TPTP Problem File: SYN003-1.006.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : SYN003-1.006 : TPTP v9.0.0. 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
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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 ).
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