%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV235+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 : n019.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 5.14s 1.54s
% Output : Refutation 5.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 24
% Syntax : Number of formulae : 116 ( 31 unt; 11 def)
% Number of atoms : 302 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 371 ( 185 ~; 158 |; 10 &)
% ( 11 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 12 prp; 0-1 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( ( p(crypt(xor(km,X0),X1))
& p(X0)
& p(crypt(xor(km,exp),X2)) )
=> p(crypt(xor(X2,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_export) ).
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(f15,axiom,
! [X0,X1] :
( ( p(crypt(X0,X1))
& p(X0) )
=> p(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_knowledge) ).
fof(f16,axiom,
! [X0,X1] :
( ( p(X1)
& p(X0) )
=> p(crypt(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_knowledge) ).
fof(f21,axiom,
p(pin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
fof(f22,axiom,
p(crypt(xor(km,pin),pp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
fof(f25,axiom,
p(crypt(xor(km,xor(imp,kp)),kek)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_9) ).
fof(f27,axiom,
p(exp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_11) ).
fof(f28,axiom,
p(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_account_number) ).
fof(f29,conjecture,
p(crypt(pp,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',find_pin) ).
fof(f30,negated_conjecture,
~ p(crypt(pp,a)),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
~ p(crypt(pp,a)),
inference(flattening,[],[f30]) ).
fof(f34,plain,
! [X0,X1,X2] :
( p(crypt(xor(X2,X0),X1))
| ~ p(crypt(xor(km,X0),X1))
| ~ p(X0)
| ~ p(crypt(xor(km,exp),X2)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f35,plain,
! [X0,X1,X2] :
( p(crypt(xor(X2,X0),X1))
| ~ p(crypt(xor(km,X0),X1))
| ~ p(X0)
| ~ p(crypt(xor(km,exp),X2)) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X0)
| ~ p(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X0)
| ~ p(X1) ),
inference(flattening,[],[f36]) ).
fof(f38,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(f39,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,[],[f38]) ).
fof(f40,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(f41,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,[],[f40]) ).
fof(f48,plain,
! [X0,X1] :
( p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f49,plain,
! [X0,X1] :
( p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( p(X1)
| ~ p(crypt(X0,X1))
| ~ p(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f51,plain,
! [X0,X1] :
( p(X1)
| ~ p(crypt(X0,X1))
| ~ p(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( p(crypt(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f53,plain,
! [X0,X1] :
( p(crypt(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(flattening,[],[f52]) ).
fof(f60,plain,
! [X2,X0,X1] :
( p(crypt(xor(X2,X0),X1))
| ~ p(crypt(xor(km,X0),X1))
| ~ p(X0)
| ~ p(crypt(xor(km,exp),X2)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[],[f37]) ).
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,[],[f39]) ).
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,[],[f41]) ).
fof(f67,plain,
! [X0,X1] :
( p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f68,plain,
! [X0,X1] :
( ~ p(crypt(X0,X1))
| p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f69,plain,
! [X0,X1] :
( p(crypt(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f74,plain,
p(pin),
inference(cnf_transformation,[],[f21]) ).
fof(f75,plain,
p(crypt(xor(km,pin),pp)),
inference(cnf_transformation,[],[f22]) ).
fof(f78,plain,
p(crypt(xor(km,xor(imp,kp)),kek)),
inference(cnf_transformation,[],[f25]) ).
fof(f80,plain,
p(exp),
inference(cnf_transformation,[],[f27]) ).
fof(f81,plain,
p(a),
inference(cnf_transformation,[],[f28]) ).
fof(f82,plain,
~ p(crypt(pp,a)),
inference(cnf_transformation,[],[f31]) ).
fof(f112,definition,
( spl1_6
<=> p(pp) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f130,definition,
( spl1_9
<=> p(pin) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f131,plain,
( ~ p(pin)
| spl1_9 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( ~ p(a)
| ~ p(pp) ),
inference(resolution,[],[f69,f82]) ).
fof(f136,plain,
( ~ p(pp)
| spl1_6 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f138,definition,
( spl1_10
<=> p(a) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f139,plain,
( ~ p(a)
| spl1_10 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f140,plain,
( ~ spl1_6
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f133,f138,f112]) ).
fof(f155,plain,
( $false
| spl1_10 ),
inference(resolution,[],[f139,f81]) ).
