TSTP Solution File: PUZ008-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PUZ008-3 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 18:27:12 EDT 2022
% Result : Unsatisfiable 0.39s 0.55s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of clauses : 48 ( 7 unt; 0 nHn; 48 RR)
% Number of literals : 208 ( 0 equ; 182 neg)
% Maximal clause size : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
safe(n0,u),
file('PUZ008-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ greater_or_equal(u,v)
| safe(u,v) ),
file('PUZ008-3.p',unknown),
[] ).
cnf(3,axiom,
greater_or_equal(u,n0),
file('PUZ008-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ greater_or_equal(u,v)
| greater_or_equal(s(u),s(v)) ),
file('PUZ008-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ safe(u,v)
| ~ safe(w,s(x))
| ~ achievable(west(m(w),c(x)),boatoneast,east(m(u),c(s(v))))
| achievable(west(m(w),c(s(x))),boatonwest,east(m(u),c(v))) ),
file('PUZ008-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ safe(u,v)
| ~ safe(w,s(s(x)))
| ~ achievable(west(m(u),c(s(s(v)))),boatonwest,east(m(w),c(x)))
| achievable(west(m(u),c(v)),boatoneast,east(m(w),c(s(s(x))))) ),
file('PUZ008-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ safe(u,v)
| ~ safe(s(s(w)),x)
| ~ achievable(west(m(s(s(u))),c(v)),boatonwest,east(m(w),c(x)))
| achievable(west(m(u),c(v)),boatoneast,east(m(s(s(w))),c(x))) ),
file('PUZ008-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ safe(u,v)
| ~ safe(s(w),s(x))
| ~ achievable(west(m(w),c(x)),boatoneast,east(m(s(u)),c(s(v))))
| achievable(west(m(s(w)),c(s(x))),boatonwest,east(m(u),c(v))) ),
file('PUZ008-3.p',unknown),
[] ).
cnf(15,axiom,
achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))),
file('PUZ008-3.p',unknown),
[] ).
cnf(16,axiom,
~ achievable(west(m(n0),c(n0)),u,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
file('PUZ008-3.p',unknown),
[] ).
cnf(18,plain,
( ~ achievable(west(m(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(s(n0))))
| ~ safe(n0,n0)
| ~ safe(s(s(s(n0))),s(s(s(n0)))) ),
inference(res,[status(thm),theory(equality)],[7,16]),
[iquote('0:Res:7.3,16.0')] ).
cnf(25,plain,
( ~ safe(s(s(s(n0))),s(s(s(n0))))
| ~ achievable(west(m(n0),c(s(s(n0)))),boatonwest,east(m(s(s(s(n0)))),c(s(n0)))) ),
inference(mrr,[status(thm)],[18,1]),
[iquote('0:MRR:18.1,1.0')] ).
cnf(32,plain,
( ~ safe(s(s(s(n0))),s(n0))
| ~ safe(n0,s(s(n0)))
| ~ achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0)))))
| ~ safe(s(s(s(n0))),s(s(s(n0)))) ),
inference(res,[status(thm),theory(equality)],[6,25]),
[iquote('0:Res:6.3,25.1')] ).
cnf(33,plain,
( ~ safe(s(s(s(n0))),s(n0))
| ~ achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0)))))
| ~ safe(s(s(s(n0))),s(s(s(n0)))) ),
inference(mrr,[status(thm)],[32,1]),
[iquote('0:MRR:32.1,1.0')] ).
cnf(53,plain,
( ~ safe(u,v)
| ~ safe(s(s(w)),s(x))
| ~ achievable(west(m(s(w)),c(x)),boatoneast,east(m(s(u)),c(s(v))))
| ~ safe(w,s(x))
| ~ safe(s(s(u)),v)
| achievable(west(m(w),c(s(x))),boatoneast,east(m(s(s(u))),c(v))) ),
inference(res,[status(thm),theory(equality)],[14,11]),
[iquote('0:Res:14.3,11.2')] ).
cnf(54,plain,
( ~ safe(u,v)
| ~ safe(s(s(w)),s(x))
| ~ achievable(west(m(s(s(w))),c(x)),boatoneast,east(m(u),c(s(v))))
| ~ safe(w,s(x))
| ~ safe(s(s(u)),v)
| achievable(west(m(w),c(s(x))),boatoneast,east(m(s(s(u))),c(v))) ),
inference(res,[status(thm),theory(equality)],[6,11]),
[iquote('0:Res:6.3,11.2')] ).
