%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PRO009+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:30:24 PM UTC 2026
% Result : Theorem 2.14s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 130 ( 19 unt; 7 def)
% Number of atoms : 403 ( 23 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 469 ( 196 ~; 187 |; 65 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 8 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 167 ( 0 sgn 145 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( occurrence_of(X1,X0)
& subactivity_occurrence(X2,X1)
& leaf_occ(X3,X1)
& arboreal(X2)
& ~ min_precedes(X2,X3,X0) )
=> X3 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(f9,axiom,
! [X0,X1,X2] :
( ( occurrence_of(X0,X1)
& occurrence_of(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( occurrence_of(X0,X2)
& root_occ(X1,X0) )
=> ~ ? [X3] : min_precedes(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
fof(f12,axiom,
! [X0,X1] :
( subactivity_occurrence(X0,X1)
=> ( activity_occurrence(X0)
& activity_occurrence(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
fof(f13,axiom,
! [X0] :
( activity_occurrence(X0)
=> ? [X1] :
( activity(X1)
& occurrence_of(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(f14,axiom,
! [X0] :
( legal(X0)
=> arboreal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(f18,axiom,
! [X0,X1] :
( root(X0,X1)
=> legal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_17) ).
fof(f20,axiom,
! [X0,X1] :
( root_occ(X0,X1)
<=> ? [X2] :
( occurrence_of(X1,X2)
& subactivity_occurrence(X0,X1)
& root(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_19) ).
fof(f27,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_26) ).
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(f51,plain,
! [X0] :
( activity_occurrence(X0)
=> ? [X1] : occurrence_of(X0,X1) ),
inference(pure_predicate_removal,[],[f13]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| ~ occurrence_of(X1,X0)
| ~ subactivity_occurrence(X2,X1)
| ~ leaf_occ(X3,X1)
| ~ arboreal(X2)
| min_precedes(X2,X3,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| ~ occurrence_of(X1,X0)
| ~ subactivity_occurrence(X2,X1)
| ~ leaf_occ(X3,X1)
| ~ arboreal(X2)
| min_precedes(X2,X3,X0) ),
inference(flattening,[],[f58]) ).
fof(f67,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X1)
| ~ occurrence_of(X0,X2) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X1)
| ~ occurrence_of(X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ! [X3] : ~ min_precedes(X3,X1,X2)
| ~ occurrence_of(X0,X2)
| ~ root_occ(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ! [X3] : ~ min_precedes(X3,X1,X2)
| ~ occurrence_of(X0,X2)
| ~ root_occ(X1,X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( activity_occurrence(X0)
& activity_occurrence(X1) )
| ~ subactivity_occurrence(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f74,plain,
! [X0] :
( ? [X1] : occurrence_of(X0,X1)
| ~ activity_occurrence(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f75,plain,
! [X0] :
( arboreal(X0)
| ~ legal(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f79,plain,
! [X0,X1] :
( legal(X0)
| ~ root(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f85,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,[],[f27]) ).
fof(f96,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(f97,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(f102,plain,
! [X0] :
( occurrence_of(X0,sK4(X0))
| ~ activity_occurrence(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f74]) ).
fof(f112,plain,
! [X0,X1] :
( ( root_occ(X0,X1)
| ! [X2] :
( ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ root(X0,X2) ) )
& ( ? [X2] :
( occurrence_of(X1,X2)
& subactivity_occurrence(X0,X1)
& root(X0,X2) )
| ~ root_occ(X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f113,plain,
! [X0,X1] :
( ( root_occ(X0,X1)
| ! [X2] :
( ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ root(X0,X2) ) )
& ( ? [X3] :
( occurrence_of(X1,X3)
& subactivity_occurrence(X0,X1)
& root(X0,X3) )
| ~ root_occ(X0,X1) ) ),
inference(rectify,[],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( ( root_occ(X0,X1)
| ! [X2] :
( ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ root(X0,X2) ) )
& ( ( occurrence_of(X1,sK9(X0,X1))
& subactivity_occurrence(X0,X1)
& root(X0,sK9(X0,X1)) )
| ~ root_occ(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1))],[f113]) ).
