SET007 Axioms: SET007+351.ax
%------------------------------------------------------------------------------
% File : SET007+351 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Properties of Go-Board - Part III
% 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 : goboard3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 2 ( 0 unt; 0 def)
% Number of atoms : 50 ( 8 equ)
% Maximal formula atoms : 28 ( 25 avg)
% Number of connectives : 58 ( 10 ~; 0 |; 36 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 20 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 17 ( 16 usr; 0 prp; 1-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% 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(t1_goboard3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k4_finseq_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E) ) ) ) ) )
& v2_funct_1(A)
& v2_topreal1(A)
& v3_topreal1(A)
& v1_topreal1(A)
& ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& v2_funct_1(C)
& v2_topreal1(C)
& v3_topreal1(C)
& v1_topreal1(C)
& k5_topreal1(np__2,A) = k5_topreal1(np__2,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))
& r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) ) ) ) ) ) ).
fof(t2_goboard3,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k4_finseq_1(A))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,D,E) ) ) ) ) )
& v4_topreal1(A)
& ! [C] :
( m2_finseq_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& v4_topreal1(C)
& k5_topreal1(np__2,A) = k5_topreal1(np__2,C)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,k3_finseq_1(A)) = k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C))
& r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) ) ) ) ) ) ).
%------------------------------------------------------------------------------