TSTP Solution File: PUZ027-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : PUZ027-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:11:24 EDT 2022
% Result : Unsatisfiable 1.75s 1.96s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 6 unt; 6 nHn; 19 RR)
% Number of literals : 45 ( 0 equ; 17 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 6 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ a_truth(truthteller(A))
| ~ a_truth(says(A,B))
| a_truth(B) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ a_truth(lower(A,B))
| ~ a_truth(truthteller(A)) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(21,axiom,
( ~ a_truth(normal(a))
| ~ a_truth(truthteller(b))
| answer(a_normal_b_truthteller) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ a_truth(normal(a))
| ~ a_truth(normal(b))
| answer(a_and_b_normal) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ a_truth(normal(a))
| ~ a_truth(liar(b))
| answer(a_normal_b_liar) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ a_truth(liar(a))
| ~ a_truth(truthteller(b))
| answer(a_liar_b_truthteller) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(25,axiom,
( ~ a_truth(liar(a))
| ~ a_truth(normal(b))
| answer(a_liar_b_normal) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ a_truth(liar(a))
| ~ a_truth(liar(b))
| answer(a_and_b_liar) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(27,axiom,
~ answer(A),
file('PUZ027-1.p',unknown),
[] ).
cnf(31,axiom,
( a_truth(truthteller(A))
| a_truth(liar(A))
| a_truth(normal(A)) ),
file('PUZ027-1.p',unknown),
[] ).
cnf(34,axiom,
a_truth(says(a,lower(a,b))),
file('PUZ027-1.p',unknown),
[] ).
cnf(36,plain,
( a_truth(liar(b))
| a_truth(normal(b))
| a_truth(truthteller(a))
| a_truth(normal(a)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[31,24,31]),27]),
[iquote('hyper,31,24,31,unit_del,27')] ).
cnf(57,plain,
( a_truth(normal(b))
| a_truth(truthteller(a))
| a_truth(normal(a)) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[36,26,31]),27])])]),
[iquote('hyper,36,26,31,unit_del,27,factor_simp,factor_simp')] ).
cnf(61,plain,
( a_truth(truthteller(a))
| a_truth(normal(a)) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[57,25,31]),27])])]),
[iquote('hyper,57,25,31,unit_del,27,factor_simp,factor_simp')] ).
cnf(74,plain,
( a_truth(normal(a))
| a_truth(lower(a,b)) ),
inference(hyper,[status(thm)],[61,4,34]),
[iquote('hyper,61,4,34')] ).
cnf(90,plain,
a_truth(normal(a)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[74,11,61])]),
[iquote('hyper,74,11,61,factor_simp')] ).
cnf(125,plain,
( a_truth(truthteller(b))
| a_truth(normal(b)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[90,23,31]),27]),
[iquote('hyper,90,23,31,unit_del,27')] ).
cnf(132,plain,
a_truth(normal(b)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[125,21,90]),27]),
[iquote('hyper,125,21,90,unit_del,27')] ).
cnf(134,plain,
answer(a_and_b_normal),
inference(hyper,[status(thm)],[132,22,90]),
[iquote('hyper,132,22,90')] ).
cnf(135,plain,
$false,
inference(binary,[status(thm)],[134,27]),
[iquote('binary,134.1,27.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : PUZ027-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 01:31:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.94 ----- Otter 3.3f, August 2004 -----
% 1.75/1.94 The process was started by sandbox2 on n007.cluster.edu,
% 1.75/1.94 Wed Jul 27 01:31:46 2022
% 1.75/1.94 The command was "./otter". The process ID is 14908.
% 1.75/1.94
% 1.75/1.94 set(prolog_style_variables).
% 1.75/1.94 set(auto).
% 1.75/1.94 dependent: set(auto1).
% 1.75/1.94 dependent: set(process_input).
% 1.75/1.94 dependent: clear(print_kept).
% 1.75/1.94 dependent: clear(print_new_demod).
% 1.75/1.94 dependent: clear(print_back_demod).
% 1.75/1.94 dependent: clear(print_back_sub).
