%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:30:36 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 15 unt; 3 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 225 ( 88 ~; 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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] :
( ~ occurrence_of(X0,tptp0)
| root_occ(sK14(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f187,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK14(X0),tptp3) ),
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(f215,plain,
leaf_occ(sK16(sK17),sK17),
inference(resolution,[],[f181,f200]) ).
fof(f216,plain,
! [X0] :
( ~ root_occ(X0,sK17)
| ~ occurrence_of(sK16(sK17),tptp2)
| ~ min_precedes(X0,sK16(sK17),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f215,f202]) ).
fof(f217,plain,
! [X0] :
( ~ root_occ(X0,sK17)
| ~ occurrence_of(sK16(sK17),tptp1)
| ~ min_precedes(X0,sK16(sK17),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f215,f201]) ).
fof(f220,definition,
( spl18_1
<=> occurrence_of(sK16(sK17),tptp1) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f222,plain,
( ~ occurrence_of(sK16(sK17),tptp1)
| spl18_1 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f224,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(f225,plain,
( ! [X0] :
( ~ root_occ(X0,sK17)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,sK16(sK17),tptp0) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( ~ spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f217,f224,f220]) ).
fof(f228,definition,
( spl18_3
<=> occurrence_of(sK16(sK17),tptp2) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f230,plain,
( ~ occurrence_of(sK16(sK17),tptp2)
| spl18_3 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
( ~ spl18_3
| spl18_2 ),
inference(avatar_split_clause,[],[f216,f224,f228]) ).
fof(f236,plain,
root_occ(sK14(sK17),sK17),
inference(resolution,[],[f186,f200]) ).
fof(f238,plain,
occurrence_of(sK14(sK17),tptp3),
inference(resolution,[],[f187,f200]) ).
fof(f262,plain,
next_subocc(sK15(sK17),sK16(sK17),tptp0),
inference(resolution,[],[f182,f200]) ).
fof(f265,plain,
next_subocc(sK14(sK17),sK15(sK17),tptp0),
inference(resolution,[],[f184,f200]) ).
fof(f276,plain,
min_precedes(sK15(sK17),sK16(sK17),tptp0),
inference(resolution,[],[f262,f124]) ).
fof(f280,plain,
min_precedes(sK14(sK17),sK15(sK17),tptp0),
inference(resolution,[],[f265,f124]) ).
fof(f341,plain,
( occurrence_of(sK16(sK17),tptp1)
| occurrence_of(sK16(sK17),tptp2) ),
inference(resolution,[],[f183,f200]) ).
fof(f342,plain,
( occurrence_of(sK16(sK17),tptp2)
| spl18_1 ),
inference(forward_subsumption_resolution,[],[f341,f222]) ).
fof(f343,plain,
( $false
| spl18_1
| spl18_3 ),
inference(forward_subsumption_resolution,[],[f342,f230]) ).
fof(f344,plain,
( spl18_1
| spl18_3 ),
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f491,plain,
! [X0] :
( ~ min_precedes(sK15(sK17),X0,tptp0)
| min_precedes(sK14(sK17),X0,tptp0) ),
inference(resolution,[],[f280,f119]) ).
fof(f653,plain,
( ~ occurrence_of(sK14(sK17),tptp3)
| ~ min_precedes(sK14(sK17),sK16(sK17),tptp0)
| ~ spl18_2 ),
inference(resolution,[],[f225,f236]) ).
fof(f655,plain,
( ~ min_precedes(sK14(sK17),sK16(sK17),tptp0)
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f653,f238]) ).
fof(f1159,plain,
min_precedes(sK14(sK17),sK16(sK17),tptp0),
inference(resolution,[],[f491,f276]) ).
fof(f1162,plain,
( $false
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f1159,f655]) ).
fof(f1163,plain,
~ spl18_2,
inference(avatar_contradiction_clause,[],[f1162]) ).
cnf(s1,plain,
( ~ spl18_1
| spl18_2 ),
inference(sat_conversion,[],[f226]) ).
cnf(s2,plain,
( spl18_2
| ~ spl18_3 ),
inference(sat_conversion,[],[f231]) ).
cnf(s3,plain,
( spl18_1
| spl18_3 ),
inference(sat_conversion,[],[f344]) ).
cnf(s48,plain,
~ spl18_2,
inference(sat_conversion,[],[f1163]) ).
cnf(s56,plain,
~ spl18_3,
inference(rat,[],[s2,s48]) ).
cnf(s57,plain,
spl18_1,
inference(rat,[],[s3,s56]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s1,s48,s57]) ).
fof(f1164,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:20:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.17/0.47 % (3467290)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3467297)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3645172481:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3467296)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3467295)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1607745803_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (3467296)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1571603745:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3467299)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=394085685:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3467298)dis+10_1_sil=32000:sp=arity:random_seed=1622173013:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3467300)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=388630178:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (3467301)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2435188976:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % Detected minimum model sizes of [4]
% 0.17/0.47 % Detected maximum model sizes of [max]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % TRYING [5]
% 0.17/0.47 % (3467300) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3467290-3467300"...
% 0.17/0.47 % (3467300)...printing done.
% 0.17/0.47 % (3467300)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3467300)------------------------------
% 0.17/0.48 % (3467300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3467300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3467300)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3467300)Termination reason: Refutation
% 0.17/0.48 % (3467300)Time elapsed: 0.020 s
% 0.17/0.48 % (3467300)Peak memory usage: 13 MB
% 0.17/0.48 % (3467300)Instructions burned: 26 (million)
% 0.17/0.48 % (3467290)Success in time 0.054 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------