%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV014-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:06:39 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.64s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 59 ( 18 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 173 ( 94 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 81 ( 10 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nonce_a_is_fresh_to_b_9,axiom,
fresh_to_b(an_a_nonce),
file('theBenchmark.p',nonce_a_is_fresh_to_b_9) ).
cnf(c_3,plain,
fresh_to_b(an_a_nonce),
inference(clausify,[status(thm)],[nonce_a_is_fresh_to_b_9]) ).
fof(b_creates_freash_nonces_in_time_10,axiom,
! [VAR_0,VAR_1] :
( ~ message(sent(VAR_1,b,pair(VAR_1,VAR_0)))
| ~ fresh_to_b(VAR_0)
| message(sent(b,t,triple(b,generate_b_nonce(VAR_0),encrypt(triple(VAR_1,VAR_0,generate_expiration_time(VAR_0)),bt)))) ),
file('theBenchmark.p',b_creates_freash_nonces_in_time_10) ).
cnf(c_4,plain,
( ~ message(sent(B,b,pair(B,A)))
| ~ fresh_to_b(A)
| message(sent(b,t,triple(b,generate_b_nonce(A),encrypt(triple(B,A,generate_expiration_time(A)),bt)))) ),
inference(clausify,[status(thm)],[b_creates_freash_nonces_in_time_10]) ).
fof(b_creates_freash_nonces_in_time_11,axiom,
! [VAR_0,VAR_1] :
( ~ message(sent(VAR_0,b,pair(VAR_0,VAR_1)))
| ~ fresh_to_b(VAR_1)
| b_stored(pair(VAR_0,VAR_1)) ),
file('theBenchmark.p',b_creates_freash_nonces_in_time_11) ).
cnf(c_5,plain,
( ~ message(sent(A,b,pair(A,B)))
| ~ fresh_to_b(B)
| b_stored(pair(A,B)) ),
inference(clausify,[status(thm)],[b_creates_freash_nonces_in_time_11]) ).
fof(b_accepts_secure_session_key_12,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ message(sent(VAR_1,b,pair(encrypt(triple(VAR_1,VAR_0,generate_expiration_time(VAR_2)),bt),encrypt(generate_b_nonce(VAR_2),VAR_0))))
| ~ b_stored(pair(VAR_1,VAR_2))
| b_holds(key(VAR_0,VAR_1)) ),
file('theBenchmark.p',b_accepts_secure_session_key_12) ).
cnf(c_6,plain,
( ~ message(sent(B,b,pair(encrypt(triple(B,A,generate_expiration_time(C)),bt),encrypt(generate_b_nonce(C),A))))
| ~ b_stored(pair(B,C))
| b_holds(key(A,B)) ),
inference(clausify,[status(thm)],[b_accepts_secure_session_key_12]) ).
cnf(c_7,plain,
( ~ message(sent(A,b,pair(A,an_a_nonce)))
| b_stored(pair(A,an_a_nonce)) ),
inference(resolve,[status(thm)],[c_3,c_5]) ).
fof(co1_38,axiom,
! [VAR_0] :
( ~ intruder_holds(key(VAR_0,b))
| ~ b_holds(key(VAR_0,a)) ),
file('theBenchmark.p',co1_38) ).
cnf(c_8,plain,
( ~ intruder_holds(key(A,b))
| ~ b_holds(key(A,a)) ),
inference(clausify,[status(thm)],[co1_38]) ).
cnf(c_9,plain,
( ~ message(sent(B,b,pair(B,an_a_nonce)))
| ~ message(sent(B,b,pair(encrypt(triple(B,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A))))
| b_holds(key(A,B)) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
fof(intruder_holds_key_32,axiom,
! [VAR_0,VAR_1] :
( ~ party_of_protocol(VAR_1)
| ~ intruder_message(VAR_0)
| intruder_holds(key(VAR_0,VAR_1)) ),
file('theBenchmark.p',intruder_holds_key_32) ).
cnf(c_14,plain,
( ~ party_of_protocol(B)
| ~ intruder_message(A)
| intruder_holds(key(A,B)) ),
inference(clausify,[status(thm)],[intruder_holds_key_32]) ).
fof(intruder_key_encrypts_33,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ party_of_protocol(VAR_2)
| ~ intruder_message(VAR_0)
| ~ intruder_holds(key(VAR_1,VAR_2))
| intruder_message(encrypt(VAR_0,VAR_1)) ),
file('theBenchmark.p',intruder_key_encrypts_33) ).
