%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:08:27 PM UTC 2026
% Result : Theorem 3.56s 1.05s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 14 unt; 6 def)
% Number of atoms : 188 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 247 ( 125 ~; 104 |; 8 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 79 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1] :
( ( p(X0)
& p(X1) )
=> p(crypt(xor(km,xor(kp,X1)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_1) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( p(X0)
& p(crypt(xor(km,xor(kp,X1)),X2))
& p(X1) )
=> p(crypt(xor(km,xor(X1,kp)),xor(X0,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_2) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( p(X0)
& p(crypt(xor(km,xor(X1,kp)),X2))
& p(X1) )
=> p(crypt(xor(km,X1),xor(X2,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_3) ).
fof(f14,axiom,
! [X0,X1] :
( ( p(X0)
& p(X1) )
=> p(xor(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',combine_with_XOR) ).
fof(f24,axiom,
p(crypt(xor(km,exp),eurk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_7) ).
fof(f26,axiom,
p(exp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_9) ).
fof(f28,conjecture,
? [X0] :
( p(crypt(xor(km,exp),X0))
& p(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',find_known_exporter) ).
fof(f29,negated_conjecture,
~ ? [X0] :
( p(crypt(xor(km,exp),X0))
& p(X0) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f34,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X0)
| ~ p(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X0)
| ~ p(X1) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( p(crypt(xor(km,xor(X1,kp)),xor(X0,X2)))
| ~ p(X0)
| ~ p(crypt(xor(km,xor(kp,X1)),X2))
| ~ p(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f37,plain,
! [X0,X1,X2] :
( p(crypt(xor(km,xor(X1,kp)),xor(X0,X2)))
| ~ p(X0)
| ~ p(crypt(xor(km,xor(kp,X1)),X2))
| ~ p(X1) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( p(crypt(xor(km,X1),xor(X2,X0)))
| ~ p(X0)
| ~ p(crypt(xor(km,xor(X1,kp)),X2))
| ~ p(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f39,plain,
! [X0,X1,X2] :
( p(crypt(xor(km,X1),xor(X2,X0)))
| ~ p(X0)
| ~ p(crypt(xor(km,xor(X1,kp)),X2))
| ~ p(X1) ),
inference(flattening,[],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f47,plain,
! [X0,X1] :
( p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ),
inference(flattening,[],[f46]) ).
fof(f53,plain,
! [X0] :
( ~ p(crypt(xor(km,exp),X0))
| ~ p(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f62,plain,
! [X2,X0,X1] :
( p(crypt(xor(km,xor(X1,kp)),xor(X0,X2)))
| ~ p(X0)
| ~ p(crypt(xor(km,xor(kp,X1)),X2))
| ~ p(X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f63,plain,
! [X2,X0,X1] :
( p(crypt(xor(km,X1),xor(X2,X0)))
| ~ p(X0)
| ~ p(crypt(xor(km,xor(X1,kp)),X2))
| ~ p(X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f67,plain,
! [X0,X1] :
( p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f77,plain,
p(crypt(xor(km,exp),eurk)),
inference(cnf_transformation,[],[f24]) ).
fof(f79,plain,
p(exp),
inference(cnf_transformation,[],[f26]) ).
fof(f81,plain,
! [X0] :
( ~ p(crypt(xor(km,exp),X0))
| ~ p(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f122,definition,
( spl1_8
<=> p(exp) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f123,plain,
( ~ p(exp)
| spl1_8 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f147,definition,
( spl1_11
<=> ! [X0] : ~ p(X0) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f148,plain,
( ! [X0] : ~ p(X0)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f720,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(crypt(xor(km,xor(exp,kp)),X1))
| ~ p(exp)
| ~ p(xor(X1,X0)) ),
inference(resolution,[],[f63,f81]) ).
fof(f730,definition,
( spl1_54
<=> ! [X0,X1] :
( ~ p(X0)
| ~ p(crypt(xor(km,xor(exp,kp)),X1))
| ~ p(xor(X1,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_54])],[avatar_definition]) ).
fof(f731,plain,
( ! [X0,X1] :
( ~ p(crypt(xor(km,xor(exp,kp)),X1))
| ~ p(xor(X1,X0))
| ~ p(X0) )
| ~ spl1_54 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f732,plain,
( ~ spl1_8
| spl1_54 ),
inference(avatar_split_clause,[],[f720,f730,f122]) ).