fof(f156,plain,
spl1_10,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f160,plain,
! [X2,X0,X1] :
( p(X1)
| ~ p(X0)
| ~ p(crypt(xor(km,exp),X2))
| ~ p(crypt(xor(km,X0),X1))
| ~ p(xor(X2,X0)) ),
inference(resolution,[],[f60,f68]) ).
fof(f170,plain,
( ! [X0,X1] :
( ~ p(crypt(xor(km,exp),X1))
| ~ p(crypt(xor(km,X0),pp))
| ~ p(xor(X1,X0))
| ~ p(X0) )
| spl1_6 ),
inference(resolution,[],[f160,f136]) ).
fof(f188,definition,
( spl1_13
<=> p(exp) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f189,plain,
( ~ p(exp)
| spl1_13 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f201,definition,
( spl1_17
<=> ! [X0] :
( ~ p(crypt(xor(km,exp),X0))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f202,plain,
( ! [X0] :
( ~ p(crypt(xor(km,exp),X0))
| ~ p(X0) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f230,plain,
( ! [X0,X1] :
( ~ p(crypt(xor(km,exp),X0))
| ~ p(crypt(xor(km,X1),pp))
| ~ p(X1)
| ~ p(X0)
| ~ p(X1) )
| spl1_6 ),
inference(resolution,[],[f170,f67]) ).
fof(f233,plain,
( ! [X0,X1] :
( ~ p(crypt(xor(km,exp),X0))
| ~ p(crypt(xor(km,X1),pp))
| ~ p(X1)
| ~ p(X0) )
| spl1_6 ),
inference(duplicate_literal_removal,[],[f230]) ).
fof(f243,definition,
( spl1_24
<=> ! [X1] :
( ~ p(crypt(xor(km,X1),pp))
| ~ p(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_24])],[avatar_definition]) ).
fof(f244,plain,
( ! [X1] :
( ~ p(crypt(xor(km,X1),pp))
| ~ p(X1) )
| ~ spl1_24 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( spl1_24
| spl1_17
| spl1_6 ),
inference(avatar_split_clause,[],[f233,f112,f201,f243]) ).
fof(f259,plain,
( $false
| spl1_13 ),
inference(resolution,[],[f189,f80]) ).
fof(f261,plain,
spl1_13,
inference(avatar_contradiction_clause,[],[f259]) ).
fof(f262,plain,
( $false
| spl1_9 ),
inference(resolution,[],[f131,f74]) ).
fof(f264,plain,
spl1_9,
inference(avatar_contradiction_clause,[],[f262]) ).
fof(f357,definition,
( spl1_40
<=> ! [X0] : ~ p(X0) ),
introduced(definition,[new_symbols(definition,[spl1_40])],[avatar_definition]) ).
fof(f358,plain,
( ! [X0] : ~ p(X0)
| ~ spl1_40 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f361,definition,
( spl1_41
<=> ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(crypt(xor(km,xor(exp,kp)),X0))
| ~ p(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_41])],[avatar_definition]) ).
fof(f362,plain,
( ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(crypt(xor(km,xor(exp,kp)),X0))
| ~ p(X1) )
| ~ spl1_41 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f476,plain,
( ! [X0,X1] :
( ~ p(crypt(xor(km,xor(exp,kp)),X0))
| ~ p(X1)
| ~ p(X0)
| ~ p(X1) )
| ~ spl1_41 ),
inference(resolution,[],[f362,f67]) ).
fof(f484,plain,
( ! [X0,X1] :
( ~ p(crypt(xor(km,xor(exp,kp)),X0))
| ~ p(X1)
| ~ p(X0) )
| ~ spl1_41 ),
inference(duplicate_literal_removal,[],[f476]) ).
fof(f489,definition,
( spl1_55
<=> ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) ) ),
introduced(definition,[new_symbols(definition,[spl1_55])],[avatar_definition]) ).
fof(f490,plain,
( ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(X0)
| ~ p(X1) )
| ~ spl1_55 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f508,definition,
( spl1_60
<=> ! [X0] :
( ~ p(crypt(xor(km,xor(exp,kp)),X0))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_60])],[avatar_definition]) ).
fof(f509,plain,
( ! [X0] :
( ~ p(crypt(xor(km,xor(exp,kp)),X0))
| ~ p(X0) )
| ~ spl1_60 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f627,plain,
( spl1_40
| spl1_60
| ~ spl1_41 ),
inference(avatar_split_clause,[],[f484,f361,f508,f357]) ).
fof(f632,plain,
( $false
| ~ spl1_40 ),
inference(resolution,[],[f358,f78]) ).
