%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:30:24 PM UTC 2026
% Result : Theorem 2.71s 1.32s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 13 unt; 3 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 228 ( 91 ~; 82 |; 46 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 81 ( 0 sgn 66 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( min_precedes(X0,X1,X3)
& min_precedes(X1,X2,X3) )
=> min_precedes(X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
fof(f5,axiom,
! [X0,X1,X2] :
( next_subocc(X0,X1,X2)
<=> ( min_precedes(X0,X1,X2)
& ~ ? [X3] :
( min_precedes(X0,X3,X2)
& min_precedes(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(f33,axiom,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2,X3] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& occurrence_of(X2,tptp4)
& next_subocc(X1,X2,tptp0)
& ( occurrence_of(X3,tptp2)
| occurrence_of(X3,tptp1) )
& next_subocc(X2,X3,tptp0)
& leaf_occ(X3,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_32) ).
fof(f46,conjecture,
! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& ( occurrence_of(X2,tptp2)
| occurrence_of(X2,tptp1) )
& min_precedes(X1,X2,tptp0)
& leaf_occ(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( occurrence_of(X0,tptp0)
=> ? [X1,X2] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& ( occurrence_of(X2,tptp2)
| occurrence_of(X2,tptp1) )
& min_precedes(X1,X2,tptp0)
& leaf_occ(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( min_precedes(X0,X2,X3)
| ~ min_precedes(X0,X1,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( min_precedes(X0,X2,X3)
| ~ min_precedes(X0,X1,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(flattening,[],[f49]) ).
fof(f57,plain,
! [X0,X1,X2] :
( next_subocc(X0,X1,X2)
<=> ( min_precedes(X0,X1,X2)
& ! [X3] :
( ~ min_precedes(X0,X3,X2)
| ~ min_precedes(X3,X1,X2) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f90,plain,
! [X0] :
( ? [X1,X2,X3] :
( occurrence_of(X1,tptp3)
& root_occ(X1,X0)
& occurrence_of(X2,tptp4)
& next_subocc(X1,X2,tptp0)
& ( occurrence_of(X3,tptp2)
| occurrence_of(X3,tptp1) )
& next_subocc(X2,X3,tptp0)
& leaf_occ(X3,X0) )
| ~ occurrence_of(X0,tptp0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f91,plain,
? [X0] :
( ! [X1,X2] :
( ~ occurrence_of(X1,tptp3)
| ~ root_occ(X1,X0)
| ( ~ occurrence_of(X2,tptp2)
& ~ occurrence_of(X2,tptp1) )
| ~ min_precedes(X1,X2,tptp0)
| ~ leaf_occ(X2,X0) )
& occurrence_of(X0,tptp0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( next_subocc(X0,X1,X2)
| ~ min_precedes(X0,X1,X2)
| ? [X3] :
( min_precedes(X0,X3,X2)
& min_precedes(X3,X1,X2) ) )
& ( ( min_precedes(X0,X1,X2)
& ! [X3] :
( ~ min_precedes(X0,X3,X2)
| ~ min_precedes(X3,X1,X2) ) )
| ~ next_subocc(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( next_subocc(X0,X1,X2)
| ~ min_precedes(X0,X1,X2)
| ? [X3] :
( min_precedes(X0,X3,X2)
& min_precedes(X3,X1,X2) ) )
& ( ( min_precedes(X0,X1,X2)
& ! [X3] :
( ~ min_precedes(X0,X3,X2)
| ~ min_precedes(X3,X1,X2) ) )
| ~ next_subocc(X0,X1,X2) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( next_subocc(X0,X1,X2)
| ~ min_precedes(X0,X1,X2)
| ? [X3] :
( min_precedes(X0,X3,X2)
& min_precedes(X3,X1,X2) ) )
& ( ( min_precedes(X0,X1,X2)
& ! [X4] :
( ~ min_precedes(X0,X4,X2)
| ~ min_precedes(X4,X1,X2) ) )
| ~ next_subocc(X0,X1,X2) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( next_subocc(X0,X1,X2)
| ~ min_precedes(X0,X1,X2)
| ( min_precedes(X0,sK0(X0,X1,X2),X2)
& min_precedes(sK0(X0,X1,X2),X1,X2) ) )
& ( ( min_precedes(X0,X1,X2)
& ! [X4] :
( ~ min_precedes(X0,X4,X2)
| ~ min_precedes(X4,X1,X2) ) )
| ~ next_subocc(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f94]) ).
fof(f117,plain,
! [X0] :
( ( occurrence_of(sK14(X0),tptp3)
& root_occ(sK14(X0),X0)
& occurrence_of(sK15(X0),tptp4)
& next_subocc(sK14(X0),sK15(X0),tptp0)
& ( occurrence_of(sK16(X0),tptp2)
| occurrence_of(sK16(X0),tptp1) )
& next_subocc(sK15(X0),sK16(X0),tptp0)
& leaf_occ(sK16(X0),X0) )
| ~ occurrence_of(X0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f90]) ).