fof(f118,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,[],[f85]) ).
fof(f119,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,[],[f118]) ).
fof(f120,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,[],[f119]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( next_subocc(X0,X1,X2)
| ~ min_precedes(X0,X1,X2)
| ( min_precedes(X0,sK11(X0,X1,X2),X2)
& min_precedes(sK11(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,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f120]) ).
fof(f122,plain,
! [X0] :
( ( occurrence_of(sK12(X0),tptp3)
& root_occ(sK12(X0),X0)
& occurrence_of(sK13(X0),tptp4)
& next_subocc(sK12(X0),sK13(X0),tptp0)
& ( occurrence_of(sK14(X0),tptp2)
| occurrence_of(sK14(X0),tptp1) )
& next_subocc(sK13(X0),sK14(X0),tptp0)
& leaf_occ(sK14(X0),X0) )
| ~ occurrence_of(X0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0)),skolemize(X3,sK14(X0))],[f96]) ).
fof(f123,plain,
( ! [X1,X2] :
( ~ occurrence_of(X1,tptp3)
| ~ root_occ(X1,sK15)
| ( ~ occurrence_of(X2,tptp2)
& ~ occurrence_of(X2,tptp1) )
| ~ min_precedes(X1,X2,tptp0)
| ~ leaf_occ(X2,sK15) )
& occurrence_of(sK15,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f97]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( ~ leaf_occ(X3,X1)
| ~ occurrence_of(X1,X0)
| ~ subactivity_occurrence(X2,X1)
| X2 = X3
| ~ arboreal(X2)
| min_precedes(X2,X3,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ occurrence_of(X0,X1)
| X1 = X2
| ~ occurrence_of(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ min_precedes(X3,X1,X2)
| ~ occurrence_of(X0,X2)
| ~ root_occ(X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f140,plain,
! [X0,X1] :
( activity_occurrence(X0)
| ~ subactivity_occurrence(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f141,plain,
! [X0] :
( occurrence_of(X0,sK4(X0))
| ~ activity_occurrence(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f142,plain,
! [X0] :
( ~ legal(X0)
| arboreal(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f151,plain,
! [X0,X1] :
( ~ root(X0,X1)
| legal(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f156,plain,
! [X0,X1] :
( ~ root_occ(X0,X1)
| root(X0,sK9(X0,X1)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f157,plain,
! [X0,X1] :
( ~ root_occ(X0,X1)
| subactivity_occurrence(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f158,plain,
! [X0,X1] :
( occurrence_of(X1,sK9(X0,X1))
| ~ root_occ(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ next_subocc(X0,X1,X2)
| min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f121]) ).
fof(f179,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK14(X0),X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f180,plain,
! [X0] :
( next_subocc(sK13(X0),sK14(X0),tptp0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f181,plain,
! [X0] :
( occurrence_of(sK14(X0),tptp1)
| occurrence_of(sK14(X0),tptp2)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f184,plain,
! [X0] :
( root_occ(sK12(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f185,plain,
! [X0] :
( occurrence_of(sK12(X0),tptp3)
| ~ occurrence_of(X0,tptp0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f197,plain,
occurrence_of(sK15,tptp0),
inference(cnf_transformation,[],[f123]) ).
fof(f198,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK15)
| ~ root_occ(X1,sK15)
| ~ occurrence_of(X2,tptp1)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f199,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK15)
| ~ root_occ(X1,sK15)
| ~ occurrence_of(X2,tptp2)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f205,plain,
leaf_occ(sK14(sK15),sK15),
inference(resolution,[],[f179,f197]) ).
fof(f206,plain,
! [X0] :
( ~ root_occ(X0,sK15)
| ~ occurrence_of(sK14(sK15),tptp2)
| ~ min_precedes(X0,sK14(sK15),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f205,f199]) ).
