%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV803_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 01:19:33 PM UTC 2026
% Result : Theorem 3.04s 1.13s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 95 ( 22 unt; 0 typ; 6 def)
% Number of atoms : 255 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 284 ( 124 ~; 122 |; 20 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-4 aty)
% Number of functors : 47 ( 47 usr; 22 con; 0-4 aty)
% Number of variables : 158 ( 0 sgn 158 !; 0 ?; 158 :)
% 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,
agent1: $tType ).
tff(type_def_9,type,
msg: $tType ).
tff(type_def_10,type,
nat: $tType ).
tff(type_def_11,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
bad: fun(agent1,bool) ).
tff(func_def_1,type,
notes: ( agent1 * msg ) > event ).
tff(func_def_2,type,
says: ( agent1 * agent1 * msg ) > event ).
tff(func_def_3,type,
knows: ( agent1 * list(event) ) > fun(msg,bool) ).
tff(func_def_4,type,
used: list(event) > fun(msg,bool) ).
tff(func_def_5,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_7,type,
server: agent1 ).
tff(func_def_8,type,
spy: agent1 ).
tff(func_def_9,type,
analz: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_10,type,
agent: agent1 > msg ).
tff(func_def_11,type,
crypt: ( nat * msg ) > msg ).
tff(func_def_12,type,
key: nat > msg ).
tff(func_def_13,type,
mPair: ( msg * msg ) > msg ).
tff(func_def_14,type,
nonce: nat > msg ).
tff(func_def_15,type,
parts: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_16,type,
symKeys: fun(nat,bool) ).
tff(func_def_17,type,
nS_Sha254967238shared: fun(list(event),bool) ).
tff(func_def_18,type,
shrK: agent1 > nat ).
tff(func_def_19,type,
aa1:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
a: agent1 ).
tff(func_def_23,type,
aa: agent1 ).
tff(func_def_24,type,
b: agent1 ).
tff(func_def_25,type,
b1: agent1 ).
tff(func_def_26,type,
ba: agent1 ).
tff(func_def_27,type,
k: nat ).
tff(func_def_28,type,
ka: nat ).
tff(func_def_29,type,
na: nat ).
tff(func_def_30,type,
nAa: nat ).
tff(func_def_31,type,
nb: nat ).
tff(func_def_32,type,
nBa: nat ).
tff(func_def_33,type,
s: agent1 ).
tff(func_def_34,type,
x: msg ).
tff(func_def_35,type,
xa: msg ).
tff(func_def_36,type,
evs5: list(event) ).
tff(func_def_37,type,
sK0: ( list(event) * nat ) > msg ).
tff(func_def_38,type,
sK1: ( list(event) * nat ) > msg ).
tff(func_def_39,type,
sK2: ( msg * list(event) * nat ) > msg ).
tff(func_def_40,type,
sK3: ( msg * agent1 * list(event) ) > agent1 ).
tff(func_def_41,type,
sK4: ( list(event) * agent1 * nat * agent1 ) > msg ).
tff(func_def_42,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_43,type,
sK6: ( list(event) * nat * msg ) > msg ).
tff(func_def_44,type,
sK7: ( list(event) * nat * msg ) > msg ).
tff(pred_def_1,type,
nS_Sha512322870Issues: ( agent1 * agent1 * msg * list(event) ) > $o ).
tff(pred_def_2,type,
nS_Sha993195050haredp: list(event) > $o ).
tff(pred_def_3,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(f8,axiom,
! [X0: list(event),X1: msg,X2: agent1] :
( member(msg,crypt(shrK(X2),X1),analz(knows(spy,X0)))
=> ( member(agent1,X2,bad)
=> member(msg,X1,analz(knows(spy,X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Crypt__Spy__analz__bad) ).
tff(f12,axiom,
! [X0: list(event),X1: msg,X2: agent1,X3: agent1] :
( member(event,says(X3,X2,X1),set(event,X0))
=> member(msg,X1,analz(knows(spy,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Says__imp__analz__Spy) ).
tff(f27,axiom,
! [X0: fun(msg,bool),X1: msg,X2: msg] :
( member(msg,mPair(X2,X1),analz(X0))
=> ~ ( member(msg,X2,analz(X0))
=> ~ member(msg,X1,analz(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_MPair__analz) ).