fof(f833,plain,
( $false
| spl1_8 ),
inference(resolution,[],[f123,f79]) ).
fof(f834,plain,
spl1_8,
inference(avatar_contradiction_clause,[],[f833]) ).
fof(f951,definition,
( spl1_97
<=> ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_97])],[avatar_definition]) ).
fof(f952,plain,
( ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) )
| ~ spl1_97 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f1272,plain,
( $false
| ~ spl1_11 ),
inference(resolution,[],[f148,f77]) ).
fof(f1311,plain,
~ spl1_11,
inference(avatar_contradiction_clause,[],[f1272]) ).
fof(f1488,plain,
( ! [X2,X0,X1] :
( ~ p(X0)
| ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(exp)
| ~ p(xor(xor(X0,X1),X2))
| ~ p(X2) )
| ~ spl1_54 ),
inference(resolution,[],[f62,f731]) ).
fof(f1496,definition,
( spl1_142
<=> ! [X2,X0,X1] :
( ~ p(X0)
| ~ p(X2)
| ~ p(xor(xor(X0,X1),X2))
| ~ p(crypt(xor(km,xor(kp,exp)),X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_142])],[avatar_definition]) ).
fof(f1497,plain,
( ! [X2,X0,X1] :
( ~ p(xor(xor(X0,X1),X2))
| ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(X0)
| ~ p(X2) )
| ~ spl1_142 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1498,plain,
( ~ spl1_8
| spl1_142
| ~ spl1_54 ),
inference(avatar_split_clause,[],[f1488,f730,f1496,f122]) ).
fof(f1499,plain,
( ! [X2,X0,X1] :
( ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(X0)
| ~ p(X2)
| ~ p(xor(X0,X1))
| ~ p(X2) )
| ~ spl1_142 ),
inference(resolution,[],[f1497,f67]) ).
fof(f1518,plain,
( ! [X2,X0,X1] :
( ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(X0)
| ~ p(X2)
| ~ p(xor(X0,X1)) )
| ~ spl1_142 ),
inference(duplicate_literal_removal,[],[f1499]) ).
fof(f1591,definition,
( spl1_161
<=> ! [X0,X1] :
( ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(X0)
| ~ p(xor(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[spl1_161])],[avatar_definition]) ).
fof(f1592,plain,
( ! [X0,X1] :
( ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(xor(X0,X1))
| ~ p(X0) )
| ~ spl1_161 ),
inference(avatar_component_clause,[],[f1591]) ).
fof(f1593,plain,
( spl1_11
| spl1_161
| ~ spl1_142 ),
inference(avatar_split_clause,[],[f1518,f1496,f1591,f147]) ).
fof(f1636,plain,
( ! [X0,X1] :
( ~ p(xor(X1,X0))
| ~ p(X1)
| ~ p(X0)
| ~ p(exp) )
| ~ spl1_161 ),
inference(resolution,[],[f1592,f61]) ).
fof(f1680,plain,
( ~ spl1_8
| spl1_97
| ~ spl1_161 ),
inference(avatar_split_clause,[],[f1636,f1591,f951,f122]) ).
fof(f1681,plain,
( ! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X0)
| ~ p(X1) )
| ~ spl1_97 ),
inference(resolution,[],[f952,f67]) ).
fof(f1682,plain,
( ! [X0,X1] :
( ~ p(X0)
| ~ p(X1) )
| ~ spl1_97 ),
inference(duplicate_literal_removal,[],[f1681]) ).
fof(f1683,plain,
( spl1_11
| spl1_11
| ~ spl1_97 ),
inference(avatar_split_clause,[],[f1682,f951,f147,f147]) ).
cnf(s95,plain,
( ~ spl1_8
| spl1_54 ),
inference(sat_conversion,[],[f732]) ).
cnf(s116,plain,
spl1_8,
inference(sat_conversion,[],[f834]) ).
cnf(s190,plain,
~ spl1_11,
inference(sat_conversion,[],[f1311]) ).
cnf(s196,plain,
( ~ spl1_8
| ~ spl1_54
| spl1_142 ),
inference(sat_conversion,[],[f1498]) ).
cnf(s214,plain,
( spl1_11
| ~ spl1_142
| spl1_161 ),
inference(sat_conversion,[],[f1593]) ).
cnf(s234,plain,
( ~ spl1_8
| spl1_97
| ~ spl1_161 ),
inference(sat_conversion,[],[f1680]) ).