fof(f207,plain,
! [X0] :
( ~ root_occ(X0,sK15)
| ~ occurrence_of(sK14(sK15),tptp1)
| ~ min_precedes(X0,sK14(sK15),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f205,f198]) ).
fof(f210,definition,
( spl16_1
<=> occurrence_of(sK14(sK15),tptp1) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
fof(f212,plain,
( ~ occurrence_of(sK14(sK15),tptp1)
| spl16_1 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f214,definition,
( spl16_2
<=> ! [X0] :
( ~ root_occ(X0,sK15)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,sK14(sK15),tptp0) ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
fof(f215,plain,
( ! [X0] :
( ~ min_precedes(X0,sK14(sK15),tptp0)
| ~ occurrence_of(X0,tptp3)
| ~ root_occ(X0,sK15) )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f216,plain,
( ~ spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f207,f214,f210]) ).
fof(f218,definition,
( spl16_3
<=> occurrence_of(sK14(sK15),tptp2) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
fof(f221,plain,
( ~ spl16_3
| spl16_2 ),
inference(avatar_split_clause,[],[f206,f214,f218]) ).
fof(f222,plain,
! [X0] :
( subactivity_occurrence(sK12(X0),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[],[f184,f157]) ).
fof(f241,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| root(sK12(X0),sK9(sK12(X0),X0)) ),
inference(resolution,[],[f156,f184]) ).
fof(f249,plain,
! [X0,X1] :
( ~ occurrence_of(X1,tptp0)
| ~ occurrence_of(sK12(X1),X0)
| tptp3 = X0 ),
inference(resolution,[],[f136,f185]) ).
fof(f251,plain,
! [X0] :
( ~ occurrence_of(sK15,X0)
| tptp0 = X0 ),
inference(resolution,[],[f136,f197]) ).
fof(f255,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| min_precedes(sK13(X0),sK14(X0),tptp0) ),
inference(resolution,[],[f180,f171]) ).
fof(f260,plain,
! [X0] :
( ~ root_occ(X0,sK15)
| tptp0 = sK9(X0,sK15) ),
inference(resolution,[],[f251,f158]) ).
fof(f290,plain,
( occurrence_of(sK14(sK15),tptp2)
| ~ occurrence_of(sK15,tptp0)
| spl16_1 ),
inference(resolution,[],[f181,f212]) ).
fof(f295,plain,
( occurrence_of(sK14(sK15),tptp2)
| spl16_1 ),
inference(forward_subsumption_resolution,[],[f290,f197]) ).
fof(f296,plain,
( spl16_3
| spl16_1 ),
inference(avatar_split_clause,[],[f295,f210,f218]) ).
fof(f369,plain,
( tptp0 = sK9(sK12(sK15),sK15)
| ~ occurrence_of(sK15,tptp0) ),
inference(resolution,[],[f260,f184]) ).
fof(f370,plain,
tptp0 = sK9(sK12(sK15),sK15),
inference(forward_subsumption_resolution,[],[f369,f197]) ).
fof(f371,plain,
! [X0,X1] :
( ~ subactivity_occurrence(X1,sK15)
| ~ occurrence_of(sK15,X0)
| sK14(sK15) = X1
| ~ arboreal(X1)
| min_precedes(X1,sK14(sK15),X0) ),
inference(resolution,[],[f127,f205]) ).
fof(f422,plain,
min_precedes(sK13(sK15),sK14(sK15),tptp0),
inference(resolution,[],[f255,f197]) ).
fof(f426,plain,
! [X0] :
( ~ root_occ(sK14(sK15),X0)
| ~ occurrence_of(X0,tptp0) ),
inference(resolution,[],[f422,f138]) ).
fof(f457,plain,
root(sK12(sK15),sK9(sK12(sK15),sK15)),
inference(resolution,[],[f241,f197]) ).
fof(f458,plain,
root(sK12(sK15),tptp0),
inference(forward_demodulation,[],[f457,f370]) ).