tff(f28,axiom,
! [X0: fun(msg,bool),X1: msg] :
( ( member(msg,X1,analz(X0))
| member(msg,X1,parts(X0)) )
<=> member(msg,X1,parts(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_analz__disj__parts) ).
tff(f68,axiom,
! [X0: list(event),X1: msg,X2: nat,X3: agent1,X4: msg,X5: agent1] :
( member(msg,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1)))),parts(knows(spy,X0)))
=> ( ~ member(agent1,X5,bad)
=> ( member(list(event),X0,nS_Sha254967238shared)
=> member(event,says(server,X5,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1))))),set(event,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_A__trusts__NS2) ).
tff(f89,axiom,
! [X0: msg,X1: agent1,X2: msg,X3: agent1,X4: list(event),X5: msg,X6: nat,X7: agent1,X8: msg,X9: agent1] :
( member(event,says(server,X9,crypt(shrK(X9),mPair(X8,mPair(agent(X7),mPair(key(X6),X5))))),set(event,X4))
=> ( member(event,says(server,X3,crypt(shrK(X3),mPair(X2,mPair(agent(X1),mPair(key(X6),X0))))),set(event,X4))
=> ( member(list(event),X4,nS_Sha254967238shared)
=> ( ( X9 = X3 )
& ( X8 = X2 )
& ( X7 = X1 )
& ( X5 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_unique__session__keys) ).
tff(f103,axiom,
~ member(agent1,a,bad),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f105,axiom,
member(list(event),evs5,nS_Sha254967238shared),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f108,axiom,
member(event,says(s,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(ka),xa))))),set(event,evs5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
tff(f109,axiom,
~ member(msg,key(k),analz(knows(spy,evs5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
tff(f111,conjecture,
( ~ member(msg,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),parts(knows(spy,evs5)))
| ( k != ka )
| ( nb != nBa )
| ( ( a = aa )
& ( b = ba ) )
| member(event,says(a,b,crypt(ka,mPair(nonce(nBa),nonce(nBa)))),set(event,evs5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_8) ).
tff(f112,negated_conjecture,
~ ( ~ member(msg,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),parts(knows(spy,evs5)))
| ( k != ka )
| ( nb != nBa )
| ( ( a = aa )
& ( b = ba ) )
| member(event,says(a,b,crypt(ka,mPair(nonce(nBa),nonce(nBa)))),set(event,evs5)) ),
inference(negated_conjecture,[status(cth)],[f111]) ).
tff(f120,plain,
! [X0: list(event),X1: msg,X2: agent1] :
( member(msg,X1,analz(knows(spy,X0)))
| ~ member(agent1,X2,bad)
| ~ member(msg,crypt(shrK(X2),X1),analz(knows(spy,X0))) ),
inference(ennf_transformation,[],[f8]) ).
tff(f121,plain,
! [X0: list(event),X1: msg,X2: agent1] :
( member(msg,X1,analz(knows(spy,X0)))
| ~ member(agent1,X2,bad)
| ~ member(msg,crypt(shrK(X2),X1),analz(knows(spy,X0))) ),
inference(flattening,[],[f120]) ).
tff(f123,plain,
! [X0: list(event),X1: msg,X2: agent1,X3: agent1] :
( member(msg,X1,analz(knows(spy,X0)))
| ~ member(event,says(X3,X2,X1),set(event,X0)) ),
inference(ennf_transformation,[],[f12]) ).
tff(f127,plain,
! [X0: fun(msg,bool),X1: msg,X2: msg] :
( ( member(msg,X1,analz(X0))
& member(msg,X2,analz(X0)) )
| ~ member(msg,mPair(X2,X1),analz(X0)) ),
inference(ennf_transformation,[],[f27]) ).
tff(f151,plain,
! [X0: list(event),X1: msg,X2: nat,X3: agent1,X4: msg,X5: agent1] :
( member(event,says(server,X5,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1))))),set(event,X0))
| ~ member(list(event),X0,nS_Sha254967238shared)
| member(agent1,X5,bad)
| ~ member(msg,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1)))),parts(knows(spy,X0))) ),
inference(ennf_transformation,[],[f68]) ).
