%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PRO009+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:30:36 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 141 ( 28 unt; 9 def)
% Number of atoms : 435 ( 24 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 500 ( 206 ~; 200 |; 72 &)
% ( 12 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 10 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 178 ( 0 sgn 155 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( occurrence_of(X1,X0)
=> ( activity(X0)
& activity_occurrence(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
fof(f2,axiom,
! [X0] :
( activity_occurrence(X0)
=> ? [X1] :
( activity(X1)
& occurrence_of(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( occurrence_of(X0,X1)
& occurrence_of(X0,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f15,axiom,
! [X0,X1,X2] :
( min_precedes(X0,X1,X2)
=> ~ root(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_14) ).
fof(f23,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_22) ).
fof(f28,axiom,
! [X0,X1] :
( ( occurrence_of(X1,X0)
& ~ atomic(X0) )
=> ? [X2] :
( root(X2,X0)
& subactivity_occurrence(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_27) ).
fof(f34,axiom,
! [X0,X1] :
( root_occ(X0,X1)
<=> ? [X2] :
( occurrence_of(X1,X2)
& subactivity_occurrence(X0,X1)
& root(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_33) ).
fof(f36,axiom,
! [X0,X1,X2,X3] :
( ( occurrence_of(X2,X3)
& root_occ(X0,X2)
& root_occ(X1,X2) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_35) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ( occurrence_of(X0,X3)
& leaf_occ(X1,X0)
& root_occ(X2,X0)
& X1 != X2 )
=> min_precedes(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_41) ).
fof(f50,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_49) ).
fof(f52,axiom,
~ atomic(tptp0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_51) ).
fof(f63,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(f64,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)],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( activity(X0)
& activity_occurrence(X1) )
| ~ occurrence_of(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f66,plain,
! [X0] :
( ? [X1] :
( activity(X1)
& occurrence_of(X0,X1) )
| ~ activity_occurrence(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f67,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X1)
| ~ occurrence_of(X0,X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f68,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ occurrence_of(X0,X1)
| ~ occurrence_of(X0,X2) ),
inference(flattening,[],[f67]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ root(X1,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
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) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2] :
( root(X2,X0)
& subactivity_occurrence(X2,X1) )
| ~ occurrence_of(X1,X0)
| atomic(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f99,plain,
! [X0,X1] :
( ? [X2] :
( root(X2,X0)
& subactivity_occurrence(X2,X1) )
| ~ occurrence_of(X1,X0)
| atomic(X0) ),
inference(flattening,[],[f98]) ).
fof(f110,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ occurrence_of(X2,X3)
| ~ root_occ(X0,X2)
| ~ root_occ(X1,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ occurrence_of(X2,X3)
| ~ root_occ(X0,X2)
| ~ root_occ(X1,X2) ),
inference(flattening,[],[f110]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( min_precedes(X2,X1,X3)
| ~ occurrence_of(X0,X3)
| ~ leaf_occ(X1,X0)
| ~ root_occ(X2,X0)
| X1 = X2 ),
inference(ennf_transformation,[],[f42]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( min_precedes(X2,X1,X3)
| ~ occurrence_of(X0,X3)
| ~ leaf_occ(X1,X0)
| ~ root_occ(X2,X0)
| X1 = X2 ),
inference(flattening,[],[f122]) ).
fof(f136,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,[],[f50]) ).
fof(f137,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,[],[f64]) ).
fof(f138,plain,
! [X0] :
( ( activity(sK0(X0))
& occurrence_of(X0,sK0(X0)) )
| ~ activity_occurrence(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f66]) ).
fof(f149,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,[],[f93]) ).
fof(f150,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,[],[f149]) ).
fof(f151,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,[],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ( next_subocc(X0,X1,X2)
| ~ min_precedes(X0,X1,X2)
| ( min_precedes(X0,sK7(X0,X1,X2),X2)
& min_precedes(sK7(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,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f151]) ).
