SET007 Axioms: SET007+415.ax
%------------------------------------------------------------------------------
% File : SET007+415 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Decomposing a Go-Board into Cells
% 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 : goboard5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 59 ( 0 unt; 0 def)
% Number of atoms : 642 ( 86 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 636 ( 53 ~; 30 |; 356 &)
% ( 18 <=>; 179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 12 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 27 ( 26 usr; 0 prp; 1-3 aty)
% Number of functors : 47 ( 47 usr; 5 con; 0-4 aty)
% Number of variables : 206 ( 179 !; 27 ?)
% 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_goboard5,axiom,
? [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& ~ v5_seqm_3(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A) ) ).
fof(t1_goboard5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_matrix_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(k4_tarski(B,C),k2_matrix_1(A))
=> ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(A)) ) ) ) ) ) ).
fof(t2_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(C)) )
=> k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,A)) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1,A)) ) ) ) ) ).
fof(t3_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(C)) )
=> k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,A)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,np__1)) ) ) ) ) ).
fof(t4_goboard5,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] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( v6_goboard1(D)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(D))
& r1_xreal_0(np__1,B)
& ~ r1_xreal_0(C,B)
& r1_xreal_0(C,k3_finseq_1(D))
& r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,A)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B,A))) ) ) ) ) ) ).
fof(t5_goboard5,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] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( v5_goboard1(D)
& r1_xreal_0(np__1,A)
& ~ r1_xreal_0(B,A)
& r1_xreal_0(B,k1_matrix_1(D))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(D))
& r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,B)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,A))) ) ) ) ) ) ).
fof(d3_goboard5,axiom,
! [A] :
( ( v1_matrix_1(A)
& m2_finseq_1(A,k3_finseq_2(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)
=> k3_goboard5(A,B,C) = k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_goboard5(A,B),k2_goboard5(A,C)) ) ) ) ).
fof(d4_goboard5,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_goboard5(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,k1_nat_1(B,np__1))
& ~ ( ~ ( ~ r1_xreal_0(B,np__1)
& ~ r1_xreal_0(k3_finseq_1(A),C) )
& r1_xreal_0(k3_finseq_1(A),k1_nat_1(C,np__1)) )
& ~ r1_xboole_0(k4_topreal1(np__2,A,B),k4_topreal1(np__2,A,C)) ) ) ) ) ) ).
fof(d5_goboard5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ( v2_goboard5(A)
<=> r1_goboard1(u1_struct_0(k15_euclid(np__2)),A,k3_goboard2(A)) ) ) ).
fof(t12_goboard5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(B,k4_finseq_1(A))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,D) ) ) ) ) ) ) ).
fof(t13_goboard5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v2_goboard5(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))
& r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) )
=> ! [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)
=> ( ( r2_hidden(k4_tarski(C,D),k2_matrix_1(k3_goboard2(A)))
& r2_hidden(k4_tarski(E,F),k2_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),C,D)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),E,F) )
=> k3_real_1(k18_complex1(k5_real_1(C,E)),k18_complex1(k5_real_1(D,F))) = np__1 ) ) ) ) ) ) ) ) ).
fof(d6_goboard5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( C = k4_goboard5(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k3_goboard2(A)))
& r2_hidden(k4_tarski(F,G),k2_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,E)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),F,G)
& ~ ( D = F
& k1_nat_1(E,np__1) = G
& C = k3_goboard5(k3_goboard2(A),D,E) )
& ~ ( k1_nat_1(D,np__1) = F
& E = G
& C = k3_goboard5(k3_goboard2(A),D,k5_binarith(E,np__1)) )
& ~ ( D = k1_nat_1(F,np__1)
& E = G
& C = k3_goboard5(k3_goboard2(A),F,G) )
& ~ ( D = F
& E = k1_nat_1(G,np__1)
& C = k3_goboard5(k3_goboard2(A),k5_binarith(D,np__1),G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_goboard5,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( C = k5_goboard5(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(k3_goboard2(A)))
& r2_hidden(k4_tarski(F,G),k2_matrix_1(k3_goboard2(A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,B) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),D,E)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(B,np__1)) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(A),F,G)
& ~ ( D = F
& k1_nat_1(E,np__1) = G
& C = k3_goboard5(k3_goboard2(A),k5_binarith(D,np__1),E) )
& ~ ( k1_nat_1(D,np__1) = F
& E = G
& C = k3_goboard5(k3_goboard2(A),D,E) )
& ~ ( D = k1_nat_1(F,np__1)
& E = G
& C = k3_goboard5(k3_goboard2(A),F,k5_binarith(G,np__1)) )
& ~ ( D = F
& E = k1_nat_1(G,np__1)
& C = k3_goboard5(k3_goboard2(A),D,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(C)
& v6_goboard1(C)
& r1_xreal_0(np__1,B) )
=> ( v3_relat_1(C)
| r1_xreal_0(k3_finseq_1(C),A)
| r1_xreal_0(k1_matrix_1(C),B)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k1_goboard5(C,A)) ) ) ) ) ) ).
