TPTP Problem File: PUZ064-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : PUZ064-2 : TPTP v8.2.0. Released v3.2.0.
% Domain : Puzzles
% Problem : Problem about mutilated chessboard problem
% Version : [Pau06] axioms : Reduced > Especial.
% English :
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names :
% Status : Unsatisfiable
% Rating : 0.35 v8.2.0, 0.33 v8.1.0, 0.32 v7.5.0, 0.47 v7.3.0, 0.42 v7.1.0, 0.33 v7.0.0, 0.47 v6.4.0, 0.53 v6.3.0, 0.45 v6.2.0, 0.50 v6.1.0, 0.57 v6.0.0, 0.60 v5.5.0, 0.75 v5.3.0, 0.78 v5.2.0, 0.69 v5.1.0, 0.76 v5.0.0, 0.71 v4.1.0, 0.77 v4.0.1, 0.73 v3.7.0, 0.50 v3.5.0, 0.55 v3.4.0, 0.67 v3.3.0, 0.64 v3.2.0
% Syntax : Number of clauses : 29 ( 21 unt; 1 nHn; 13 RR)
% Number of literals : 42 ( 18 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 64 ( 15 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. This version has only the necessary
% axioms.
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_a,v_A,tc_set(t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
c_inter(v_a,v_t,t_a) = c_emptyset ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ).
cnf(cls_conjecture_4,negated_conjecture,
c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a))
| c_inter(v_t,v_u,t_a) != c_emptyset
| ~ c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) ) ).
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_Relation_OImage__diag_0,axiom,
c_Relation_OImage(c_Relation_Odiag(V_A,T_a),V_B,T_a,T_a) = c_inter(V_A,V_B,T_a) ).
cnf(cls_Set_OCompl__Diff__eq_0,axiom,
c_uminus(c_minus(V_A,V_B,tc_set(T_a)),tc_set(T_a)) = c_union(c_uminus(V_A,tc_set(T_a)),V_B,T_a) ).
cnf(cls_Set_OCompl__UNIV__eq_0,axiom,
c_uminus(c_UNIV,tc_set(T_a)) = c_emptyset ).
cnf(cls_Set_ODiff__Compl_0,axiom,
c_minus(V_A,c_uminus(V_B,tc_set(T_a)),tc_set(T_a)) = c_inter(V_A,V_B,T_a) ).
cnf(cls_Set_OInt__UNIV__left_0,axiom,
c_inter(c_UNIV,V_y,T_a) = V_y ).
cnf(cls_Set_OInt__iff_1,axiom,
( ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| c_in(V_c,V_B,T_a) ) ).
cnf(cls_Set_OUn__Diff__cancel2_0,axiom,
c_union(c_minus(V_B,V_A,tc_set(T_a)),V_A,T_a) = c_union(V_B,V_A,T_a) ).
cnf(cls_Set_OUn__Diff__cancel_0,axiom,
c_union(V_A,c_minus(V_B,V_A,tc_set(T_a)),T_a) = c_union(V_A,V_B,T_a) ).
cnf(cls_Set_OUn__UNIV__left_0,axiom,
c_union(c_UNIV,V_B,T_a) = c_UNIV ).
cnf(cls_Set_OUn__absorb_0,axiom,
c_union(V_y,V_y,T_a) = V_y ).
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_Set_OUn__empty__left_0,axiom,
c_union(c_emptyset,V_y,T_a) = V_y ).
cnf(cls_Set_OUn__empty__right_0,axiom,
c_union(V_y,c_emptyset,T_a) = V_y ).
cnf(cls_Set_OUn__subset__iff_0,axiom,
( ~ c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| c_lessequals(V_A,V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUn__subset__iff_1,axiom,
( ~ c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a))
| c_lessequals(V_B,V_C,tc_set(T_a)) ) ).
cnf(cls_Set_OUn__subset__iff_2,axiom,
( ~ c_lessequals(V_B,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_C,tc_set(T_a))
| c_lessequals(c_union(V_A,V_B,T_a),V_C,tc_set(T_a)) ) ).
cnf(cls_Set_Odouble__complement_0,axiom,
c_uminus(c_uminus(V_y,tc_set(T_a)),tc_set(T_a)) = V_y ).
cnf(cls_Set_Oempty__iff_0,axiom,
~ c_in(V_c,c_emptyset,T_a) ).
cnf(cls_Set_Oempty__subsetI_0,axiom,
c_lessequals(c_emptyset,V_A,tc_set(T_a)) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| V_A = V_B ) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)) ).
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