% 1.75/1.94 dependent: set(control_memory).
% 1.75/1.94 dependent: assign(max_mem, 12000).
% 1.75/1.94 dependent: assign(pick_given_ratio, 4).
% 1.75/1.94 dependent: assign(stats_level, 1).
% 1.75/1.94 dependent: assign(max_seconds, 10800).
% 1.75/1.94 clear(print_given).
% 1.75/1.94
% 1.75/1.94 list(usable).
% 1.75/1.94 0 [] a_truth(truthteller(X))|a_truth(liar(X))|a_truth(normal(X)).
% 1.75/1.94 0 [] -a_truth(truthteller(X))| -a_truth(normal(X)).
% 1.75/1.94 0 [] -a_truth(truthteller(X))| -a_truth(liar(X)).
% 1.75/1.94 0 [] -a_truth(liar(X))| -a_truth(normal(X)).
% 1.75/1.94 0 [] -a_truth(truthteller(X))| -a_truth(says(X,Y))|a_truth(Y).
% 1.75/1.94 0 [] -a_truth(liar(X))| -a_truth(says(X,Y))| -a_truth(Y).
% 1.75/1.94 0 [] -a_truth(X)| -a_truth(says(Y,X))|a_truth(truthteller(Y))|a_truth(normal(Y)).
% 1.75/1.94 0 [] a_truth(X)| -a_truth(says(Y,X))|a_truth(liar(Y))|a_truth(normal(Y)).
% 1.75/1.94 0 [] a_truth(not_lower(X,X)).
% 1.75/1.94 0 [] -a_truth(not_lower(X,Y))| -a_truth(lower(X,Y)).
% 1.75/1.94 0 [] a_truth(not_lower(X,Y))|a_truth(lower(X,Y)).
% 1.75/1.94 0 [] -a_truth(lower(X,Y))| -a_truth(liar(X))|a_truth(normal(Y))|a_truth(truthteller(Y)).
% 1.75/1.94 0 [] -a_truth(lower(X,Y))| -a_truth(normal(X))|a_truth(truthteller(Y)).
% 1.75/1.94 0 [] -a_truth(lower(X,Y))| -a_truth(truthteller(X)).
% 1.75/1.94 0 [] -a_truth(lower(X,Y))| -a_truth(truthteller(Y))|a_truth(normal(X))|a_truth(liar(X)).
% 1.75/1.94 0 [] -a_truth(lower(X,Y))| -a_truth(normal(Y))|a_truth(liar(X)).
% 1.75/1.94 0 [] -a_truth(lower(X,Y))| -a_truth(liar(Y)).
% 1.75/1.94 0 [] -a_truth(not_lower(X,Y))| -a_truth(truthteller(X))|a_truth(truthteller(Y))|a_truth(lower(Y,X)).
% 1.75/1.94 0 [] -a_truth(not_lower(X,Y))| -a_truth(liar(X))|a_truth(liar(Y))|a_truth(lower(Y,X)).
% 1.75/1.94 0 [] -a_truth(not_lower(X,Y))| -a_truth(normal(X))|a_truth(normal(Y))|a_truth(lower(Y,X)).
% 1.75/1.94 0 [] a_truth(says(a,lower(a,b))).
% 1.75/1.94 0 [] a_truth(says(b,not_lower(a,b))).
% 1.75/1.94 0 [] -a_truth(truthteller(a))| -a_truth(truthteller(b))|answer(a_and_b_truthteller).
% 1.75/1.94 0 [] -a_truth(truthteller(a))| -a_truth(normal(b))|answer(a_truthteller_b_normal).
% 1.75/1.94 0 [] -a_truth(truthteller(a))| -a_truth(liar(b))|answer(a_truthteller_b_liar).
% 1.75/1.94 0 [] -a_truth(normal(a))| -a_truth(truthteller(b))|answer(a_normal_b_truthteller).
% 1.75/1.94 0 [] -a_truth(normal(a))| -a_truth(normal(b))|answer(a_and_b_normal).
% 1.75/1.94 0 [] -a_truth(normal(a))| -a_truth(liar(b))|answer(a_normal_b_liar).
