%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : PUZ032-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:11:25 EDT 2022
% Result : Unsatisfiable 1.59s 1.77s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 7 unt; 2 nHn; 13 RR)
% Number of literals : 25 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ a_truth(truthteller(A))
| ~ a_truth(says(A,B))
| a_truth(B) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ a_truth(liar(A))
| ~ a_truth(says(A,B))
| ~ a_truth(B) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ a_truth(A)
| ~ a_truth(says(B,A))
| a_truth(truthteller(B)) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(5,axiom,
( a_truth(A)
| ~ a_truth(says(B,A))
| a_truth(liar(B)) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(6,axiom,
~ a_truth(truthteller(c)),
file('PUZ032-1.p',unknown),
[] ).
cnf(7,plain,
( ~ a_truth(liar(A))
| ~ a_truth(says(A,liar(A))) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.1.3')] ).
cnf(8,plain,
( a_truth(liar(A))
| ~ a_truth(says(A,liar(A))) ),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.1.3')] ).
cnf(9,axiom,
( a_truth(truthteller(A))
| a_truth(liar(A)) ),
file('PUZ032-1.p',unknown),
[] ).
cnf(11,axiom,
a_truth(says(b,says(a,liar(a)))),
file('PUZ032-1.p',unknown),
[] ).
cnf(12,axiom,
a_truth(says(c,liar(b))),
file('PUZ032-1.p',unknown),
[] ).
cnf(15,plain,
a_truth(truthteller(b)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[12,4,9]),6]),
[iquote('hyper,12,4,9,unit_del,6')] ).
cnf(17,plain,
a_truth(says(a,liar(a))),
inference(hyper,[status(thm)],[11,2,15]),
[iquote('hyper,11,2,15')] ).
cnf(18,plain,
a_truth(liar(a)),
inference(hyper,[status(thm)],[17,8]),
[iquote('hyper,17,8')] ).
cnf(21,plain,
$false,
inference(hyper,[status(thm)],[18,7,17]),
[iquote('hyper,18,7,17')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ032-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n005.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 : 300
% 0.13/0.33 % DateTime : Wed Jul 27 01:47:05 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.59/1.77 ----- Otter 3.3f, August 2004 -----
% 1.59/1.77 The process was started by sandbox2 on n005.cluster.edu,
% 1.59/1.77 Wed Jul 27 01:47:05 2022
% 1.59/1.77 The command was "./otter". The process ID is 9473.
% 1.59/1.77
% 1.59/1.77 set(prolog_style_variables).
% 1.59/1.77 set(auto).
% 1.59/1.77 dependent: set(auto1).
% 1.59/1.77 dependent: set(process_input).
% 1.59/1.77 dependent: clear(print_kept).
% 1.59/1.77 dependent: clear(print_new_demod).
% 1.59/1.77 dependent: clear(print_back_demod).
% 1.59/1.77 dependent: clear(print_back_sub).
% 1.59/1.77 dependent: set(control_memory).
% 1.59/1.77 dependent: assign(max_mem, 12000).
% 1.59/1.77 dependent: assign(pick_given_ratio, 4).
% 1.59/1.77 dependent: assign(stats_level, 1).
% 1.59/1.77 dependent: assign(max_seconds, 10800).
% 1.59/1.77 clear(print_given).
% 1.59/1.77
% 1.59/1.77 list(usable).
% 1.59/1.77 0 [] a_truth(truthteller(X))|a_truth(liar(X)).
% 1.59/1.77 0 [] -a_truth(truthteller(X))| -a_truth(liar(X)).
% 1.59/1.77 0 [] -a_truth(truthteller(Truthteller))| -a_truth(says(Truthteller,Statement))|a_truth(Statement).
% 1.59/1.77 0 [] -a_truth(liar(Liar))| -a_truth(says(Liar,Statement))| -a_truth(Statement).
% 1.59/1.77 0 [] -a_truth(Statement)| -a_truth(says(Truthteller,Statement))|a_truth(truthteller(Truthteller)).
% 1.59/1.77 0 [] a_truth(Statement)| -a_truth(says(Liar,Statement))|a_truth(liar(Liar)).
% 1.59/1.77 0 [] a_truth(says(a,mumble)).