tff(f152,plain,
! [X0: list(event),X1: msg,X2: nat,X3: agent1,X4: msg,X5: agent1] :
( member(event,says(server,X5,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1))))),set(event,X0))
| ~ member(list(event),X0,nS_Sha254967238shared)
| member(agent1,X5,bad)
| ~ member(msg,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1)))),parts(knows(spy,X0))) ),
inference(flattening,[],[f151]) ).
tff(f174,plain,
! [X0: msg,X1: agent1,X2: msg,X3: agent1,X4: list(event),X5: msg,X6: nat,X7: agent1,X8: msg,X9: agent1] :
( ( ( X9 = X3 )
& ( X8 = X2 )
& ( X7 = X1 )
& ( X5 = X0 ) )
| ~ member(list(event),X4,nS_Sha254967238shared)
| ~ member(event,says(server,X3,crypt(shrK(X3),mPair(X2,mPair(agent(X1),mPair(key(X6),X0))))),set(event,X4))
| ~ member(event,says(server,X9,crypt(shrK(X9),mPair(X8,mPair(agent(X7),mPair(key(X6),X5))))),set(event,X4)) ),
inference(ennf_transformation,[],[f89]) ).
tff(f175,plain,
! [X0: msg,X1: agent1,X2: msg,X3: agent1,X4: list(event),X5: msg,X6: nat,X7: agent1,X8: msg,X9: agent1] :
( ( ( X9 = X3 )
& ( X8 = X2 )
& ( X7 = X1 )
& ( X5 = X0 ) )
| ~ member(list(event),X4,nS_Sha254967238shared)
| ~ member(event,says(server,X3,crypt(shrK(X3),mPair(X2,mPair(agent(X1),mPair(key(X6),X0))))),set(event,X4))
| ~ member(event,says(server,X9,crypt(shrK(X9),mPair(X8,mPair(agent(X7),mPair(key(X6),X5))))),set(event,X4)) ),
inference(flattening,[],[f174]) ).
tff(f194,plain,
( member(msg,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),parts(knows(spy,evs5)))
& ( ka = k )
& ( nBa = nb )
& ( ( a != aa )
| ( b != ba ) )
& ~ member(event,says(a,b,crypt(ka,mPair(nonce(nBa),nonce(nBa)))),set(event,evs5)) ),
inference(ennf_transformation,[],[f112]) ).
tff(f207,plain,
! [X0: fun(msg,bool),X1: msg] :
( ( member(msg,X1,analz(X0))
| member(msg,X1,parts(X0))
| ~ member(msg,X1,parts(X0)) )
& ( member(msg,X1,parts(X0))
| ( ~ member(msg,X1,analz(X0))
& ~ member(msg,X1,parts(X0)) ) ) ),
inference(nnf_transformation,[],[f28]) ).
tff(f208,plain,
! [X0: fun(msg,bool),X1: msg] :
( ( member(msg,X1,analz(X0))
| member(msg,X1,parts(X0))
| ~ member(msg,X1,parts(X0)) )
& ( member(msg,X1,parts(X0))
| ( ~ member(msg,X1,analz(X0))
& ~ member(msg,X1,parts(X0)) ) ) ),
inference(flattening,[],[f207]) ).
tff(f230,plain,
! [X2: agent1,X0: list(event),X1: msg] :
( ~ member(msg,crypt(shrK(X2),X1),analz(knows(spy,X0)))
| ~ member(agent1,X2,bad)
| member(msg,X1,analz(knows(spy,X0))) ),
inference(cnf_transformation,[],[f121]) ).
tff(f234,plain,
! [X2: agent1,X3: agent1,X0: list(event),X1: msg] :
( ~ member(event,says(X3,X2,X1),set(event,X0))
| member(msg,X1,analz(knows(spy,X0))) ),
inference(cnf_transformation,[],[f123]) ).
tff(f261,plain,
! [X2: msg,X0: fun(msg,bool),X1: msg] :
( ~ member(msg,mPair(X2,X1),analz(X0))
| member(msg,X2,analz(X0)) ),
inference(cnf_transformation,[],[f127]) ).
tff(f262,plain,
! [X2: msg,X0: fun(msg,bool),X1: msg] :
( ~ member(msg,mPair(X2,X1),analz(X0))
| member(msg,X1,analz(X0)) ),
inference(cnf_transformation,[],[f127]) ).
