%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV811_5 : TPTP v9.3.1. Released v6.0.0.
% 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 09:00:40 AM UTC 2026
% Result : Theorem 56.84s 18.96s
% Output : Refutation 56.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 574 ( 19 ~; 12 |; 4 &; 536 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 9 con; 0-5 aty)
% Number of variables : 36 ( 0 ^; 33 !; 3 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(event_type,type,
event: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(agent_type,type,
agent: $tType ).
thf(msg_type,type,
msg: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(says_decl,type,
says: agent > agent > msg > event ).
thf(initState_decl,type,
initState: agent > ( bool @ ( msg @ fun ) ) ).
thf(knows_decl,type,
knows: agent > ( event @ list ) > ( bool @ ( msg @ fun ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(rev_decl,type,
rev:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(set_decl,type,
set:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( TA @ fun ) ) ) ).
thf(takeWhile_decl,type,
takeWhile:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(spy_decl,type,
spy: agent ).
thf(analz_decl,type,
analz: ( bool @ ( msg @ fun ) ) > ( bool @ ( msg @ fun ) ) ).
thf(crypt_decl,type,
crypt: nat > msg > msg ).
thf(key_decl,type,
key: nat > msg ).
thf(mPair_decl,type,
mPair: msg > msg > msg ).
thf(nonce_decl,type,
nonce: nat > msg ).
thf(parts_decl,type,
parts: ( bool @ ( msg @ fun ) ) > ( bool @ ( msg @ fun ) ) ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(a_decl,type,
a: agent ).
thf(b_decl,type,
b: agent ).
thf(k_decl,type,
k: nat ).
thf(nb_decl,type,
nb: nat ).
thf(90,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_takeWhile_Osimps_I1_J) ).
thf(467,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(468,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
inference(cnf,[status(esa)],[467]) ).
thf(469,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ takeWhile ) ) )
= ( TA @ nil ) ),
inference(lifteq,[status(thm)],[468]) ).
thf(56,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rev__is__Nil__conv) ).
thf(348,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(349,plain,
! [TA: $tType,A: TA @ list] :
( ( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
| ( ( A @ ( TA @ rev ) )
!= ( TA @ nil ) ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(351,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) ) ),
inference(cnfConj,[status(thm)],[349]) ).
thf(353,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rev ) )
= ( TA @ nil ) )
| ( A
!= ( TA @ nil ) ) ),
inference(lifteq,[status(thm)],[351]) ).
thf(354,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ rev ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[353]) ).
thf(1,conjecture,
( ~ ( event @ nil @ ( event @ rev ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ) )
| ~ ( event @ nil @ ( event @ set ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ member ) ) )
| ( event @ nil @ ( spy @ knows ) @ analz @ ( k @ key @ ( msg @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( ~ ( event @ nil @ ( event @ rev ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ) )
| ~ ( event @ nil @ ( event @ set ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ member ) ) )
| ( event @ nil @ ( spy @ knows ) @ analz @ ( k @ key @ ( msg @ member ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( ~ ( event @ nil @ ( event @ rev ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ) )
| ~ ( event @ nil @ ( event @ set ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ member ) ) )
| ( event @ nil @ ( spy @ knows ) @ analz @ ( k @ key @ ( msg @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(114,plain,
( ( event @ nil @ ( event @ rev ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ) )
& ( event @ nil @ ( event @ set ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ member ) ) )
& ~ ( event @ nil @ ( spy @ knows ) @ analz @ ( k @ key @ ( msg @ member ) ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(117,plain,
event @ nil @ ( event @ rev ) @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(591,plain,
( ( ( event @ nil @ ( event @ rev ) )
!= ( event @ nil @ ( event @ rev ) ) )
| ( event @ nil @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ) ) ),
inference(paramod_ordered,[status(thm)],[354,117]) ).
thf(592,plain,
event @ nil @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ),
inference(pattern_uni,[status(thm)],[591:[]]) ).
thf(614,plain,
! [A: bool @ ( event @ fun )] :
( ( ( event @ nil @ ( A @ ( event @ takeWhile ) ) )
!= ( event @ nil @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) @ ( event @ takeWhile ) ) ) )
| ( event @ nil @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ) ) ),
inference(paramod_ordered,[status(thm)],[469,592]) ).