fof(f463,plain,
! [X0] :
( ~ occurrence_of(sK12(sK15),X0)
| tptp3 = X0 ),
inference(resolution,[],[f249,f197]) ).
fof(f468,plain,
legal(sK12(sK15)),
inference(resolution,[],[f458,f151]) ).
fof(f481,plain,
arboreal(sK12(sK15)),
inference(resolution,[],[f468,f142]) ).
fof(f587,plain,
( tptp3 = sK4(sK12(sK15))
| ~ activity_occurrence(sK12(sK15)) ),
inference(resolution,[],[f463,f141]) ).
fof(f600,definition,
( spl16_30
<=> activity_occurrence(sK12(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_30])],[avatar_definition]) ).
fof(f601,plain,
( activity_occurrence(sK12(sK15))
| ~ spl16_30 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f602,plain,
( ~ activity_occurrence(sK12(sK15))
| spl16_30 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f604,definition,
( spl16_31
<=> tptp3 = sK4(sK12(sK15)) ),
introduced(definition,[new_symbols(definition,[spl16_31])],[avatar_definition]) ).
fof(f606,plain,
( tptp3 = sK4(sK12(sK15))
| ~ spl16_31 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f607,plain,
( ~ spl16_30
| spl16_31 ),
inference(avatar_split_clause,[],[f587,f604,f600]) ).
fof(f608,plain,
( ! [X0] : ~ subactivity_occurrence(sK12(sK15),X0)
| spl16_30 ),
inference(resolution,[],[f602,f140]) ).
fof(f650,plain,
! [X0] :
( ~ occurrence_of(sK15,X0)
| sK14(sK15) = sK12(sK15)
| ~ arboreal(sK12(sK15))
| min_precedes(sK12(sK15),sK14(sK15),X0)
| ~ occurrence_of(sK15,tptp0) ),
inference(resolution,[],[f371,f222]) ).
fof(f652,plain,
! [X0] :
( ~ occurrence_of(sK15,X0)
| sK14(sK15) = sK12(sK15)
| min_precedes(sK12(sK15),sK14(sK15),X0)
| ~ occurrence_of(sK15,tptp0) ),
inference(forward_subsumption_resolution,[],[f650,f481]) ).
fof(f654,plain,
! [X0] :
( ~ occurrence_of(sK15,X0)
| sK14(sK15) = sK12(sK15)
| min_precedes(sK12(sK15),sK14(sK15),X0) ),
inference(forward_subsumption_resolution,[],[f652,f197]) ).
fof(f656,definition,
( spl16_38
<=> sK14(sK15) = sK12(sK15) ),
introduced(definition,[new_symbols(definition,[spl16_38])],[avatar_definition]) ).
fof(f658,plain,
( sK14(sK15) = sK12(sK15)
| ~ spl16_38 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f660,definition,
( spl16_39
<=> ! [X0] :
( ~ occurrence_of(sK15,X0)
| min_precedes(sK12(sK15),sK14(sK15),X0) ) ),
introduced(definition,[new_symbols(definition,[spl16_39])],[avatar_definition]) ).
fof(f661,plain,
( ! [X0] :
( ~ occurrence_of(sK15,X0)
| min_precedes(sK12(sK15),sK14(sK15),X0) )
| ~ spl16_39 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f662,plain,
( spl16_38
| spl16_39 ),
inference(avatar_split_clause,[],[f654,f660,f656]) ).
fof(f666,plain,
( ~ occurrence_of(sK15,tptp0)
| spl16_30 ),
inference(resolution,[],[f608,f222]) ).
fof(f671,plain,
( $false
| spl16_30 ),
inference(forward_subsumption_resolution,[],[f666,f197]) ).
fof(f672,plain,
spl16_30,
inference(avatar_contradiction_clause,[],[f671]) ).
fof(f702,plain,
( occurrence_of(sK12(sK15),tptp3)
| ~ activity_occurrence(sK12(sK15))
| ~ spl16_31 ),
inference(superposition,[],[f141,f606]) ).