cnf(62,plain,
( ~ safe(s(s(s(n0))),s(n0))
| ~ safe(n0,s(s(n0)))
| achievable(west(m(s(s(s(n0)))),c(s(n0))),boatoneast,east(m(n0),c(s(s(n0))))) ),
inference(res,[status(thm),theory(equality)],[15,7]),
[iquote('0:Res:15.0,7.2')] ).
cnf(66,plain,
( ~ safe(u,v)
| ~ safe(w,s(s(x)))
| ~ achievable(west(m(w),c(s(x))),boatoneast,east(m(u),c(s(v))))
| ~ safe(w,x)
| ~ safe(u,s(s(v)))
| achievable(west(m(w),c(x)),boatoneast,east(m(u),c(s(s(v))))) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.3,7.2')] ).
cnf(68,plain,
( ~ safe(s(s(s(n0))),s(n0))
| achievable(west(m(s(s(s(n0)))),c(s(n0))),boatoneast,east(m(n0),c(s(s(n0))))) ),
inference(mrr,[status(thm)],[62,1]),
[iquote('0:MRR:62.1,1.0')] ).
cnf(139,plain,
( ~ safe(s(s(s(n0))),s(n0))
| ~ safe(n0,s(n0))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(n0,s(s(s(n0))))
| achievable(west(m(s(s(s(n0)))),c(n0)),boatoneast,east(m(n0),c(s(s(s(n0)))))) ),
inference(res,[status(thm),theory(equality)],[68,66]),
[iquote('0:Res:68.1,66.2')] ).
cnf(144,plain,
( ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| achievable(west(m(s(s(s(n0)))),c(n0)),boatoneast,east(m(n0),c(s(s(s(n0)))))) ),
inference(mrr,[status(thm)],[139,1]),
[iquote('0:MRR:139.1,139.4,1.0,1.0')] ).
cnf(178,plain,
( ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(n0,s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(res,[status(thm),theory(equality)],[144,54]),
[iquote('0:Res:144.3,54.2')] ).
cnf(184,plain,
( ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(n0,s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(obv,[status(thm),theory(equality)],[178]),
[iquote('0:Obv:178.0')] ).
cnf(185,plain,
( ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0))))) ),
inference(mrr,[status(thm)],[184,1]),
[iquote('0:MRR:184.2,1.0')] ).
cnf(410,plain,
( ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(n0,s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))) ),
inference(res,[status(thm),theory(equality)],[185,53]),
[iquote('0:Res:185.5,53.2')] ).
cnf(411,plain,
( ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(n0,s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))) ),
inference(obv,[status(thm),theory(equality)],[410]),
[iquote('0:Obv:410.4')] ).
cnf(412,plain,
( ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))) ),
inference(mrr,[status(thm)],[411,1]),
[iquote('0:MRR:411.4,1.0')] ).
cnf(436,plain,
( ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(n0,s(s(s(n0))))
| ~ safe(n0,s(n0))
| ~ safe(s(s(s(n0))),s(s(n0)))
| achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))) ),
inference(res,[status(thm),theory(equality)],[412,66]),
[iquote('0:Res:412.5,66.2')] ).
cnf(437,plain,
( ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(n0,s(s(s(n0))))
| ~ safe(n0,s(n0))
| ~ safe(s(s(s(n0))),s(s(n0)))
| achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))) ),
inference(obv,[status(thm),theory(equality)],[436]),
[iquote('0:Obv:436.1')] ).
cnf(438,plain,
( ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(s(n0)))
| achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))) ),
inference(mrr,[status(thm)],[437,1]),
[iquote('0:MRR:437.4,437.5,1.0,1.0')] ).
cnf(442,plain,
( ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),s(s(s(n0)))) ),
inference(res,[status(thm),theory(equality)],[438,33]),
[iquote('0:Res:438.5,33.1')] ).
cnf(444,plain,
( ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0))
| ~ safe(s(s(s(n0))),s(s(s(n0)))) ),
inference(obv,[status(thm),theory(equality)],[442]),
[iquote('0:Obv:442.2')] ).
cnf(448,plain,
( ~ greater_or_equal(s(s(s(n0))),s(s(s(n0))))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(res,[status(thm),theory(equality)],[2,444]),
[iquote('0:Res:2.1,444.5')] ).
cnf(449,plain,
( ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(n0)),s(s(n0)))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(res,[status(thm),theory(equality)],[4,448]),
[iquote('0:Res:4.1,448.0')] ).
cnf(450,plain,
( ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(s(n0)))
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(mrr,[status(thm)],[449,2]),
[iquote('0:MRR:449.2,2.1')] ).
cnf(468,plain,
( ~ greater_or_equal(s(s(s(n0))),s(s(n0)))
| ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(res,[status(thm),theory(equality)],[2,450]),
[iquote('0:Res:2.1,450.3')] ).
