%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n009.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 08:58:29 AM UTC 2026
% Result : Theorem 8.61s 4.34s
% Output : Refutation 8.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 60 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 465 ( 2 ~; 0 |; 34 &; 407 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 82 ( 0 ^; 82 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(p_decl,type,
p: $i > $o ).
thf(crypt_decl,type,
crypt: $i > $i > $i ).
thf(pp_decl,type,
pp: $i ).
thf(a_decl,type,
a: $i ).
thf(xor_decl,type,
xor: $i > $i > $i ).
thf(id_decl,type,
id: $i ).
thf(km_decl,type,
km: $i ).
thf(imp_decl,type,
imp: $i ).
thf(rand_decl,type,
rand: $i ).
thf(exp_decl,type,
exp: $i ).
thf(decrypt_decl,type,
decrypt: $i > $i > $i ).
thf(kp_decl,type,
kp: $i ).
thf(data_decl,type,
data: $i ).
thf(kek_decl,type,
kek: $i ).
thf(pin_decl,type,
pin: $i ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ ( A @ crypt ) @ p ) )
=> ( B @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_knowledge) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ ( A @ crypt ) @ p ) )
=> ( B @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ crypt ) @ ( A @ decrypt ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encryption_decryption_cancellation) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ crypt ) @ ( A @ decrypt ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ p )
& ( C @ ( kp @ ( B @ xor ) @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( A @ ( C @ xor ) @ ( B @ ( km @ xor ) @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import___part_3) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ p )
& ( C @ ( kp @ ( B @ xor ) @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( A @ ( C @ xor ) @ ( B @ ( km @ xor ) @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,axiom,
pp @ ( pin @ ( km @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
thf(78,plain,
pp @ ( pin @ ( km @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( data @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( A @ ( B @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_data) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ( B @ ( data @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( A @ ( B @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(16,axiom,
data @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_3) ).
thf(60,plain,
data @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ xor ) )
= id ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_rules_2) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( A @ xor ) )
= id ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ p )
& ( C @ ( B @ ( kp @ xor ) @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( C @ ( A @ xor ) @ ( kp @ ( B @ xor ) @ ( km @ xor ) @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import___part_2) ).
thf(65,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ p )
& ( C @ ( B @ ( kp @ xor ) @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( C @ ( A @ xor ) @ ( kp @ ( B @ xor ) @ ( km @ xor ) @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
pin @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
thf(77,plain,
pin @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ xor ) @ ( A @ xor ) )
= ( C @ ( B @ ( A @ xor ) @ xor ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_associative) ).
thf(41,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ xor ) @ ( A @ xor ) )
= ( C @ ( B @ ( A @ xor ) @ xor ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( exp @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p )
& ( B @ ( A @ ( km @ xor ) @ crypt ) @ p ) )
=> ( B @ ( A @ ( C @ xor ) @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_export) ).
thf(73,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( exp @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p )
& ( B @ ( A @ ( km @ xor ) @ crypt ) @ p ) )
=> ( B @ ( A @ ( C @ xor ) @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
a @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_account_number) ).
thf(76,plain,
a @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(25,axiom,
imp @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_2) ).
thf(75,plain,
imp @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
kp @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).
thf(51,plain,
kp @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(29,axiom,
kek @ ( imp @ ( rand @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_10) ).
thf(79,plain,
kek @ ( imp @ ( rand @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutative) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( imp @ ( km @ xor ) @ crypt ) @ p )
& ( D @ p )
& ( C @ ( B @ ( A @ xor ) @ crypt ) @ p ) )
=> ( C @ ( B @ ( A @ xor ) @ crypt ) @ ( D @ ( E @ xor ) @ decrypt ) @ ( D @ ( km @ xor ) @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_import) ).
thf(45,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ ( imp @ ( km @ xor ) @ crypt ) @ p )
& ( D @ p )
& ( C @ ( B @ ( A @ xor ) @ crypt ) @ p ) )
=> ( C @ ( B @ ( A @ xor ) @ crypt ) @ ( D @ ( E @ xor ) @ decrypt ) @ ( D @ ( km @ xor ) @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
exp @ ( imp @ xor ) @ ( rand @ xor ) @ ( imp @ ( km @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_7) ).
