%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV751_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 01:26:21 PM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 48 ~; 46 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 15 con; 0-4 aty)
% Number of variables : 86 ( 84 !; 2 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
event: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
agent: $tType ).
tff(type_def_9,type,
msg: $tType ).
tff(type_def_10,type,
nat: $tType ).
tff(type_def_11,type,
keymode: $tType ).
tff(type_def_12,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
bad: fun(agent,bool) ).
tff(func_def_1,type,
notes: ( agent * msg ) > event ).
tff(func_def_2,type,
says: ( agent * agent * msg ) > event ).
tff(func_def_3,type,
knows: ( agent * list(event) ) > fun(msg,bool) ).
tff(func_def_4,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_5,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_6,type,
server: agent ).
tff(func_def_7,type,
spy: agent ).
tff(func_def_8,type,
analz: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_9,type,
agent1: agent > msg ).
tff(func_def_10,type,
crypt: ( nat * msg ) > msg ).
tff(func_def_11,type,
key: nat > msg ).
tff(func_def_12,type,
mPair: ( msg * msg ) > msg ).
tff(func_def_13,type,
nonce: nat > msg ).
tff(func_def_14,type,
parts: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_15,type,
symKeys: fun(nat,bool) ).
tff(func_def_16,type,
nS_Sha254967238shared: fun(list(event),bool) ).
tff(func_def_17,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_18,type,
publicKey: keymode > fun(agent,nat) ).
tff(func_def_19,type,
shrK: fun(agent,nat) ).
tff(func_def_20,type,
image:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > fun(X1,bool) ) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fFalse: bool ).
tff(func_def_23,type,
fTrue: bool ).
tff(func_def_24,type,
a: agent ).
tff(func_def_25,type,
b: agent ).
tff(func_def_26,type,
k: nat ).
tff(func_def_27,type,
k1: nat ).
tff(func_def_28,type,
na: msg ).
tff(func_def_29,type,
x: msg ).
tff(func_def_30,type,
evs: list(event) ).
tff(func_def_31,type,
sK0: ( list(event) * nat * msg ) > msg ).
tff(func_def_32,type,
sK1: fun(msg,bool) > msg ).
tff(func_def_33,type,
sK2: fun(msg,bool) > msg ).
tff(func_def_34,type,
sK3: fun(msg,bool) > msg ).
tff(func_def_35,type,
sK4: fun(msg,bool) > nat ).
tff(func_def_36,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
nS_Sha993195050haredp: list(event) > $o ).
tff(pred_def_2,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_3,type,
pp: bool > $o ).
tff(f8,axiom,
! [X0: list(event),X1: nat,X2: agent,X3: msg,X4: agent] :
( member(event,says(server,X4,crypt(aa(agent,nat,shrK,X4),mPair(X3,mPair(agent1(X2),mPair(key(X1),crypt(aa(agent,nat,shrK,X2),mPair(key(X1),agent1(X4)))))))),set(event,X0))
=> ( ~ member(agent,X4,bad)
=> ( ~ member(agent,X2,bad)
=> ( member(list(event),X0,nS_Sha254967238shared)
=> ( ! [X5: msg] : ~ member(event,notes(spy,mPair(X3,mPair(X5,key(X1)))),set(event,X0))
=> ~ member(msg,key(X1),analz(knows(spy,X0))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_secrecy__lemma) ).
tff(f92,axiom,
! [X0: list(event),X1: msg,X2: nat,X3: agent,X4: msg,X5: nat,X6: agent] :
( member(event,says(server,X6,crypt(X5,mPair(X4,mPair(agent1(X3),mPair(key(X2),X1))))),set(event,X0))
=> ( member(list(event),X0,nS_Sha254967238shared)
=> ( ~ member(nat,X2,image(agent,nat,shrK,top_top(fun(agent,bool))))
& ( X1 = crypt(aa(agent,nat,shrK,X3),mPair(key(X2),agent1(X6))) )
& ( X5 = aa(agent,nat,shrK,X6) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Says__Server__message__form) ).
tff(f103,axiom,
member(event,says(server,a,crypt(k1,mPair(na,mPair(agent1(b),mPair(key(k),x))))),set(event,evs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f104,axiom,
! [X0: msg] : ~ member(event,notes(spy,mPair(na,mPair(X0,key(k)))),set(event,evs)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f105,axiom,
~ member(agent,a,bad),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f106,axiom,
~ member(agent,b,bad),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
tff(f107,axiom,
member(list(event),evs,nS_Sha254967238shared),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(f108,conjecture,
~ member(msg,key(k),analz(knows(spy,evs))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
tff(f109,negated_conjecture,
~ ~ member(msg,key(k),analz(knows(spy,evs))),
inference(negated_conjecture,[status(cth)],[f108]) ).
