%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV811_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 2.40s 0.81s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 8 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 41 ( 41 usr; 10 con; 0-5 aty)
% Number of variables : 32 ( 32 !; 0 ?; 32 :)
% 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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
bad: fun(agent,bool) ).
tff(func_def_3,type,
gets: ( agent * msg ) > event ).
tff(func_def_4,type,
notes: ( agent * msg ) > event ).
tff(func_def_5,type,
says: ( agent * agent * msg ) > event ).
tff(func_def_6,type,
initState: agent > fun(msg,bool) ).
tff(func_def_7,type,
knows: ( agent * list(event) ) > fun(msg,bool) ).
tff(func_def_8,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_9,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_10,type,
rev:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_11,type,
set:
!>[X0: $tType] : ( list(X0) > fun(X0,bool) ) ).
tff(func_def_12,type,
takeWhile:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > list(X0) ) ).
tff(func_def_13,type,
spy: agent ).
tff(func_def_14,type,
analz: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_15,type,
crypt: ( nat * msg ) > msg ).
tff(func_def_16,type,
key: nat > msg ).
tff(func_def_17,type,
mPair: ( msg * msg ) > msg ).
tff(func_def_18,type,
nonce: nat > msg ).
tff(func_def_19,type,
parts: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_20,type,
nS_Sha254967238shared: fun(list(event),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,
fNot: fun(bool,bool) ).
tff(func_def_24,type,
fTrue: bool ).
tff(func_def_25,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_26,type,
a: agent ).
tff(func_def_27,type,
b: agent ).
tff(func_def_28,type,
k: nat ).
tff(func_def_29,type,
nb: nat ).
tff(func_def_30,type,
sK0:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_31,type,
sK1:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) * list(X0) ) > X0 ) ).
tff(func_def_32,type,
sK2: fun(msg,bool) > msg ).
tff(func_def_33,type,
sK3: fun(msg,bool) > nat ).
tff(func_def_34,type,
sK4: fun(msg,bool) > msg ).
tff(func_def_35,type,
sK5: fun(msg,bool) > msg ).
tff(func_def_36,type,
sK6: ( list(event) * agent * msg ) > agent ).
tff(func_def_37,type,
sK7: ( list(event) * msg ) > agent ).
tff(func_def_38,type,
sK8: ( list(event) * msg ) > agent ).
tff(pred_def_1,type,
nS_Sha512322870Issues: ( agent * agent * msg * list(event) ) > $o ).
tff(pred_def_2,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_3,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sQ9_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f19,axiom,
! [X0: fun(msg,bool),X1: msg] :
( member(msg,X1,X0)
=> member(msg,X1,parts(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_parts_OInj) ).
tff(f54,axiom,
! [X0: list(event),X1: msg,X2: agent,X3: agent] :
( member(event,says(X3,X2,X1),set(event,X0))
=> member(msg,X1,knows(X3,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Says__imp__knows) ).
tff(f60,axiom,
! [X0: agent] : ( knows(X0,nil(event)) = initState(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_knows__Nil) ).
tff(f90,axiom,
! [X0: agent,X1: msg,X2: nat] : ~ member(msg,crypt(X2,X1),parts(initState(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Crypt__notin__initState) ).
tff(f111,conjecture,
( member(msg,key(k),analz(knows(spy,nil(event))))
| ~ member(event,says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))),set(event,nil(event)))
| ~ member(msg,crypt(k,mPair(nonce(nb),nonce(nb))),parts(knows(spy,takeWhile(event,combb(bool,bool,event,fNot,combc(event,event,bool,fequal(event),says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))))),rev(event,nil(event)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f112,negated_conjecture,
~ ( member(msg,key(k),analz(knows(spy,nil(event))))
| ~ member(event,says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))),set(event,nil(event)))
| ~ member(msg,crypt(k,mPair(nonce(nb),nonce(nb))),parts(knows(spy,takeWhile(event,combb(bool,bool,event,fNot,combc(event,event,bool,fequal(event),says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))))),rev(event,nil(event)))))) ),
inference(negated_conjecture,[status(cth)],[f111]) ).
tff(f122,plain,
! [X0: fun(msg,bool),X1: msg] :
( member(msg,X1,parts(X0))
| ~ member(msg,X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
tff(f137,plain,
! [X0: list(event),X1: msg,X2: agent,X3: agent] :
( member(msg,X1,knows(X3,X0))
| ~ member(event,says(X3,X2,X1),set(event,X0)) ),
inference(ennf_transformation,[],[f54]) ).