cnf(469,plain,
( ~ greater_or_equal(s(s(n0)),s(n0))
| ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(s(n0))),n0)
| ~ safe(s(s(s(n0))),s(n0)) ),
inference(res,[status(thm),theory(equality)],[4,468]),
[iquote('0:Res:4.1,468.0')] ).
cnf(470,plain,
( ~ greater_or_equal(s(s(s(n0))),s(n0))
| ~ greater_or_equal(s(s(n0)),s(n0))
| ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(s(n0))),n0) ),
inference(res,[status(thm),theory(equality)],[2,469]),
[iquote('0:Res:2.1,469.4')] ).
cnf(471,plain,
( ~ greater_or_equal(s(s(n0)),n0)
| ~ greater_or_equal(s(s(n0)),s(n0))
| ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(s(n0))),n0) ),
inference(res,[status(thm),theory(equality)],[4,470]),
[iquote('0:Res:4.1,470.0')] ).
cnf(472,plain,
( ~ greater_or_equal(s(s(n0)),s(n0))
| ~ greater_or_equal(s(s(n0)),s(s(n0)))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(s(n0))),n0) ),
inference(mrr,[status(thm)],[471,3]),
[iquote('0:MRR:471.0,3.0')] ).
cnf(485,plain,
( ~ greater_or_equal(s(n0),s(n0))
| ~ greater_or_equal(s(s(n0)),s(n0))
| ~ safe(s(n0),s(n0))
| ~ safe(s(s(s(n0))),n0) ),
inference(res,[status(thm),theory(equality)],[4,472]),
[iquote('0:Res:4.1,472.1')] ).
cnf(486,plain,
( ~ greater_or_equal(s(n0),s(n0))
| ~ greater_or_equal(s(s(n0)),s(n0))
| ~ safe(s(s(s(n0))),n0) ),
inference(mrr,[status(thm)],[485,2]),
[iquote('0:MRR:485.2,2.1')] ).
cnf(487,plain,
( ~ greater_or_equal(s(s(s(n0))),n0)
| ~ greater_or_equal(s(n0),s(n0))
| ~ greater_or_equal(s(s(n0)),s(n0)) ),
inference(res,[status(thm),theory(equality)],[2,486]),
[iquote('0:Res:2.1,486.2')] ).
cnf(488,plain,
( ~ greater_or_equal(s(n0),s(n0))
| ~ greater_or_equal(s(s(n0)),s(n0)) ),
inference(mrr,[status(thm)],[487,3]),
[iquote('0:MRR:487.0,3.0')] ).
cnf(489,plain,
( ~ greater_or_equal(s(n0),n0)
| ~ greater_or_equal(s(n0),s(n0)) ),
inference(res,[status(thm),theory(equality)],[4,488]),
[iquote('0:Res:4.1,488.1')] ).
cnf(490,plain,
~ greater_or_equal(s(n0),s(n0)),
inference(mrr,[status(thm)],[489,3]),
[iquote('0:MRR:489.0,3.0')] ).
cnf(491,plain,
~ greater_or_equal(n0,n0),
inference(res,[status(thm),theory(equality)],[4,490]),
[iquote('0:Res:4.1,490.0')] ).
cnf(492,plain,
$false,
inference(mrr,[status(thm)],[491,3]),
[iquote('0:MRR:491.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : PUZ008-3 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 01:14:26 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.39/0.55
% 0.39/0.55 SPASS V 3.9
% 0.39/0.55 SPASS beiseite: Proof found.
% 0.39/0.55 % SZS status Theorem
% 0.39/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.55 SPASS derived 323 clauses, backtracked 0 clauses, performed 0 splits and kept 144 clauses.
% 0.39/0.55 SPASS allocated 63872 KBytes.
% 0.39/0.55 SPASS spent 0:00:00.21 on the problem.
% 0.39/0.55 0:00:00.04 for the input.
% 0.39/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.39/0.55 0:00:00.02 for inferences.
% 0.39/0.55 0:00:00.00 for the backtracking.
% 0.39/0.55 0:00:00.14 for the reduction.
% 0.39/0.55
% 0.39/0.55
% 0.39/0.55 Here is a proof with depth 16, length 48 :
% 0.39/0.55 % SZS output start Refutation
% See solution above
% 0.39/0.55 Formulae used in the proof : no_missionaries_is_safe same_or_more_missionaries_is_safe great_eq_base great_eq_recursive cannibal_east_to_west two_cannibals_west_to_east two_missionaries_west_to_east missionary_and_cannibal_east_to_west start_on_west_bank prove_can_get_to_east_bank
% 0.39/0.56
%------------------------------------------------------------------------------