## TPTP Problem File: SYN003-1.006.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SYN003-1.006 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Syntactic
% Problem  : Implications that form a contradiction
% Version  : Biased.
% English  : P1 & Q1 -> P2     P1 & R1 -> P2     Q -> Q1     R -> R1   :
%            P2 & Q2 -> P3     P2 & R2 -> P3     Q -> Q2     R -> R2   :
%              ......           ......        ....      ....           :
%            Pk-1 & Qk-1 ->Pk  Pk-1 & Rk-1 -> Pk Q -> Qk-1   R -> Rk-1 :
%            P1                ~Pk               Q           R         :
%          : The size is k, in the above.

% Refs     : [Pla82] Plaisted (1982), A Simplified Problem Reduction Format
% Source   : [Pla82]
% Names    : Problem 5.2 [Pla82]

% Status   : Unsatisfiable
% Rating   : 0.00 v2.1.0
% Syntax   : Number of clauses     :   24 (   4 unt;   0 nHn;  24 RR)
%            Number of literals    :   54 (   0 equ;  31 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of predicates  :   18 (  18 usr;  18 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0 sgn)
% SPC      : CNF_UNS_PRP

% Comments : "This set of clauses can cause the following strategies to
%            generate a search space which is exponential in k: All-negative
%            resolution, set-of-support with ~Pk as the support set, input
%            resolution, SL-resolution, locking resolution with a bad choice
%            of indices, and ancestor-filter form (linear resolution)."
%            [Pla82] p.243.
%          : tptp2X: -f tptp -s6 SYN003-1.g
%--------------------------------------------------------------------------
cnf(pqp_1,negated_conjecture,
( ~ p_1
| ~ q_1
| p_2 ) ).

cnf(pqp_2,negated_conjecture,
( ~ p_2
| ~ q_2
| p_3 ) ).

cnf(pqp_3,negated_conjecture,
( ~ p_3
| ~ q_3
| p_4 ) ).

cnf(pqp_4,negated_conjecture,
( ~ p_4
| ~ q_4
| p_5 ) ).

cnf(pqp_5,negated_conjecture,
( ~ p_5
| ~ q_5
| p_6 ) ).

cnf(prp_1,negated_conjecture,
( ~ p_1
| ~ r_1
| p_2 ) ).

cnf(prp_2,negated_conjecture,
( ~ p_2
| ~ r_2
| p_3 ) ).

cnf(prp_3,negated_conjecture,
( ~ p_3
| ~ r_3
| p_4 ) ).

cnf(prp_4,negated_conjecture,
( ~ p_4
| ~ r_4
| p_5 ) ).

cnf(prp_5,negated_conjecture,
( ~ p_5
| ~ r_5
| p_6 ) ).

cnf(qq_1,negated_conjecture,
( ~ q
| q_1 ) ).

cnf(qq_2,negated_conjecture,
( ~ q
| q_2 ) ).

cnf(qq_3,negated_conjecture,
( ~ q
| q_3 ) ).

cnf(qq_4,negated_conjecture,
( ~ q
| q_4 ) ).

cnf(qq_5,negated_conjecture,
( ~ q
| q_5 ) ).

cnf(rr_1,negated_conjecture,
( ~ r
| r_1 ) ).

cnf(rr_2,negated_conjecture,
( ~ r
| r_2 ) ).

cnf(rr_3,negated_conjecture,
( ~ r
| r_3 ) ).

cnf(rr_4,negated_conjecture,
( ~ r
| r_4 ) ).

cnf(rr_5,negated_conjecture,
( ~ r
| r_5 ) ).

cnf(base_1,negated_conjecture,
p_1 ).

cnf(base_2,negated_conjecture,
~ p_6 ).

cnf(base_3,negated_conjecture,
q ).

cnf(base_4,negated_conjecture,
r ).

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