thf(44,plain,
exp @ ( imp @ xor ) @ ( rand @ xor ) @ ( imp @ ( km @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
exp @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_11) ).
thf(59,plain,
exp @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( data @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( A @ ( B @ decrypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_data) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( B @ ( data @ ( km @ xor ) @ crypt ) @ p )
& ( A @ p ) )
=> ( A @ ( B @ decrypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ p ) )
=> ( B @ ( A @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_knowledge) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ p ) )
=> ( B @ ( A @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( kp @ xor ) @ ( km @ xor ) @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import___part_1) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( kp @ xor ) @ ( km @ xor ) @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,axiom,
! [A: $i] :
( ( id @ ( A @ xor ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_rules_1) ).
thf(35,plain,
! [A: $i] :
( ( id @ ( A @ xor ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( exp @ ( km @ xor ) @ crypt ) @ p )
& ( D @ ( imp @ ( km @ xor ) @ crypt ) @ p )
& ( C @ p )
& ( B @ ( A @ crypt ) @ p ) )
=> ( B @ ( A @ crypt ) @ ( D @ ( C @ xor ) @ decrypt ) @ ( F @ ( E @ xor ) @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_translate) ).
thf(48,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( exp @ ( km @ xor ) @ crypt ) @ p )
& ( D @ ( imp @ ( km @ xor ) @ crypt ) @ p )
& ( C @ p )
& ( B @ ( A @ crypt ) @ p ) )
=> ( B @ ( A @ crypt ) @ ( D @ ( C @ xor ) @ decrypt ) @ ( F @ ( E @ xor ) @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ xor ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',combine_with_XOR) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ xor ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
id @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_4) ).
thf(67,plain,
id @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
a @ ( pp @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',find_pin) ).
thf(2,negated_conjecture,
~ ( a @ ( pp @ crypt ) @ p ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ( a @ ( pp @ crypt ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
rand @ ( imp @ ( km @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_8) ).
thf(47,plain,
rand @ ( imp @ ( km @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
kek @ ( kp @ ( imp @ xor ) @ ( km @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_9) ).
thf(68,plain,
kek @ ( kp @ ( imp @ xor ) @ ( km @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(111,plain,
$false,
inference(e,[status(thm)],[69,56,52,78,61,60,38,65,77,41,73,76,75,51,79,32,45,44,59,71,54,80,35,48,63,67,31,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.23/0.49 % Computer : n009.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 13:21:14 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.41/1.39 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.15/1.71 % [INFO] Parsing done (318ms).
% 2.15/1.74 % [INFO] Running in sequential loop mode.
% 3.24/2.38 % [INFO] eprover registered as external prover.
% 3.24/2.40 % [INFO] Scanning for conjecture ...
% 3.64/2.55 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 3.81/2.66 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 4.06/2.77 % [INFO] Problem is first-order (TPTP FOF).
% 4.06/2.78 % [INFO] Type checking passed.
% 4.06/2.79 % [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 ...
% 8.61/4.33 % External prover 'e' found a proof!
% 8.61/4.33 % [INFO] Killing All external provers ...
% 8.61/4.34 % Time passed: 3618ms (effective reasoning time: 2588ms)
% 8.61/4.34 % 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)>
% 8.61/4.34 % Axioms used in derivation (28): initial_knowledge_of_intruder_1, key_import, encrypt_data, xor_associative, initial_knowledge_of_intruder_7, key_part_import___part_2, initial_knowledge_of_intruder_6, key_export, decrypt_knowledge, encryption_decryption_cancellation, initial_knowledge_of_intruder_9, initial_knowledge_of_intruder_4, key_translate, encrypt_knowledge, initial_knowledge_of_intruder_8, key_part_import___part_3, xor_rules_2, an_account_number, initial_knowledge_of_intruder_11, combine_with_XOR, xor_rules_1, initial_knowledge_of_intruder_10, initial_knowledge_of_intruder_2, xor_commutative, initial_knowledge_of_intruder_3, key_part_import___part_1, decrypt_data, initial_knowledge_of_intruder_5
% 8.61/4.34 % No. of inferences in proof: 60
% 8.61/4.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3618 ms resp. 2588 ms w/o parsing
% 8.91/4.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.91/4.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------