%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV763_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 01:26:22 PM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 17 unt; 0 typ; 1 def)
% Number of atoms : 86 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 97 ( 47 ~; 38 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 20 con; 0-4 aty)
% Number of variables : 23 ( 0 sgn 21 !; 2 ?; 23 :)
% 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,
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,
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: agent ).
tff(func_def_8,type,
spy: agent ).
tff(func_def_9,type,
analz: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_10,type,
keysFor: fun(msg,bool) > fun(nat,bool) ).
tff(func_def_11,type,
agent1: agent > msg ).
tff(func_def_12,type,
crypt: ( nat * msg ) > msg ).
tff(func_def_13,type,
key: nat > msg ).
tff(func_def_14,type,
mPair: ( msg * msg ) > msg ).
tff(func_def_15,type,
nonce: nat > msg ).
tff(func_def_16,type,
parts: fun(msg,bool) > fun(msg,bool) ).
tff(func_def_17,type,
symKeys: fun(nat,bool) ).
tff(func_def_18,type,
nS_Sha254967238shared: fun(list(event),bool) ).
tff(func_def_19,type,
shrK: agent > nat ).
tff(func_def_20,type,
aa1:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
a: agent ).
tff(func_def_24,type,
a1: agent ).
tff(func_def_25,type,
aa: agent ).
tff(func_def_26,type,
b: agent ).
tff(func_def_27,type,
ba: agent ).
tff(func_def_28,type,
k: nat ).
tff(func_def_29,type,
kab: nat ).
tff(func_def_30,type,
na: msg ).
tff(func_def_31,type,
nAa: nat ).
tff(func_def_32,type,
nb: nat ).
tff(func_def_33,type,
x: msg ).
tff(func_def_34,type,
evs2: list(event) ).
tff(func_def_35,type,
sK0: ( list(event) * agent * nat * agent ) > msg ).
tff(func_def_36,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_37,type,
sK2: agent ).
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(f79,axiom,
! [X0: list(event),X1: nat] :
( ~ member(msg,key(X1),used(X0))
=> ( member(nat,X1,symKeys)
=> ( member(list(event),X0,nS_Sha254967238shared)
=> ~ member(nat,X1,keysFor(parts(knows(spy,X0)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_new__keys__not__used) ).
tff(f84,axiom,
! [X0: fun(msg,bool),X1: msg,X2: nat] :
( member(msg,crypt(X2,X1),X0)
=> ( member(nat,X2,symKeys)
=> member(nat,X2,keysFor(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Crypt__imp__keysFor) ).
tff(f103,axiom,
member(list(event),evs2,nS_Sha254967238shared),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f104,axiom,
~ member(msg,key(kab),used(evs2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f105,axiom,
member(nat,kab,symKeys),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f109,conjecture,
( ( a != aa )
| ( na != nonce(nAa) )
| ( b != ba )
| ( k != kab )
| ( x != crypt(shrK(ba),mPair(key(kab),agent1(aa))) )
| ~ member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2)))
| ? [X0: agent] : member(event,says(X0,ba,crypt(shrK(ba),mPair(key(kab),agent1(aa)))),set(event,evs2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
tff(f110,negated_conjecture,
~ ( ( a != aa )
| ( na != nonce(nAa) )
| ( b != ba )
| ( k != kab )
| ( x != crypt(shrK(ba),mPair(key(kab),agent1(aa))) )
| ~ member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2)))
| ? [X0: agent] : member(event,says(X0,ba,crypt(shrK(ba),mPair(key(kab),agent1(aa)))),set(event,evs2)) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
tff(f162,plain,
! [X0: list(event),X1: nat] :
( ~ member(nat,X1,keysFor(parts(knows(spy,X0))))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(nat,X1,symKeys)
| member(msg,key(X1),used(X0)) ),
inference(ennf_transformation,[],[f79]) ).
tff(f163,plain,
! [X0: list(event),X1: nat] :
( ~ member(nat,X1,keysFor(parts(knows(spy,X0))))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(nat,X1,symKeys)
| member(msg,key(X1),used(X0)) ),
inference(flattening,[],[f162]) ).
tff(f166,plain,
! [X0: fun(msg,bool),X1: msg,X2: nat] :
( member(nat,X2,keysFor(X0))
| ~ member(nat,X2,symKeys)
| ~ member(msg,crypt(X2,X1),X0) ),
inference(ennf_transformation,[],[f84]) ).
tff(f167,plain,
! [X0: fun(msg,bool),X1: msg,X2: nat] :
( member(nat,X2,keysFor(X0))
| ~ member(nat,X2,symKeys)
| ~ member(msg,crypt(X2,X1),X0) ),
inference(flattening,[],[f166]) ).
