TPTP Problem File: COM010-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : COM010-1 : TPTP v9.0.0. Released v3.2.0.
% Domain : Computing Theory
% Problem : Problem about UNITY theory
% Version : [Pau06] axioms : Especial.
% English :
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names : UNITY__program_equalityI [Pau06]
% Status : Unsatisfiable
% Rating : 0.25 v9.0.0, 0.20 v8.2.0, 0.19 v8.1.0, 0.16 v7.5.0, 0.37 v7.4.0, 0.35 v7.3.0, 0.25 v7.1.0, 0.17 v7.0.0, 0.40 v6.3.0, 0.27 v6.2.0, 0.50 v6.1.0, 0.64 v6.0.0, 0.60 v5.5.0, 0.75 v5.3.0, 0.78 v5.2.0, 0.75 v5.1.0, 0.82 v5.0.0, 0.79 v4.1.0, 0.77 v4.0.1, 0.82 v3.7.0, 0.70 v3.5.0, 0.73 v3.4.0, 0.75 v3.3.0, 0.71 v3.2.0
% Syntax : Number of clauses : 2740 ( 657 unt; 248 nHn;1963 RR)
% Number of literals : 6001 (1288 equ;3073 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 : 239 ( 239 usr; 47 con; 0-18 aty)
% Number of variables : 5695 (1163 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_UNITY_OActs__eq_0,axiom,
c_UNITY_OActs(c_UNITY_Omk__program(c_Pair(V_init,c_Pair(V_acts,V_allowed,tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a),T_a) = c_insert(c_Relation_OId,V_acts,tc_set(tc_prod(T_a,T_a))) ).
cnf(cls_UNITY_OActs__nonempty_0,axiom,
c_UNITY_OActs(V_F,T_a) != c_emptyset ).
cnf(cls_UNITY_OAllowedActs__eq_0,axiom,
c_UNITY_OAllowedActs(c_UNITY_Omk__program(c_Pair(V_init,c_Pair(V_acts,V_allowed,tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a),T_a) = c_insert(c_Relation_OId,V_allowed,tc_set(tc_prod(T_a,T_a))) ).
cnf(cls_UNITY_OId__in__Acts_0,axiom,
c_in(c_Relation_OId,c_UNITY_OActs(V_F,T_a),tc_set(tc_prod(T_a,T_a))) ).
cnf(cls_UNITY_OId__in__AllowedActs_0,axiom,
c_in(c_Relation_OId,c_UNITY_OAllowedActs(V_F,T_a),tc_set(tc_prod(T_a,T_a))) ).
cnf(cls_UNITY_OInit__eq_0,axiom,
c_UNITY_OInit(c_UNITY_Omk__program(c_Pair(V_y,c_Pair(V_acts,V_allowed,tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a),T_a) = V_y ).
cnf(cls_UNITY_Oinsert__Id__Acts_0,axiom,
c_insert(c_Relation_OId,c_UNITY_OActs(V_F,T_a),tc_set(tc_prod(T_a,T_a))) = c_UNITY_OActs(V_F,T_a) ).
cnf(cls_UNITY_Oinsert__Id__AllowedActs_0,axiom,
c_insert(c_Relation_OId,c_UNITY_OAllowedActs(V_F,T_a),tc_set(tc_prod(T_a,T_a))) = c_UNITY_OAllowedActs(V_F,T_a) ).
cnf(cls_UNITY_Osurjective__mk__program_0,axiom,
c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(V_y,T_a),c_Pair(c_UNITY_OActs(V_y,T_a),c_UNITY_OAllowedActs(V_y,T_a),tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a)))),tc_set(T_a),tc_prod(tc_set(tc_set(tc_prod(T_a,T_a))),tc_set(tc_set(tc_prod(T_a,T_a))))),T_a) = V_y ).
cnf(cls_conjecture_0,negated_conjecture,
c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a) ).
cnf(cls_conjecture_1,negated_conjecture,
c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a) ).
cnf(cls_conjecture_2,negated_conjecture,
c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a) ).
cnf(cls_conjecture_3,negated_conjecture,
v_F != v_G ).
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