fof(f118,plain,
( ! [X1,X2] :
( ~ occurrence_of(X1,tptp3)
| ~ root_occ(X1,sK17)
| ( ~ occurrence_of(X2,tptp2)
& ~ occurrence_of(X2,tptp1) )
| ~ min_precedes(X1,X2,tptp0)
| ~ leaf_occ(X2,sK17) )
& occurrence_of(sK17,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f91]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ min_precedes(X0,X1,X3)
| min_precedes(X0,X2,X3)
| ~ min_precedes(X1,X2,X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ next_subocc(X0,X1,X2)
| min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f181,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK16(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f182,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sK15(X0),sK16(X0),tptp0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f183,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK16(X0),tptp1)
| occurrence_of(sK16(X0),tptp2) ),
inference(cnf_transformation,[],[f117]) ).
fof(f184,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sK14(X0),sK15(X0),tptp0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f186,plain,
! [X0] :
( root_occ(sK14(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f187,plain,
! [X0] :
( occurrence_of(sK14(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f200,plain,
occurrence_of(sK17,tptp0),
inference(cnf_transformation,[],[f118]) ).
fof(f201,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK17)
| ~ root_occ(X1,sK17)
| ~ occurrence_of(X2,tptp1)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f118]) ).
fof(f202,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK17)
| ~ root_occ(X1,sK17)
| ~ occurrence_of(X2,tptp2)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f118]) ).
fof(f205,plain,
leaf_occ(sK16(sK17),sK17),
inference(resolution,[],[f181,f200]) ).
fof(f206,plain,
! [X0] :
( ~ root_occ(X0,sK17)
| ~ occurrence_of(sK16(sK17),tptp2)
| ~ min_precedes(X0,sK16(sK17),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f205,f202]) ).
fof(f207,plain,
! [X0] :
( ~ root_occ(X0,sK17)
| ~ occurrence_of(sK16(sK17),tptp1)
| ~ min_precedes(X0,sK16(sK17),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f205,f201]) ).
fof(f209,definition,
( spl18_1
<=> occurrence_of(sK16(sK17),tptp1) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f211,plain,
( ~ occurrence_of(sK16(sK17),tptp1)
| spl18_1 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f213,definition,
( spl18_2
<=> ! [X0] :
( ~ root_occ(X0,sK17)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,sK16(sK17),tptp0) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f214,plain,
( ! [X0] :
( ~ root_occ(X0,sK17)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,sK16(sK17),tptp0) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f215,plain,
( ~ spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f207,f213,f209]) ).
fof(f217,definition,
( spl18_3
<=> occurrence_of(sK16(sK17),tptp2) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f220,plain,
( ~ spl18_3
| spl18_2 ),
inference(avatar_split_clause,[],[f206,f213,f217]) ).
fof(f246,plain,
next_subocc(sK15(sK17),sK16(sK17),tptp0),
inference(resolution,[],[f182,f200]) ).
fof(f250,plain,
next_subocc(sK14(sK17),sK15(sK17),tptp0),
inference(resolution,[],[f184,f200]) ).
fof(f264,plain,
min_precedes(sK15(sK17),sK16(sK17),tptp0),
inference(resolution,[],[f246,f124]) ).
fof(f269,plain,
min_precedes(sK14(sK17),sK15(sK17),tptp0),
inference(resolution,[],[f250,f124]) ).
fof(f290,plain,
( occurrence_of(sK16(sK17),tptp1)
| occurrence_of(sK16(sK17),tptp2) ),
inference(resolution,[],[f183,f200]) ).
fof(f291,plain,
( occurrence_of(sK16(sK17),tptp2)
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f290,f211]) ).
fof(f294,plain,
( spl18_3
| spl18_1 ),
inference(avatar_split_clause,[],[f291,f209,f217]) ).
fof(f298,plain,
! [X0] :
( ~ min_precedes(sK15(sK17),X0,tptp0)
| min_precedes(sK14(sK17),X0,tptp0) ),
inference(resolution,[],[f119,f269]) ).
fof(f596,plain,
( ~ occurrence_of(sK14(sK17),tptp3)
| ~ min_precedes(sK14(sK17),sK16(sK17),tptp0)
| ~ occurrence_of(sK17,tptp0)
| ~ spl18_2 ),
inference(resolution,[],[f214,f186]) ).
fof(f597,plain,
( ~ min_precedes(sK14(sK17),sK16(sK17),tptp0)
| ~ occurrence_of(sK17,tptp0)
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f596,f187]) ).
fof(f598,plain,
( ~ min_precedes(sK14(sK17),sK16(sK17),tptp0)
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f597,f200]) ).
