%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV234+2 : 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 : n002.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 6.22s 3.65s
% Output : Refutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 261 ( 2 ~; 0 |; 16 &; 229 @)
% ( 0 <=>; 14 =>; 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 : 16 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(public_decl,type,
public: $i > $o ).
thf(enc_decl,type,
enc: $i > $i > $i ).
thf(pp_decl,type,
pp: $i ).
thf(a_decl,type,
a: $i ).
thf(xor_decl,type,
xor: $i > $i > $i ).
thf(z_decl,type,
z: $i ).
thf(k3_decl,type,
k3: $i ).
thf(km_decl,type,
km: $i ).
thf(imp_decl,type,
imp: $i ).
thf(inv_decl,type,
inv: $i > $i ).
thf(kp_decl,type,
kp: $i > $i ).
thf(data_decl,type,
data: $i ).
thf(kek_decl,type,
kek: $i ).
thf(pin_decl,type,
pin: $i ).
thf(18,axiom,
data @ ( pin @ xor ) @ ( kek @ xor ) @ ( imp @ ( km @ xor ) @ enc ) @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge9) ).
thf(56,plain,
data @ ( pin @ xor ) @ ( kek @ xor ) @ ( imp @ ( km @ xor ) @ enc ) @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
imp @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge1) ).
thf(52,plain,
imp @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
pp @ ( pin @ ( kek @ xor ) @ enc ) @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge5) ).
thf(61,plain,
pp @ ( pin @ ( kek @ xor ) @ enc ) @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(21,axiom,
pin @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge4) ).
thf(60,plain,
pin @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ inv @ enc ) @ public ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ability_to_decrypt) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ inv @ enc ) @ public ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( imp @ ( km @ xor ) @ enc ) @ public )
& ( C @ ( B @ ( A @ xor ) @ enc ) @ public )
& ( B @ public ) )
=> ( C @ ( B @ ( km @ xor ) @ enc ) @ public ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_import_cmd) ).
thf(41,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( imp @ ( km @ xor ) @ enc ) @ public )
& ( C @ ( B @ ( A @ xor ) @ enc ) @ public )
& ( B @ public ) )
=> ( C @ ( B @ ( km @ xor ) @ enc ) @ public ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( z @ ( A @ xor ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_zero) ).
thf(34,plain,
! [A: $i] :
( ( z @ ( A @ xor ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ xor ) @ public ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ability_to_xor) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ xor ) @ public ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ inv @ enc ) @ ( A @ enc ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_decrypt_cancel) ).
thf(43,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ inv @ enc ) @ ( A @ enc ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ public )
=> ( A @ kp @ public ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kp_set) ).
thf(58,plain,
! [A: $i] :
( ( A @ public )
=> ( A @ kp @ public ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
data @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge2) ).
thf(62,plain,
data @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
a @ ( pp @ enc ) @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( a @ ( pp @ enc ) @ public ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(24,plain,
~ ( a @ ( pp @ enc ) @ public ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
k3 @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge6) ).
thf(37,plain,
k3 @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ xor ) )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_self_cancel) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( A @ xor ) )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ kp @ ( km @ xor ) @ enc ) @ public )
& ( C @ public )
& ( B @ kp @ public ) )
=> ( C @ ( A @ xor ) @ ( B @ ( km @ xor ) @ enc ) @ public ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import_cmd) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ kp @ ( km @ xor ) @ enc ) @ public )
& ( C @ public )
& ( B @ kp @ public ) )
=> ( C @ ( A @ xor ) @ ( B @ ( km @ xor ) @ enc ) @ public ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
k3 @ ( kek @ xor ) @ ( imp @ kp @ ( km @ xor ) @ enc ) @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge7) ).
thf(57,plain,
k3 @ ( kek @ xor ) @ ( imp @ kp @ ( km @ xor ) @ enc ) @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutes) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ xor ) )
= ( A @ ( B @ xor ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ enc ) @ public ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ability_to_encrypt) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ enc ) @ public ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ ( km @ ( data @ xor ) @ inv @ enc ) @ enc ) @ public ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_data_cmd) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( ( B @ public )
& ( A @ public ) )
=> ( B @ ( A @ ( km @ ( data @ xor ) @ inv @ enc ) @ enc ) @ public ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,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_assosciative) ).
thf(31,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)],[5]) ).
thf(9,axiom,
a @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge8) ).
thf(40,plain,
a @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
z @ public,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge3) ).
thf(55,plain,
z @ public,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(75,plain,
$false,
inference(e,[status(thm)],[56,52,61,60,53,41,34,48,43,58,62,24,37,25,46,57,28,38,50,31,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.21/0.48 % Computer : n002.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Sat Sep 26 13:23:36 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 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
% 1.44/1.31 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.78/1.60 % [INFO] Parsing done (285ms).
% 2.02/1.62 % [INFO] Running in sequential loop mode.
% 3.07/2.22 % [INFO] eprover registered as external prover.
% 3.07/2.23 % [INFO] Scanning for conjecture ...
% 3.27/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 3.45/2.46 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 3.66/2.53 % [INFO] Problem is first-order (TPTP FOF).
% 3.66/2.54 % [INFO] Type checking passed.
% 3.66/2.55 % [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 ...
% 6.22/3.64 % External prover 'e' found a proof!
% 6.22/3.64 % [INFO] Killing All external provers ...
% 6.22/3.64 % Time passed: 2957ms (effective reasoning time: 2014ms)
% 6.22/3.64 % 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)>
% 6.22/3.65 % Axioms used in derivation (21): kp_set, encrypt_decrypt_cancel, initial_knowledge7, initial_knowledge3, encrypt_data_cmd, xor_commutes, xor_zero, initial_knowledge4, initial_knowledge1, initial_knowledge8, initial_knowledge2, key_part_import_cmd, xor_assosciative, xor_self_cancel, initial_knowledge6, initial_knowledge5, key_import_cmd, ability_to_xor, ability_to_encrypt, initial_knowledge9, ability_to_decrypt
% 6.22/3.65 % No. of inferences in proof: 46
% 6.22/3.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2957 ms resp. 2014 ms w/o parsing
% 6.65/3.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.65/3.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------