fof(f158,plain,
! [X0,X1] :
( ( root(sK11(X0,X1),X0)
& subactivity_occurrence(sK11(X0,X1),X1) )
| ~ occurrence_of(X1,X0)
| atomic(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f99]) ).
fof(f160,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,[],[f34]) ).
fof(f161,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,[],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( ( root_occ(X0,X1)
| ! [X2] :
( ~ occurrence_of(X1,X2)
| ~ subactivity_occurrence(X0,X1)
| ~ root(X0,X2) ) )
& ( ( occurrence_of(X1,sK13(X0,X1))
& subactivity_occurrence(X0,X1)
& root(X0,sK13(X0,X1)) )
| ~ root_occ(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1))],[f161]) ).
fof(f167,plain,
! [X0] :
( ( occurrence_of(sK16(X0),tptp3)
& root_occ(sK16(X0),X0)
& occurrence_of(sK17(X0),tptp4)
& next_subocc(sK16(X0),sK17(X0),tptp0)
& ( occurrence_of(sK18(X0),tptp2)
| occurrence_of(sK18(X0),tptp1) )
& next_subocc(sK17(X0),sK18(X0),tptp0)
& leaf_occ(sK18(X0),X0) )
| ~ occurrence_of(X0,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X1,sK16(X0)),skolemize(X2,sK17(X0)),skolemize(X3,sK18(X0))],[f136]) ).
fof(f168,plain,
( ! [X1,X2] :
( ~ occurrence_of(X1,tptp3)
| ~ root_occ(X1,sK19)
| ( ~ occurrence_of(X2,tptp2)
& ~ occurrence_of(X2,tptp1) )
| ~ min_precedes(X1,X2,tptp0)
| ~ leaf_occ(X2,sK19) )
& occurrence_of(sK19,tptp0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f137]) ).
fof(f169,plain,
! [X0,X1] :
( ~ occurrence_of(X1,X0)
| activity_occurrence(X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f171,plain,
! [X0] :
( ~ activity_occurrence(X0)
| occurrence_of(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f138]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ occurrence_of(X0,X1)
| X1 = X2
| ~ occurrence_of(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ root(X1,X2)
| ~ min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f205,plain,
! [X2,X0,X1] :
( ~ next_subocc(X0,X1,X2)
| min_precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f219,plain,
! [X0,X1] :
( ~ occurrence_of(X1,X0)
| subactivity_occurrence(sK11(X0,X1),X1)
| atomic(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f220,plain,
! [X0,X1] :
( ~ occurrence_of(X1,X0)
| root(sK11(X0,X1),X0)
| atomic(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ subactivity_occurrence(X0,X1)
| ~ occurrence_of(X1,X2)
| root_occ(X0,X1)
| ~ root(X0,X2) ),
inference(cnf_transformation,[],[f162]) ).
fof(f235,plain,
! [X2,X3,X0,X1] :
( ~ root_occ(X0,X2)
| ~ occurrence_of(X2,X3)
| X0 = X1
| ~ root_occ(X1,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f241,plain,
! [X2,X3,X0,X1] :
( ~ leaf_occ(X1,X0)
| ~ occurrence_of(X0,X3)
| min_precedes(X2,X1,X3)
| ~ root_occ(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f251,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| leaf_occ(sK18(X0),X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f252,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| next_subocc(sK17(X0),sK18(X0),tptp0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f253,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK18(X0),tptp1)
| occurrence_of(sK18(X0),tptp2) ),
inference(cnf_transformation,[],[f167]) ).
fof(f256,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| root_occ(sK16(X0),X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f257,plain,
! [X0] :
( ~ occurrence_of(X0,tptp0)
| occurrence_of(sK16(X0),tptp3) ),
inference(cnf_transformation,[],[f167]) ).
fof(f259,plain,
~ atomic(tptp0),
inference(cnf_transformation,[],[f52]) ).
fof(f270,plain,
occurrence_of(sK19,tptp0),
inference(cnf_transformation,[],[f168]) ).
fof(f271,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK19)
| ~ root_occ(X1,sK19)
| ~ occurrence_of(X2,tptp1)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f168]) ).
