%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ023-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 18:27:18 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 12 unt; 1 nHn; 21 RR)
% Number of literals : 34 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(12,axiom,
( ~ a_truth(liar(b))
| ~ a_truth(liar(c))
| an_answer(b_and_c_liars) ),
file('PUZ023-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ a_truth(liar(b))
| ~ a_truth(truthteller(c))
| an_answer(b_liar_and_c_truthteller) ),
file('PUZ023-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ a_truth(truthteller(b))
| ~ a_truth(liar(c))
| an_answer(b_truthteller_and_c_liar) ),
file('PUZ023-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ a_truth(truthteller(b))
| ~ a_truth(truthteller(c))
| an_answer(b_and_c_truthtellers) ),
file('PUZ023-1.p',unknown),
[] ).
cnf(16,axiom,
~ an_answer(u),
file('PUZ023-1.p',unknown),
[] ).
cnf(17,axiom,
( a_truth(liar(u))
| a_truth(truthteller(u)) ),
file('PUZ023-1.p',unknown),
[] ).
cnf(23,plain,
( ~ a_truth(truthteller(c))
| ~ a_truth(truthteller(b)) ),
inference(mrr,[status(thm)],[15,16]),
[iquote('0:MRR:15.2,16.0')] ).
cnf(24,plain,
( ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
inference(mrr,[status(thm)],[14,16]),
[iquote('0:MRR:14.2,16.0')] ).
cnf(25,plain,
( ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(mrr,[status(thm)],[13,16]),
[iquote('0:MRR:13.2,16.0')] ).
cnf(26,plain,
( ~ a_truth(liar(c))
| ~ a_truth(liar(b)) ),
inference(mrr,[status(thm)],[12,16]),
[iquote('0:MRR:12.2,16.0')] ).
cnf(57,plain,
~ a_truth(truthteller(b)),
inference(spt,[spt(split,[position(s1)])],[24]),
[iquote('1:Spt:24.1')] ).
cnf(59,plain,
a_truth(liar(b)),
inference(res,[status(thm),theory(equality)],[17,57]),
[iquote('1:Res:17.1,57.0')] ).
cnf(60,plain,
~ a_truth(truthteller(c)),
inference(mrr,[status(thm)],[25,59]),
[iquote('1:MRR:25.1,59.0')] ).
cnf(61,plain,
~ a_truth(liar(c)),
inference(mrr,[status(thm)],[26,59]),
[iquote('1:MRR:26.1,59.0')] ).
cnf(63,plain,
a_truth(liar(c)),
inference(res,[status(thm),theory(equality)],[17,60]),
[iquote('1:Res:17.1,60.0')] ).
cnf(64,plain,
$false,
inference(mrr,[status(thm)],[63,61]),
[iquote('1:MRR:63.0,61.0')] ).
cnf(65,plain,
a_truth(truthteller(b)),
inference(spt,[spt(split,[position(sa)])],[64,57]),
[iquote('1:Spt:64.0,24.1,57.0')] ).
cnf(66,plain,
~ a_truth(liar(c)),
inference(spt,[spt(split,[position(s2)])],[24]),
[iquote('1:Spt:64.0,24.0')] ).
cnf(68,plain,
~ a_truth(truthteller(c)),
inference(mrr,[status(thm)],[23,65]),
[iquote('1:MRR:23.1,65.0')] ).
cnf(69,plain,
a_truth(liar(c)),
inference(res,[status(thm),theory(equality)],[17,68]),
[iquote('1:Res:17.1,68.0')] ).
cnf(70,plain,
$false,
inference(mrr,[status(thm)],[69,66]),
[iquote('1:MRR:69.0,66.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PUZ023-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat May 28 21:36:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.40
% 0.12/0.40 SPASS V 3.9
% 0.12/0.40 SPASS beiseite: Proof found.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40 SPASS derived 15 clauses, backtracked 8 clauses, performed 4 splits and kept 41 clauses.
% 0.12/0.40 SPASS allocated 75629 KBytes.
% 0.12/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.40 0:00:00.04 for the input.
% 0.12/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.40 0:00:00.00 for inferences.
% 0.12/0.40 0:00:00.00 for the backtracking.
% 0.12/0.40 0:00:00.00 for the reduction.
% 0.12/0.40
% 0.12/0.40
% 0.12/0.40 Here is a proof with depth 2, length 21 :
% 0.12/0.40 % SZS output start Refutation
% See solution above
% 0.12/0.40 Formulae used in the proof : b_and_c_liars b_liar_and_c_truthteller b_truthteller_and_c_liar b_and_c_truthtellers prove_there_is_an_answer truthteller_or_liar
% 0.12/0.40
%------------------------------------------------------------------------------