TPTP Problem File: COL109-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : COL109-1 : 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_parcontract_easy_10 [Pau06]
% Status : Unsatisfiable
% Rating : 0.45 v8.2.0, 0.43 v8.1.0, 0.47 v7.4.0, 0.53 v7.3.0, 0.58 v7.0.0, 0.60 v6.4.0, 0.53 v6.3.0, 0.55 v6.2.0, 0.50 v6.1.0, 0.57 v6.0.0, 0.60 v5.5.0, 0.80 v5.3.0, 0.83 v5.2.0, 0.75 v5.1.0, 0.76 v5.0.0, 0.71 v4.1.0, 0.77 v4.0.1, 0.73 v3.7.0, 0.60 v3.5.0, 0.64 v3.4.0, 0.75 v3.3.0, 0.93 v3.2.0
% Syntax : Number of clauses : 1411 ( 233 unt; 42 nHn;1316 RR)
% Number of literals : 2694 ( 253 equ;1263 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 82 ( 81 usr; 0 prp; 1-3 aty)
% Number of functors : 148 ( 148 usr; 29 con; 0-6 aty)
% Number of variables : 2024 ( 227 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/COL002-1.ax').
include('Axioms/COL002-0.ax').
include('Axioms/MSC001-2.ax').
include('Axioms/MSC001-0.ax').
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(c_Pair(v_z,v_w,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(c_Pair(v_xb,v_x_H,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(c_Pair(v_yb,v_y_Ha,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(v_xb,v_z),c_Comb_Ocomb_Oop_A_D_D(v_yb,v_z)),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_x_H),v_y_Ha),v_w),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_x_H),v_y_Ha),v_xc(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_xb),v_yb),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_in(c_Pair(V_U,v_xc(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_xb),v_yb),V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_in(c_Pair(v_w,v_xaa(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_z,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ) ).
cnf(cls_conjecture_7,negated_conjecture,
( c_in(c_Pair(V_U,v_xaa(V_U),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_z,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ) ).
%------------------------------------------------------------------------------