SET007 Axioms: SET007+597.ax
%------------------------------------------------------------------------------
% File : SET007+597 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of Cells on 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 : gobrd13 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 70 ( 2 unt; 0 def)
% Number of atoms : 1127 ( 189 equ)
% Maximal formula atoms : 34 ( 16 avg)
% Number of connectives : 1162 ( 105 ~; 11 |; 705 &)
% ( 9 <=>; 332 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 16 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-4 aty)
% Number of functors : 42 ( 42 usr; 4 con; 0-4 aty)
% Number of variables : 315 ( 312 !; 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(cc1_gobrd13,axiom,
! [A,B] :
( m1_finseq_1(B,k3_finseq_2(A))
=> v1_matrlin(B) ) ).
fof(cc2_gobrd13,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_matrlin(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) ) ) ).
fof(fc1_gobrd13,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,k3_finseq_2(A)) )
=> v1_finset_1(k2_gobrd13(B)) ) ).
fof(d1_gobrd13,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> k2_gobrd13(A) = k3_card_3(k3_funct_6(A)) ) ).
fof(t1_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,k3_finseq_2(B))
=> m2_finseq_1(k1_funct_1(C,A),B) ) ) ) ).
fof(t2_gobrd13,axiom,
$true ).
fof(t4_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(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(D))
& k1_funct_1(D,A) = C )
=> k3_finseq_1(C) = k1_matrix_1(D) ) ) ) ) ) ).
fof(t5_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(C)) )
=> ( ( r2_hidden(A,k4_finseq_1(E))
& k1_funct_1(E,A) = D
& r2_hidden(B,k4_finseq_1(D)) )
=> r2_hidden(k4_tarski(A,B),k2_matrix_1(E)) ) ) ) ) ) ) ).
fof(t6_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m2_finseq_1(D,C)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(C)) )
=> ( ( r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
& k1_funct_1(E,A) = D )
=> ( k3_finseq_1(D) = k1_matrix_1(E)
& r2_hidden(B,k4_finseq_1(D)) ) ) ) ) ) ) ) ).
fof(t8_gobrd13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(A)) )
=> r1_xreal_0(k4_card_1(k2_gobrd13(B)),k2_nat_1(k3_finseq_1(B),k1_matrix_1(B))) ) ) ).
fof(t9_gobrd13,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B)
=> r1_tarski(k2_relat_1(A),k2_gobrd13(B)) ) ) ) ).
fof(t10_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(D),k2_gobrd13(E))
& r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(E))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,np__1,C) )
=> A = np__1 ) ) ) ) ) ) ).
fof(t11_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(D),k2_gobrd13(E))
& r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(E))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k3_finseq_1(E),C) )
=> A = k3_finseq_1(D) ) ) ) ) ) ) ).
fof(t12_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(D),k2_gobrd13(E))
& r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(E))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,np__1) )
=> B = np__1 ) ) ) ) ) ) ).
fof(t13_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(D),k2_gobrd13(E))
& r2_hidden(k4_tarski(A,B),k2_matrix_1(D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(E))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,k1_matrix_1(E)) )
=> B = k1_matrix_1(D) ) ) ) ) ) ) ).
fof(t14_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(E),k2_gobrd13(F))
& r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(E))
& r1_xreal_0(np__1,C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(F))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
=> ( r1_xreal_0(k3_finseq_1(E),A)
| r1_xreal_0(k3_finseq_1(F),C)
| r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,k1_nat_1(C,np__1),D)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(A,np__1),B))) ) ) ) ) ) ) ) ) ).
fof(t15_gobrd13,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)))) )
=> ! [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)))) )
=> ( ( r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k5_binarith(A,np__1),B),k2_gobrd13(F))
& r1_xreal_0(A,k3_finseq_1(E))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(E))
& r1_xreal_0(C,k3_finseq_1(F))
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(F))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
=> ( r1_xreal_0(A,np__1)
| r1_xreal_0(C,np__1)
| r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k5_binarith(A,np__1),B)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,k5_binarith(C,np__1),D))) ) ) ) ) ) ) ) ) ).