fof(f663,plain,
~ spl1_40,
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f668,plain,
( ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(X1)
| ~ p(crypt(xor(km,xor(exp,kp)),X0))
| ~ p(exp) )
| ~ spl1_17 ),
inference(resolution,[],[f202,f63]) ).
fof(f675,plain,
( ~ spl1_13
| spl1_41
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f668,f201,f361,f188]) ).
fof(f794,plain,
( ~ p(pin)
| ~ spl1_24 ),
inference(resolution,[],[f244,f75]) ).
fof(f800,plain,
( ~ spl1_9
| ~ spl1_24 ),
inference(avatar_split_clause,[],[f794,f243,f130]) ).
fof(f876,plain,
( ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(X0)
| ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(exp) )
| ~ spl1_60 ),
inference(resolution,[],[f509,f62]) ).
fof(f894,definition,
( spl1_101
<=> ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_101])],[avatar_definition]) ).
fof(f895,plain,
( ! [X0,X1] :
( ~ p(xor(X0,X1))
| ~ p(crypt(xor(km,xor(kp,exp)),X1))
| ~ p(X0) )
| ~ spl1_101 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f896,plain,
( ~ spl1_13
| spl1_101
| ~ spl1_60 ),
inference(avatar_split_clause,[],[f876,f508,f894,f188]) ).
fof(f932,plain,
( ! [X0,X1] :
( ~ p(xor(X1,X0))
| ~ p(X1)
| ~ p(X0)
| ~ p(exp) )
| ~ spl1_101 ),
inference(resolution,[],[f895,f61]) ).
fof(f959,plain,
( ~ spl1_13
| spl1_55
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f932,f894,f489,f188]) ).
fof(f990,plain,
( ! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| ~ p(X0)
| ~ p(X1) )
| ~ spl1_55 ),
inference(resolution,[],[f490,f67]) ).
fof(f992,plain,
( ! [X0,X1] :
( ~ p(X0)
| ~ p(X1) )
| ~ spl1_55 ),
inference(duplicate_literal_removal,[],[f990]) ).
fof(f993,plain,
( spl1_40
| spl1_40
| ~ spl1_55 ),
inference(avatar_split_clause,[],[f992,f489,f357,f357]) ).
cnf(s8,plain,
( ~ spl1_6
| ~ spl1_10 ),
inference(sat_conversion,[],[f140]) ).
cnf(s11,plain,
spl1_10,
inference(sat_conversion,[],[f156]) ).
cnf(s18,plain,
( spl1_6
| spl1_17
| spl1_24 ),
inference(sat_conversion,[],[f245]) ).
cnf(s23,plain,
spl1_13,
inference(sat_conversion,[],[f261]) ).
cnf(s24,plain,
spl1_9,
inference(sat_conversion,[],[f264]) ).
cnf(s78,plain,
( spl1_40
| ~ spl1_41
| spl1_60 ),
inference(sat_conversion,[],[f627]) ).
cnf(s92,plain,
~ spl1_40,
inference(sat_conversion,[],[f663]) ).
cnf(s93,plain,
( ~ spl1_13
| ~ spl1_17
| spl1_41 ),
inference(sat_conversion,[],[f675]) ).
cnf(s105,plain,
( ~ spl1_9
| ~ spl1_24 ),
inference(sat_conversion,[],[f800]) ).
cnf(s119,plain,
( ~ spl1_13
| ~ spl1_60
| spl1_101 ),
inference(sat_conversion,[],[f896]) ).
cnf(s129,plain,
( ~ spl1_13
| spl1_55
| ~ spl1_101 ),
inference(sat_conversion,[],[f959]) ).
cnf(s134,plain,
( spl1_40
| spl1_40
| ~ spl1_55 ),
inference(sat_conversion,[],[f993]) ).
cnf(s135,plain,
( spl1_40
| ~ spl1_55 ),
inference(rat,[],[s134]) ).
cnf(s137,plain,
~ spl1_55,
inference(rat,[],[s135,s92]) ).
cnf(s139,plain,
( ~ spl1_41
| spl1_60 ),
inference(rat,[],[s78,s92]) ).
cnf(s152,plain,
~ spl1_24,
inference(rat,[],[s105,s24]) ).
cnf(s154,plain,
~ spl1_101,
inference(rat,[],[s129,s137,s23]) ).
cnf(s155,plain,
~ spl1_60,
inference(rat,[],[s119,s154,s23]) ).
cnf(s159,plain,
~ spl1_41,
inference(rat,[],[s139,s155]) ).
cnf(s164,plain,
~ spl1_17,
inference(rat,[],[s93,s23,s159]) ).
cnf(s167,plain,
spl1_6,
inference(rat,[],[s18,s152,s164]) ).
cnf(s181,plain,
$false,
inference(rat,[],[s8,s11,s167]) ).
fof(f994,plain,
$false,
inference(avatar_sat_refutation,[],[s181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n019.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 10:15:03 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.30 Running first-order theorem proving
% 0.25/0.30 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
% 5.14/1.54 % (3907604)Detected formulas, will run a generic FOF schedule.
