%------------------------------------------------------------------------------
% File     : PUZ063-1 : TPTP v9.0.0. Released v3.2.0.
% Domain   : Puzzles
% Problem  : Problem about mutilated chessboard problem
% Version  : [Pau06] axioms : Especial.
% English  :

% Refs     : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source   : [Pau06]
% Names    : Mutil__tiling_UnI_1 [Pau06]

% Status   : Unsatisfiable
% Rating   : 0.20 v8.2.0, 0.14 v8.1.0, 0.11 v7.5.0, 0.16 v7.4.0, 0.12 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.20 v6.3.0, 0.09 v6.2.0, 0.20 v6.1.0, 0.36 v6.0.0, 0.20 v5.5.0, 0.35 v5.3.0, 0.28 v5.2.0, 0.38 v5.1.0, 0.41 v5.0.0, 0.29 v4.1.0, 0.38 v4.0.1, 0.27 v4.0.0, 0.36 v3.7.0, 0.30 v3.5.0, 0.36 v3.4.0, 0.42 v3.3.0, 0.43 v3.2.0
% Syntax   : Number of clauses     : 2735 ( 651 unt; 248 nHn;1962 RR)
%            Number of literals    : 5999 (1280 equ;3075 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    8 (   1 avg)
%            Number of predicates  :   87 (  86 usr;   0 prp; 1-3 aty)
%            Number of functors    :  237 ( 237 usr;  48 con; 0-18 aty)
%            Number of variables   : 5685 (1154 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments : The problems in the [Pau06] collection each have very many axioms,
%            of which only a small selection are required for the refutation.
%            The mission is to find those few axioms, after which a refutation
%            can be quite easily found.
%------------------------------------------------------------------------------
include('Axioms/MSC001-1.ax').
include('Axioms/MSC001-0.ax').
%------------------------------------------------------------------------------
cnf(cls_Mutil_Odomino_Ohoriz_0,axiom,
    c_in(c_insert(c_Pair(V_i,V_j,tc_nat,tc_nat),c_insert(c_Pair(V_i,c_Suc(V_j),tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_Mutil_Odomino,tc_set(tc_prod(tc_nat,tc_nat))) ).

cnf(cls_Mutil_Odomino_Overtl_0,axiom,
    c_in(c_insert(c_Pair(V_i,V_j,tc_nat,tc_nat),c_insert(c_Pair(c_Suc(V_i),V_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),c_Mutil_Odomino,tc_set(tc_prod(tc_nat,tc_nat))) ).

cnf(cls_Mutil_Otiling_OUn_0,axiom,
    ( ~ c_in(V_a,V_A,tc_set(T_a))
    | ~ c_in(V_t,c_Mutil_Otiling(V_A,T_a),tc_set(T_a))
    | c_inter(V_a,V_t,T_a) != c_emptyset
    | c_in(c_union(V_a,V_t,T_a),c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) ) ).

cnf(cls_Mutil_Otiling_Oempty_0,axiom,
    c_in(c_emptyset,c_Mutil_Otiling(V_A,T_a),tc_set(T_a)) ).

cnf(cls_Set_OUn__assoc_0,axiom,
    c_union(c_union(V_A,V_B,T_a),V_C,T_a) = c_union(V_A,c_union(V_B,V_C,T_a),T_a) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_inter(c_emptyset,v_u,t_a) = c_emptyset ).

cnf(cls_conjecture_2,negated_conjecture,
    ~ c_in(c_union(c_emptyset,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ).

%------------------------------------------------------------------------------