thf(615,plain,
event @ nil @ ( spy @ knows ) @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ),
inference(pattern_uni,[status(thm)],[614:[bind(A,$thf( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( b @ ( a @ says ) ) @ ( event @ fequal @ ( bool @ ( event @ ( event @ combc ) ) ) ) @ ( fNot @ ( event @ ( bool @ ( bool @ combb ) ) ) ) ))]]) ).
thf(13,axiom,
! [A: agent] :
( ( event @ nil @ ( A @ knows ) )
= ( A @ initState ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_knows__Nil) ).
thf(175,plain,
! [A: agent] :
( ( event @ nil @ ( A @ knows ) )
= ( A @ initState ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(176,plain,
! [A: agent] :
( ( event @ nil @ ( A @ knows ) )
= ( A @ initState ) ),
inference(cnf,[status(esa)],[175]) ).
thf(177,plain,
! [A: agent] :
( ( event @ nil @ ( A @ knows ) )
= ( A @ initState ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(782,plain,
spy @ initState @ parts @ ( nb @ nonce @ ( nb @ nonce @ mPair ) @ ( k @ crypt ) @ ( msg @ member ) ),
inference(rewrite,[status(thm)],[615,177]) ).
thf(89,axiom,
! [A: agent,B: msg,C: nat] :
~ ( A @ initState @ parts @ ( B @ ( C @ crypt ) @ ( msg @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Crypt__notin__initState) ).
thf(464,plain,
! [A: agent,B: msg,C: nat] :
~ ( A @ initState @ parts @ ( B @ ( C @ crypt ) @ ( msg @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(465,plain,
~ ? [A: agent,B: msg,C: nat] : ( A @ initState @ parts @ ( B @ ( C @ crypt ) @ ( msg @ member ) ) ),
inference(miniscope,[status(thm)],[464]) ).
thf(466,plain,
! [C: nat,B: msg,A: agent] :
~ ( A @ initState @ parts @ ( B @ ( C @ crypt ) @ ( msg @ member ) ) ),
inference(cnf,[status(esa)],[465]) ).
thf(2479,plain,
$false,
inference(rewrite,[status(thm)],[782,466]) ).
thf(2480,plain,
$false,
inference(simp,[status(thm)],[2479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV811_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.12 % 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
% 0.21/0.49 % Computer : n005.cluster.edu
% 0.21/0.49 % Model : x86_64 x86_64
% 0.21/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.49 % Memory : 8046.5625MB
% 0.21/0.49 % OS : Linux 6.8.0-71-generic
% 0.21/0.49 % CPULimit : 300
% 0.21/0.49 % WCLimit : 300
% 0.21/0.49 % DateTime : Sat Sep 26 14:59:47 UTC 2026
% 0.21/0.49 % CPUTime :
% 0.21/0.49 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
% 1.26/1.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.35/1.50 % [INFO] Parsing done (306ms).
% 2.35/1.52 % [INFO] Running in sequential loop mode.
% 3.48/1.91 % [INFO] eprover registered as external prover.
% 3.48/1.92 % [INFO] Scanning for conjecture ...
% 4.03/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 110 axioms. Running axiom selection ...
% 4.44/2.37 % [INFO] Axiom selection finished. Selected 110 axioms (removed 0 axioms).
% 5.40/2.65 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.68/2.70 % [INFO] Type checking passed.
% 5.68/2.71 % [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 ...
% 56.84/18.95 % [INFO] Killing All external provers ...
% 56.84/18.95 % Time passed: 18237ms (effective reasoning time: 17428ms)
% 56.84/18.95 % 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)>
% 56.84/18.96 % Axioms used in derivation (4): fact_5_takeWhile_Osimps_I1_J, fact_9_rev__is__Nil__conv, fact_59_knows__Nil, fact_89_Crypt__notin__initState
% 56.84/18.96 % No. of inferences in proof: 30
% 56.84/18.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18237 ms resp. 17428 ms w/o parsing
% 56.84/19.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 56.84/19.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------