tff(f264,plain,
! [X0: fun(msg,bool),X1: msg] :
( member(msg,X1,parts(X0))
| ~ member(msg,X1,analz(X0)) ),
inference(cnf_transformation,[],[f208]) ).
tff(f309,plain,
! [X2: nat,X3: agent1,X0: list(event),X1: msg,X4: msg,X5: agent1] :
( ~ member(msg,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1)))),parts(knows(spy,X0)))
| ~ member(list(event),X0,nS_Sha254967238shared)
| member(agent1,X5,bad)
| member(event,says(server,X5,crypt(shrK(X5),mPair(X4,mPair(agent(X3),mPair(key(X2),X1))))),set(event,X0)) ),
inference(cnf_transformation,[],[f152]) ).
tff(f333,plain,
! [X2: msg,X3: agent1,X0: msg,X1: agent1,X8: msg,X6: nat,X9: agent1,X7: agent1,X4: list(event),X5: msg] :
( ~ member(event,says(server,X3,crypt(shrK(X3),mPair(X2,mPair(agent(X1),mPair(key(X6),X0))))),set(event,X4))
| ~ member(list(event),X4,nS_Sha254967238shared)
| ( X0 = X5 )
| ~ member(event,says(server,X9,crypt(shrK(X9),mPair(X8,mPair(agent(X7),mPair(key(X6),X5))))),set(event,X4)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f334,plain,
! [X2: msg,X3: agent1,X0: msg,X1: agent1,X8: msg,X6: nat,X9: agent1,X7: agent1,X4: list(event),X5: msg] :
( ~ member(event,says(server,X3,crypt(shrK(X3),mPair(X2,mPair(agent(X1),mPair(key(X6),X0))))),set(event,X4))
| ~ member(list(event),X4,nS_Sha254967238shared)
| ( X1 = X7 )
| ~ member(event,says(server,X9,crypt(shrK(X9),mPair(X8,mPair(agent(X7),mPair(key(X6),X5))))),set(event,X4)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f336,plain,
! [X2: msg,X3: agent1,X0: msg,X1: agent1,X8: msg,X6: nat,X9: agent1,X7: agent1,X4: list(event),X5: msg] :
( ~ member(event,says(server,X3,crypt(shrK(X3),mPair(X2,mPair(agent(X1),mPair(key(X6),X0))))),set(event,X4))
| ~ member(list(event),X4,nS_Sha254967238shared)
| ( X3 = X9 )
| ~ member(event,says(server,X9,crypt(shrK(X9),mPair(X8,mPair(agent(X7),mPair(key(X6),X5))))),set(event,X4)) ),
inference(cnf_transformation,[],[f175]) ).
tff(f352,plain,
~ member(agent1,a,bad),
inference(cnf_transformation,[],[f103]) ).
tff(f354,plain,
member(list(event),evs5,nS_Sha254967238shared),
inference(cnf_transformation,[],[f105]) ).
tff(f357,plain,
member(event,says(s,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(ka),xa))))),set(event,evs5)),
inference(cnf_transformation,[],[f108]) ).
tff(f358,plain,
~ member(msg,key(k),analz(knows(spy,evs5))),
inference(cnf_transformation,[],[f109]) ).
tff(f361,plain,
( ( a != aa )
| ( b != ba ) ),
inference(cnf_transformation,[],[f194]) ).
tff(f363,plain,
ka = k,
inference(cnf_transformation,[],[f194]) ).
tff(f364,plain,
member(msg,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),parts(knows(spy,evs5))),
inference(cnf_transformation,[],[f194]) ).
tff(f381,definition,
( spl8_1
<=> ( b = ba ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
tff(f382,plain,
( ( b = ba )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f381]) ).
tff(f385,definition,
( spl8_2
<=> ( a = aa ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
tff(f387,plain,
( ( a != aa )
| spl8_2 ),
inference(avatar_component_clause,[],[f385]) ).
tff(f388,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f361,f385,f381]) ).
tff(f390,definition,
( spl8_3
<=> member(msg,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),parts(knows(spy,evs5))) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
tff(f391,plain,
( member(msg,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x)))),parts(knows(spy,evs5)))
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f390]) ).