% 1.59/1.77 0 [] a_truth(says(b,says(a,liar(a)))).
% 1.59/1.77 0 [] a_truth(says(c,liar(b))).
% 1.59/1.77 0 [] -a_truth(truthteller(c)).
% 1.59/1.77 end_of_list.
% 1.59/1.77
% 1.59/1.77 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.59/1.77
% 1.59/1.77 This is a non-Horn set without equality. The strategy will
% 1.59/1.77 be ordered hyper_res, unit deletion, and factoring, with
% 1.59/1.77 satellites in sos and with nuclei in usable.
% 1.59/1.77
% 1.59/1.77 dependent: set(hyper_res).
% 1.59/1.77 dependent: set(factor).
% 1.59/1.77 dependent: set(unit_deletion).
% 1.59/1.77
% 1.59/1.77 ------------> process usable:
% 1.59/1.77 ** KEPT (pick-wt=6): 1 [] -a_truth(truthteller(A))| -a_truth(liar(A)).
% 1.59/1.77 ** KEPT (pick-wt=9): 2 [] -a_truth(truthteller(A))| -a_truth(says(A,B))|a_truth(B).
% 1.59/1.77 ** KEPT (pick-wt=9): 3 [] -a_truth(liar(A))| -a_truth(says(A,B))| -a_truth(B).
% 1.59/1.77 ** KEPT (pick-wt=9): 4 [] -a_truth(A)| -a_truth(says(B,A))|a_truth(truthteller(B)).
% 1.59/1.77 ** KEPT (pick-wt=9): 5 [] a_truth(A)| -a_truth(says(B,A))|a_truth(liar(B)).
% 1.59/1.77 ** KEPT (pick-wt=3): 6 [] -a_truth(truthteller(c)).
% 1.59/1.77
% 1.59/1.77 ------------> process sos:
% 1.59/1.77 ** KEPT (pick-wt=6): 9 [] a_truth(truthteller(A))|a_truth(liar(A)).
% 1.59/1.77 ** KEPT (pick-wt=4): 10 [] a_truth(says(a,mumble)).
% 1.59/1.77 ** KEPT (pick-wt=7): 11 [] a_truth(says(b,says(a,liar(a)))).
% 1.59/1.77 ** KEPT (pick-wt=5): 12 [] a_truth(says(c,liar(b))).
% 1.59/1.77
% 1.59/1.77 ======= end of input processing =======
% 1.59/1.77
% 1.59/1.77 =========== start of search ===========
% 1.59/1.77
% 1.59/1.77 -------- PROOF --------
% 1.59/1.77
% 1.59/1.77 -----> EMPTY CLAUSE at 0.00 sec ----> 21 [hyper,18,7,17] $F.
% 1.59/1.77
% 1.59/1.77 Length of proof is 5. Level of proof is 3.
% 1.59/1.77
% 1.59/1.77 ---------------- PROOF ----------------
% 1.59/1.77 % SZS status Unsatisfiable
% 1.59/1.77 % SZS output start Refutation
% See solution above
% 1.59/1.77 ------------ end of proof -------------
% 1.59/1.77
% 1.59/1.77
% 1.59/1.77 Search stopped by max_proofs option.
% 1.59/1.77
% 1.59/1.77
% 1.59/1.77 Search stopped by max_proofs option.
% 1.59/1.77
% 1.59/1.77 ============ end of search ============
% 1.59/1.77
% 1.59/1.77 -------------- statistics -------------
% 1.59/1.77 clauses given 10
% 1.59/1.77 clauses generated 38
% 1.59/1.77 clauses kept 20
% 1.59/1.77 clauses forward subsumed 27
% 1.59/1.77 clauses back subsumed 2
% 1.59/1.77 Kbytes malloced 976
% 1.59/1.77
% 1.59/1.77 ----------- times (seconds) -----------
% 1.59/1.77 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/1.77 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/1.77 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.59/1.77
% 1.59/1.77 That finishes the proof of the theorem.
% 1.59/1.77
% 1.59/1.77 Process 9473 finished Wed Jul 27 01:47:07 2022
% 1.59/1.77 Otter interrupted
% 1.59/1.77 PROOF FOUND
%------------------------------------------------------------------------------