% 1.75/1.94 0 [] -a_truth(liar(a))| -a_truth(truthteller(b))|answer(a_liar_b_truthteller).
% 1.75/1.94 0 [] -a_truth(liar(a))| -a_truth(normal(b))|answer(a_liar_b_normal).
% 1.75/1.94 0 [] -a_truth(liar(a))| -a_truth(liar(b))|answer(a_and_b_liar).
% 1.75/1.94 0 [] -answer(Answer).
% 1.75/1.94 end_of_list.
% 1.75/1.94
% 1.75/1.94 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.75/1.94
% 1.75/1.94 This is a non-Horn set without equality. The strategy will
% 1.75/1.94 be ordered hyper_res, unit deletion, and factoring, with
% 1.75/1.94 satellites in sos and with nuclei in usable.
% 1.75/1.94
% 1.75/1.94 dependent: set(hyper_res).
% 1.75/1.94 dependent: set(factor).
% 1.75/1.94 dependent: set(unit_deletion).
% 1.75/1.94
% 1.75/1.94 ------------> process usable:
% 1.75/1.94 ** KEPT (pick-wt=6): 1 [] -a_truth(truthteller(A))| -a_truth(normal(A)).
% 1.75/1.94 ** KEPT (pick-wt=6): 2 [] -a_truth(truthteller(A))| -a_truth(liar(A)).
% 1.75/1.94 ** KEPT (pick-wt=6): 3 [] -a_truth(liar(A))| -a_truth(normal(A)).
% 1.75/1.94 ** KEPT (pick-wt=9): 4 [] -a_truth(truthteller(A))| -a_truth(says(A,B))|a_truth(B).
% 1.75/1.94 ** KEPT (pick-wt=9): 5 [] -a_truth(liar(A))| -a_truth(says(A,B))| -a_truth(B).
% 1.75/1.94 ** KEPT (pick-wt=12): 6 [] -a_truth(A)| -a_truth(says(B,A))|a_truth(truthteller(B))|a_truth(normal(B)).
% 1.75/1.94 ** KEPT (pick-wt=12): 7 [] a_truth(A)| -a_truth(says(B,A))|a_truth(liar(B))|a_truth(normal(B)).
% 1.75/1.94 ** KEPT (pick-wt=8): 8 [] -a_truth(not_lower(A,B))| -a_truth(lower(A,B)).
% 1.75/1.94 ** KEPT (pick-wt=13): 9 [] -a_truth(lower(A,B))| -a_truth(liar(A))|a_truth(normal(B))|a_truth(truthteller(B)).
% 1.75/1.94 ** KEPT (pick-wt=10): 10 [] -a_truth(lower(A,B))| -a_truth(normal(A))|a_truth(truthteller(B)).
% 1.75/1.94 ** KEPT (pick-wt=7): 11 [] -a_truth(lower(A,B))| -a_truth(truthteller(A)).
% 1.75/1.94 ** KEPT (pick-wt=13): 12 [] -a_truth(lower(A,B))| -a_truth(truthteller(B))|a_truth(normal(A))|a_truth(liar(A)).
% 1.75/1.96 ** KEPT (pick-wt=10): 13 [] -a_truth(lower(A,B))| -a_truth(normal(B))|a_truth(liar(A)).
% 1.75/1.96 ** KEPT (pick-wt=7): 14 [] -a_truth(lower(A,B))| -a_truth(liar(B)).
% 1.75/1.96 ** KEPT (pick-wt=14): 15 [] -a_truth(not_lower(A,B))| -a_truth(truthteller(A))|a_truth(truthteller(B))|a_truth(lower(B,A)).
% 1.75/1.96 ** KEPT (pick-wt=14): 16 [] -a_truth(not_lower(A,B))| -a_truth(liar(A))|a_truth(liar(B))|a_truth(lower(B,A)).
% 1.75/1.96 ** KEPT (pick-wt=14): 17 [] -a_truth(not_lower(A,B))| -a_truth(normal(A))|a_truth(normal(B))|a_truth(lower(B,A)).
