TSTP Solution File: PUZ008-3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : PUZ008-3 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n021.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  : 300s
% DateTime : Wed Jul 27 13:11:02 EDT 2022

% Result   : Unsatisfiable 1.84s 2.01s
% Output   : Refutation 1.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   31 (  23 unt;   0 nHn;  22 RR)
%            Number of literals    :   51 (   0 equ;  21 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (  10 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ greater_or_e_qual(A,B)
    | safe(A,B) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(2,axiom,
    ( greater_or_e_qual(s(A),s(B))
    | ~ greater_or_e_qual(A,B) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(D))))
    | ~ safe(A,s(B))
    | ~ safe(C,D)
    | achievable(west(m(A),c(s(B))),boatonwest,east(m(C),c(D))) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ achievable(west(m(A),c(s(s(B)))),boatonwest,east(m(C),c(D)))
    | ~ safe(A,B)
    | ~ safe(C,s(s(D)))
    | achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(s(D))))) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(D)))
    | ~ safe(s(A),B)
    | ~ safe(C,D)
    | achievable(west(m(s(A)),c(B)),boatonwest,east(m(C),c(D))) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ achievable(west(m(s(s(A))),c(B)),boatonwest,east(m(C),c(D)))
    | ~ safe(A,B)
    | ~ safe(s(s(C)),D)
    | achievable(west(m(A),c(B)),boatoneast,east(m(s(s(C))),c(D))) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ achievable(west(m(s(A)),c(s(B))),boatonwest,east(m(C),c(D)))
    | ~ safe(A,B)
    | ~ safe(s(C),s(D))
    | achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(s(D)))) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(s(D))))
    | ~ safe(s(A),s(B))
    | ~ safe(C,D)
    | achievable(west(m(s(A)),c(s(B))),boatonwest,east(m(C),c(D))) ),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(13,axiom,
    ~ achievable(west(m(n0),c(n0)),A,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(14,axiom,
    safe(n0,A),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(15,axiom,
    greater_or_e_qual(A,n0),
    file('PUZ008-3.p',unknown),
    [] ).

cnf(16,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(17,plain,
    greater_or_e_qual(s(A),s(n0)),
    inference(hyper,[status(thm)],[15,2]),
    [iquote('hyper,15,2')] ).

cnf(18,plain,
    safe(A,n0),
    inference(hyper,[status(thm)],[15,1]),
    [iquote('hyper,15,1')] ).

cnf(19,plain,
    greater_or_e_qual(s(s(A)),s(s(n0))),
    inference(hyper,[status(thm)],[17,2]),
    [iquote('hyper,17,2')] ).

cnf(20,plain,
    safe(s(A),s(n0)),
    inference(hyper,[status(thm)],[17,1]),
    [iquote('hyper,17,1')] ).

cnf(21,plain,
    achievable(west(m(s(s(s(n0)))),c(s(n0))),boatoneast,east(m(n0),c(s(s(n0))))),
    inference(hyper,[status(thm)],[16,5,20,14]),
    [iquote('hyper,16,5,20,14')] ).

cnf(22,plain,
    greater_or_e_qual(s(s(s(A))),s(s(s(n0)))),
    inference(hyper,[status(thm)],[19,2]),
    [iquote('hyper,19,2')] ).

cnf(23,plain,
    safe(s(s(A)),s(s(n0))),
    inference(hyper,[status(thm)],[19,1]),
    [iquote('hyper,19,1')] ).

cnf(27,plain,
    safe(s(s(s(A))),s(s(s(n0)))),
    inference(hyper,[status(thm)],[22,1]),
    [iquote('hyper,22,1')] ).

cnf(28,plain,
    achievable(west(m(s(s(s(n0)))),c(s(s(n0)))),boatonwest,east(m(n0),c(s(n0)))),
    inference(hyper,[status(thm)],[21,4,23,14]),
    [iquote('hyper,21,4,23,14')] ).

cnf(37,plain,
    achievable(west(m(s(s(s(n0)))),c(n0)),boatoneast,east(m(n0),c(s(s(s(n0)))))),
    inference(hyper,[status(thm)],[28,5,18,14]),
    [iquote('hyper,28,5,18,14')] ).