cnf(c_15,plain,
( ~ party_of_protocol(C)
| ~ intruder_message(A)
| ~ intruder_holds(key(B,C))
| intruder_message(encrypt(A,B)) ),
inference(clausify,[status(thm)],[intruder_key_encrypts_33]) ).
cnf(c_17,plain,
( ~ message(sent(a,b,pair(a,an_a_nonce)))
| ~ message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A))))
| ~ intruder_holds(key(A,b)) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_18,plain,
( ~ party_of_protocol(b)
| ~ intruder_message(A)
| ~ message(sent(a,b,pair(a,an_a_nonce)))
| ~ message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_19,plain,
( ~ party_of_protocol(B)
| ~ intruder_message(C)
| intruder_message(encrypt(C,A))
| ~ party_of_protocol(B)
| ~ intruder_message(A) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_20,plain,
( ~ intruder_message(C)
| intruder_message(encrypt(C,A))
| ~ party_of_protocol(B)
| ~ intruder_message(A) ),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_21,plain,
( ~ message(sent(A,b,pair(A,an_a_nonce)))
| 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)))) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
fof(a_is_party_of_protocol_2,axiom,
party_of_protocol(a),
file('theBenchmark.p',a_is_party_of_protocol_2) ).
cnf(c_22,plain,
party_of_protocol(a),
inference(clausify,[status(thm)],[a_is_party_of_protocol_2]) ).
fof(a_sent_message_i_to_b_3,axiom,
message(sent(a,b,pair(a,an_a_nonce))),
file('theBenchmark.p',a_sent_message_i_to_b_3) ).
cnf(c_23,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(clausify,[status(thm)],[a_sent_message_i_to_b_3]) ).
fof(b_is_party_of_protocol_8,axiom,
party_of_protocol(b),
file('theBenchmark.p',b_is_party_of_protocol_8) ).
cnf(c_24,plain,
party_of_protocol(b),
inference(clausify,[status(thm)],[b_is_party_of_protocol_8]) ).
fof(t_is_party_of_protocol_15,axiom,
party_of_protocol(t),
file('theBenchmark.p',t_is_party_of_protocol_15) ).
cnf(c_27,plain,
party_of_protocol(t),
inference(clausify,[status(thm)],[t_is_party_of_protocol_15]) ).
fof(intruder_can_record_17,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ message(sent(VAR_1,VAR_2,VAR_0))
| intruder_message(VAR_0) ),
file('theBenchmark.p',intruder_can_record_17) ).
cnf(c_28,plain,
( ~ message(sent(B,C,A))
| intruder_message(A) ),
inference(clausify,[status(thm)],[intruder_can_record_17]) ).
fof(intruder_decomposes_pairs_19,axiom,
! [VAR_0,VAR_1] :
( ~ intruder_message(pair(VAR_1,VAR_0))
| intruder_message(VAR_0) ),
file('theBenchmark.p',intruder_decomposes_pairs_19) ).
cnf(c_30,plain,
( ~ intruder_message(pair(B,A))
| intruder_message(A) ),
inference(clausify,[status(thm)],[intruder_decomposes_pairs_19]) ).
fof(intruder_decomposes_triples_21,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ intruder_message(triple(VAR_1,VAR_0,VAR_2))
| intruder_message(VAR_0) ),
file('theBenchmark.p',intruder_decomposes_triples_21) ).
cnf(c_32,plain,
( ~ intruder_message(triple(B,A,C))
| intruder_message(A) ),
inference(clausify,[status(thm)],[intruder_decomposes_triples_21]) ).
fof(intruder_decomposes_triples_22,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ intruder_message(triple(VAR_1,VAR_2,VAR_0))
| intruder_message(VAR_0) ),
file('theBenchmark.p',intruder_decomposes_triples_22) ).
cnf(c_33,plain,
( ~ intruder_message(triple(B,C,A))
| intruder_message(A) ),
inference(clausify,[status(thm)],[intruder_decomposes_triples_22]) ).
fof(intruder_composes_pairs_27,axiom,
! [VAR_0,VAR_1] :
( ~ intruder_message(VAR_0)
| ~ intruder_message(VAR_1)
| intruder_message(pair(VAR_0,VAR_1)) ),
file('theBenchmark.p',intruder_composes_pairs_27) ).
cnf(c_38,plain,
( ~ intruder_message(A)
| ~ intruder_message(B)
| intruder_message(pair(A,B)) ),
inference(clausify,[status(thm)],[intruder_composes_pairs_27]) ).