tff(f405,plain,
spl8_3,
inference(avatar_split_clause,[],[f364,f390]) ).
tff(f560,plain,
member(event,says(s,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))))),set(event,evs5)),
inference(forward_demodulation,[],[f357,f363]) ).
tff(f566,plain,
member(msg,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa)))),analz(knows(spy,evs5))),
inference(resolution,[],[f560,f234]) ).
tff(f592,plain,
( ~ member(list(event),evs5,nS_Sha254967238shared)
| member(agent1,a,bad)
| member(event,says(server,a,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x))))),set(event,evs5))
| ~ spl8_3 ),
inference(resolution,[],[f309,f391]) ).
tff(f593,plain,
! [X2: msg,X3: agent1,X0: list(event),X1: agent1,X4: nat,X5: msg] :
( ~ member(msg,crypt(shrK(X1),mPair(X2,mPair(agent(X3),mPair(key(X4),X5)))),analz(knows(spy,X0)))
| member(agent1,X1,bad)
| member(event,says(server,X1,crypt(shrK(X1),mPair(X2,mPair(agent(X3),mPair(key(X4),X5))))),set(event,X0))
| ~ member(list(event),X0,nS_Sha254967238shared) ),
inference(resolution,[],[f309,f264]) ).
tff(f594,plain,
( member(agent1,a,bad)
| member(event,says(server,a,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x))))),set(event,evs5))
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f592,f354]) ).
tff(f595,plain,
( member(event,says(server,a,crypt(shrK(a),mPair(nonce(na),mPair(agent(b),mPair(key(k),x))))),set(event,evs5))
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f594,f352]) ).
tff(f688,plain,
( ~ member(agent1,aa,bad)
| member(msg,mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))),analz(knows(spy,evs5))) ),
inference(resolution,[],[f566,f230]) ).
tff(f698,definition,
( spl8_6
<=> member(msg,mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))),analz(knows(spy,evs5))) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
tff(f700,plain,
( member(msg,mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))),analz(knows(spy,evs5)))
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f698]) ).
tff(f707,definition,
( spl8_8
<=> member(agent1,aa,bad) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
tff(f710,plain,
( spl8_6
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f688,f707,f698]) ).
tff(f757,plain,
( ! [X2: agent1,X3: msg,X0: agent1,X1: msg] :
( ~ member(list(event),evs5,nS_Sha254967238shared)
| ( a = X0 )
| ~ member(event,says(server,X0,crypt(shrK(X0),mPair(X1,mPair(agent(X2),mPair(key(k),X3))))),set(event,evs5)) )
| ~ spl8_3 ),
inference(resolution,[],[f595,f336]) ).
tff(f759,plain,
( ! [X2: msg,X3: msg,X0: agent1,X1: agent1] :
( ~ member(list(event),evs5,nS_Sha254967238shared)
| ( b = X0 )
| ~ member(event,says(server,X1,crypt(shrK(X1),mPair(X2,mPair(agent(X0),mPair(key(k),X3))))),set(event,evs5)) )
| ~ spl8_3 ),
inference(resolution,[],[f595,f334]) ).
tff(f760,plain,
( ! [X2: msg,X3: agent1,X0: msg,X1: agent1] :
( ~ member(list(event),evs5,nS_Sha254967238shared)
| ( x = X0 )
| ~ member(event,says(server,X1,crypt(shrK(X1),mPair(X2,mPair(agent(X3),mPair(key(k),X0))))),set(event,evs5)) )
| ~ spl8_3 ),
inference(resolution,[],[f595,f333]) ).
tff(f764,plain,
( ! [X2: msg,X3: agent1,X0: msg,X1: agent1] :
( ~ member(event,says(server,X1,crypt(shrK(X1),mPair(X2,mPair(agent(X3),mPair(key(k),X0))))),set(event,evs5))
| ( x = X0 ) )
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f760,f354]) ).
tff(f765,plain,
( ! [X2: msg,X3: msg,X0: agent1,X1: agent1] :
( ~ member(event,says(server,X1,crypt(shrK(X1),mPair(X2,mPair(agent(X0),mPair(key(k),X3))))),set(event,evs5))
| ( b = X0 ) )
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f759,f354]) ).
