TSTP Solution File: SWV011+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWV011+1 : TPTP v8.1.0. Released v2.4.0.
% 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 13:19:40 EDT 2022
% Result : Theorem 1.71s 1.90s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 3
% Syntax : Number of clauses : 4 ( 3 unt; 0 nHn; 4 RR)
% Number of literals : 5 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 1 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ a_holds(key(A,b))
| ~ b_holds(key(A,a)) ),
file('SWV011+1.p',unknown),
[] ).
cnf(12,axiom,
b_holds(key(generate_key(an_a_nonce),a)),
file('SWV011+1.p',unknown),
[] ).
cnf(14,axiom,
a_holds(key(generate_key(an_a_nonce),b)),
file('SWV011+1.p',unknown),
[] ).
cnf(18,plain,
$false,
inference(hyper,[status(thm)],[14,1,12]),
[iquote('hyper,14,1,12')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV011+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n005.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:56:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.71/1.90 ----- Otter 3.3f, August 2004 -----
% 1.71/1.90 The process was started by sandbox on n005.cluster.edu,
% 1.71/1.90 Wed Jul 27 05:56:35 2022
% 1.71/1.90 The command was "./otter". The process ID is 8383.
% 1.71/1.90
% 1.71/1.90 set(prolog_style_variables).
% 1.71/1.90 set(auto).
% 1.71/1.90 dependent: set(auto1).
% 1.71/1.90 dependent: set(process_input).
% 1.71/1.90 dependent: clear(print_kept).
% 1.71/1.90 dependent: clear(print_new_demod).
% 1.71/1.90 dependent: clear(print_back_demod).
% 1.71/1.90 dependent: clear(print_back_sub).
% 1.71/1.90 dependent: set(control_memory).
% 1.71/1.90 dependent: assign(max_mem, 12000).
% 1.71/1.90 dependent: assign(pick_given_ratio, 4).
% 1.71/1.90 dependent: assign(stats_level, 1).
% 1.71/1.90 dependent: assign(max_seconds, 10800).
% 1.71/1.90 clear(print_given).
% 1.71/1.90
% 1.71/1.90 formula_list(usable).
% 1.71/1.90 a_holds(key(at,t)).
% 1.71/1.90 party_of_protocol(a).
% 1.71/1.90 message(sent(a,b,pair(a,an_a_nonce))).
% 1.71/1.90 a_stored(pair(b,an_a_nonce)).
% 1.71/1.90 b_holds(key(bt,t)).
% 1.71/1.90 party_of_protocol(b).
% 1.71/1.90 fresh_to_b(an_a_nonce).
% 1.71/1.90 t_holds(key(at,a)).
% 1.71/1.90 t_holds(key(bt,b)).
% 1.71/1.90 party_of_protocol(t).
% 1.71/1.90 b_holds(key(generate_key(an_a_nonce),a)).
% 1.71/1.90 message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))).
% 1.71/1.90 a_holds(key(generate_key(an_a_nonce),b)).
% 1.71/1.90 message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))).
% 1.71/1.90 message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))).
% 1.71/1.90 b_stored(pair(a,an_a_nonce)).
% 1.71/1.90 -(exists U (a_holds(key(U,b))&b_holds(key(U,a)))).
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 -------> usable clausifies to:
% 1.71/1.90
% 1.71/1.90 list(usable).
% 1.71/1.90 0 [] a_holds(key(at,t)).
% 1.71/1.90 0 [] party_of_protocol(a).
% 1.71/1.90 0 [] message(sent(a,b,pair(a,an_a_nonce))).
% 1.71/1.90 0 [] a_stored(pair(b,an_a_nonce)).
% 1.71/1.90 0 [] b_holds(key(bt,t)).
% 1.71/1.90 0 [] party_of_protocol(b).
% 1.71/1.90 0 [] fresh_to_b(an_a_nonce).
% 1.71/1.90 0 [] t_holds(key(at,a)).
% 1.71/1.90 0 [] t_holds(key(bt,b)).
% 1.71/1.90 0 [] party_of_protocol(t).
% 1.71/1.90 0 [] b_holds(key(generate_key(an_a_nonce),a)).
% 1.71/1.90 0 [] message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))).
% 1.71/1.90 0 [] a_holds(key(generate_key(an_a_nonce),b)).
% 1.71/1.90 0 [] message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))).
% 1.71/1.90 0 [] message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))).
