%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ032-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 18:27:20 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 16 ( 9 unt; 3 nHn; 16 RR)
% Number of literals : 25 ( 0 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
a_truth(says(b,says(a,liar(a)))),
file('PUZ032-1.p',unknown),
[] ).
cnf(3,axiom,
a_truth(says(c,liar(b))),
file('PUZ032-1.p',unknown),
[] ).
cnf(4,axiom,
~ a_truth(truthteller(c)),
file('PUZ032-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ a_truth(liar(u))
| ~ a_truth(truthteller(u)) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ a_truth(u)
| ~ a_truth(says(v,u))
| a_truth(truthteller(v)) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ a_truth(says(u,v))
| a_truth(v)
| a_truth(liar(u)) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(12,plain,
( ~ a_truth(u)
| ~ a_truth(says(c,u)) ),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.2,4.0')] ).
cnf(27,plain,
~ a_truth(liar(b)),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.0,12.1')] ).
cnf(31,plain,
( a_truth(says(a,liar(a)))
| a_truth(liar(b)) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(32,plain,
a_truth(says(a,liar(a))),
inference(mrr,[status(thm)],[31,27]),
[iquote('0:MRR:31.1,27.0')] ).
cnf(34,plain,
( a_truth(liar(a))
| a_truth(liar(a)) ),
inference(res,[status(thm),theory(equality)],[32,10]),
[iquote('0:Res:32.0,10.0')] ).
cnf(35,plain,
a_truth(liar(a)),
inference(obv,[status(thm),theory(equality)],[34]),
[iquote('0:Obv:34.0')] ).
cnf(36,plain,
~ a_truth(truthteller(a)),
inference(res,[status(thm),theory(equality)],[35,6]),
[iquote('0:Res:35.0,6.0')] ).
cnf(38,plain,
( ~ a_truth(liar(a))
| a_truth(truthteller(a)) ),
inference(res,[status(thm),theory(equality)],[32,9]),
[iquote('0:Res:32.0,9.1')] ).
cnf(42,plain,
a_truth(truthteller(a)),
inference(ssi,[status(thm)],[38,35]),
[iquote('0:SSi:38.0,35.0')] ).
cnf(43,plain,
$false,
inference(mrr,[status(thm)],[42,36]),
[iquote('0:MRR:42.0,36.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ032-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat May 28 19:47:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 16 clauses, backtracked 0 clauses, performed 0 splits and kept 21 clauses.
% 0.20/0.41 SPASS allocated 75612 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.04 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 3, length 16 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : b_says_a_says_hes_a_liar c_says_b_is_a_liar prove_c_is_a_truthteller not_both truths_are_told_by_truthtellers liars_are_told_by_liars
% 0.20/0.41
%------------------------------------------------------------------------------