cnf(38,plain,
    achievable(west(m(s(s(s(n0)))),c(s(n0))),boatonwest,east(m(n0),c(s(s(n0))))),
    inference(hyper,[status(thm)],[37,4,20,14]),
    [iquote('hyper,37,4,20,14')] ).

cnf(39,plain,
    achievable(west(m(s(n0)),c(s(n0))),boatoneast,east(m(s(s(n0))),c(s(s(n0))))),
    inference(hyper,[status(thm)],[38,9,20,23]),
    [iquote('hyper,38,9,20,23')] ).

cnf(40,plain,
    achievable(west(m(s(s(n0))),c(s(s(n0)))),boatonwest,east(m(s(n0)),c(s(n0)))),
    inference(hyper,[status(thm)],[39,12,23,20]),
    [iquote('hyper,39,12,23,20')] ).

cnf(43,plain,
    achievable(west(m(n0),c(s(s(n0)))),boatoneast,east(m(s(s(s(n0)))),c(s(n0)))),
    inference(hyper,[status(thm)],[40,9,14,20]),
    [iquote('hyper,40,9,14,20')] ).

cnf(44,plain,
    achievable(west(m(n0),c(s(s(s(n0))))),boatonwest,east(m(s(s(s(n0)))),c(n0))),
    inference(hyper,[status(thm)],[43,4,14,18]),
    [iquote('hyper,43,4,14,18')] ).

cnf(45,plain,
    achievable(west(m(n0),c(s(n0))),boatoneast,east(m(s(s(s(n0)))),c(s(s(n0))))),
    inference(hyper,[status(thm)],[44,5,14,23]),
    [iquote('hyper,44,5,14,23')] ).

cnf(46,plain,
    achievable(west(m(s(n0)),c(s(n0))),boatonwest,east(m(s(s(n0))),c(s(s(n0))))),
    inference(hyper,[status(thm)],[45,8,20,23]),
    [iquote('hyper,45,8,20,23')] ).

cnf(50,plain,
    achievable(west(m(n0),c(n0)),boatoneast,east(m(s(s(s(n0)))),c(s(s(s(n0)))))),
    inference(hyper,[status(thm)],[46,11,18,27]),
    [iquote('hyper,46,11,18,27')] ).