fof(t16_gobrd13,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)))) )
=> ! [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)))) )
=> ( ( r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,k1_nat_1(B,np__1)),k2_gobrd13(F))
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(E))
& r1_xreal_0(np__1,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(F))
& r1_xreal_0(np__1,D)
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
=> ( r1_xreal_0(k1_matrix_1(E),B)
| r1_xreal_0(k1_matrix_1(F),D)
| r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,k1_nat_1(D,np__1))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,k1_nat_1(B,np__1)))) ) ) ) ) ) ) ) ) ).
fof(t17_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(E),k2_gobrd13(F))
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(E))
& r1_xreal_0(B,k1_matrix_1(E))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(F))
& r1_xreal_0(D,k1_matrix_1(F))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
=> ( r1_xreal_0(B,np__1)
| r1_xreal_0(D,np__1)
| r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,k5_binarith(B,np__1))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,k5_binarith(D,np__1)))) ) ) ) ) ) ) ) ) ).
fof(t18_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(E),k2_gobrd13(F))
& r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(F))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
=> r1_tarski(k3_goboard5(F,C,D),k3_goboard5(E,A,B)) ) ) ) ) ) ) ) ).
fof(t19_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(E),k2_gobrd13(F))
& r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(F))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
=> r1_tarski(k3_goboard5(F,k5_binarith(C,np__1),D),k3_goboard5(E,k5_binarith(A,np__1),B)) ) ) ) ) ) ) ) ).
fof(t20_gobrd13,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)))) )
=> ! [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_tarski(k2_gobrd13(E),k2_gobrd13(F))
& r2_hidden(k4_tarski(A,B),k2_matrix_1(E))
& r2_hidden(k4_tarski(C,D),k2_matrix_1(F))
& k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),F,C,D) )
=> r1_tarski(k3_goboard5(F,C,k5_binarith(D,np__1)),k3_goboard5(E,A,k5_binarith(B,np__1))) ) ) ) ) ) ) ) ).
fof(t21_gobrd13,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] :
( ( ~ 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)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,A)
=> r1_tarski(k2_gobrd13(k3_goboard2(B)),k2_gobrd13(A)) ) ) ) ).
fof(d2_gobrd13,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)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( D = k3_gobrd13(A,B,C)
<=> ! [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(B))
& r2_hidden(k4_tarski(G,H),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,E,F)
& 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,G,H)
& ~ ( E = G
& k1_nat_1(F,np__1) = H
& D = k3_goboard5(B,E,F) )
& ~ ( k1_nat_1(E,np__1) = G
& F = H
& D = k3_goboard5(B,E,k5_binarith(F,np__1)) )
& ~ ( E = k1_nat_1(G,np__1)
& F = H
& D = k3_goboard5(B,G,H) )
& ~ ( E = G
& F = k1_nat_1(H,np__1)
& D = k3_goboard5(B,k5_binarith(E,np__1),H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_gobrd13,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)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( D = k4_gobrd13(A,B,C)
<=> ! [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(B))
& r2_hidden(k4_tarski(G,H),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,E,F)
& 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,G,H)
& ~ ( E = G
& k1_nat_1(F,np__1) = H
& D = k3_goboard5(B,k5_binarith(E,np__1),F) )
& ~ ( k1_nat_1(E,np__1) = G
& F = H
& D = k3_goboard5(B,E,F) )
& ~ ( E = k1_nat_1(G,np__1)
& F = H
& D = k3_goboard5(B,G,k5_binarith(H,np__1)) )
& ~ ( E = G
& F = k1_nat_1(H,np__1)
& D = k3_goboard5(B,E,H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
=> k4_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),C) ) ) ) ) ) ) ).
fof(t23_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
=> k3_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) ).
fof(t24_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
=> k4_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) ).
fof(t25_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
=> k3_gobrd13(D,E,A) = k3_goboard5(E,B,k5_binarith(C,np__1)) ) ) ) ) ) ) ).
fof(t26_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k4_gobrd13(D,E,A) = k3_goboard5(E,B,k5_binarith(C,np__1)) ) ) ) ) ) ) ).
fof(t27_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k3_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) ).