tff(f767,plain,
( ! [X2: agent1,X3: msg,X0: agent1,X1: msg] :
( ~ member(event,says(server,X0,crypt(shrK(X0),mPair(X1,mPair(agent(X2),mPair(key(k),X3))))),set(event,evs5))
| ( a = X0 ) )
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f757,f354]) ).
tff(f784,plain,
( member(agent1,aa,bad)
| member(event,says(server,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))))),set(event,evs5))
| ~ member(list(event),evs5,nS_Sha254967238shared) ),
inference(resolution,[],[f593,f566]) ).
tff(f959,definition,
( spl8_14
<=> member(event,says(server,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))))),set(event,evs5)) ),
introduced(definition,[new_symbols(definition,[spl8_14])],[avatar_definition]) ).
tff(f961,plain,
( member(event,says(server,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))))),set(event,evs5))
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f959]) ).
tff(f963,plain,
( member(agent1,aa,bad)
| member(event,says(server,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),xa))))),set(event,evs5)) ),
inference(forward_subsumption_resolution,[],[f784,f354]) ).
tff(f980,plain,
( spl8_14
| spl8_8 ),
inference(avatar_split_clause,[],[f963,f707,f959]) ).
tff(f986,plain,
( member(msg,mPair(agent(ba),mPair(key(k),xa)),analz(knows(spy,evs5)))
| ~ spl8_6 ),
inference(resolution,[],[f700,f262]) ).
tff(f1154,plain,
( ( xa = x )
| ~ spl8_3
| ~ spl8_14 ),
inference(resolution,[],[f764,f961]) ).
tff(f1193,plain,
( ( b = ba )
| ~ spl8_3
| ~ spl8_14 ),
inference(resolution,[],[f765,f961]) ).
tff(f1248,plain,
( member(msg,mPair(key(k),xa),analz(knows(spy,evs5)))
| ~ spl8_6 ),
inference(resolution,[],[f986,f262]) ).
tff(f1269,plain,
( member(msg,key(k),analz(knows(spy,evs5)))
| ~ spl8_6 ),
inference(resolution,[],[f1248,f261]) ).
tff(f1277,plain,
( $false
| ~ spl8_6 ),
inference(forward_subsumption_resolution,[],[f1269,f358]) ).
tff(f1278,plain,
~ spl8_6,
inference(avatar_contradiction_clause,[],[f1277]) ).
tff(f1279,plain,
( spl8_1
| ~ spl8_3
| ~ spl8_14 ),
inference(avatar_split_clause,[],[f1193,f959,f390,f381]) ).
tff(f1472,plain,
( member(event,says(server,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(ba),mPair(key(k),x))))),set(event,evs5))
| ~ spl8_3
| ~ spl8_14 ),
inference(forward_demodulation,[],[f961,f1154]) ).
tff(f1473,plain,
( member(event,says(server,aa,crypt(shrK(aa),mPair(nonce(nAa),mPair(agent(b),mPair(key(k),x))))),set(event,evs5))
| ~ spl8_1
| ~ spl8_3
| ~ spl8_14 ),
inference(forward_demodulation,[],[f1472,f382]) ).
tff(f1479,plain,
( ( a = aa )
| ~ spl8_1
| ~ spl8_3
| ~ spl8_14 ),
inference(resolution,[],[f1473,f767]) ).
tff(f1498,plain,
( $false
| ~ spl8_1
| spl8_2
| ~ spl8_3
| ~ spl8_14 ),
inference(forward_subsumption_resolution,[],[f1479,f387]) ).
tff(f1499,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_3
| ~ spl8_14 ),
inference(avatar_contradiction_clause,[],[f1498]) ).
cnf(s1,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f388]) ).
cnf(s4,plain,
spl8_3,
inference(sat_conversion,[],[f405]) ).
cnf(s6,plain,
( spl8_6
| ~ spl8_8 ),
inference(sat_conversion,[],[f710]) ).
cnf(s16,plain,
( spl8_8
| spl8_14 ),
inference(sat_conversion,[],[f980]) ).
cnf(s22,plain,
~ spl8_6,
inference(sat_conversion,[],[f1278]) ).
cnf(s23,plain,
( spl8_1
| ~ spl8_3
| ~ spl8_14 ),
inference(sat_conversion,[],[f1279]) ).