fof(t15_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(C)
& v6_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(np__1,B) )
=> ( v3_relat_1(C)
| r1_xreal_0(k1_matrix_1(C),B)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))),k1_goboard5(C,A)) ) ) ) ) ) ).
fof(t16_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(C)
& v5_goboard1(C)
& r1_xreal_0(np__1,B) )
=> ( v3_relat_1(C)
| r1_xreal_0(k1_matrix_1(C),A)
| r1_xreal_0(k3_finseq_1(C),B)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,k1_nat_1(A,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1),k1_nat_1(A,np__1))),k2_goboard5(C,A)) ) ) ) ) ) ).
fof(t17_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(C)
& v5_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(C))
& r1_xreal_0(np__1,B) )
=> ( v3_relat_1(C)
| r1_xreal_0(k3_finseq_1(C),B)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,A),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1),A)),k2_goboard5(C,A)) ) ) ) ) ) ).
fof(t18_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(C)
& v5_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k1_matrix_1(C)) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))),k2_goboard5(C,B)) ) ) ) ) ).
fof(t19_goboard5,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)))) )
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k3_finseq_1(C),A)
| r1_xreal_0(k1_matrix_1(C),B)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))),k3_goboard5(C,A,B)) ) ) ) ) ) ).
fof(t20_goboard5,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)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(np__1,B) )
=> ( r1_xreal_0(k1_matrix_1(C),B)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_nat_1(B,np__1))),k3_goboard5(C,A,B)) ) ) ) ) ) ).
fof(t21_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(C)
& v6_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(k1_nat_1(B,np__1),k3_finseq_1(C)) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,A),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1),A)),k1_goboard5(C,B)) ) ) ) ) ).
fof(t22_goboard5,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)))) )
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k1_matrix_1(C),A)
| r1_xreal_0(k3_finseq_1(C),B)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,k1_nat_1(A,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1),k1_nat_1(A,np__1))),k3_goboard5(C,B,A)) ) ) ) ) ) ).
fof(t23_goboard5,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)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(C)) )
=> ( r1_xreal_0(k3_finseq_1(C),A)
| r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B)),k3_goboard5(C,A,B)) ) ) ) ) ) ).
fof(t26_goboard5,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)))) )
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k3_finseq_1(C),A)
| r1_xreal_0(k1_matrix_1(C),B)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_goboard5(C,A,B),k3_goboard5(C,k1_nat_1(A,np__1),B)) = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(A,np__1),k1_nat_1(B,np__1))) ) ) ) ) ) ).
fof(t27_goboard5,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)))) )
=> ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k1_matrix_1(C),A)
| r1_xreal_0(k3_finseq_1(C),B)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_goboard5(C,B,A),k3_goboard5(C,B,k1_nat_1(A,np__1))) = k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,k1_nat_1(A,np__1)),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1),k1_nat_1(A,np__1))) ) ) ) ) ) ).
fof(t28_goboard5,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& m2_finseq_1(D,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))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(k3_goboard2(D)))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),k1_nat_1(C,np__1)),k2_matrix_1(k3_goboard2(D)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),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)),k3_goboard2(D),k1_nat_1(B,np__1),k1_nat_1(C,np__1)) )
=> ( k5_goboard5(D,A) = k3_goboard5(k3_goboard2(D),B,C)
& k4_goboard5(D,A) = k3_goboard5(k3_goboard2(D),k1_nat_1(B,np__1),C) ) ) ) ) ) ) ).