fof(t28_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k4_gobrd13(D,E,A) = k3_goboard5(E,B,C) ) ) ) ) ) ) ).
fof(t29_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k3_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),C) ) ) ) ) ) ) ).
fof(t30_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,C) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_gobrd13(B,C,A),k3_gobrd13(B,C,A)) = k4_topreal1(np__2,B,A) ) ) ) ) ).
fof(t31_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),B,C) )
=> v4_pre_topc(k3_gobrd13(B,C,A),k15_euclid(np__2)) ) ) ) ) ).
fof(t32_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [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)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,D)
& r1_xreal_0(k1_nat_1(A,np__1),B) )
=> ( k4_gobrd13(C,D,A) = k4_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A)
& k3_gobrd13(C,D,A) = k3_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A) ) ) ) ) ) ) ).
fof(t33_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [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)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),C,B)))
& r1_xreal_0(B,k3_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,D) )
=> ( k4_gobrd13(C,D,k1_nat_1(A,B)) = k4_gobrd13(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),C,B),D,A)
& k3_gobrd13(C,D,k1_nat_1(A,B)) = k3_gobrd13(k1_rfinseq(u1_struct_0(k15_euclid(np__2)),C,B),D,A) ) ) ) ) ) ) ).
fof(t34_gobrd13,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] :
( ( ~ v1_xboole_0(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B) )
=> ( r1_tarski(k4_gobrd13(C,B,A),k5_goboard5(C,A))
& r1_tarski(k3_gobrd13(C,B,A),k4_goboard5(C,A)) ) ) ) ) ) ).
fof(d4_gobrd13,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)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( D = k5_gobrd13(A,B,C)
<=> ! [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(B))
& r2_hidden(k4_tarski(G,H),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,E,F)
& 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,G,H)
& ~ ( E = G
& k1_nat_1(F,np__1) = H
& D = k3_goboard5(B,G,H) )
& ~ ( k1_nat_1(E,np__1) = G
& F = H
& D = k3_goboard5(B,G,k5_binarith(H,np__1)) )
& ~ ( E = k1_nat_1(G,np__1)
& F = H
& D = k3_goboard5(B,k5_binarith(G,np__1),H) )
& ~ ( E = G
& F = k1_nat_1(H,np__1)
& D = k3_goboard5(B,k5_binarith(G,np__1),k5_binarith(H,np__1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_gobrd13,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)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( D = k6_gobrd13(A,B,C)
<=> ! [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(B))
& r2_hidden(k4_tarski(G,H),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,E,F)
& 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,G,H)
& ~ ( E = G
& k1_nat_1(F,np__1) = H
& D = k3_goboard5(B,k5_binarith(G,np__1),H) )
& ~ ( k1_nat_1(E,np__1) = G
& F = H
& D = k3_goboard5(B,G,H) )
& ~ ( E = k1_nat_1(G,np__1)
& F = H
& D = k3_goboard5(B,k5_binarith(G,np__1),k5_binarith(H,np__1)) )
& ~ ( E = G
& F = k1_nat_1(H,np__1)
& D = k3_goboard5(B,G,k5_binarith(H,np__1)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t35_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
=> k6_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),k1_nat_1(C,np__1)) ) ) ) ) ) ) ).
fof(t36_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1)) )
=> k5_gobrd13(D,E,A) = k3_goboard5(E,B,k1_nat_1(C,np__1)) ) ) ) ) ) ) ).
fof(t37_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
=> k6_gobrd13(D,E,A) = k3_goboard5(E,k1_nat_1(B,np__1),C) ) ) ) ) ) ) ).
fof(t38_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C) )
=> k5_gobrd13(D,E,A) = k3_goboard5(E,k1_nat_1(B,np__1),k5_binarith(C,np__1)) ) ) ) ) ) ) ).
fof(t39_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k6_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),k5_binarith(C,np__1)) ) ) ) ) ) ) ).
fof(t40_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,k1_nat_1(B,np__1),C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k5_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),C) ) ) ) ) ) ) ).
fof(t41_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k6_gobrd13(D,E,A) = k3_goboard5(E,B,k5_binarith(C,np__1)) ) ) ) ) ) ) ).
