%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV236+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 : n017.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 4.30s 2.69s
% Output : Refutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 58 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 119 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 463 ( 2 ~; 0 |; 37 &; 400 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 89 ( 0 ^; 86 !; 3 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(p_decl,type,
p: $i > $o ).
thf(crypt_decl,type,
crypt: $i > $i > $i ).
thf(xor_decl,type,
xor: $i > $i > $i ).
thf(km_decl,type,
km: $i ).
thf(exp_decl,type,
exp: $i ).
thf(data_decl,type,
data: $i ).
thf(decrypt_decl,type,
decrypt: $i > $i > $i ).
thf(imp_decl,type,
imp: $i ).
thf(kp_decl,type,
kp: $i ).
thf(eurk_decl,type,
eurk: $i ).
thf(id_decl,type,
id: $i ).
thf(a_decl,type,
a: $i ).
thf(pin_decl,type,
pin: $i ).
thf(pp_decl,type,
pp: $i ).
thf(22,axiom,
eurk @ ( data @ ( km @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_8) ).
thf(69,plain,
eurk @ ( data @ ( km @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,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(56,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)],[15]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( data @ ( A @ xor ) @ crypt ) @ p )
=> ( B @ ( A @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',data_cv_is_known_to_be_zero) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( B @ ( data @ ( A @ xor ) @ crypt ) @ p )
=> ( B @ ( A @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ crypt ) @ ( A @ decrypt ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encryption_decryption_cancellation) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ crypt ) @ ( A @ decrypt ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
eurk @ ( exp @ ( km @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_7) ).
thf(60,plain,
eurk @ ( exp @ ( km @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,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(65,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)],[20]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( A @ xor ) )
= id ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_rules_2) ).
thf(77,plain,
! [A: $i] :
( ( A @ ( A @ xor ) )
= id ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(26,axiom,
pp @ ( pin @ ( km @ xor ) @ crypt ) @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
thf(73,plain,
pp @ ( pin @ ( km @ xor ) @ crypt ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(3,axiom,
exp @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_9) ).
thf(32,plain,
exp @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,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(44,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)],[9]) ).
thf(24,axiom,
a @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_account_number) ).
thf(71,plain,
a @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ p ) )
=> ( B @ ( A @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_knowledge) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ p ) )
=> ( B @ ( A @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,axiom,
pin @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
thf(72,plain,
pin @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(16,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(58,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)],[16]) ).
thf(1,conjecture,
? [A: $i] :
( ( A @ p )
& ( A @ ( exp @ ( km @ xor ) @ crypt ) @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',find_known_exporter) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( A @ p )
& ( A @ ( exp @ ( km @ xor ) @ crypt ) @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(30,plain,
~ ? [A: $i] :
( ( A @ p )
& ( A @ ( exp @ ( km @ xor ) @ crypt ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(61,plain,
! [A: $i,B: $i] :
( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ xor ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
! [A: $i] :
( ( id @ ( A @ xor ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_rules_1) ).
thf(74,plain,
! [A: $i] :
( ( id @ ( A @ xor ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,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(38,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)],[6]) ).
thf(23,axiom,
imp @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_2) ).
thf(70,plain,
imp @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ ( A @ crypt ) @ p ) )
=> ( B @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_knowledge) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( A @ p )
& ( B @ ( A @ crypt ) @ p ) )
=> ( B @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,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)],[29]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutative) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,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(48,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)],[11]) ).
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(63,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(7,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(40,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)],[7]) ).
thf(14,axiom,
data @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_3) ).
thf(55,plain,
data @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
kp @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).
thf(47,plain,
kp @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,axiom,
id @ p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_4) ).
thf(68,plain,
id @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(109,plain,
$false,
inference(e,[status(thm)],[69,56,42,52,60,65,77,73,32,44,71,50,72,58,30,61,74,38,70,33,80,35,48,63,40,55,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.13/0.40 % Computer : n017.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 13:16:34 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.19 % [INFO] Parsing done (206ms).
% 1.40/1.21 % [INFO] Running in sequential loop mode.
% 2.02/1.60 % [INFO] eprover registered as external prover.
% 2.02/1.61 % [INFO] Scanning for conjecture ...
% 2.21/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 27 axioms. Running axiom selection ...
% 2.21/1.78 % [INFO] Axiom selection finished. Selected 27 axioms (removed 0 axioms).
% 2.39/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.85 % [INFO] Type checking passed.
% 2.39/1.85 % [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 ...
% 4.30/2.69 % External prover 'e' found a proof!
% 4.30/2.69 % [INFO] Killing All external provers ...
% 4.30/2.69 % Time passed: 2143ms (effective reasoning time: 1472ms)
% 4.30/2.69 % 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)>
% 4.30/2.69 % Axioms used in derivation (27): initial_knowledge_of_intruder_1, key_import, encrypt_data, xor_associative, initial_knowledge_of_intruder_7, key_part_import___part_2, data_cv_is_known_to_be_zero, 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, combine_with_XOR, xor_rules_1, initial_knowledge_of_intruder_2, xor_commutative, initial_knowledge_of_intruder_3, key_part_import___part_1, decrypt_data, initial_knowledge_of_intruder_5
% 4.30/2.69 % No. of inferences in proof: 58
% 4.30/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2143 ms resp. 1472 ms w/o parsing
% 4.68/2.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.68/2.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------