%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV237+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 : 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 3.94s 2.58s
% Output : Refutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 52 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 415 ( 2 ~; 0 |; 48 &; 339 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(p_decl,type,
p: $i > $o ).
thf(enc_decl,type,
enc: $i > $i > $i ).
thf(pp_decl,type,
pp: $i ).
thf(a_decl,type,
a: $i ).
thf(i_decl,type,
i: $i > $i ).
thf(tc_decl,type,
tc: $i ).
thf(wk_decl,type,
wk: $i ).
thf(tmk_decl,type,
tmk: $i ).
thf(zcmk_decl,type,
zcmk: $i ).
thf(k_decl,type,
k: $i ).
thf(kk_decl,type,
kk: $i ).
thf(lp_decl,type,
lp: $i ).
thf(w_decl,type,
w: $i ).
thf(t1_decl,type,
t1: $i ).
thf(t2_decl,type,
t2: $i ).
thf(21,axiom,
t1 @ ( w @ enc ) @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_3) ).
thf(69,plain,
t1 @ ( w @ enc ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tmk @ i @ enc ) @ ( wk @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',receive_working_key_from_switch) ).
thf(52,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tmk @ i @ enc ) @ ( wk @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
pp @ ( tmk @ enc ) @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_1) ).
thf(65,plain,
pp @ ( tmk @ enc ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( tc @ i @ enc ) @ i @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_decrypt) ).
thf(73,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( tc @ i @ enc ) @ i @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tmk @ i @ enc ) @ ( B @ ( zcmk @ i @ enc ) @ i @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_translate_from_TMK_to_ZCMK) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tmk @ i @ enc ) @ ( B @ ( zcmk @ i @ enc ) @ i @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tc @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_clear_key_as_Tcomms_key) ).
thf(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tc @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( zcmk @ i @ enc ) @ i @ enc ) @ ( tmk @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_translate_from_ZCMK_to_TMK) ).
thf(48,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( zcmk @ i @ enc ) @ i @ enc ) @ ( tmk @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
a @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_8) ).
thf(31,plain,
a @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ p )
=> ( A @ i @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keys_are_symmetric) ).
thf(43,plain,
! [A: $i] :
( ( A @ p )
=> ( A @ i @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
kk @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_6) ).
thf(58,plain,
kk @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
k @ ( tc @ enc ) @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_5) ).
thf(51,plain,
k @ ( tc @ enc ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,axiom,
w @ ( wk @ enc ) @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_2) ).
thf(79,plain,
w @ ( wk @ enc ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( wk @ i @ enc ) @ i @ enc ) @ ( C @ ( wk @ i @ enc ) @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_translate_between_interchange_keys) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( wk @ i @ enc ) @ i @ enc ) @ ( C @ ( wk @ i @ enc ) @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ i @ enc ) @ ( A @ enc ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dec_enc_cancel) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ i @ enc ) @ ( A @ enc ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ i @ i )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',double_inverse_cancel) ).
thf(28,plain,
! [A: $i] :
( ( A @ i @ i )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( tmk @ i @ enc ) @ i @ enc ) @ ( C @ ( wk @ i @ enc ) @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_translate_PIN_from_local_to_interchange_key) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( B @ ( tmk @ i @ enc ) @ i @ enc ) @ ( C @ ( wk @ i @ enc ) @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( tc @ i @ enc ) @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_encrypt) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( tc @ i @ enc ) @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tc @ i @ enc ) @ ( B @ ( tmk @ i @ enc ) @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_a_stored_comms_key) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tc @ i @ enc ) @ ( B @ ( tmk @ i @ enc ) @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
kk @ i @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_7) ).
thf(64,plain,
kk @ i @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( lp @ i @ enc ) @ ( B @ ( wk @ i @ enc ) @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_translate_PIN_from_local_storage_to_interchange_key) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( lp @ i @ enc ) @ ( B @ ( wk @ i @ enc ) @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
a @ ( pp @ enc ) @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( a @ ( pp @ enc ) @ p ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ( a @ ( pp @ enc ) @ p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
t2 @ ( lp @ enc ) @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_4) ).
thf(80,plain,
t2 @ ( lp @ enc ) @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ enc ) @ ( A @ i @ enc ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',enc_dec_cancel) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ enc ) @ ( A @ i @ enc ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',attacker_can_encrypt) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tmk @ i @ enc ) @ ( B @ ( tmk @ i @ enc ) @ enc ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_a_PIN_derivation_key_under_a_TMK) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ p )
& ( B @ p )
& ( A @ p ) )
=> ( A @ ( tmk @ i @ enc ) @ ( B @ ( tmk @ i @ enc ) @ enc ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(90,plain,
$false,
inference(e,[status(thm)],[69,52,65,73,76,66,48,31,43,58,51,79,62,70,28,38,32,45,64,59,27,80,35,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV237+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.13/0.40 % 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 13:16:33 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.18 % [INFO] Parsing done (204ms).
% 1.41/1.20 % [INFO] Running in sequential loop mode.
% 1.87/1.59 % [INFO] eprover registered as external prover.
% 2.05/1.60 % [INFO] Scanning for conjecture ...
% 2.05/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 24 axioms. Running axiom selection ...
% 2.21/1.76 % [INFO] Axiom selection finished. Selected 24 axioms (removed 0 axioms).
% 2.40/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.40/1.83 % [INFO] Type checking passed.
% 2.40/1.84 % [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 ...
% 3.94/2.58 % External prover 'e' found a proof!
% 3.94/2.58 % [INFO] Killing All external provers ...
% 3.94/2.58 % Time passed: 2050ms (effective reasoning time: 1373ms)
% 3.94/2.58 % 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)>
% 3.94/2.58 % Axioms used in derivation (24): intruder_knows_3, receive_working_key_from_switch, data_translate_between_interchange_keys, key_translate_from_ZCMK_to_TMK, data_translate_PIN_from_local_storage_to_interchange_key, data_decrypt, intruder_knows_1, data_encrypt, key_translate_from_TMK_to_ZCMK, intruder_knows_7, intruder_knows_4, data_translate_PIN_from_local_to_interchange_key, keys_are_symmetric, dec_enc_cancel, intruder_knows_6, intruder_knows_8, encrypt_clear_key_as_Tcomms_key, intruder_knows_2, attacker_can_encrypt, double_inverse_cancel, encrypt_a_stored_comms_key, intruder_knows_5, enc_dec_cancel, encrypt_a_PIN_derivation_key_under_a_TMK
% 3.94/2.58 % No. of inferences in proof: 52
% 3.94/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2050 ms resp. 1373 ms w/o parsing
% 4.31/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.31/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------