fof(f272,plain,
! [X2,X1] :
( ~ leaf_occ(X2,sK19)
| ~ root_occ(X1,sK19)
| ~ occurrence_of(X2,tptp2)
| ~ min_precedes(X1,X2,tptp0)
| ~ occurrence_of(X1,tptp3) ),
inference(cnf_transformation,[],[f168]) ).
fof(f273,plain,
activity_occurrence(sK19),
inference(resolution,[],[f169,f270]) ).
fof(f278,plain,
occurrence_of(sK19,sK0(sK19)),
inference(resolution,[],[f171,f273]) ).
fof(f289,plain,
leaf_occ(sK18(sK19),sK19),
inference(resolution,[],[f251,f270]) ).
fof(f290,plain,
! [X0] :
( ~ root_occ(X0,sK19)
| ~ occurrence_of(sK18(sK19),tptp2)
| ~ min_precedes(X0,sK18(sK19),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f289,f272]) ).
fof(f291,plain,
! [X0] :
( ~ root_occ(X0,sK19)
| ~ occurrence_of(sK18(sK19),tptp1)
| ~ min_precedes(X0,sK18(sK19),tptp0)
| ~ occurrence_of(X0,tptp3) ),
inference(resolution,[],[f289,f271]) ).
fof(f294,definition,
( spl20_1
<=> occurrence_of(sK18(sK19),tptp1) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f296,plain,
( ~ occurrence_of(sK18(sK19),tptp1)
| spl20_1 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f298,definition,
( spl20_2
<=> ! [X0] :
( ~ root_occ(X0,sK19)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,sK18(sK19),tptp0) ) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f299,plain,
( ! [X0] :
( ~ root_occ(X0,sK19)
| ~ occurrence_of(X0,tptp3)
| ~ min_precedes(X0,sK18(sK19),tptp0) )
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f300,plain,
( ~ spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f291,f298,f294]) ).
fof(f302,definition,
( spl20_3
<=> occurrence_of(sK18(sK19),tptp2) ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f304,plain,
( ~ occurrence_of(sK18(sK19),tptp2)
| spl20_3 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f305,plain,
( ~ spl20_3
| spl20_2 ),
inference(avatar_split_clause,[],[f290,f298,f302]) ).
fof(f310,plain,
root_occ(sK16(sK19),sK19),
inference(resolution,[],[f256,f270]) ).
fof(f312,plain,
occurrence_of(sK16(sK19),tptp3),
inference(resolution,[],[f257,f270]) ).
fof(f332,plain,
! [X0] :
( ~ occurrence_of(sK19,X0)
| tptp0 = X0 ),
inference(resolution,[],[f173,f270]) ).
fof(f342,plain,
next_subocc(sK17(sK19),sK18(sK19),tptp0),
inference(resolution,[],[f252,f270]) ).
fof(f346,plain,
tptp0 = sK0(sK19),
inference(resolution,[],[f332,f278]) ).
fof(f350,plain,
min_precedes(sK17(sK19),sK18(sK19),tptp0),
inference(resolution,[],[f342,f205]) ).
fof(f382,plain,
( subactivity_occurrence(sK11(tptp0,sK19),sK19)
| atomic(tptp0) ),
inference(resolution,[],[f219,f270]) ).
fof(f391,plain,
subactivity_occurrence(sK11(tptp0,sK19),sK19),
inference(forward_subsumption_resolution,[],[f382,f259]) ).
fof(f399,plain,
( root(sK11(tptp0,sK19),tptp0)
| atomic(tptp0) ),
inference(resolution,[],[f220,f270]) ).
fof(f408,plain,
root(sK11(tptp0,sK19),tptp0),
inference(forward_subsumption_resolution,[],[f399,f259]) ).
fof(f423,plain,
! [X0] : ~ min_precedes(X0,sK11(tptp0,sK19),tptp0),
inference(resolution,[],[f408,f193]) ).
fof(f441,plain,
( occurrence_of(sK18(sK19),tptp1)
| occurrence_of(sK18(sK19),tptp2) ),
inference(resolution,[],[f253,f270]) ).
