TSTP Solution File: PUZ026-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ026-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 18:27:19 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of clauses : 60 ( 24 unt; 13 nHn; 60 RR)
% Number of literals : 111 ( 0 equ; 63 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( a_truth(normal(u))
| a_truth(not_normal(u)) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ a_truth(truthteller(u))
| ~ a_truth(truthteller(v))
| ~ people(v,u,w) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ a_truth(liar(u))
| ~ a_truth(liar(v))
| ~ people(v,w,u) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ a_truth(normal(u))
| ~ a_truth(normal(v))
| ~ people(v,u,w) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ a_truth(normal(u))
| ~ a_truth(normal(v))
| ~ people(v,w,u) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(10,axiom,
people(b,c,a),
file('PUZ026-1.p',unknown),
[] ).
cnf(11,axiom,
people(c,b,a),
file('PUZ026-1.p',unknown),
[] ).
cnf(12,axiom,
a_truth(says(a,normal(a))),
file('PUZ026-1.p',unknown),
[] ).
cnf(13,axiom,
a_truth(says(b,normal(a))),
file('PUZ026-1.p',unknown),
[] ).
cnf(14,axiom,
a_truth(says(c,not_normal(c))),
file('PUZ026-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ a_truth(truthteller(u))
| ~ a_truth(normal(v))
| ~ a_truth(liar(w)) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(16,axiom,
( a_truth(normal(u))
| a_truth(liar(u))
| a_truth(truthteller(u)) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ a_truth(normal(u))
| ~ a_truth(truthteller(u)) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ a_truth(normal(u))
| ~ a_truth(liar(u)) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ a_truth(truthteller(u))
| ~ a_truth(says(u,v))
| a_truth(v) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(21,axiom,
( ~ a_truth(u)
| ~ a_truth(liar(v))
| ~ a_truth(says(v,u)) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ a_truth(says(u,v))
| a_truth(v)
| a_truth(normal(u))
| a_truth(liar(u)) ),
file('PUZ026-1.p',unknown),
[] ).
cnf(38,plain,
~ a_truth(normal(u)),
inference(spt,[spt(split,[position(s1)])],[15]),
[iquote('1:Spt:15.1')] ).
cnf(41,plain,
( ~ a_truth(says(u,v))
| a_truth(v)
| a_truth(liar(u)) ),
inference(mrr,[status(thm)],[23,38]),
[iquote('1:MRR:23.2,38.0')] ).
cnf(44,plain,
( a_truth(normal(a))
| a_truth(liar(b)) ),
inference(res,[status(thm),theory(equality)],[13,41]),
[iquote('1:Res:13.0,41.0')] ).
cnf(45,plain,
( a_truth(normal(a))
| a_truth(liar(a)) ),
inference(res,[status(thm),theory(equality)],[12,41]),
[iquote('1:Res:12.0,41.0')] ).
cnf(47,plain,
a_truth(liar(b)),
inference(mrr,[status(thm)],[44,38]),
[iquote('1:MRR:44.0,38.0')] ).
cnf(48,plain,
a_truth(liar(a)),
inference(mrr,[status(thm)],[45,38]),
[iquote('1:MRR:45.0,38.0')] ).
cnf(49,plain,
( ~ a_truth(truthteller(b))
| a_truth(normal(a)) ),
inference(res,[status(thm),theory(equality)],[13,20]),
[iquote('0:Res:13.0,20.1')] ).
cnf(50,plain,
( ~ a_truth(truthteller(a))
| a_truth(normal(a)) ),
inference(res,[status(thm),theory(equality)],[12,20]),
[iquote('0:Res:12.0,20.1')] ).
cnf(62,plain,
( ~ a_truth(normal(a))
| ~ a_truth(liar(b)) ),
inference(res,[status(thm),theory(equality)],[13,21]),
[iquote('0:Res:13.0,21.2')] ).
cnf(63,plain,
( ~ a_truth(normal(a))
| ~ a_truth(liar(a)) ),
inference(res,[status(thm),theory(equality)],[12,21]),
[iquote('0:Res:12.0,21.2')] ).
cnf(64,plain,
( ~ a_truth(not_normal(c))
| ~ a_truth(liar(c)) ),
inference(res,[status(thm),theory(equality)],[14,21]),
[iquote('0:Res:14.0,21.2')] ).
cnf(66,plain,
( ~ a_truth(liar(a))
| ~ a_truth(liar(b)) ),
inference(res,[status(thm),theory(equality)],[10,6]),
[iquote('0:Res:10.0,6.2')] ).
cnf(68,plain,
$false,
inference(mrr,[status(thm)],[66,48,47]),
[iquote('1:MRR:66.0,66.1,48.0,47.0')] ).
cnf(69,plain,
( ~ a_truth(truthteller(u))
| ~ a_truth(liar(v)) ),
inference(spt,[spt(split,[position(s2)])],[15]),
[iquote('1:Spt:68.0,15.0,15.2')] ).
cnf(70,plain,
~ a_truth(truthteller(a)),
inference(mrr,[status(thm)],[50,17]),
[iquote('0:MRR:50.1,17.0')] ).
cnf(75,plain,
( ~ a_truth(liar(c))
| a_truth(normal(c)) ),
inference(sor,[status(thm)],[64,2]),
[iquote('0:SoR:64.0,2.1')] ).
cnf(76,plain,
~ a_truth(liar(c)),
inference(mrr,[status(thm)],[75,19]),
[iquote('0:MRR:75.1,19.0')] ).
cnf(81,plain,
( ~ a_truth(liar(b))
| a_truth(truthteller(a))
| a_truth(liar(a)) ),
inference(sor,[status(thm)],[62,16]),
[iquote('0:SoR:62.0,16.0')] ).