fof(t29_goboard5,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& m2_finseq_1(D,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))
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(k3_goboard2(D)))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),k1_nat_1(C,np__1)),k2_matrix_1(k3_goboard2(D)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),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)),k3_goboard2(D),k1_nat_1(B,np__1),k1_nat_1(C,np__1)) )
=> ( k5_goboard5(D,A) = k3_goboard5(k3_goboard2(D),B,k1_nat_1(C,np__1))
& k4_goboard5(D,A) = k3_goboard5(k3_goboard2(D),B,C) ) ) ) ) ) ) ).
fof(t30_goboard5,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& m2_finseq_1(D,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))
& r2_hidden(k4_tarski(B,k1_nat_1(C,np__1)),k2_matrix_1(k3_goboard2(D)))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),k1_nat_1(C,np__1)),k2_matrix_1(k3_goboard2(D)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(B,np__1),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)),k3_goboard2(D),B,k1_nat_1(C,np__1)) )
=> ( k5_goboard5(D,A) = k3_goboard5(k3_goboard2(D),B,C)
& k4_goboard5(D,A) = k3_goboard5(k3_goboard2(D),B,k1_nat_1(C,np__1)) ) ) ) ) ) ) ).
fof(t31_goboard5,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] :
( ( ~ v1_xboole_0(D)
& v1_topreal1(D)
& v2_topreal1(D)
& v1_finseq_6(D,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(D)
& v2_goboard5(D)
& m2_finseq_1(D,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))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),k1_nat_1(C,np__1)),k2_matrix_1(k3_goboard2(D)))
& r2_hidden(k4_tarski(k1_nat_1(B,np__1),C),k2_matrix_1(k3_goboard2(D)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),D,A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(D),k1_nat_1(B,np__1),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)),k3_goboard2(D),k1_nat_1(B,np__1),C) )
=> ( k5_goboard5(D,A) = k3_goboard5(k3_goboard2(D),k1_nat_1(B,np__1),C)
& k4_goboard5(D,A) = k3_goboard5(k3_goboard2(D),B,C) ) ) ) ) ) ) ).
fof(t32_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_topreal1(B)
& v2_topreal1(B)
& v1_finseq_6(B,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(B)
& v2_goboard5(B)
& m2_finseq_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_goboard5(B,A),k4_goboard5(B,A)) = k4_topreal1(np__2,B,A) ) ) ) ).
fof(dt_k1_goboard5,axiom,
! [A,B] :
( ( v1_matrix_1(A)
& m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k1_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k2_goboard5,axiom,
! [A,B] :
( ( v1_matrix_1(A)
& m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k2_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k3_goboard5,axiom,
! [A,B,C] :
( ( v1_matrix_1(A)
& m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k3_goboard5(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k4_goboard5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k4_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k5_goboard5,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,k5_numbers) )
=> m1_subset_1(k5_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(d1_goboard5,axiom,
! [A] :
( ( v1_matrix_1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k3_finseq_1(A),B)
| k1_goboard5(A,B) = a_2_0_goboard5(A,B) ) )
& ( r1_xreal_0(k3_finseq_1(A),B)
=> k1_goboard5(A,B) = a_2_1_goboard5(A,B) )
& ~ ( ~ ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k3_finseq_1(A),B) )
& ~ r1_xreal_0(k3_finseq_1(A),B)
& k1_goboard5(A,B) != a_2_2_goboard5(A,B) ) ) ) ) ).
fof(d2_goboard5,axiom,
! [A] :
( ( v1_matrix_1(A)
& m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
=> ( r1_xreal_0(k1_matrix_1(A),B)
| k2_goboard5(A,B) = a_2_3_goboard5(A,B) ) )
& ( r1_xreal_0(k1_matrix_1(A),B)
=> k2_goboard5(A,B) = a_2_4_goboard5(A,B) )
& ~ ( ~ ( r1_xreal_0(np__1,B)
& ~ r1_xreal_0(k1_matrix_1(A),B) )
& ~ r1_xreal_0(k1_matrix_1(A),B)
& k2_goboard5(A,B) != a_2_5_goboard5(A,B) ) ) ) ) ).
fof(t6_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(C)) )
=> ( r1_xreal_0(k1_matrix_1(C),A)
| k2_goboard5(C,A) = a_3_0_goboard5(A,B,C) ) ) ) ) ) ).
fof(t7_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B)) )
=> ( v3_relat_1(B)
| k2_goboard5(B,k1_matrix_1(B)) = a_2_6_goboard5(A,B) ) ) ) ) ).