fof(f442,plain,
( occurrence_of(sK18(sK19),tptp2)
| spl20_1 ),
inference(forward_subsumption_resolution,[],[f441,f296]) ).
fof(f443,plain,
( $false
| spl20_1
| spl20_3 ),
inference(forward_subsumption_resolution,[],[f442,f304]) ).
fof(f444,plain,
( spl20_1
| spl20_3 ),
inference(avatar_contradiction_clause,[],[f443]) ).
fof(f472,plain,
! [X0] :
( ~ occurrence_of(sK19,X0)
| root_occ(sK11(tptp0,sK19),sK19)
| ~ root(sK11(tptp0,sK19),X0) ),
inference(resolution,[],[f230,f391]) ).
fof(f474,definition,
( spl20_6
<=> root_occ(sK11(tptp0,sK19),sK19) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
fof(f476,plain,
( root_occ(sK11(tptp0,sK19),sK19)
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f478,definition,
( spl20_7
<=> ! [X0] :
( ~ occurrence_of(sK19,X0)
| ~ root(sK11(tptp0,sK19),X0) ) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
fof(f479,plain,
( ! [X0] :
( ~ root(sK11(tptp0,sK19),X0)
| ~ occurrence_of(sK19,X0) )
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f480,plain,
( spl20_6
| spl20_7 ),
inference(avatar_split_clause,[],[f472,f478,f474]) ).
fof(f518,plain,
! [X0,X1] :
( ~ occurrence_of(sK19,X0)
| sK16(sK19) = X1
| ~ root_occ(X1,sK19) ),
inference(resolution,[],[f235,f310]) ).
fof(f524,definition,
( spl20_15
<=> ! [X0] : ~ occurrence_of(sK19,X0) ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
fof(f525,plain,
( ! [X0] : ~ occurrence_of(sK19,X0)
| ~ spl20_15 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f528,definition,
( spl20_16
<=> ! [X1] :
( sK16(sK19) = X1
| ~ root_occ(X1,sK19) ) ),
introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition]) ).
fof(f529,plain,
( ! [X1] :
( ~ root_occ(X1,sK19)
| sK16(sK19) = X1 )
| ~ spl20_16 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f530,plain,
( spl20_16
| spl20_15 ),
inference(avatar_split_clause,[],[f518,f524,f528]) ).
fof(f628,plain,
! [X0,X1] :
( ~ root_occ(X1,sK19)
| min_precedes(X1,sK18(sK19),X0)
| ~ occurrence_of(sK19,X0)
| sK18(sK19) = X1 ),
inference(resolution,[],[f241,f289]) ).
fof(f861,plain,
( ~ occurrence_of(sK19,tptp0)
| ~ spl20_7 ),
inference(resolution,[],[f479,f408]) ).
fof(f862,plain,
( $false
| ~ spl20_7 ),
inference(forward_subsumption_resolution,[],[f861,f270]) ).
fof(f863,plain,
~ spl20_7,
inference(avatar_contradiction_clause,[],[f862]) ).
fof(f864,plain,
( sK16(sK19) = sK11(tptp0,sK19)
| ~ spl20_6
| ~ spl20_16 ),
inference(resolution,[],[f476,f529]) ).
fof(f1007,plain,
( occurrence_of(sK11(tptp0,sK19),tptp3)
| ~ spl20_6
| ~ spl20_16 ),
inference(superposition,[],[f312,f864]) ).
fof(f1044,plain,
( $false
| ~ spl20_15 ),
inference(resolution,[],[f525,f270]) ).
fof(f1051,plain,
~ spl20_15,
inference(avatar_contradiction_clause,[],[f1044]) ).
fof(f1163,plain,
( ~ occurrence_of(sK11(tptp0,sK19),tptp3)
| ~ min_precedes(sK11(tptp0,sK19),sK18(sK19),tptp0)
| ~ spl20_2
| ~ spl20_6 ),
inference(resolution,[],[f299,f476]) ).