tff(f111,plain,
member(msg,key(k),analz(knows(spy,evs))),
inference(flattening,[],[f109]) ).
tff(f119,plain,
! [X0: list(event),X1: nat,X2: agent,X3: msg,X4: agent] :
( ~ member(msg,key(X1),analz(knows(spy,X0)))
| ? [X5: msg] : member(event,notes(spy,mPair(X3,mPair(X5,key(X1)))),set(event,X0))
| ~ member(list(event),X0,nS_Sha254967238shared)
| member(agent,X2,bad)
| member(agent,X4,bad)
| ~ member(event,says(server,X4,crypt(aa(agent,nat,shrK,X4),mPair(X3,mPair(agent1(X2),mPair(key(X1),crypt(aa(agent,nat,shrK,X2),mPair(key(X1),agent1(X4)))))))),set(event,X0)) ),
inference(ennf_transformation,[],[f8]) ).
tff(f120,plain,
! [X0: list(event),X1: nat,X2: agent,X3: msg,X4: agent] :
( ~ member(msg,key(X1),analz(knows(spy,X0)))
| ? [X5: msg] : member(event,notes(spy,mPair(X3,mPair(X5,key(X1)))),set(event,X0))
| ~ member(list(event),X0,nS_Sha254967238shared)
| member(agent,X2,bad)
| member(agent,X4,bad)
| ~ member(event,says(server,X4,crypt(aa(agent,nat,shrK,X4),mPair(X3,mPair(agent1(X2),mPair(key(X1),crypt(aa(agent,nat,shrK,X2),mPair(key(X1),agent1(X4)))))))),set(event,X0)) ),
inference(flattening,[],[f119]) ).
tff(f164,plain,
! [X0: list(event),X1: msg,X2: nat,X3: agent,X4: msg,X5: nat,X6: agent] :
( ( ~ member(nat,X2,image(agent,nat,shrK,top_top(fun(agent,bool))))
& ( X1 = crypt(aa(agent,nat,shrK,X3),mPair(key(X2),agent1(X6))) )
& ( X5 = aa(agent,nat,shrK,X6) ) )
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(event,says(server,X6,crypt(X5,mPair(X4,mPair(agent1(X3),mPair(key(X2),X1))))),set(event,X0)) ),
inference(ennf_transformation,[],[f92]) ).
tff(f165,plain,
! [X0: list(event),X1: msg,X2: nat,X3: agent,X4: msg,X5: nat,X6: agent] :
( ( ~ member(nat,X2,image(agent,nat,shrK,top_top(fun(agent,bool))))
& ( X1 = crypt(aa(agent,nat,shrK,X3),mPair(key(X2),agent1(X6))) )
& ( X5 = aa(agent,nat,shrK,X6) ) )
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(event,says(server,X6,crypt(X5,mPair(X4,mPair(agent1(X3),mPair(key(X2),X1))))),set(event,X0)) ),
inference(flattening,[],[f164]) ).
tff(f183,plain,
! [X2: agent,X3: msg,X0: list(event),X1: nat,X4: agent] :
( ~ member(event,says(server,X4,crypt(aa(agent,nat,shrK,X4),mPair(X3,mPair(agent1(X2),mPair(key(X1),crypt(aa(agent,nat,shrK,X2),mPair(key(X1),agent1(X4)))))))),set(event,X0))
| member(agent,X4,bad)
| member(agent,X2,bad)
| ~ member(list(event),X0,nS_Sha254967238shared)
| member(event,notes(spy,mPair(X3,mPair(sK0(X0,X1,X3),key(X1)))),set(event,X0))
| ~ member(msg,key(X1),analz(knows(spy,X0))) ),
inference(cnf_transformation,[],[f120]) ).
tff(f294,plain,
! [X2: nat,X3: agent,X0: list(event),X1: msg,X6: agent,X4: msg,X5: nat] :
( ~ member(event,says(server,X6,crypt(X5,mPair(X4,mPair(agent1(X3),mPair(key(X2),X1))))),set(event,X0))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ( aa(agent,nat,shrK,X6) = X5 ) ),
inference(cnf_transformation,[],[f165]) ).