cnf(84,plain,
~ a_truth(liar(b)),
inference(mrr,[status(thm)],[81,70,66]),
[iquote('0:MRR:81.1,81.2,70.0,66.0')] ).
cnf(91,plain,
( ~ a_truth(truthteller(b))
| ~ a_truth(truthteller(c)) ),
inference(res,[status(thm),theory(equality)],[11,3]),
[iquote('0:Res:11.0,3.2')] ).
cnf(94,plain,
( ~ a_truth(normal(a))
| ~ a_truth(normal(c)) ),
inference(res,[status(thm),theory(equality)],[11,8]),
[iquote('0:Res:11.0,8.2')] ).
cnf(95,plain,
( ~ a_truth(normal(a))
| ~ a_truth(normal(b)) ),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.0,8.2')] ).
cnf(97,plain,
( ~ a_truth(normal(c))
| a_truth(liar(a))
| a_truth(truthteller(a)) ),
inference(res,[status(thm),theory(equality)],[16,94]),
[iquote('0:Res:16.0,94.0')] ).
cnf(99,plain,
( ~ a_truth(normal(c))
| a_truth(liar(a)) ),
inference(mrr,[status(thm)],[97,70]),
[iquote('0:MRR:97.2,70.0')] ).
cnf(100,plain,
( a_truth(liar(c))
| a_truth(truthteller(c))
| a_truth(liar(a)) ),
inference(res,[status(thm),theory(equality)],[16,99]),
[iquote('0:Res:16.0,99.0')] ).
cnf(101,plain,
( a_truth(truthteller(c))
| a_truth(liar(a)) ),
inference(mrr,[status(thm)],[100,76]),
[iquote('0:MRR:100.0,76.0')] ).
cnf(102,plain,
a_truth(truthteller(c)),
inference(spt,[spt(split,[position(s2s1)])],[101]),
[iquote('2:Spt:101.0')] ).
cnf(104,plain,
~ a_truth(truthteller(b)),
inference(mrr,[status(thm)],[91,102]),
[iquote('2:MRR:91.1,102.0')] ).
cnf(105,plain,
~ a_truth(liar(u)),
inference(res,[status(thm),theory(equality)],[102,69]),
[iquote('2:Res:102.0,69.0')] ).
cnf(106,plain,
( a_truth(normal(u))
| a_truth(truthteller(u)) ),
inference(mrr,[status(thm)],[16,105]),
[iquote('2:MRR:16.1,105.0')] ).
cnf(112,plain,
( ~ a_truth(normal(b))
| a_truth(truthteller(a)) ),
inference(res,[status(thm),theory(equality)],[106,95]),
[iquote('2:Res:106.0,95.0')] ).
cnf(113,plain,
~ a_truth(normal(b)),
inference(mrr,[status(thm)],[112,70]),
[iquote('2:MRR:112.1,70.0')] ).
cnf(120,plain,
a_truth(truthteller(b)),
inference(res,[status(thm),theory(equality)],[106,113]),
[iquote('2:Res:106.0,113.0')] ).
cnf(121,plain,
$false,
inference(mrr,[status(thm)],[120,104]),
[iquote('2:MRR:120.0,104.0')] ).
cnf(122,plain,
~ a_truth(truthteller(c)),
inference(spt,[spt(split,[position(s2sa)])],[121,102]),
[iquote('2:Spt:121.0,101.0,102.0')] ).
cnf(123,plain,
a_truth(liar(a)),
inference(spt,[spt(split,[position(s2s2)])],[101]),
[iquote('2:Spt:121.0,101.1')] ).
cnf(124,plain,
~ a_truth(normal(a)),
inference(mrr,[status(thm)],[63,123]),
[iquote('2:MRR:63.1,123.0')] ).
cnf(125,plain,
~ a_truth(truthteller(b)),
inference(mrr,[status(thm)],[49,124]),
[iquote('2:MRR:49.1,124.0')] ).
cnf(134,plain,
( ~ a_truth(normal(b))
| ~ a_truth(normal(c)) ),
inference(res,[status(thm),theory(equality)],[11,7]),
[iquote('0:Res:11.0,7.2')] ).
cnf(140,plain,
( ~ a_truth(normal(c))
| a_truth(liar(b))
| a_truth(truthteller(b)) ),
inference(res,[status(thm),theory(equality)],[16,134]),
[iquote('0:Res:16.0,134.0')] ).
cnf(141,plain,
~ a_truth(normal(c)),
inference(mrr,[status(thm)],[140,84,125]),
[iquote('2:MRR:140.1,140.2,84.0,125.0')] ).
cnf(142,plain,
( a_truth(liar(c))
| a_truth(truthteller(c)) ),
inference(res,[status(thm),theory(equality)],[16,141]),
[iquote('2:Res:16.0,141.0')] ).
cnf(143,plain,
$false,
inference(mrr,[status(thm)],[142,76,122]),
[iquote('2:MRR:142.0,142.1,76.0,122.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ026-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.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 19:53:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 85 clauses, backtracked 39 clauses, performed 2 splits and kept 94 clauses.
% 0.18/0.41 SPASS allocated 75664 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.03 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.00 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 5, length 60 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : normal_or_not_normal not_two_truthtellers1 not_two_liars2 not_two_normal1 not_two_normal2 b_c_a_are_people c_b_a_are_people a_says_a_normal b_says_a_normal c_says_c_not_normal prove_one_of_each person_is_one_type not_truthteller_and_normal not_liar_and_normal truthtellers_tell_truth liars_lie liars_and_normal_lie
% 0.18/0.41
%------------------------------------------------------------------------------