fof(t42_gobrd13,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_finseq_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),D,E)
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(E))
& r2_hidden(k4_tarski(B,C),k2_matrix_1(E))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,k1_nat_1(C,np__1))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(A,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,C) )
=> k5_gobrd13(D,E,A) = k3_goboard5(E,k5_binarith(B,np__1),k5_binarith(C,np__1)) ) ) ) ) ) ) ).
fof(t43_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [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)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,D)
& r1_xreal_0(k1_nat_1(A,np__1),B) )
=> ( k6_gobrd13(C,D,A) = k6_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A)
& k5_gobrd13(C,D,A) = k5_gobrd13(k16_finseq_1(u1_struct_0(k15_euclid(np__2)),C,B),D,A) ) ) ) ) ) ) ).
fof(d6_gobrd13,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_gobrd13(A,B,C,D)
<=> ! [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)
& ~ ( E = G
& k1_nat_1(F,np__1) = H
& r2_hidden(k4_tarski(k1_nat_1(G,np__1),H),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k1_nat_1(G,np__1),H) )
& ~ ( k1_nat_1(E,np__1) = G
& F = H
& r2_hidden(k4_tarski(G,k5_binarith(H,np__1)),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k5_binarith(H,np__1)) )
& ~ ( E = k1_nat_1(G,np__1)
& F = H
& r2_hidden(k4_tarski(G,k1_nat_1(H,np__1)),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k1_nat_1(H,np__1)) )
& ~ ( E = G
& F = k1_nat_1(H,np__1)
& r2_hidden(k4_tarski(k5_binarith(G,np__1),H),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k5_binarith(G,np__1),H) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_gobrd13,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_gobrd13(A,B,C,D)
<=> ! [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)
& ~ ( E = G
& k1_nat_1(F,np__1) = H
& r2_hidden(k4_tarski(k5_binarith(G,np__1),H),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k5_binarith(G,np__1),H) )
& ~ ( k1_nat_1(E,np__1) = G
& F = H
& r2_hidden(k4_tarski(G,k1_nat_1(H,np__1)),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k1_nat_1(H,np__1)) )
& ~ ( E = k1_nat_1(G,np__1)
& F = H
& r2_hidden(k4_tarski(G,k5_binarith(H,np__1)),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k5_binarith(H,np__1)) )
& ~ ( E = G
& F = k1_nat_1(H,np__1)
& r2_hidden(k4_tarski(k1_nat_1(G,np__1),H),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k1_nat_1(G,np__1),H) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_gobrd13,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r3_gobrd13(A,B,C,D)
<=> ! [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)
& ~ ( E = G
& k1_nat_1(F,np__1) = H
& r2_hidden(k4_tarski(G,k1_nat_1(H,np__1)),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k1_nat_1(H,np__1)) )
& ~ ( k1_nat_1(E,np__1) = G
& F = H
& r2_hidden(k4_tarski(k1_nat_1(G,np__1),H),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k1_nat_1(G,np__1),H) )
& ~ ( E = k1_nat_1(G,np__1)
& F = H
& r2_hidden(k4_tarski(k5_binarith(G,np__1),H),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,k5_binarith(G,np__1),H) )
& ~ ( E = G
& F = k1_nat_1(H,np__1)
& r2_hidden(k4_tarski(G,k5_binarith(H,np__1)),k2_matrix_1(C))
& k4_finseq_4(k5_numbers,A,B,k1_nat_1(D,np__2)) = k3_matrix_1(A,C,G,k5_binarith(H,np__1)) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C,D] :
( m2_finseq_1(D,C)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(C)) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(D))
& r1_xreal_0(k1_nat_1(A,np__2),B)
& r1_gobrd13(C,k16_finseq_1(C,D,B),E,A) )
=> r1_gobrd13(C,D,E,A) ) ) ) ) ) ).
fof(t45_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C,D] :
( m2_finseq_1(D,C)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(C)) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(D))
& r1_xreal_0(k1_nat_1(A,np__2),B)
& r2_gobrd13(C,k16_finseq_1(C,D,B),E,A) )
=> r2_gobrd13(C,D,E,A) ) ) ) ) ) ).