tff(f295,plain,
! [X2: nat,X3: agent,X0: list(event),X1: msg,X6: agent,X4: msg,X5: nat] :
( ~ member(event,says(server,X6,crypt(X5,mPair(X4,mPair(agent1(X3),mPair(key(X2),X1))))),set(event,X0))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ( crypt(aa(agent,nat,shrK,X3),mPair(key(X2),agent1(X6))) = X1 ) ),
inference(cnf_transformation,[],[f165]) ).
tff(f309,plain,
member(event,says(server,a,crypt(k1,mPair(na,mPair(agent1(b),mPair(key(k),x))))),set(event,evs)),
inference(cnf_transformation,[],[f103]) ).
tff(f310,plain,
! [X0: msg] : ~ member(event,notes(spy,mPair(na,mPair(X0,key(k)))),set(event,evs)),
inference(cnf_transformation,[],[f104]) ).
tff(f311,plain,
~ member(agent,a,bad),
inference(cnf_transformation,[],[f105]) ).
tff(f312,plain,
~ member(agent,b,bad),
inference(cnf_transformation,[],[f106]) ).
tff(f313,plain,
member(list(event),evs,nS_Sha254967238shared),
inference(cnf_transformation,[],[f107]) ).
tff(f314,plain,
member(msg,key(k),analz(knows(spy,evs))),
inference(cnf_transformation,[],[f111]) ).
tff(f341,plain,
! [X2: agent,X3: msg,X0: list(event),X1: nat,X4: agent] :
( ~ member(event,notes(spy,mPair(X3,mPair(sK0(X0,X1,X3),key(X1)))),set(event,X0))
| ~ member(agent,X4,bad)
| ~ member(agent,X2,bad)
| member(list(event),X0,nS_Sha254967238shared)
| member(event,says(server,X4,crypt(aa(agent,nat,shrK,X4),mPair(X3,mPair(agent1(X2),mPair(key(X1),crypt(aa(agent,nat,shrK,X2),mPair(key(X1),agent1(X4)))))))),set(event,X0))
| member(msg,key(X1),analz(knows(spy,X0))) ),
inference(consistent_polarity_flipping,[],[f183]) ).
tff(f396,plain,
! [X2: nat,X3: agent,X0: list(event),X1: msg,X6: agent,X4: msg,X5: nat] :
( member(event,says(server,X6,crypt(X5,mPair(X4,mPair(agent1(X3),mPair(key(X2),X1))))),set(event,X0))
| member(list(event),X0,nS_Sha254967238shared)
| ( crypt(aa(agent,nat,shrK,X3),mPair(key(X2),agent1(X6))) = X1 ) ),
inference(consistent_polarity_flipping,[],[f295]) ).
tff(f397,plain,
! [X2: nat,X3: agent,X0: list(event),X1: msg,X6: agent,X4: msg,X5: nat] :
( member(event,says(server,X6,crypt(X5,mPair(X4,mPair(agent1(X3),mPair(key(X2),X1))))),set(event,X0))
| member(list(event),X0,nS_Sha254967238shared)
| ( aa(agent,nat,shrK,X6) = X5 ) ),
inference(consistent_polarity_flipping,[],[f294]) ).
tff(f410,plain,
~ member(event,says(server,a,crypt(k1,mPair(na,mPair(agent1(b),mPair(key(k),x))))),set(event,evs)),
inference(consistent_polarity_flipping,[],[f309]) ).
tff(f411,plain,
! [X0: msg] : member(event,notes(spy,mPair(na,mPair(X0,key(k)))),set(event,evs)),
inference(consistent_polarity_flipping,[],[f310]) ).
tff(f412,plain,
member(agent,a,bad),
inference(consistent_polarity_flipping,[],[f311]) ).
tff(f413,plain,
member(agent,b,bad),
inference(consistent_polarity_flipping,[],[f312]) ).
tff(f414,plain,
~ member(list(event),evs,nS_Sha254967238shared),
inference(consistent_polarity_flipping,[],[f313]) ).
tff(f415,plain,
~ member(msg,key(k),analz(knows(spy,evs))),
inference(consistent_polarity_flipping,[],[f314]) ).
tff(f489,plain,
( member(list(event),evs,nS_Sha254967238shared)
| ( k1 = aa(agent,nat,shrK,a) ) ),
inference(resolution,[],[f397,f410]) ).