% 5.14/1.54 % (3907610)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=2781029831:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.14/1.54 % (3907614)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2073609694:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.14/1.54 % (3907611)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=3197629128:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.14/1.54 % (3907613)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3957390066:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.14/1.54 % (3907612)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4220305681:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.14/1.54 % (3907609)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=2816193127:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.14/1.54 % (3907613)Refutation not found, incomplete strategy
% 5.14/1.54 % (3907613)------------------------------
% 5.14/1.54 % (3907613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.54 % (3907612)Refutation not found, incomplete strategy
% 5.14/1.54 % (3907612)------------------------------
% 5.14/1.54 % (3907612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.54 % (3907613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.54 % (3907612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.54 % (3907613)CaDiCaL version: 2.1.3
% 5.14/1.54 % (3907612)CaDiCaL version: 2.1.3
% 5.14/1.54 % (3907613)Termination reason: Refutation not found, incomplete strategy
% 5.14/1.54 % (3907613)Time elapsed: 0.002 s
% 5.14/1.54 % (3907612)Termination reason: Refutation not found, incomplete strategy
% 5.14/1.54 % (3907612)Time elapsed: 0.001 s
% 5.14/1.54 % (3907613)Peak memory usage: 87 MB
% 5.14/1.54 % (3907612)Peak memory usage: 87 MB
% 5.14/1.54 % (3907615)dis-21_1_sil=8000:lcm=predicate:random_seed=1042916118: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)
% 5.14/1.54 % (3907614)Instruction limit reached!
% 5.14/1.54 % (3907614)------------------------------
% 5.14/1.54 % (3907614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.54 % (3907614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.54 % (3907614)CaDiCaL version: 2.1.3
% 5.14/1.54 % (3907614)Termination reason: Instruction limit
% 5.14/1.54 % (3907614)Termination phase: Saturation
% 5.14/1.54 % (3907614)Time elapsed: 0.144 s
% 5.14/1.54 % (3907614)Peak memory usage: 90 MB
% 5.14/1.54 % (3907614)Instructions burned: 139 (million)
% 5.14/1.54 % (3907615)First to succeed.
% 5.14/1.54 % (3907615)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3907604"
% 5.14/1.54 % (3907623)lrs+10_1_sil=8000:sp=occurrence:random_seed=931865121:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.14/1.54 % (3907623)Refutation not found, incomplete strategy
% 5.14/1.54 % (3907623)------------------------------
% 5.14/1.54 % (3907623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.14/1.54 % (3907623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.14/1.54 % (3907623)CaDiCaL version: 2.1.3
% 5.14/1.54 % (3907623)Termination reason: Refutation not found, incomplete strategy
% 5.14/1.54 % (3907623)Time elapsed: 0.002 s
% 5.14/1.54 % (3907623)Peak memory usage: 88 MB
% 5.14/1.54 % (3907612)------------------------------
% 5.14/1.54 % (3907612)------------------------------
% 5.14/1.54 % (3907613)------------------------------
% 5.14/1.54 % (3907613)------------------------------
% 5.14/1.54 % (3907615)Refutation found. Thanks to Tanya!
% 5.14/1.54 % SZS status Theorem for theBenchmark
% 5.14/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.95/1.75 % (3907615)------------------------------
% 5.95/1.75 % (3907615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.75 % (3907615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.75 % (3907615)CaDiCaL version: 2.1.3
% 5.95/1.75 % (3907615)Termination reason: Refutation
% 5.95/1.75 % (3907615)Time elapsed: 0.025 s
% 5.95/1.75 % (3907615)Peak memory usage: 90 MB
% 5.95/1.75 % (3907615)Instructions burned: 20 (million)
% 5.95/1.75 % (3907615)------------------------------
% 5.95/1.75 % (3907615)------------------------------
% 5.95/1.75 % (3907604)Success in time 0.731 s
% 5.95/1.75 % Vampire exiting
%------------------------------------------------------------------------------