% 1.71/1.90 0 [] b_stored(pair(a,an_a_nonce)).
% 1.71/1.90 0 [] -a_holds(key(U,b))| -b_holds(key(U,a)).
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=2.
% 1.71/1.90
% 1.71/1.90 This is a Horn set without equality. The strategy will
% 1.71/1.90 be hyperresolution, with satellites in sos and nuclei
% 1.71/1.90 in usable.
% 1.71/1.90
% 1.71/1.90 dependent: set(hyper_res).
% 1.71/1.90 dependent: clear(order_hyper).
% 1.71/1.90
% 1.71/1.90 ------------> process usable:
% 1.71/1.90 ** KEPT (pick-wt=8): 1 [] -a_holds(key(A,b))| -b_holds(key(A,a)).
% 1.71/1.90
% 1.71/1.90 ------------> process sos:
% 1.71/1.90 ** KEPT (pick-wt=4): 2 [] a_holds(key(at,t)).
% 1.71/1.90 ** KEPT (pick-wt=2): 3 [] party_of_protocol(a).
% 1.71/1.90 ** KEPT (pick-wt=7): 4 [] message(sent(a,b,pair(a,an_a_nonce))).
% 1.71/1.90 ** KEPT (pick-wt=4): 5 [] a_stored(pair(b,an_a_nonce)).
% 1.71/1.90 ** KEPT (pick-wt=4): 6 [] b_holds(key(bt,t)).
% 1.71/1.90 ** KEPT (pick-wt=2): 7 [] party_of_protocol(b).
% 1.71/1.90 ** KEPT (pick-wt=2): 8 [] fresh_to_b(an_a_nonce).
% 1.71/1.90 ** KEPT (pick-wt=4): 9 [] t_holds(key(at,a)).
% 1.71/1.90 ** KEPT (pick-wt=4): 10 [] t_holds(key(bt,b)).
% 1.71/1.90 ** KEPT (pick-wt=2): 11 [] party_of_protocol(t).
% 1.71/1.90 ** KEPT (pick-wt=5): 12 [] b_holds(key(generate_key(an_a_nonce),a)).
% 1.71/1.90 ** KEPT (pick-wt=18): 13 [] message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))).
% 1.71/1.90 ** KEPT (pick-wt=5): 14 [] a_holds(key(generate_key(an_a_nonce),b)).
% 1.71/1.90 ** KEPT (pick-wt=24): 15 [] message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))).
% 1.71/1.90 ** KEPT (pick-wt=15): 16 [] message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))).
% 1.71/1.90 ** KEPT (pick-wt=4): 17 [] b_stored(pair(a,an_a_nonce)).
% 1.71/1.90
% 1.71/1.90 ======= end of input processing =======
% 1.71/1.90
% 1.71/1.90 =========== start of search ===========
% 1.71/1.90
% 1.71/1.90 -------- PROOF --------
% 1.71/1.90
% 1.71/1.90 -----> EMPTY CLAUSE at 0.00 sec ----> 18 [hyper,14,1,12] $F.
% 1.71/1.90
% 1.71/1.90 Length of proof is 0. Level of proof is 0.
% 1.71/1.90
% 1.71/1.90 ---------------- PROOF ----------------
% 1.71/1.90 % SZS status Theorem
% 1.71/1.90 % SZS output start Refutation
% See solution above
% 1.71/1.90 ------------ end of proof -------------
% 1.71/1.90
% 1.71/1.90
% 1.71/1.90 Search stopped by max_proofs option.
% 1.71/1.90
% 1.71/1.90
% 1.71/1.90 Search stopped by max_proofs option.
% 1.71/1.90
% 1.71/1.90 ============ end of search ============
% 1.71/1.90
% 1.71/1.90 -------------- statistics -------------
% 1.71/1.90 clauses given 13
% 1.71/1.90 clauses generated 1
% 1.71/1.90 clauses kept 17
% 1.71/1.90 clauses forward subsumed 0
% 1.71/1.90 clauses back subsumed 0
% 1.71/1.90 Kbytes malloced 976
% 1.71/1.90
% 1.71/1.90 ----------- times (seconds) -----------
% 1.71/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.90
% 1.71/1.90 That finishes the proof of the theorem.
% 1.71/1.90
% 1.71/1.90 Process 8383 finished Wed Jul 27 05:56:37 2022
% 1.71/1.90 Otter interrupted
% 1.71/1.90 PROOF FOUND
%------------------------------------------------------------------------------