cnf(s29,plain,
( ~ spl8_1
| spl8_2
| ~ spl8_3
| ~ spl8_14 ),
inference(sat_conversion,[],[f1499]) ).
cnf(s33,plain,
~ spl8_8,
inference(rat,[],[s6,s22]) ).
cnf(s34,plain,
spl8_14,
inference(rat,[],[s16,s33]) ).
cnf(s39,plain,
spl8_1,
inference(rat,[],[s23,s34,s4]) ).
cnf(s42,plain,
spl8_2,
inference(rat,[],[s29,s34,s4,s39]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s1,s42,s39]) ).
tff(f1502,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV803_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 12:38:22 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.04/1.13 % (324396)Detected formulas, will run a generic FOF schedule.
% 3.04/1.13 % (324401)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3780337925:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.04/1.13 % (324402)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1485426539:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.04/1.13 % (324403)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=142813204:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.04/1.13 % (324404)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2027050411:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.04/1.13 % (324405)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1433626764:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.04/1.13 % (324407)dis-21_1_sil=8000:lcm=predicate:random_seed=3964660063:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.04/1.13 % (324404)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.04/1.13 % (324406)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=31732680:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.04/1.13 % (324403)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.04/1.13 % (324404)Refutation not found, incomplete strategy
% 3.04/1.13 % (324404)------------------------------
% 3.04/1.13 % (324404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.13 % (324404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.13 % (324404)CaDiCaL version: 2.1.3
% 3.04/1.13 % (324404)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.13 % (324404)Time elapsed: 0.008 s
% 3.04/1.13 % (324404)Peak memory usage: 88 MB
% 3.04/1.13 % (324404)Instructions burned: 12 (million)
% 3.04/1.13 % (324406)First to succeed.
% 3.04/1.13 % (324406)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-324396"
% 3.04/1.13 % (324405)Instruction limit reached!
% 3.04/1.13 % (324405)------------------------------
% 3.04/1.13 % (324405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.13 % (324405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.13 % (324405)CaDiCaL version: 2.1.3
% 3.04/1.13 % (324405)Termination reason: Instruction limit
% 3.04/1.13 % (324405)Termination phase: Saturation
% 3.04/1.13 % (324405)Time elapsed: 0.067 s
% 3.04/1.13 % (324405)Peak memory usage: 88 MB
% 3.04/1.13 % (324405)Instructions burned: 119 (million)
% 3.04/1.13 % (324407)Instruction limit reached!
% 3.04/1.13 % (324407)------------------------------
% 3.04/1.13 % (324407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.04/1.13 % (324407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.04/1.13 % (324407)CaDiCaL version: 2.1.3
% 3.04/1.13 % (324407)Termination reason: Instruction limit
% 3.04/1.13 % (324407)Termination phase: Saturation
% 3.04/1.13 % (324407)Time elapsed: 0.076 s
% 3.04/1.13 % (324407)Peak memory usage: 89 MB
% 3.04/1.13 % (324407)Instructions burned: 130 (million)
% 3.04/1.13 % Exception at run slice level
% 3.04/1.13 User error: GNN currently only supports monomorphic FOL.
% 3.04/1.13 % (324415)lrs+10_1_sil=8000:sp=occurrence:random_seed=3577512557:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.04/1.13 % (324416)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2569613442:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.04/1.13 % (324404)------------------------------
% 3.04/1.13 % (324404)------------------------------
% 3.04/1.13 % (324417)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4207329378:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.04/1.13 % (324406)Refutation found. Thanks to Tanya!
% 3.04/1.13 % SZS status Theorem for theBenchmark
% 3.04/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/1.33 % (324406)------------------------------
% 3.99/1.33 % (324406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.33 % (324406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.33 % (324406)CaDiCaL version: 2.1.3
% 3.99/1.33 % (324406)Termination reason: Refutation
% 3.99/1.33 % (324406)Time elapsed: 0.047 s
% 3.99/1.33 % (324406)Peak memory usage: 90 MB
% 3.99/1.33 % (324406)Instructions burned: 76 (million)
% 3.99/1.33 % (324406)------------------------------
% 3.99/1.33 % (324406)------------------------------
% 3.99/1.33 % (324396)Success in time 0.479 s
% 3.99/1.33 % Vampire exiting
%------------------------------------------------------------------------------