fof(intruder_message_sent_31,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ party_of_protocol(VAR_0)
| ~ party_of_protocol(VAR_1)
| ~ intruder_message(VAR_2)
| message(sent(VAR_0,VAR_1,VAR_2)) ),
file('theBenchmark.p',intruder_message_sent_31) ).
cnf(c_41,plain,
( ~ party_of_protocol(A)
| ~ party_of_protocol(B)
| ~ intruder_message(C)
| message(sent(A,B,C)) ),
inference(clausify,[status(thm)],[intruder_message_sent_31]) ).
cnf(c_2169,plain,
( ~ party_of_protocol(b)
| ~ intruder_message(A)
| ~ message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))) ),
inference(resolve,[status(thm)],[c_23,c_18]) ).
cnf(c_46,plain,
( ~ intruder_message(A)
| ~ message(sent(a,b,pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))) ),
inference(resolve,[status(thm)],[c_24,c_2169]) ).
cnf(c_47,plain,
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)))),
inference(resolve,[status(thm)],[c_21,c_23]) ).
cnf(c_48,plain,
intruder_message(pair(a,an_a_nonce)),
inference(resolve,[status(thm)],[c_28,c_23]) ).
cnf(c_2170,plain,
( ~ party_of_protocol(a)
| ~ party_of_protocol(b)
| ~ intruder_message(pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))
| ~ intruder_message(A) ),
inference(resolve,[status(thm)],[c_46,c_41]) ).
cnf(c_2171,plain,
( ~ party_of_protocol(a)
| ~ intruder_message(pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))
| ~ intruder_message(A) ),
inference(resolve,[status(thm)],[c_24,c_2170]) ).
cnf(c_49,plain,
( ~ intruder_message(pair(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),A)))
| ~ intruder_message(A) ),
inference(resolve,[status(thm)],[c_22,c_2171]) ).
cnf(c_50,plain,
intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),
inference(resolve,[status(thm)],[c_28,c_47]) ).
cnf(c_62,plain,
intruder_message(an_a_nonce),
inference(resolve,[status(thm)],[c_30,c_48]) ).
cnf(c_76,plain,
( ~ intruder_message(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),A))
| ~ intruder_message(A) ),
inference(resolve,[status(thm)],[c_49,c_38]) ).
cnf(c_2172,plain,
( ~ intruder_message(generate_b_nonce(an_a_nonce))
| ~ party_of_protocol(B)
| ~ intruder_message(A)
| ~ intruder_message(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(A) ),
inference(resolve,[status(thm)],[c_76,c_20]) ).
cnf(c_105,plain,
( ~ intruder_message(generate_b_nonce(an_a_nonce))
| ~ party_of_protocol(B)
| ~ intruder_message(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(A) ),
inference(copy,[status(thm)],[c_2172]) ).
cnf(c_142,plain,
( ~ intruder_message(generate_b_nonce(an_a_nonce))
| ~ intruder_message(encrypt(triple(a,A,generate_expiration_time(an_a_nonce)),bt))
| ~ intruder_message(A) ),
inference(resolve,[status(thm)],[c_105,c_27]) ).
cnf(c_209,plain,
( ~ intruder_message(generate_b_nonce(an_a_nonce))
| ~ intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)) ),
inference(resolve,[status(thm)],[c_62,c_142]) ).
cnf(c_2152,plain,
intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)),
inference(resolve,[status(thm)],[c_33,c_50]) ).
cnf(c_2153,plain,
intruder_message(generate_b_nonce(an_a_nonce)),
inference(resolve,[status(thm)],[c_32,c_50]) ).
cnf(c_2173,plain,
~ intruder_message(generate_b_nonce(an_a_nonce)),
inference(resolve,[status(thm)],[c_2152,c_209]) ).
cnf(c_2168,plain,
$false,
inference(resolve,[status(thm)],[c_2153,c_2173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV014-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 13:08:26 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1058205 was started by sandbox2 on n026,
% 0.18/0.45 % Sat Sep 26 13:08:26 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.64
% 0.23/0.64 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.64
% 0.23/0.64 % Proof 1 at 0.10 (+ 0.07) seconds.
% 0.23/0.64 % Length of proof is 37.
% 0.23/0.64 % Level of proof is 11.
% 0.23/0.64 % Maximum clause weight is 39.000.
% 0.23/0.64 % Given clauses 40.
% 0.23/0.64
% 0.23/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------