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  
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