%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV233+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 6.26s 3.23s
% Output : Refutation 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 24 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 389 ( 2 ~; 0 |; 48 &; 321 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 10 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(knows_decl,type,
knows: $i > $o ).
thf(secret_decl,type,
secret: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(concatenate_decl,type,
concatenate: $i > $i > $i ).
thf(decrypt_decl,type,
decrypt: $i > $i > $i ).
thf(encrypt_decl,type,
encrypt: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(fourth_decl,type,
fourth: $i > $i ).
thf(head_decl,type,
head: $i > $i ).
thf(symmetric_decrypt_decl,type,
symmetric_decrypt: $i > $i > $i ).
thf(symmetric_encrypt_decl,type,
symmetric_encrypt: $i > $i > $i ).
thf(first_decl,type,
first: $i > $i ).
thf(third_decl,type,
third: $i > $i ).
thf(extract_decl,type,
extract: $i > $i > $i ).
thf(sign_decl,type,
sign: $i > $i > $i ).
thf(second_decl,type,
second: $i > $i ).
thf(hash_decl,type,
hash: $i > $i ).
thf(mac_decl,type,
mac: $i > $i > $i ).
thf(n_decl,type,
n: $i ).
thf(k_c_decl,type,
k_c: $i ).
thf(c_decl,type,
c: $i ).
thf(eol_decl,type,
eol: $i ).
thf(k_ca_decl,type,
k_ca: $i ).
thf(s_decl,type,
s: $i ).
thf(kgen_decl,type,
kgen: $i > $i ).
thf(k_s_decl,type,
k_s: $i ).
thf(k_a_decl,type,
k_a: $i ).
thf(11,axiom,
! [A: $i] :
( ( A @ second )
= ( A @ tail @ head ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_axiom) ).
thf(46,plain,
! [A: $i] :
( ( A @ second )
= ( A @ tail @ head ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
( ( k_a @ knows )
& ( k_a @ inverse @ knows )
& ( k_ca @ knows ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',previous_knowledge) ).
thf(84,plain,
( ( k_a @ knows )
& ( k_a @ inverse @ knows )
& ( k_ca @ knows ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( B @ inverse @ ( A @ sign ) @ knows ) )
=> ( A @ knows ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sign_equation) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( B @ inverse @ ( A @ sign ) @ knows ) )
=> ( A @ knows ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ first )
= ( A @ head ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_axiom) ).
thf(34,plain,
! [A: $i] :
( ( A @ first )
= ( A @ head ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ concatenate ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tail_axiom) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ concatenate ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( B @ ( A @ symmetric_encrypt ) @ knows ) )
=> ( A @ knows ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_encrypt_equation) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( B @ ( A @ symmetric_encrypt ) @ knows ) )
=> ( A @ knows ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ concatenate ) @ knows )
=> ( ( B @ knows )
& ( A @ knows ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_2) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ concatenate ) @ knows )
=> ( ( B @ knows )
& ( A @ knows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ inverse @ knows )
& ( B @ ( A @ encrypt ) @ knows ) )
=> ( A @ knows ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_equation) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( ( B @ inverse @ knows )
& ( B @ ( A @ encrypt ) @ knows ) )
=> ( A @ knows ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ symmetric_encrypt ) @ symmetric_decrypt ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_decrypt_axiom) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ symmetric_encrypt ) @ symmetric_decrypt ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ concatenate ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_axiom) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ concatenate ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ third )
= ( A @ tail @ tail @ head ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',third_axiom) ).
thf(37,plain,
! [A: $i] :
( ( A @ third )
= ( A @ tail @ tail @ head ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ inverse @ ( B @ ( A @ encrypt ) @ decrypt ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_axiom) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( B @ inverse @ ( B @ ( A @ encrypt ) @ decrypt ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ fourth )
= ( A @ tail @ tail @ tail @ head ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fourth_axiom) ).
thf(28,plain,
! [A: $i] :
( ( A @ fourth )
= ( A @ tail @ tail @ tail @ head ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( A @ knows ) )
=> ( B @ ( A @ mac ) @ knows ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmac_axiom) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( A @ knows ) )
=> ( B @ ( A @ mac ) @ knows ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
secret @ knows,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',attack) ).
thf(2,negated_conjecture,
~ ( secret @ knows ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ( secret @ knows ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( A @ knows ) )
=> ( ( B @ ( A @ sign ) @ knows )
& ( B @ ( A @ extract ) @ knows )
& ( B @ ( A @ symmetric_decrypt ) @ knows )
& ( B @ ( A @ decrypt ) @ knows )
& ( B @ ( A @ symmetric_encrypt ) @ knows )
& ( B @ ( A @ encrypt ) @ knows )
& ( B @ ( A @ concatenate ) @ knows ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_1) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( B @ knows )
& ( A @ knows ) )
=> ( ( B @ ( A @ sign ) @ knows )
& ( B @ ( A @ extract ) @ knows )
& ( B @ ( A @ symmetric_decrypt ) @ knows )
& ( B @ ( A @ decrypt ) @ knows )
& ( B @ ( A @ symmetric_encrypt ) @ knows )
& ( B @ ( A @ encrypt ) @ knows )
& ( B @ ( A @ concatenate ) @ knows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ knows )
=> ( ( A @ hash @ knows )
& ( A @ tail @ knows )
& ( A @ head @ knows ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_3) ).