% 1.75/1.96 ** KEPT (pick-wt=8): 18 [] -a_truth(truthteller(a))| -a_truth(truthteller(b))|answer(a_and_b_truthteller).
% 1.75/1.96 ** KEPT (pick-wt=8): 19 [] -a_truth(truthteller(a))| -a_truth(normal(b))|answer(a_truthteller_b_normal).
% 1.75/1.96 ** KEPT (pick-wt=8): 20 [] -a_truth(truthteller(a))| -a_truth(liar(b))|answer(a_truthteller_b_liar).
% 1.75/1.96 ** KEPT (pick-wt=8): 21 [] -a_truth(normal(a))| -a_truth(truthteller(b))|answer(a_normal_b_truthteller).
% 1.75/1.96 ** KEPT (pick-wt=8): 22 [] -a_truth(normal(a))| -a_truth(normal(b))|answer(a_and_b_normal).
% 1.75/1.96 ** KEPT (pick-wt=8): 23 [] -a_truth(normal(a))| -a_truth(liar(b))|answer(a_normal_b_liar).
% 1.75/1.96 ** KEPT (pick-wt=8): 24 [] -a_truth(liar(a))| -a_truth(truthteller(b))|answer(a_liar_b_truthteller).
% 1.75/1.96 ** KEPT (pick-wt=8): 25 [] -a_truth(liar(a))| -a_truth(normal(b))|answer(a_liar_b_normal).
% 1.75/1.96 ** KEPT (pick-wt=8): 26 [] -a_truth(liar(a))| -a_truth(liar(b))|answer(a_and_b_liar).
% 1.75/1.96 ** KEPT (pick-wt=2): 27 [] -answer(A).
% 1.75/1.96
% 1.75/1.96 ------------> process sos:
% 1.75/1.96 ** KEPT (pick-wt=9): 31 [] a_truth(truthteller(A))|a_truth(liar(A))|a_truth(normal(A)).
% 1.75/1.96 ** KEPT (pick-wt=4): 32 [] a_truth(not_lower(A,A)).
% 1.75/1.96 ** KEPT (pick-wt=8): 33 [] a_truth(not_lower(A,B))|a_truth(lower(A,B)).
% 1.75/1.96 ** KEPT (pick-wt=6): 34 [] a_truth(says(a,lower(a,b))).
% 1.75/1.96 ** KEPT (pick-wt=6): 35 [] a_truth(says(b,not_lower(a,b))).
% 1.75/1.96
% 1.75/1.96 ======= end of input processing =======
% 1.75/1.96
% 1.75/1.96 =========== start of search ===========
% 1.75/1.96
% 1.75/1.96 -------- PROOF --------
% 1.75/1.96
% 1.75/1.96 ----> UNIT CONFLICT at 0.02 sec ----> 135 [binary,134.1,27.1] $F.
% 1.75/1.96
% 1.75/1.96 Length of proof is 8. Level of proof is 8.
% 1.75/1.96
% 1.75/1.96 ---------------- PROOF ----------------
% 1.75/1.96 % SZS status Unsatisfiable
% 1.75/1.96 % SZS output start Refutation
% See solution above
% 1.75/1.96 ------------ end of proof -------------
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96 ============ end of search ============
% 1.75/1.96
% 1.75/1.96 -------------- statistics -------------
% 1.75/1.96 clauses given 14
% 1.75/1.96 clauses generated 492
% 1.75/1.96 clauses kept 134
% 1.75/1.96 clauses forward subsumed 390
% 1.75/1.96 clauses back subsumed 74
% 1.75/1.96 Kbytes malloced 976
% 1.75/1.96
% 1.75/1.96 ----------- times (seconds) -----------
% 1.75/1.96 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.75/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.96 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.96
% 1.75/1.96 That finishes the proof of the theorem.
% 1.75/1.96
% 1.75/1.96 Process 14908 finished Wed Jul 27 01:31:47 2022
% 1.75/1.96 Otter interrupted
% 1.75/1.96 PROOF FOUND
%------------------------------------------------------------------------------