tff(f172,plain,
( ~ member(msg,key(k),analz(knows(spy,nil(event))))
& member(event,says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))),set(event,nil(event)))
& member(msg,crypt(k,mPair(nonce(nb),nonce(nb))),parts(knows(spy,takeWhile(event,combb(bool,bool,event,fNot,combc(event,event,bool,fequal(event),says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))))),rev(event,nil(event)))))) ),
inference(ennf_transformation,[],[f112]) ).
tff(f234,plain,
! [X0: fun(msg,bool),X1: msg] :
( member(msg,X1,parts(X0))
| ~ member(msg,X1,X0) ),
inference(cnf_transformation,[],[f122]) ).
tff(f284,plain,
! [X2: agent,X3: agent,X0: list(event),X1: msg] :
( ~ member(event,says(X3,X2,X1),set(event,X0))
| member(msg,X1,knows(X3,X0)) ),
inference(cnf_transformation,[],[f137]) ).
tff(f291,plain,
! [X0: agent] : ( knows(X0,nil(event)) = initState(X0) ),
inference(cnf_transformation,[],[f60]) ).
tff(f328,plain,
! [X2: nat,X0: agent,X1: msg] : ~ member(msg,crypt(X2,X1),parts(initState(X0))),
inference(cnf_transformation,[],[f90]) ).
tff(f353,plain,
member(event,says(a,b,crypt(k,mPair(nonce(nb),nonce(nb)))),set(event,nil(event))),
inference(cnf_transformation,[],[f172]) ).
tff(f359,plain,
! [X2: nat,X0: agent,X1: msg] : ~ member(msg,crypt(X2,X1),parts(knows(X0,nil(event)))),
inference(definition_unfolding,[],[f328,f291]) ).
tff(f489,plain,
! [X2: agent,X0: nat,X1: msg] : ~ member(msg,crypt(X0,X1),knows(X2,nil(event))),
inference(resolution,[],[f359,f234]) ).
tff(f626,plain,
member(msg,crypt(k,mPair(nonce(nb),nonce(nb))),knows(a,nil(event))),
inference(resolution,[],[f284,f353]) ).
tff(f627,plain,
$false,
inference(resolution,[],[f626,f489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV811_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 12:37:24 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.40/0.81 % (2225174)Detected formulas, will run a generic FOF schedule.
% 2.40/0.81 % (2225185)dis-21_1_sil=8000:lcm=predicate:random_seed=2415483401: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)
% 2.40/0.81 % (2225185)First to succeed.
% 2.40/0.81 % (2225185)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2225174"
% 2.40/0.81 % (2225184)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2338786786:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.40/0.81 % (2225182)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1190762500:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.40/0.81 % (2225179)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=3285242902:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.40/0.81 % (2225181)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=4197094950:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.40/0.81 % (2225183)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1590945042:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.40/0.81 % (2225180)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=758496396:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.40/0.81 % (2225182)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.40/0.81 % (2225181)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.40/0.81 % (2225182)Refutation not found, incomplete strategy
% 2.40/0.81 % (2225182)------------------------------
% 2.40/0.81 % (2225182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/0.81 % (2225182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.81 % (2225182)CaDiCaL version: 2.1.3
% 2.40/0.81 % (2225182)Termination reason: Refutation not found, incomplete strategy
% 2.40/0.81 % (2225182)Time elapsed: 0.005 s
% 2.40/0.81 % (2225182)Peak memory usage: 88 MB
% 2.40/0.81 % (2225182)Instructions burned: 7 (million)
% 2.40/0.81 % (2225184)Also succeeded, but the first one will report.
% 2.40/0.81 % (2225183)Also succeeded, but the first one will report.
% 2.40/0.81 % (2225185)Refutation found. Thanks to Tanya!
% 2.40/0.81 % SZS status Theorem for theBenchmark
% 2.40/0.81 % SZS output start Proof for theBenchmark
% See solution above
% 2.40/0.81 % (2225185)------------------------------
% 2.40/0.81 % (2225185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.40/0.81 % (2225185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.40/0.81 % (2225185)CaDiCaL version: 2.1.3
% 2.40/0.81 % (2225185)Termination reason: Refutation
% 2.40/0.81 % (2225185)Time elapsed: 0.005 s
% 2.40/0.81 % (2225185)Peak memory usage: 89 MB
% 2.40/0.81 % (2225185)Instructions burned: 14 (million)
% 2.40/0.81 % (2225185)------------------------------
% 2.40/0.81 % (2225185)------------------------------
% 2.40/0.81 % (2225174)Success in time 0.291 s
% 2.40/0.81 % Vampire exiting
%------------------------------------------------------------------------------