fof(f703,plain,
( occurrence_of(sK12(sK15),tptp3)
| ~ spl16_30
| ~ spl16_31 ),
inference(forward_subsumption_resolution,[],[f702,f601]) ).
fof(f1112,plain,
( min_precedes(sK12(sK15),sK14(sK15),tptp0)
| ~ spl16_39 ),
inference(resolution,[],[f661,f197]) ).
fof(f1158,plain,
( ~ occurrence_of(sK12(sK15),tptp3)
| ~ root_occ(sK12(sK15),sK15)
| ~ spl16_2
| ~ spl16_39 ),
inference(resolution,[],[f1112,f215]) ).
fof(f1185,plain,
( ~ root_occ(sK12(sK15),sK15)
| ~ spl16_2
| ~ spl16_30
| ~ spl16_31
| ~ spl16_39 ),
inference(forward_subsumption_resolution,[],[f1158,f703]) ).
fof(f1212,plain,
( root_occ(sK14(sK15),sK15)
| ~ occurrence_of(sK15,tptp0)
| ~ spl16_38 ),
inference(superposition,[],[f184,f658]) ).
fof(f1213,plain,
( ~ occurrence_of(sK15,tptp0)
| ~ spl16_38 ),
inference(forward_subsumption_resolution,[],[f1212,f426]) ).
fof(f1230,plain,
( $false
| ~ spl16_38 ),
inference(forward_subsumption_resolution,[],[f1213,f197]) ).
fof(f1231,plain,
~ spl16_38,
inference(avatar_contradiction_clause,[],[f1230]) ).
fof(f1235,plain,
( ~ occurrence_of(sK15,tptp0)
| ~ spl16_2
| ~ spl16_30
| ~ spl16_31
| ~ spl16_39 ),
inference(resolution,[],[f1185,f184]) ).
fof(f1236,plain,
( $false
| ~ spl16_2
| ~ spl16_30
| ~ spl16_31
| ~ spl16_39 ),
inference(forward_subsumption_resolution,[],[f1235,f197]) ).
fof(f1237,plain,
( ~ spl16_2
| ~ spl16_30
| ~ spl16_31
| ~ spl16_39 ),
inference(avatar_contradiction_clause,[],[f1236]) ).
cnf(s1,plain,
( ~ spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f216]) ).
cnf(s2,plain,
( spl16_2
| ~ spl16_3 ),
inference(sat_conversion,[],[f221]) ).
cnf(s6,plain,
( spl16_1
| spl16_3 ),
inference(sat_conversion,[],[f296]) ).
cnf(s25,plain,
( ~ spl16_30
| spl16_31 ),
inference(sat_conversion,[],[f607]) ).
cnf(s29,plain,
( spl16_38
| spl16_39 ),
inference(sat_conversion,[],[f662]) ).
cnf(s30,plain,
spl16_30,
inference(sat_conversion,[],[f672]) ).
cnf(s75,plain,
~ spl16_38,
inference(sat_conversion,[],[f1231]) ).
cnf(s76,plain,
( ~ spl16_2
| ~ spl16_30
| ~ spl16_31
| ~ spl16_39 ),
inference(sat_conversion,[],[f1237]) ).
cnf(s78,plain,
spl16_39,
inference(rat,[],[s29,s75]) ).
cnf(s80,plain,
spl16_31,
inference(rat,[],[s25,s30]) ).
cnf(s81,plain,
~ spl16_2,
inference(rat,[],[s76,s78,s30,s80]) ).
cnf(s87,plain,
~ spl16_3,
inference(rat,[],[s2,s81]) ).
cnf(s88,plain,
spl16_1,
inference(rat,[],[s6,s87]) ).
cnf(s89,plain,
$false,
inference(rat,[],[s1,s81,s88]) ).
fof(f1238,plain,
$false,
inference(avatar_sat_refutation,[],[s89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PRO009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 22:23:31 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.14/1.30 % (2074851)Detected formulas, will run a generic FOF schedule.
