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