cnf(51,plain,
    $false,
    inference(binary,[status(thm)],[50,13]),
    [iquote('binary,50.1,13.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : PUZ008-3 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n021.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Jul 27 01:43:38 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 1.84/2.01  ----- Otter 3.3f, August 2004 -----
% 1.84/2.01  The process was started by sandbox on n021.cluster.edu,
% 1.84/2.01  Wed Jul 27 01:43:38 2022
% 1.84/2.01  The command was "./otter".  The process ID is 30200.
% 1.84/2.01  
% 1.84/2.01  set(prolog_style_variables).
% 1.84/2.01  set(auto).
% 1.84/2.01     dependent: set(auto1).
% 1.84/2.01     dependent: set(process_input).
% 1.84/2.01     dependent: clear(print_kept).
% 1.84/2.01     dependent: clear(print_new_demod).
% 1.84/2.01     dependent: clear(print_back_demod).
% 1.84/2.01     dependent: clear(print_back_sub).
% 1.84/2.01     dependent: set(control_memory).
% 1.84/2.01     dependent: assign(max_mem, 12000).
% 1.84/2.01     dependent: assign(pick_given_ratio, 4).
% 1.84/2.01     dependent: assign(stats_level, 1).
% 1.84/2.01     dependent: assign(max_seconds, 10800).
% 1.84/2.01  clear(print_given).
% 1.84/2.01  
% 1.84/2.01  list(usable).
% 1.84/2.01  0 [] safe(n0,X).
% 1.84/2.01  0 [] -greater_or_e_qual(X,Y)|safe(X,Y).
% 1.84/2.01  0 [] greater_or_e_qual(X,n0).
% 1.84/2.01  0 [] greater_or_e_qual(s(X),s(Y))| -greater_or_e_qual(X,Y).
% 1.84/2.01  0 [] -achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W)))| -safe(X,Y)| -safe(Z,s(W))|achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W)))).
% 1.84/2.01  0 [] -achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(W))))| -safe(X,s(Y))| -safe(Z,W)|achievable(west(m(X),c(s(Y))),boatonwest,east(m(Z),c(W))).
% 1.84/2.01  0 [] -achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W)))| -safe(X,Y)| -safe(Z,s(s(W)))|achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W))))).
% 1.84/2.01  0 [] -achievable(west(m(X),c(Y)),boatoneast,east(m(Z),c(s(s(W)))))| -safe(X,s(s(Y)))| -safe(Z,W)|achievable(west(m(X),c(s(s(Y)))),boatonwest,east(m(Z),c(W))).
% 1.84/2.01  0 [] -achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W)))| -safe(X,Y)| -safe(s(Z),W)|achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W))).
% 1.84/2.01  0 [] -achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(W)))| -safe(s(X),Y)| -safe(Z,W)|achievable(west(m(s(X)),c(Y)),boatonwest,east(m(Z),c(W))).
% 1.84/2.01  0 [] -achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W)))| -safe(X,Y)| -safe(s(s(Z)),W)|achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W))).
% 1.84/2.01  0 [] -achievable(west(m(X),c(Y)),boatoneast,east(m(s(s(Z))),c(W)))| -safe(s(s(X)),Y)| -safe(Z,W)|achievable(west(m(s(s(X))),c(Y)),boatonwest,east(m(Z),c(W))).
% 1.84/2.01  0 [] -achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W)))| -safe(X,Y)| -safe(s(Z),s(W))|achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W)))).
% 1.84/2.01  0 [] -achievable(west(m(X),c(Y)),boatoneast,east(m(s(Z)),c(s(W))))| -safe(s(X),s(Y))| -safe(Z,W)|achievable(west(m(s(X)),c(s(Y))),boatonwest,east(m(Z),c(W))).
% 1.84/2.01  0 [] achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))).
% 1.84/2.01  0 [] -achievable(west(m(n0),c(n0)),X,east(m(s(s(s(n0)))),c(s(s(s(n0)))))).
% 1.84/2.01  end_of_list.
% 1.84/2.01  
% 1.84/2.01  SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.84/2.01  
% 1.84/2.01  This is a Horn set without equality.  The strategy will
% 1.84/2.01  be hyperresolution, with satellites in sos and nuclei
% 1.84/2.01  in usable.
% 1.84/2.01  
% 1.84/2.01     dependent: set(hyper_res).
% 1.84/2.01     dependent: clear(order_hyper).
% 1.84/2.01  
% 1.84/2.01  ------------> process usable:
% 1.84/2.01  ** KEPT (pick-wt=6): 1 [] -greater_or_e_qual(A,B)|safe(A,B).
% 1.84/2.01  ** KEPT (pick-wt=8): 2 [] greater_or_e_qual(s(A),s(B))| -greater_or_e_qual(A,B).
