TPTP Problem File: COL120-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : COL120-1 : TPTP v8.2.0. Released v3.2.0.
% Domain : Combinatory Logic
% Problem : Problem about combinators
% Version : [Pau06] axioms : Especial.
% English :
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names : Comb__diamond_rtrancl_1 [Pau06]
% Status : Unsatisfiable
% Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.25 v5.3.0, 0.22 v5.2.0, 0.19 v5.1.0, 0.29 v4.1.0, 0.23 v4.0.1, 0.36 v4.0.0, 0.18 v3.7.0, 0.20 v3.5.0, 0.18 v3.4.0, 0.25 v3.3.0, 0.36 v3.2.0
% Syntax : Number of clauses : 1371 ( 224 unt; 28 nHn;1285 RR)
% Number of literals : 2585 ( 203 equ;1233 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 83 ( 82 usr; 0 prp; 1-3 aty)
% Number of functors : 128 ( 128 usr; 23 con; 0-6 aty)
% Number of variables : 1940 ( 222 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/MSC001-2.ax').
include('Axioms/MSC001-0.ax').
%------------------------------------------------------------------------------
cnf(cls_Comb_Ocomb_Odistinct__1__iff1_0,axiom,
c_Comb_Ocomb_OK != c_Comb_Ocomb_OS ).
cnf(cls_Comb_Ocomb_Odistinct__2__iff1_0,axiom,
c_Comb_Ocomb_OS != c_Comb_Ocomb_OK ).
cnf(cls_Comb_Ocomb_Odistinct__3__iff1_0,axiom,
c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(V_comb1_H,V_comb2_H) ).
cnf(cls_Comb_Ocomb_Odistinct__4__iff1_0,axiom,
c_Comb_Ocomb_Oop_A_D_D(V_comb1_H,V_comb2_H) != c_Comb_Ocomb_OK ).
cnf(cls_Comb_Ocomb_Odistinct__5__iff1_0,axiom,
c_Comb_Ocomb_OS != c_Comb_Ocomb_Oop_A_D_D(V_comb1_H,V_comb2_H) ).
cnf(cls_Comb_Ocomb_Odistinct__6__iff1_0,axiom,
c_Comb_Ocomb_Oop_A_D_D(V_comb1_H,V_comb2_H) != c_Comb_Ocomb_OS ).
cnf(cls_Comb_Ocomb_Oinject__iff1_0,axiom,
( c_Comb_Ocomb_Oop_A_D_D(V_comb1,V_comb2) != c_Comb_Ocomb_Oop_A_D_D(V_comb1_H,V_comb2_H)
| V_comb1 = V_comb1_H ) ).
cnf(cls_Comb_Ocomb_Oinject__iff1_1,axiom,
( c_Comb_Ocomb_Oop_A_D_D(V_comb1,V_comb2) != c_Comb_Ocomb_Oop_A_D_D(V_comb1_H,V_comb2_H)
| V_comb2 = V_comb2_H ) ).
cnf(cls_Comb_Odiamond__strip__lemmaE_0,axiom,
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y_H,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_Comb_Odiamond__strip__lemmaE_1,axiom,
( ~ c_Comb_Odiamond(V_r,T_a)
| ~ c_in(c_Pair(V_x,V_y_H,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,c_Comb_Odiamond__strip__lemmaE__1(V_r,V_y,V_y_H,T_a),T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_Transitive__Closure_Ortrancl__trans_0,axiom,
( ~ c_in(c_Pair(V_b,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a))
| c_in(c_Pair(V_a,V_c,T_a,T_a),c_Transitive__Closure_Ortrancl(V_r,T_a),tc_prod(T_a,T_a)) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Comb_Odiamond(v_r,t_a) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(c_Pair(v_y,v_x,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ c_in(c_Pair(v_x,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_y,V_U,t_a,t_a),c_Transitive__Closure_Ortrancl(v_r,t_a),tc_prod(t_a,t_a)) ) ).
%------------------------------------------------------------------------------