden(A,k4_finseq_1(D))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(D))
& r2_hidden(B,k4_finseq_1(C))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
& ~ r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E)))
& r2_hidden(E,k4_finseq_1(C))
& k18_complex1(k5_real_1(B,E)) != np__1 ) ) ) ) ) ) ).
fof(t44_goboard1,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)))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,k3_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
& r2_hidden(A,k4_finseq_1(C))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(C))
& r2_hidden(B,k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,B),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A)))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A))) )
=> r1_xreal_0(E,B) ) ) )
=> ( r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(B,np__1)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1)))) ) ) ) ) ) ) ).
fof(t45_goboard1,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)))
=> ( ( r1_xreal_0(np__1,k3_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A))))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,D),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) ) ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(np__2,k3_finseq_1(B))
& r1_xboole_0(k5_topreal1(np__2,B),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) )
& ! [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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A))
& r2_hidden(E,k4_finseq_1(B))
& r2_hidden(F,k4_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r2_hidden(G,k4_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,G),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) )
=> r1_xreal_0(G,E) ) )
& ~ r1_xreal_0(F,E)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,F),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
& r1_xreal_0(D,C) ) ) ) ) ) ) ) ) ) ).
fof(t46_goboard1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [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_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& r2_hidden(A,k4_finseq_1(C))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k2_finseq_1(k1_matrix_1(B)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D))) ) ) ) ) ) ) ).
fof(t47_goboard1,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)))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
& r2_hidden(A,k4_finseq_1(D))
& r2_hidden(k1_nat_1(A,np__1),k4_finseq_1(D))
& r2_hidden(B,k2_finseq_1(k1_matrix_1(C)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
& ~ r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E)))
& r2_hidden(E,k2_finseq_1(k1_matrix_1(C)))
& k18_complex1(k5_real_1(B,E)) != np__1 ) ) ) ) ) ) ).
fof(t48_goboard1,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)))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r1_xreal_0(np__1,k3_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_matrix_1(C))))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
& r2_hidden(A,k2_finseq_1(k1_matrix_1(C)))
& r2_hidden(k1_nat_1(A,np__1),k2_finseq_1(k1_matrix_1(C)))
& r2_hidden(B,k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A)))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A))) )
=> r1_xreal_0(E,B) ) ) )
=> ( r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(B,np__1)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1)))) ) ) ) ) ) ) ).
fof(t49_goboard1,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)))
=> ( ( r1_xreal_0(np__1,k3_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A))))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A) )
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,D),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) ) ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(A))
& r1_xreal_0(np__2,k3_finseq_1(B))
& r1_xboole_0(k5_topreal1(np__2,B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) ) )
& ! [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)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(A))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(A))
& r2_hidden(E,k4_finseq_1(B))
& r2_hidden(F,k4_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C)))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r2_hidden(G,k4_finseq_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,G),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,C))) )
=> r1_xreal_0(G,E) ) )
& ~ r1_xreal_0(F,E)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,F),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,D)))
& r1_xreal_0(D,C) ) ) ) ) ) ) ) ) ) ).
fof(t50_goboard1,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)))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(A,k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B)))
& r2_hidden(B,k2_finseq_1(k1_matrix_1(C)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1)))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B))) )
=> r1_xreal_0(A,E) ) ) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(E,k4_finseq_1(D))
& r1_xreal_0(E,A) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r2_hidden(F,k2_finseq_1(k1_matrix_1(C)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,E),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),C,F))) )
=> r1_xreal_0(F,B) ) ) ) ) ) ) ) ) ) ).
fof(t51_goboard1,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)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A))))
& ~ r1_xreal_0(k1_matrix_1(A),np__1)
& r1_xreal_0(np__1,k3_finseq_1(B))
& ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(A,k1_matrix_1(A)),np__1)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),k4_goboard1(A,k1_matrix_1(A)),k1_matrix_1(k4_goboard1(A,k1_matrix_1(A))))))
& r1_xreal_0(np__1,k3_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,k4_goboard1(A,k1_matrix_1(A)))
& r1_tarski(k2_relat_1(C),k2_relat_1(B)) ) ) ) ) ) ).
fof(t52_goboard1,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)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
& k3_xboole_0(k2_relat_1(B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1))) != k1_xboole_0
& k3_xboole_0(k2_relat_1(B),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A)))) != k1_xboole_0
& ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_tarski(k2_relat_1(C),k2_relat_1(B))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,np__1)))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C)),k2_relat_1(k8_matrix_1(u1_struct_0(k15_euclid(np__2)),A,k1_matrix_1(A))))
& r1_xreal_0(np__1,k3_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,A) ) ) ) ) ) ).
fof(t53_goboard1,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)))) )
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(A,k4_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,C)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k3_finseq_1(D)),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))))
& r2_hidden(B,k4_finseq_1(D))
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,B),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A))) )
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(A,E)
& r1_xreal_0(E,k3_finseq_1(C))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(F,k4_finseq_1(D))
& r1_xreal_0(B,F)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,F),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E))) ) ) ) )
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(E,A)
& r1_xreal_0(E,k3_finseq_1(C))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(F,k4_finseq_1(D))
& ~ r1_xreal_0(F,B)
& r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,F),k2_relat_1(k7_matrix_1(u1_struct_0(k15_euclid(np__2)),C,E))) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_goboard1,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(A,k2_finseq_1(f2_s1_goboard1))
& ! [B] :
( m1_subset_1(B,f1_s1_goboard1)
=> ~ p1_s1_goboard1(A,B) ) ) )
=> ? [A] :
( m2_finseq_1(A,f1_s1_goboard1)
& k3_finseq_1(A) = f2_s1_goboard1
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_finseq_1(f2_s1_goboard1))
=> p1_s1_goboard1(B,k4_finseq_4(k5_numbers,f1_s1_goboard1,A,B)) ) ) ) ) ).
fof(redefinition_v2_goboard1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_matrix_1(B)
& m1_finseq_1(B,k3_finseq_2(A)) )
=> ( v2_goboard1(B,A)
<=> v3_relat_1(B) ) ) ).
fof(dt_k1_goboard1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k1_numbers)
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k1_goboard1(A,B),k1_numbers) ) ).
fof(redefinition_k1_goboard1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k1_numbers)
& m1_subset_1(B,k5_numbers) )
=> k1_goboard1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k2_goboard1,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> m2_finseq_1(k2_goboard1(A),k1_numbers) ) ).
fof(dt_k3_goboard1,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> m2_finseq_1(k3_goboard1(A),k1_numbers) ) ).
fof(dt_k4_goboard1,axiom,
! [A,B] :
( ( ~ v3_relat_1(A)
& v1_matrix_1(A)
& v3_goboard1(A)
& v4_goboard1(A)
& v5_goboard1(A)
& v6_goboard1(A)
& m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v3_relat_1(k4_goboard1(A,B))
& v1_matrix_1(k4_goboard1(A,B))
& v3_goboard1(k4_goboard1(A,B))
& v4_goboard1(k4_goboard1(A,B))
& v5_goboard1(k4_goboard1(A,B))
& v6_goboard1(k4_goboard1(A,B))
& m2_finseq_1(k4_goboard1(A,B),k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) ) ) ).
%------------------------------------------------------------------------------