% 2.14/1.30 % (2074860)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2244173103:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.14/1.30 % (2074860)Instruction limit reached!
% 2.14/1.30 % (2074860)------------------------------
% 2.14/1.30 % (2074860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/1.30 % (2074860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/1.30 % (2074860)CaDiCaL version: 2.1.3
% 2.14/1.30 % (2074860)Termination reason: Instruction limit
% 2.14/1.30 % (2074860)Termination phase: Saturation
% 2.14/1.30 % (2074860)Time elapsed: 0.030 s
% 2.14/1.30 % (2074860)Peak memory usage: 88 MB
% 2.14/1.30 % (2074860)Instructions burned: 119 (million)
% 2.14/1.30 % (2074857)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=1404180381:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.14/1.30 % (2074858)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=408130505:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.14/1.30 % (2074856)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=2906337202:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.14/1.30 % (2074862)dis-21_1_sil=8000:lcm=predicate:random_seed=268638039: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)
% 2.14/1.30 % (2074859)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=614944538:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.14/1.30 % (2074861)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2862154965:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.14/1.30 % (2074859)Refutation not found, incomplete strategy
% 2.14/1.30 % (2074859)------------------------------
% 2.14/1.30 % (2074859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/1.30 % (2074859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/1.30 % (2074859)CaDiCaL version: 2.1.3
% 2.14/1.30 % (2074859)Termination reason: Refutation not found, incomplete strategy
% 2.14/1.30 % (2074859)Time elapsed: 0.001 s
% 2.14/1.30 % (2074859)Peak memory usage: 87 MB
% 2.14/1.30 % (2074861)First to succeed.
% 2.14/1.30 % (2074861)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2074851"
% 2.14/1.30 % (2074862)Instruction limit reached!
% 2.14/1.30 % (2074862)------------------------------
% 2.14/1.30 % (2074862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/1.30 % (2074862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/1.30 % (2074862)CaDiCaL version: 2.1.3
% 2.14/1.30 % (2074862)Termination reason: Instruction limit
% 2.14/1.30 % (2074862)Termination phase: Saturation
% 2.14/1.30 % (2074862)Time elapsed: 0.082 s
% 2.14/1.30 % (2074862)Peak memory usage: 89 MB
% 2.14/1.30 % (2074862)Instructions burned: 129 (million)
% 2.14/1.30 % (2074864)lrs+10_1_sil=8000:sp=occurrence:random_seed=2976441518:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.14/1.30 % (2074864)Also succeeded, but the first one will report.
% 2.14/1.30 % (2074859)------------------------------
% 2.14/1.30 % (2074859)------------------------------
% 2.14/1.30 % (2074871)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3167634847:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.14/1.30 % (2074871)Refutation not found, incomplete strategy
% 2.14/1.30 % (2074871)------------------------------
% 2.14/1.30 % (2074871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/1.30 % (2074871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/1.30 % (2074871)CaDiCaL version: 2.1.3
% 2.14/1.30 % (2074871)Termination reason: Refutation not found, incomplete strategy
% 2.14/1.30 % (2074871)Time elapsed: 0.004 s
% 2.14/1.30 % (2074871)Peak memory usage: 88 MB
% 2.14/1.30 % (2074871)Instructions burned: 3 (million)
% 2.14/1.30 % (2074861)Refutation found. Thanks to Tanya!
% 2.14/1.30 % SZS status Theorem for theBenchmark
% 2.14/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (2074861)------------------------------
% 0.17/1.50 % (2074861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2074861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2074861)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2074861)Termination reason: Refutation
% 0.17/1.50 % (2074861)Time elapsed: 0.032 s
% 0.17/1.50 % (2074861)Peak memory usage: 90 MB
% 0.17/1.50 % (2074861)Instructions burned: 39 (million)
% 0.17/1.50 % (2074861)------------------------------
% 0.17/1.50 % (2074861)------------------------------
% 0.17/1.50 % (2074851)Success in time 0.463 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------