tff(f490,plain,
k1 = aa(agent,nat,shrK,a),
inference(forward_subsumption_resolution,[],[f489,f414]) ).
tff(f493,plain,
( member(list(event),evs,nS_Sha254967238shared)
| ( x = crypt(aa(agent,nat,shrK,b),mPair(key(k),agent1(a))) ) ),
inference(resolution,[],[f396,f410]) ).
tff(f494,plain,
x = crypt(aa(agent,nat,shrK,b),mPair(key(k),agent1(a))),
inference(forward_subsumption_resolution,[],[f493,f414]) ).
tff(f546,plain,
! [X0: agent,X1: agent] :
( ~ member(agent,X0,bad)
| ~ member(agent,X1,bad)
| member(list(event),evs,nS_Sha254967238shared)
| member(event,says(server,X0,crypt(aa(agent,nat,shrK,X0),mPair(na,mPair(agent1(X1),mPair(key(k),crypt(aa(agent,nat,shrK,X1),mPair(key(k),agent1(X0)))))))),set(event,evs))
| member(msg,key(k),analz(knows(spy,evs))) ),
inference(resolution,[],[f341,f411]) ).
tff(f550,plain,
! [X0: agent,X1: agent] :
( ~ member(agent,X0,bad)
| ~ member(agent,X1,bad)
| member(event,says(server,X0,crypt(aa(agent,nat,shrK,X0),mPair(na,mPair(agent1(X1),mPair(key(k),crypt(aa(agent,nat,shrK,X1),mPair(key(k),agent1(X0)))))))),set(event,evs))
| member(msg,key(k),analz(knows(spy,evs))) ),
inference(forward_subsumption_resolution,[],[f546,f414]) ).
tff(f551,plain,
! [X0: agent,X1: agent] :
( member(event,says(server,X0,crypt(aa(agent,nat,shrK,X0),mPair(na,mPair(agent1(X1),mPair(key(k),crypt(aa(agent,nat,shrK,X1),mPair(key(k),agent1(X0)))))))),set(event,evs))
| ~ member(agent,X1,bad)
| ~ member(agent,X0,bad) ),
inference(forward_subsumption_resolution,[],[f550,f415]) ).
tff(f558,plain,
( member(event,says(server,a,crypt(aa(agent,nat,shrK,a),mPair(na,mPair(agent1(b),mPair(key(k),x))))),set(event,evs))
| ~ member(agent,b,bad)
| ~ member(agent,a,bad) ),
inference(superposition,[],[f551,f494]) ).
tff(f567,plain,
( member(event,says(server,a,crypt(aa(agent,nat,shrK,a),mPair(na,mPair(agent1(b),mPair(key(k),x))))),set(event,evs))
| ~ member(agent,a,bad) ),
inference(forward_subsumption_resolution,[],[f558,f413]) ).
tff(f568,plain,
member(event,says(server,a,crypt(aa(agent,nat,shrK,a),mPair(na,mPair(agent1(b),mPair(key(k),x))))),set(event,evs)),
inference(forward_subsumption_resolution,[],[f567,f412]) ).
tff(f569,plain,
member(event,says(server,a,crypt(k1,mPair(na,mPair(agent1(b),mPair(key(k),x))))),set(event,evs)),
inference(forward_demodulation,[],[f568,f490]) ).
tff(f570,plain,
$false,
inference(forward_subsumption_resolution,[],[f569,f410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV751_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 12:26:17 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.28 % (755131)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (755138)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1671469136:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (755137)% WARNING: option uhcvi not known.
% 0.20/0.28 % (755136)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=535591509_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (755137)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=463076303:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (755139)dis+10_1_sil=32000:sp=arity:random_seed=645241574:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (755140)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2670774045:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (755142)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2513471606:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (755141)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=248317184:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (755137) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-755131-755137"...
% 0.20/0.28 % (755137)...printing done.
% 0.20/0.28 % (755137)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (755137)------------------------------
% 0.20/0.28 % (755137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (755137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (755137)CaDiCaL version: 2.1.3
% 0.20/0.28 % (755137)Termination reason: Refutation
% 0.20/0.28 % (755137)Time elapsed: 0.020 s
% 0.20/0.28 % (755137)Peak memory usage: 12 MB
% 0.20/0.28 % (755137)Instructions burned: 31 (million)
% 0.20/0.28 % (755131)Success in time 0.063 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------