%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 08:57:55 AM UTC 2026
% Result : Theorem 3.89s 7.60s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 203 ( 2 ~; 0 |; 3 &; 198 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 23 usr; 7 con; 0-4 aty)
% Number of variables : 3 ( 0 ^; 0 !; 3 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_holds_decl,type,
a_holds: $i > $o ).
thf(key_decl,type,
key: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(b_holds_decl,type,
b_holds: $i > $o ).
thf(a_decl,type,
a: $i ).
thf(party_of_protocol_decl,type,
party_of_protocol: $i > $o ).
thf(t_decl,type,
t: $i ).
thf(fresh_to_b_decl,type,
fresh_to_b: $i > $o ).
thf(an_a_nonce_decl,type,
an_a_nonce: $i ).
thf(b_stored_decl,type,
b_stored: $i > $o ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(generate_key_decl,type,
generate_key: $i > $i ).
thf(bt_decl,type,
bt: $i ).
thf(a_stored_decl,type,
a_stored: $i > $o ).
thf(message_decl,type,
message: $i > $o ).
thf(sent_decl,type,
sent: $i > $i > $i > $i ).
thf(triple_decl,type,
triple: $i > $i > $i > $i ).
thf(generate_b_nonce_decl,type,
generate_b_nonce: $i > $i ).
thf(encrypt_decl,type,
encrypt: $i > $i > $i ).
thf(generate_expiration_time_decl,type,
generate_expiration_time: $i > $i ).
thf(t_holds_decl,type,
t_holds: $i > $o ).
thf(at_decl,type,
at: $i ).
thf(quadruple_decl,type,
quadruple: $i > $i > $i > $i > $i ).
thf(11,axiom,
an_a_nonce @ generate_key @ ( an_a_nonce @ generate_b_nonce @ encrypt ) @ ( bt @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ generate_key @ ( a @ triple ) ) @ encrypt ) @ pair ) @ ( b @ ( a @ sent ) ) @ message,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(29,plain,
an_a_nonce @ generate_key @ ( an_a_nonce @ generate_b_nonce @ encrypt ) @ ( bt @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ generate_key @ ( a @ triple ) ) @ encrypt ) @ pair ) @ ( b @ ( a @ sent ) ) @ message,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
an_a_nonce @ generate_b_nonce @ ( bt @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ generate_key @ ( a @ triple ) ) @ encrypt ) @ ( at @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ generate_key @ ( an_a_nonce @ ( b @ quadruple ) ) ) @ encrypt ) @ triple ) ) @ ( a @ ( t @ sent ) ) @ message,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(35,plain,
an_a_nonce @ generate_b_nonce @ ( bt @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ generate_key @ ( a @ triple ) ) @ encrypt ) @ ( at @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ generate_key @ ( an_a_nonce @ ( b @ quadruple ) ) ) @ encrypt ) @ triple ) ) @ ( a @ ( t @ sent ) ) @ message,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
b @ ( bt @ key ) @ t_holds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_holds_key_bt_for_b) ).
thf(31,plain,
b @ ( bt @ key ) @ t_holds,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
b @ ( an_a_nonce @ generate_key @ key ) @ a_holds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(24,plain,
b @ ( an_a_nonce @ generate_key @ key ) @ a_holds,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
a @ ( an_a_nonce @ generate_key @ key ) @ b_holds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(25,plain,
a @ ( an_a_nonce @ generate_key @ key ) @ b_holds,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
bt @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ ( a @ triple ) ) @ encrypt ) @ ( an_a_nonce @ generate_b_nonce @ ( b @ triple ) ) @ ( t @ ( b @ sent ) ) @ message,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
thf(28,plain,
bt @ ( an_a_nonce @ generate_expiration_time @ ( an_a_nonce @ ( a @ triple ) ) @ encrypt ) @ ( an_a_nonce @ generate_b_nonce @ ( b @ triple ) ) @ ( t @ ( b @ sent ) ) @ message,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
t @ party_of_protocol,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_is_party_of_protocol) ).