% 1.84/2.01  ** KEPT (pick-wt=33): 3 [] -achievable(west(m(A),c(s(B))),boatonwest,east(m(C),c(D)))| -safe(A,B)| -safe(C,s(D))|achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(D)))).
% 1.84/2.01  ** KEPT (pick-wt=33): 4 [] -achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(D))))| -safe(A,s(B))| -safe(C,D)|achievable(west(m(A),c(s(B))),boatonwest,east(m(C),c(D))).
% 1.84/2.01  ** KEPT (pick-wt=36): 5 [] -achievable(west(m(A),c(s(s(B)))),boatonwest,east(m(C),c(D)))| -safe(A,B)| -safe(C,s(s(D)))|achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(s(D))))).
% 1.84/2.01  ** KEPT (pick-wt=36): 6 [] -achievable(west(m(A),c(B)),boatoneast,east(m(C),c(s(s(D)))))| -safe(A,s(s(B)))| -safe(C,D)|achievable(west(m(A),c(s(s(B)))),boatonwest,east(m(C),c(D))).
% 1.84/2.01  ** KEPT (pick-wt=33): 7 [] -achievable(west(m(s(A)),c(B)),boatonwest,east(m(C),c(D)))| -safe(A,B)| -safe(s(C),D)|achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(D))).
% 1.84/2.01  ** KEPT (pick-wt=33): 8 [] -achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(D)))| -safe(s(A),B)| -safe(C,D)|achievable(west(m(s(A)),c(B)),boatonwest,east(m(C),c(D))).
% 1.84/2.01  ** KEPT (pick-wt=36): 9 [] -achievable(west(m(s(s(A))),c(B)),boatonwest,east(m(C),c(D)))| -safe(A,B)| -safe(s(s(C)),D)|achievable(west(m(A),c(B)),boatoneast,east(m(s(s(C))),c(D))).
% 1.84/2.01  ** KEPT (pick-wt=36): 10 [] -achievable(west(m(A),c(B)),boatoneast,east(m(s(s(C))),c(D)))| -safe(s(s(A)),B)| -safe(C,D)|achievable(west(m(s(s(A))),c(B)),boatonwest,east(m(C),c(D))).
% 1.84/2.01  ** KEPT (pick-wt=36): 11 [] -achievable(west(m(s(A)),c(s(B))),boatonwest,east(m(C),c(D)))| -safe(A,B)| -safe(s(C),s(D))|achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(s(D)))).
% 1.84/2.01  ** KEPT (pick-wt=36): 12 [] -achievable(west(m(A),c(B)),boatoneast,east(m(s(C)),c(s(D))))| -safe(s(A),s(B))| -safe(C,D)|achievable(west(m(s(A)),c(s(B))),boatonwest,east(m(C),c(D))).
% 1.84/2.01  ** KEPT (pick-wt=18): 13 [] -achievable(west(m(n0),c(n0)),A,east(m(s(s(s(n0)))),c(s(s(s(n0)))))).
% 1.84/2.01  
% 1.84/2.01  ------------> process sos:
% 1.84/2.01  ** KEPT (pick-wt=3): 14 [] safe(n0,A).
% 1.84/2.01  ** KEPT (pick-wt=3): 15 [] greater_or_e_qual(A,n0).
% 1.84/2.01  ** KEPT (pick-wt=18): 16 [] achievable(west(m(s(s(s(n0)))),c(s(s(s(n0))))),boatonwest,east(m(n0),c(n0))).
% 1.84/2.01  
% 1.84/2.01  ======= end of input processing =======
% 1.84/2.01  
% 1.84/2.01  =========== start of search ===========
% 1.84/2.01  
% 1.84/2.01  -------- PROOF -------- 
% 1.84/2.01  
% 1.84/2.01  ----> UNIT CONFLICT at   0.00 sec ----> 51 [binary,50.1,13.1] $F.
% 1.84/2.01  
% 1.84/2.01  Length of proof is 18.  Level of proof is 13.
% 1.84/2.01  
% 1.84/2.01  ---------------- PROOF ----------------
% 1.84/2.01  % SZS status Unsatisfiable
% 1.84/2.01  % SZS output start Refutation
% See solution above
% 1.84/2.01  ------------ end of proof -------------
% 1.84/2.01  
% 1.84/2.01  
% 1.84/2.01  Search stopped by max_proofs option.
% 1.84/2.01  
% 1.84/2.01  
% 1.84/2.01  Search stopped by max_proofs option.
% 1.84/2.01  
% 1.84/2.01  ============ end of search ============
% 1.84/2.01  
% 1.84/2.01  -------------- statistics -------------
% 1.84/2.01  clauses given                 32
% 1.84/2.01  clauses generated             50
% 1.84/2.01  clauses kept                  50
% 1.84/2.01  clauses forward subsumed      16
% 1.84/2.01  clauses back subsumed          0
% 1.84/2.01  Kbytes malloced              976
% 1.84/2.01  
% 1.84/2.01  ----------- times (seconds) -----------
% 1.84/2.01  user CPU time          0.00          (0 hr, 0 min, 0 sec)
% 1.84/2.01  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 1.84/2.01  wall-clock time        1             (0 hr, 0 min, 1 sec)
% 1.84/2.01  
% 1.84/2.01  That finishes the proof of the theorem.
% 1.84/2.01  
% 1.84/2.01  Process 30200 finished Wed Jul 27 01:43:39 2022
% 1.84/2.01  Otter interrupted
% 1.84/2.01  PROOF FOUND
%------------------------------------------------------------------------------