fof(t46_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C,D] :
( m2_finseq_1(D,C)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(C)) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__2),k3_finseq_1(D))
& r1_xreal_0(k1_nat_1(A,np__2),B)
& r3_gobrd13(C,k16_finseq_1(C,D,B),E,A) )
=> r3_gobrd13(C,D,E,A) ) ) ) ) ) ).
fof(t47_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( m2_finseq_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(B)) )
=> ( ( r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(B,C,E)
& k16_finseq_1(B,C,A) = k16_finseq_1(B,D,A)
& r1_gobrd13(B,C,E,k5_binarith(A,np__1))
& r1_gobrd13(B,D,E,k5_binarith(A,np__1)) )
=> ( r1_xreal_0(A,np__1)
| k16_finseq_1(B,C,k1_nat_1(A,np__1)) = k16_finseq_1(B,D,k1_nat_1(A,np__1)) ) ) ) ) ) ) ).
fof(t48_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( m2_finseq_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(B)) )
=> ( ( r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(B,C,E)
& k16_finseq_1(B,C,A) = k16_finseq_1(B,D,A)
& r2_gobrd13(B,C,E,k5_binarith(A,np__1))
& r2_gobrd13(B,D,E,k5_binarith(A,np__1)) )
=> ( r1_xreal_0(A,np__1)
| k16_finseq_1(B,C,k1_nat_1(A,np__1)) = k16_finseq_1(B,D,k1_nat_1(A,np__1)) ) ) ) ) ) ) ).
fof(t49_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( m2_finseq_1(C,B)
=> ! [D] :
( m2_finseq_1(D,B)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(B)) )
=> ( ( r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(C))
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(D))
& r1_goboard1(B,C,E)
& k16_finseq_1(B,C,A) = k16_finseq_1(B,D,A)
& r3_gobrd13(B,C,E,k5_binarith(A,np__1))
& r3_gobrd13(B,D,E,k5_binarith(A,np__1)) )
=> ( r1_xreal_0(A,np__1)
| k16_finseq_1(B,C,k1_nat_1(A,np__1)) = k16_finseq_1(B,D,k1_nat_1(A,np__1)) ) ) ) ) ) ) ).
fof(t50_gobrd13,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(C)) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(D))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(D)) )
=> r2_hidden(k3_matrix_1(C,D,A,B),k2_gobrd13(D)) ) ) ) ) ) ).
fof(dt_k1_gobrd13,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_finseq_2(B,u1_struct_0(k15_euclid(np__2)))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> m2_finseq_1(k1_gobrd13(A,B,C,D),u1_struct_0(k15_euclid(np__2))) ) ).
fof(redefinition_k1_gobrd13,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_finseq_2(B,u1_struct_0(k15_euclid(np__2)))
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(D,A) )
=> k1_gobrd13(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k2_gobrd13,axiom,
$true ).
fof(dt_k3_gobrd13,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k3_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k4_gobrd13,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k4_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k5_gobrd13,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k5_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k6_gobrd13,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k6_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t3_gobrd13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,k3_finseq_2(A))
=> k2_gobrd13(B) = k3_tarski(a_2_0_gobrd13(A,B)) ) ) ).
fof(t7_gobrd13,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(A)) )
=> k2_gobrd13(B) = a_2_1_gobrd13(A,B) ) ) ).
fof(fraenkel_a_2_0_gobrd13,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& m2_finseq_1(C,k3_finseq_2(B)) )
=> ( r2_hidden(A,a_2_0_gobrd13(B,C))
<=> ? [D] :
( m2_finseq_2(D,B,k3_finseq_2(B))
& A = k2_relat_1(D)
& r2_hidden(D,k2_relat_1(C)) ) ) ) ).
fof(fraenkel_a_2_1_gobrd13,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(B)) )
=> ( r2_hidden(A,a_2_1_gobrd13(B,C))
<=> ? [D,E] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& m2_subset_1(E,k1_numbers,k5_numbers)
& A = k3_matrix_1(B,C,D,E)
& r2_hidden(k4_tarski(D,E),k2_matrix_1(C)) ) ) ) ).
%------------------------------------------------------------------------------