thf(21,plain,
t @ party_of_protocol,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
t @ ( at @ key ) @ a_holds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_holds_key_at_for_t) ).
thf(33,plain,
t @ ( at @ key ) @ a_holds,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
b @ party_of_protocol,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_party_of_protocol) ).
thf(32,plain,
b @ party_of_protocol,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
an_a_nonce @ ( a @ pair ) @ ( b @ ( a @ sent ) ) @ message,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_sent_message_i_to_b) ).
thf(34,plain,
an_a_nonce @ ( a @ pair ) @ ( b @ ( a @ sent ) ) @ message,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
an_a_nonce @ fresh_to_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonce_a_is_fresh_to_b) ).
thf(22,plain,
an_a_nonce @ fresh_to_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
an_a_nonce @ ( b @ pair ) @ a_stored,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_stored_message_i) ).
thf(27,plain,
an_a_nonce @ ( b @ pair ) @ a_stored,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
t @ ( bt @ key ) @ b_holds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_hold_key_bt_for_t) ).
thf(26,plain,
t @ ( bt @ key ) @ b_holds,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
an_a_nonce @ ( a @ pair ) @ b_stored,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(23,plain,
an_a_nonce @ ( a @ pair ) @ b_stored,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
a @ party_of_protocol,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_party_of_protocol) ).
thf(36,plain,
a @ party_of_protocol,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
a @ ( at @ key ) @ t_holds,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_holds_key_at_for_a) ).
thf(30,plain,
a @ ( at @ key ) @ t_holds,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
? [A: $i] :
( ( a @ ( A @ key ) @ b_holds )
& ( b @ ( A @ key ) @ a_holds ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( a @ ( A @ key ) @ b_holds )
& ( b @ ( A @ key ) @ a_holds ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ? [A: $i] :
( ( a @ ( A @ key ) @ b_holds )
& ( b @ ( A @ key ) @ a_holds ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
$false,
inference(e,[status(thm)],[29,35,31,24,25,28,21,33,32,34,22,27,26,23,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/5.62 % Computer : n020.cluster.edu
% 0.16/5.62 % Model : x86_64 x86_64
% 0.16/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.62 % Memory : 8046.5625MB
% 0.16/5.62 % OS : Linux 6.8.0-71-generic
% 0.16/5.62 % CPULimit : 300
% 0.16/5.62 % WCLimit : 300
% 0.16/5.62 % DateTime : Sat Sep 26 13:06:26 UTC 2026
% 0.16/5.62 % CPUTime :
% 0.16/5.62 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.01/6.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/6.41 % [INFO] Parsing done (193ms).
% 1.19/6.43 % [INFO] Running in sequential loop mode.
% 2.02/6.84 % [INFO] eprover registered as external prover.
% 2.02/6.84 % [INFO] Scanning for conjecture ...
% 2.23/6.95 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.23/7.02 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.45/7.04 % [INFO] Problem is first-order (TPTP FOF).
% 2.45/7.05 % [INFO] Type checking passed.
% 2.45/7.06 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.60/7.59 % External prover 'e' found a proof!
% 3.60/7.60 % [INFO] Killing All external provers ...
% 3.60/7.60 % Time passed: 1826ms (effective reasoning time: 1164ms)
% 3.89/7.60 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.89/7.60 % Axioms used in derivation (16): ax4, a_holds_key_at_for_t, t_holds_key_at_for_a, ax1, a_stored_message_i, ax6, b_is_party_of_protocol, a_is_party_of_protocol, ax2, t_is_party_of_protocol, b_hold_key_bt_for_t, t_holds_key_bt_for_b, nonce_a_is_fresh_to_b, a_sent_message_i_to_b, ax3, ax5
% 3.89/7.60 % No. of inferences in proof: 36
% 3.89/7.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1826 ms resp. 1164 ms w/o parsing
% 3.89/7.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.89/7.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------