tff(f191,plain,
( ( aa = a )
& ( nonce(nAa) = na )
& ( ba = b )
& ( kab = k )
& ( x = crypt(shrK(ba),mPair(key(kab),agent1(aa))) )
& member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2)))
& ! [X0: agent] : ~ member(event,says(X0,ba,crypt(shrK(ba),mPair(key(kab),agent1(aa)))),set(event,evs2)) ),
inference(ennf_transformation,[],[f110]) ).
tff(f319,plain,
! [X0: list(event),X1: nat] :
( ~ member(nat,X1,keysFor(parts(knows(spy,X0))))
| ~ member(list(event),X0,nS_Sha254967238shared)
| ~ member(nat,X1,symKeys)
| member(msg,key(X1),used(X0)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f325,plain,
! [X2: nat,X0: fun(msg,bool),X1: msg] :
( ~ member(msg,crypt(X2,X1),X0)
| ~ member(nat,X2,symKeys)
| member(nat,X2,keysFor(X0)) ),
inference(cnf_transformation,[],[f167]) ).
tff(f348,plain,
member(list(event),evs2,nS_Sha254967238shared),
inference(cnf_transformation,[],[f103]) ).
tff(f349,plain,
~ member(msg,key(kab),used(evs2)),
inference(cnf_transformation,[],[f104]) ).
tff(f350,plain,
member(nat,kab,symKeys),
inference(cnf_transformation,[],[f105]) ).
tff(f355,plain,
member(msg,crypt(kab,nonce(nb)),parts(knows(spy,evs2))),
inference(cnf_transformation,[],[f191]) ).
tff(f357,plain,
kab = k,
inference(cnf_transformation,[],[f191]) ).
tff(f361,plain,
~ member(msg,key(k),used(evs2)),
inference(definition_unfolding,[],[f349,f357]) ).
tff(f362,plain,
member(nat,k,symKeys),
inference(definition_unfolding,[],[f350,f357]) ).
tff(f365,plain,
member(msg,crypt(k,nonce(nb)),parts(knows(spy,evs2))),
inference(definition_unfolding,[],[f355,f357]) ).
tff(f389,definition,
( spl3_2
<=> member(msg,crypt(k,nonce(nb)),parts(knows(spy,evs2))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f390,plain,
( member(msg,crypt(k,nonce(nb)),parts(knows(spy,evs2)))
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f389]) ).
tff(f397,plain,
spl3_2,
inference(avatar_split_clause,[],[f365,f389]) ).
tff(f511,plain,
( ~ member(nat,k,symKeys)
| member(nat,k,keysFor(parts(knows(spy,evs2))))
| ~ spl3_2 ),
inference(resolution,[],[f325,f390]) ).
tff(f518,plain,
( member(nat,k,keysFor(parts(knows(spy,evs2))))
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f511,f362]) ).
tff(f572,plain,
( ~ member(list(event),evs2,nS_Sha254967238shared)
| ~ member(nat,k,symKeys)
| member(msg,key(k),used(evs2))
| ~ spl3_2 ),
inference(resolution,[],[f319,f518]) ).
tff(f573,plain,
( ~ member(nat,k,symKeys)
| member(msg,key(k),used(evs2))
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f572,f348]) ).
tff(f574,plain,
( member(msg,key(k),used(evs2))
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f573,f362]) ).
tff(f575,plain,
( $false
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f574,f361]) ).
tff(f576,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f575]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f397]) ).
cnf(s4,plain,
~ spl3_2,
inference(sat_conversion,[],[f576]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4]) ).
tff(f577,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV763_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 12:29:36 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.29 % (1143178)Will run a generic schedule for satisfiability detection.
% 0.19/0.29 % (1143183)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1462410199_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (1143184)% WARNING: option uhcvi not known.
% 0.19/0.29 % (1143184)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=565862686:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.29 % (1143185)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=422069116:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.29 % (1143186)dis+10_1_sil=32000:sp=arity:random_seed=3225178761:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.29 % (1143187)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4006522346:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.29 % (1143188)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3950817470:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.29 % (1143189)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3726589748:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.29 % (1143191)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2739849793:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.29 % Exception at run slice level
% 0.19/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.29 % (1143186) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1143178-1143186"...
% 0.19/0.29 % (1143186)...printing done.
% 0.19/0.29 % (1143188) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1143178-1143188"...
% 0.19/0.29 % (1143186)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (1143186)------------------------------
% 0.19/0.29 % (1143186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1143186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1143186)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1143186)Termination reason: Refutation
% 0.19/0.29 % (1143186)Time elapsed: 0.014 s
% 0.19/0.29 % (1143186)Peak memory usage: 12 MB
% 0.19/0.29 % (1143186)Instructions burned: 22 (million)
% 0.19/0.29 % (1143178)Success in time 0.059 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------