fof(t8_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B)) )
=> ( v3_relat_1(B)
| k2_goboard5(B,np__0) = a_2_7_goboard5(A,B) ) ) ) ) ).
fof(t9_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(C)
& r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(C)) )
=> ( r1_xreal_0(k3_finseq_1(C),A)
| k1_goboard5(C,A) = a_3_1_goboard5(A,B,C) ) ) ) ) ) ).
fof(t10_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(B)) )
=> ( v3_relat_1(B)
| k1_goboard5(B,k3_finseq_1(B)) = a_2_8_goboard5(A,B) ) ) ) ) ).
fof(t11_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(B)) )
=> ( v3_relat_1(B)
| k1_goboard5(B,np__0) = a_2_9_goboard5(A,B) ) ) ) ) ).
fof(t24_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v3_goboard1(B)
& v6_goboard1(B)
& r1_xreal_0(k1_nat_1(A,np__1),k3_finseq_1(B)) )
=> ( v3_relat_1(B)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k1_goboard5(B,A),k1_goboard5(B,k1_nat_1(A,np__1))) = a_2_10_goboard5(A,B) ) ) ) ) ).
fof(t25_goboard5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( v4_goboard1(B)
& v5_goboard1(B)
& r1_xreal_0(k1_nat_1(A,np__1),k1_matrix_1(B)) )
=> ( v3_relat_1(B)
| k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_goboard5(B,A),k2_goboard5(B,k1_nat_1(A,np__1))) = a_2_11_goboard5(A,B) ) ) ) ) ).
fof(fraenkel_a_2_0_goboard5,axiom,
! [A,B,C] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_0_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,np__1)),D)
& r1_xreal_0(D,k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),np__1))) ) ) ) ).
fof(fraenkel_a_2_1_goboard5,axiom,
! [A,B,C] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_1_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,C,np__1)),D) ) ) ) ).
fof(fraenkel_a_2_2_goboard5,axiom,
! [A,B,C] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_2_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(D,k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k1_nat_1(C,np__1),np__1))) ) ) ) ).
fof(fraenkel_a_2_3_goboard5,axiom,
! [A,B,C] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_3_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,C)),E)
& r1_xreal_0(E,k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,k1_nat_1(C,np__1)))) ) ) ) ).
fof(fraenkel_a_2_4_goboard5,axiom,
! [A,B,C] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_4_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,C)),E) ) ) ) ).
fof(fraenkel_a_2_5_goboard5,axiom,
! [A,B,C] :
( ( v1_matrix_1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2))))
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_5_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(E,k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,k1_nat_1(C,np__1)))) ) ) ) ).
fof(fraenkel_a_3_0_goboard5,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers)
& v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_3_0_goboard5(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,k1_numbers)
& m1_subset_1(F,k1_numbers)
& A = k23_euclid(E,F)
& r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,B)),F)
& r1_xreal_0(F,k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,C,k1_nat_1(B,np__1)))) ) ) ) ).
fof(fraenkel_a_2_6_goboard5,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_2_6_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,k1_matrix_1(C))),E) ) ) ) ).
fof(fraenkel_a_2_7_goboard5,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_2_7_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(E,k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,B,np__1))) ) ) ) ).
fof(fraenkel_a_3_1_goboard5,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers)
& v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_3_1_goboard5(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,k1_numbers)
& m1_subset_1(F,k1_numbers)
& A = k23_euclid(E,F)
& r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,B,C)),E)
& r1_xreal_0(E,k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),D,k1_nat_1(B,np__1),C))) ) ) ) ).
fof(fraenkel_a_2_8_goboard5,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_2_8_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C),B)),D) ) ) ) ).
fof(fraenkel_a_2_9_goboard5,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_2_9_goboard5(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_numbers)
& m1_subset_1(E,k1_numbers)
& A = k23_euclid(D,E)
& r1_xreal_0(D,k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1,B))) ) ) ) ).
fof(fraenkel_a_2_10_goboard5,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_2_10_goboard5(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& A = D
& k21_euclid(D) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k1_nat_1(B,np__1),np__1)) ) ) ) ).
fof(fraenkel_a_2_11_goboard5,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,a_2_11_goboard5(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
& A = D
& k22_euclid(D) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1,k1_nat_1(B,np__1))) ) ) ) ).
%------------------------------------------------------------------------------