## TPTP Problem File: PUZ030-1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : PUZ030-1 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Puzzles
% Problem  : Salt and Mustard Problem
% Version  : Especial.
% English  :

% Refs     : [LO85]  Lusk & Overbeek (1985), Non-Horn Problems
%          : [Car86] Carroll (1986), Lewis Carroll's Symbolic Logic
%          : [MB88]  Manthey & Bry (1988), SATCHMO: A Theorem Prover Implem
% Source   : [LO85]
% Names    : Salt and Mustard Problem [LO85]
%          : Salt-and-Mustard Problem [MB88]

% Status   : Unsatisfiable
% Rating   : 0.00 v5.5.0, 0.20 v5.4.0, 0.00 v2.2.0, 0.25 v2.1.0, 0.00 v2.0.0
% Syntax   : Number of clauses     :   43 (   0 unt;  13 nHn;  41 RR)
%            Number of literals    :  106 (   0 equ;  55 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   5 usr;   0 prp; 1-1 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   12 (   0 sgn)
% SPC      : CNF_UNS_EPR_NEQ_NHN

%--------------------------------------------------------------------------
cnf(both1,axiom,
( ~ both(X)
| salt(X) ) ).

cnf(both2,axiom,
( ~ both(X)
| mustard(X) ) ).

cnf(both3,axiom,
( ~ salt(X)
| ~ mustard(X)
| both(X) ) ).

cnf(oneof1,axiom,
( ~ oneof(X)
| salt(X)
| mustard(X) ) ).

cnf(oneof2,axiom,
( ~ oneof(X)
| ~ both(X) ) ).

cnf(oneof3,axiom,
( ~ oneof(X)
| ~ neither(X) ) ).

cnf(one_condition_holds1,axiom,
( both(X)
| neither(X)
| oneof(X) ) ).

cnf(oneof4,axiom,
( ~ oneof(X)
| ~ salt(X)
| ~ mustard(X) ) ).

cnf(neither1,axiom,
( ~ both(X)
| ~ neither(X) ) ).

cnf(neither2,axiom,
( ~ neither(X)
| ~ salt(X) ) ).

cnf(neither3,axiom,
( ~ neither(X)
| ~ mustard(X) ) ).

cnf(neither4,axiom,
( salt(X)
| mustard(X)
| neither(X) ) ).

cnf(rule1_1,hypothesis,
( ~ salt(barry)
| oneof(cole)
| oneof(lang) ) ).

cnf(rule1_2,hypothesis,
( ~ oneof(cole)
| salt(barry) ) ).

cnf(rule1_3,hypothesis,
( ~ oneof(lang)
| salt(barry) ) ).

cnf(rule2_1,hypothesis,
( ~ mustard(barry)
| neither(dix)
| both(mill) ) ).

cnf(rule2_2,hypothesis,
( ~ neither(dix)
| mustard(barry) ) ).

cnf(rule2_3,hypothesis,
( ~ both(mill)
| mustard(barry) ) ).

cnf(rule3_1,hypothesis,
( ~ salt(cole)
| oneof(barry)
| neither(mill) ) ).

cnf(rule3_2,hypothesis,
( ~ oneof(barry)
| salt(cole) ) ).

cnf(rule3_3,hypothesis,
( ~ neither(mill)
| salt(cole) ) ).

cnf(rule4_1,hypothesis,
( ~ mustard(cole)
| both(dix)
| both(lang) ) ).

cnf(rule4_2,hypothesis,
( ~ both(dix)
| mustard(cole) ) ).

cnf(rule4_3,hypothesis,
( ~ both(lang)
| mustard(cole) ) ).

cnf(rule5_1,hypothesis,
( ~ salt(dix)
| neither(barry)
| both(cole) ) ).

cnf(rule5_2,hypothesis,
( ~ neither(barry)
| salt(dix) ) ).

cnf(rule5_3,hypothesis,
( ~ both(cole)
| salt(dix) ) ).

cnf(rule6_1,hypothesis,
( ~ mustard(dix)
| neither(lang)
| neither(mill) ) ).

cnf(rule6_2,hypothesis,
( ~ neither(lang)
| mustard(dix) ) ).

cnf(rule6_3,hypothesis,
( ~ neither(mill)
| mustard(dix) ) ).

cnf(rule7_1,hypothesis,
( ~ salt(lang)
| oneof(barry)
| oneof(dix) ) ).

cnf(rule7_2,hypothesis,
( ~ oneof(barry)
| salt(lang) ) ).

cnf(rule7_3,hypothesis,
( ~ oneof(dix)
| salt(lang) ) ).

cnf(rule8_1,hypothesis,
( ~ mustard(lang)
| neither(cole)
| neither(mill) ) ).

cnf(rule8_2,hypothesis,
( ~ neither(cole)
| mustard(lang) ) ).

cnf(rule8_3,hypothesis,
( ~ neither(mill)
| mustard(lang) ) ).

cnf(rule9_1,hypothesis,
( ~ salt(mill)
| both(barry)
| both(lang) ) ).

cnf(rule9_2,hypothesis,
( ~ both(barry)
| salt(mill) ) ).

cnf(rule9_3,hypothesis,
( ~ both(lang)
| mustard(mill) ) ).

cnf(rule10_1,hypothesis,
( ~ mustard(mill)
| oneof(cole)
| oneof(dix) ) ).

cnf(rule10_2,hypothesis,
( ~ oneof(cole)
| mustard(mill) ) ).

cnf(rule10_3,hypothesis,
( ~ oneof(dix)
| mustard(mill) ) ).

cnf(prove_who_takes_what,negated_conjecture,
( ~ neither(cole)
| ~ neither(dix)
| ~ both(barry)
| ~ oneof(lang)
| ~ salt(mill)
| ~ mustard(lang)
| ~ oneof(mill) ) ).

%--------------------------------------------------------------------------
```