thf(49,plain,
! [A: $i] :
( ( A @ knows )
=> ( ( A @ hash @ knows )
& ( A @ tail @ knows )
& ( A @ head @ knows ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( B @ ( C @ extract ) @ second )
= B )
& ( C @ knows )
& ( B @ knows )
& ( A @ knows ) )
=> ( k_ca @ inverse @ ( eol @ ( k_s @ concatenate ) @ ( s @ concatenate ) @ sign ) @ ( B @ ( k_s @ inverse @ ( eol @ ( A @ concatenate ) @ ( B @ kgen @ concatenate ) @ sign ) @ encrypt ) @ concatenate ) @ knows ) )
& ( ( ( ( k_ca @ ( E @ extract ) @ second @ ( k_c @ inverse @ ( D @ decrypt ) @ extract ) @ second )
= n )
& ( ( k_ca @ ( E @ extract ) @ first )
= s )
& ( E @ knows )
& ( D @ knows ) )
=> ( k_ca @ ( E @ extract ) @ second @ ( k_c @ inverse @ ( D @ decrypt ) @ extract ) @ first @ ( secret @ symmetric_encrypt ) @ knows ) )
& ( k_c @ inverse @ ( eol @ ( k_c @ concatenate ) @ ( c @ concatenate ) @ sign ) @ ( k_c @ concatenate ) @ ( n @ concatenate ) @ knows ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',protocol) ).
thf(72,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( B @ ( C @ extract ) @ second )
= B )
& ( C @ knows )
& ( B @ knows )
& ( A @ knows ) )
=> ( k_ca @ inverse @ ( eol @ ( k_s @ concatenate ) @ ( s @ concatenate ) @ sign ) @ ( B @ ( k_s @ inverse @ ( eol @ ( A @ concatenate ) @ ( B @ kgen @ concatenate ) @ sign ) @ encrypt ) @ concatenate ) @ knows ) )
& ( ( ( ( k_ca @ ( E @ extract ) @ second @ ( k_c @ inverse @ ( D @ decrypt ) @ extract ) @ second )
= n )
& ( ( k_ca @ ( E @ extract ) @ first )
= s )
& ( E @ knows )
& ( D @ knows ) )
=> ( k_ca @ ( E @ extract ) @ second @ ( k_c @ inverse @ ( D @ decrypt ) @ extract ) @ first @ ( secret @ symmetric_encrypt ) @ knows ) )
& ( k_c @ inverse @ ( eol @ ( k_c @ concatenate ) @ ( c @ concatenate ) @ sign ) @ ( k_c @ concatenate ) @ ( n @ concatenate ) @ knows ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ inverse @ ( A @ sign ) @ extract ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sign_axiom) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ inverse @ ( A @ sign ) @ extract ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(133,plain,
$false,
inference(e,[status(thm)],[46,84,89,34,22,81,66,63,31,40,37,25,28,70,21,54,49,72,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV233+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.38 % Computer : n005.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 13:20:47 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.10/1.07 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.51/1.36 % [INFO] Parsing done (285ms).
% 1.51/1.38 % [INFO] Running in sequential loop mode.
% 2.60/1.95 % [INFO] eprover registered as external prover.
% 2.60/1.96 % [INFO] Scanning for conjecture ...
% 2.88/2.09 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.04/2.18 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.13/2.27 % [INFO] Problem is first-order (TPTP FOF).
% 3.13/2.28 % [INFO] Type checking passed.
% 3.13/2.29 % [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 ...
% 6.26/3.23 % External prover 'e' found a proof!
% 6.26/3.23 % [INFO] Killing All external provers ...
% 6.26/3.23 % Time passed: 2694ms (effective reasoning time: 1843ms)
% 6.26/3.23 % 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)>
% 6.26/3.23 % Axioms used in derivation (18): decrypt_axiom, construct_message_2, symmac_axiom, symmetric_encrypt_equation, construct_message_3, tail_axiom, first_axiom, previous_knowledge, construct_message_1, fourth_axiom, sign_equation, symmetric_decrypt_axiom, head_axiom, encrypt_equation, third_axiom, second_axiom, protocol, sign_axiom
% 6.26/3.23 % No. of inferences in proof: 40
% 6.26/3.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2694 ms resp. 1843 ms w/o parsing
% 6.26/3.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.26/3.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------