fof(f926,plain,
min_precedes(sK14(sK17),sK16(sK17),tptp0),
inference(resolution,[],[f298,f264]) ).
fof(f928,plain,
( $false
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f926,f598]) ).
fof(f929,plain,
~ spl18_2,
inference(avatar_contradiction_clause,[],[f928]) ).
cnf(s1,plain,
( ~ spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f215]) ).
cnf(s2,plain,
( spl18_2
| ~ spl18_3 ),
inference(sat_conversion,[],[f220]) ).
cnf(s6,plain,
( spl18_1
| spl18_3 ),
inference(sat_conversion,[],[f294]) ).
cnf(s46,plain,
~ spl18_2,
inference(sat_conversion,[],[f929]) ).
cnf(s59,plain,
~ spl18_3,
inference(rat,[],[s2,s46]) ).
cnf(s60,plain,
spl18_1,
inference(rat,[],[s6,s59]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s1,s46,s60]) ).
fof(f930,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:22:11 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.71/1.32 % (976243)Detected formulas, will run a generic FOF schedule.
% 2.71/1.32 % (976248)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=3967763587:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.32 % (976253)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3540326860:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.32 % (976249)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=1331419731:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.32 % (976251)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3995167470:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.32 % (976252)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3550578718:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.32 % (976254)dis-21_1_sil=8000:lcm=predicate:random_seed=3513225571: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)
% 2.71/1.32 % (976250)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=1612056654:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.32 % (976251)Refutation not found, incomplete strategy
% 2.71/1.32 % (976251)------------------------------
% 2.71/1.32 % (976251)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.32 % (976251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.32 % (976251)CaDiCaL version: 2.1.3
% 2.71/1.32 % (976251)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.32 % (976251)Time elapsed: 0.001 s
% 2.71/1.32 % (976251)Peak memory usage: 87 MB
% 2.71/1.32 % (976253)First to succeed.
% 2.71/1.32 % (976253)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-976243"
% 2.71/1.32 % (976254)Instruction limit reached!
% 2.71/1.32 % (976254)------------------------------
% 2.71/1.32 % (976254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.32 % (976254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.32 % (976254)CaDiCaL version: 2.1.3
% 2.71/1.32 % (976254)Termination reason: Instruction limit
% 2.71/1.32 % (976254)Termination phase: Saturation
% 2.71/1.32 % (976254)Time elapsed: 0.050 s
% 2.71/1.32 % (976254)Peak memory usage: 88 MB
% 2.71/1.32 % (976254)Instructions burned: 131 (million)
% 2.71/1.32 % (976252)Instruction limit reached!
% 2.71/1.32 % (976252)------------------------------
% 2.71/1.32 % (976252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.32 % (976252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.32 % (976252)CaDiCaL version: 2.1.3
% 2.71/1.32 % (976252)Termination reason: Instruction limit
% 2.71/1.32 % (976252)Termination phase: Saturation
% 2.71/1.32 % (976252)Time elapsed: 0.072 s
% 2.71/1.32 % (976252)Peak memory usage: 88 MB
% 2.71/1.32 % (976252)Instructions burned: 120 (million)
% 2.71/1.32 % (976262)lrs+10_1_sil=8000:sp=occurrence:random_seed=1030930019:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.71/1.32 % (976262)Also succeeded, but the first one will report.
% 2.71/1.32 % (976251)------------------------------
% 2.71/1.32 % (976251)------------------------------
% 2.71/1.32 % (976263)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2964607354:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.71/1.32 % (976263)Refutation not found, incomplete strategy
% 2.71/1.32 % (976263)------------------------------
% 2.71/1.32 % (976263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.32 % (976263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.32 % (976263)CaDiCaL version: 2.1.3
% 2.71/1.32 % (976263)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.32 % (976263)Time elapsed: 0.003 s
% 2.71/1.32 % (976263)Peak memory usage: 88 MB
% 2.71/1.32 % (976263)Instructions burned: 3 (million)
% 2.71/1.32 % (976253)Refutation found. Thanks to Tanya!
% 2.71/1.32 % SZS status Theorem for theBenchmark
% 2.71/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.41 % (976253)------------------------------
% 3.77/1.41 % (976253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.41 % (976253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.41 % (976253)CaDiCaL version: 2.1.3
% 3.77/1.41 % (976253)Termination reason: Refutation
% 3.77/1.41 % (976253)Time elapsed: 0.023 s
% 3.77/1.41 % (976253)Peak memory usage: 90 MB
% 3.77/1.41 % (976253)Instructions burned: 28 (million)
% 3.77/1.41 % (976253)------------------------------
% 3.77/1.41 % (976253)------------------------------
% 3.77/1.41 % (976243)Success in time 0.452 s
% 3.77/1.41 % Vampire exiting
%------------------------------------------------------------------------------