cnf(s235,plain,
( spl1_11
| spl1_11
| ~ spl1_97 ),
inference(sat_conversion,[],[f1683]) ).
cnf(s236,plain,
( spl1_11
| ~ spl1_97 ),
inference(rat,[],[s235]) ).
cnf(s237,plain,
~ spl1_97,
inference(rat,[],[s236,s190]) ).
cnf(s248,plain,
~ spl1_161,
inference(rat,[],[s234,s237,s116]) ).
cnf(s251,plain,
~ spl1_142,
inference(rat,[],[s214,s190,s248]) ).
cnf(s253,plain,
~ spl1_54,
inference(rat,[],[s196,s116,s251]) ).
cnf(s273,plain,
$false,
inference(rat,[],[s95,s253,s116]) ).
fof(f1684,plain,
$false,
inference(avatar_sat_refutation,[],[s273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n015.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 10:18:16 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
% 3.56/1.05 % (2520174)Detected formulas, will run a generic FOF schedule.
% 3.56/1.05 % (2520180)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=2553054812:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.56/1.05 % (2520182)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1091763557:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.56/1.05 % (2520181)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=3089973339:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.56/1.05 % (2520185)dis-21_1_sil=8000:lcm=predicate:random_seed=3707287256: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)
% 3.56/1.05 % (2520179)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=16321583:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.56/1.05 % (2520183)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3145287208:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.56/1.05 % (2520182)Refutation not found, incomplete strategy
% 3.56/1.05 % (2520182)------------------------------
% 3.56/1.05 % (2520182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.05 % (2520182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.05 % (2520182)CaDiCaL version: 2.1.3
% 3.56/1.05 % (2520182)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.05 % (2520182)Time elapsed: 0.001 s
% 3.56/1.05 % (2520182)Peak memory usage: 88 MB
% 3.56/1.05 % (2520183)Refutation not found, incomplete strategy
% 3.56/1.05 % (2520183)------------------------------
% 3.56/1.05 % (2520183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.05 % (2520183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.05 % (2520183)CaDiCaL version: 2.1.3
% 3.56/1.05 % (2520183)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.05 % (2520183)Time elapsed: 0.002 s
% 3.56/1.05 % (2520183)Peak memory usage: 87 MB
% 3.56/1.05 % (2520183)Instructions burned: 1 (million)
% 3.56/1.05 % (2520184)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3047432237:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.56/1.05 % (2520185)First to succeed.
% 3.56/1.05 % (2520185)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2520174"
% 3.56/1.05 % (2520184)Instruction limit reached!
% 3.56/1.05 % (2520184)------------------------------
% 3.56/1.05 % (2520184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.05 % (2520184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.05 % (2520184)CaDiCaL version: 2.1.3
% 3.56/1.05 % (2520184)Termination reason: Instruction limit
% 3.56/1.05 % (2520184)Termination phase: Saturation
% 3.56/1.05 % (2520184)Time elapsed: 0.048 s
% 3.56/1.05 % (2520184)Peak memory usage: 89 MB
% 3.56/1.05 % (2520184)Instructions burned: 142 (million)
% 3.56/1.05 % (2520193)lrs+10_1_sil=8000:sp=occurrence:random_seed=909757645:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.56/1.05 % (2520193)Also succeeded, but the first one will report.
% 3.56/1.05 % (2520182)------------------------------
% 3.56/1.05 % (2520182)------------------------------
% 3.56/1.05 % (2520183)------------------------------
% 3.56/1.05 % (2520183)------------------------------
% 3.56/1.05 % (2520185)Refutation found. Thanks to Tanya!
% 3.56/1.05 % SZS status Theorem for theBenchmark
% 3.56/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.06 % (2520185)------------------------------
% 3.56/1.06 % (2520185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.06 % (2520185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.06 % (2520185)CaDiCaL version: 2.1.3
% 3.56/1.06 % (2520185)Termination reason: Refutation
% 3.56/1.06 % (2520185)Time elapsed: 0.019 s
% 3.56/1.06 % (2520185)Peak memory usage: 90 MB
% 3.56/1.06 % (2520185)Instructions burned: 29 (million)
% 3.56/1.06 % (2520185)------------------------------
% 3.56/1.06 % (2520185)------------------------------
% 3.56/1.06 % (2520174)Success in time 0.443 s
% 3.56/1.06 % Vampire exiting
%------------------------------------------------------------------------------