fof(f1164,plain,
( ~ min_precedes(sK11(tptp0,sK19),sK18(sK19),tptp0)
| ~ spl20_2
| ~ spl20_6
| ~ spl20_16 ),
inference(forward_subsumption_resolution,[],[f1163,f1007]) ).
fof(f1200,plain,
! [X0] :
( min_precedes(sK16(sK19),sK18(sK19),X0)
| ~ occurrence_of(sK19,X0)
| sK18(sK19) = sK16(sK19) ),
inference(resolution,[],[f628,f310]) ).
fof(f1203,definition,
( spl20_58
<=> sK18(sK19) = sK11(tptp0,sK19) ),
introduced(definition,[new_symbols(definition,[spl20_58])],[avatar_definition]) ).
fof(f1205,plain,
( sK18(sK19) = sK11(tptp0,sK19)
| ~ spl20_58 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f1207,definition,
( spl20_59
<=> ! [X0] :
( min_precedes(sK11(tptp0,sK19),sK18(sK19),X0)
| ~ occurrence_of(sK19,X0) ) ),
introduced(definition,[new_symbols(definition,[spl20_59])],[avatar_definition]) ).
fof(f1208,plain,
( ! [X0] :
( ~ occurrence_of(sK19,X0)
| min_precedes(sK11(tptp0,sK19),sK18(sK19),X0) )
| ~ spl20_59 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1210,plain,
( ! [X0] :
( min_precedes(sK11(tptp0,sK19),sK18(sK19),X0)
| ~ occurrence_of(sK19,X0)
| sK18(sK19) = sK16(sK19) )
| ~ spl20_6
| ~ spl20_16 ),
inference(forward_demodulation,[],[f1200,f864]) ).
fof(f1211,plain,
( ! [X0] :
( sK18(sK19) = sK11(tptp0,sK19)
| min_precedes(sK11(tptp0,sK19),sK18(sK19),X0)
| ~ occurrence_of(sK19,X0) )
| ~ spl20_6
| ~ spl20_16 ),
inference(forward_demodulation,[],[f1210,f864]) ).
fof(f1212,plain,
( spl20_59
| spl20_58
| ~ spl20_6
| ~ spl20_16 ),
inference(avatar_split_clause,[],[f1211,f528,f474,f1203,f1207]) ).
fof(f1972,plain,
( min_precedes(sK11(tptp0,sK19),sK18(sK19),sK0(sK19))
| ~ spl20_59 ),
inference(resolution,[],[f1208,f278]) ).
fof(f1979,plain,
( min_precedes(sK11(tptp0,sK19),sK18(sK19),tptp0)
| ~ spl20_59 ),
inference(forward_demodulation,[],[f1972,f346]) ).
fof(f1988,plain,
( $false
| ~ spl20_2
| ~ spl20_6
| ~ spl20_16
| ~ spl20_59 ),
inference(forward_subsumption_resolution,[],[f1979,f1164]) ).
fof(f1989,plain,
( ~ spl20_2
| ~ spl20_6
| ~ spl20_16
| ~ spl20_59 ),
inference(avatar_contradiction_clause,[],[f1988]) ).
fof(f2000,plain,
( min_precedes(sK17(sK19),sK11(tptp0,sK19),tptp0)
| ~ spl20_58 ),
inference(superposition,[],[f350,f1205]) ).
fof(f2054,plain,
( $false
| ~ spl20_58 ),
inference(forward_subsumption_resolution,[],[f2000,f423]) ).
fof(f2055,plain,
~ spl20_58,
inference(avatar_contradiction_clause,[],[f2054]) ).
cnf(s1,plain,
( ~ spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f300]) ).
cnf(s2,plain,
( spl20_2
| ~ spl20_3 ),
inference(sat_conversion,[],[f305]) ).
cnf(s3,plain,
( spl20_1
| spl20_3 ),
inference(sat_conversion,[],[f444]) ).
cnf(s5,plain,
( spl20_6
| spl20_7 ),
inference(sat_conversion,[],[f480]) ).
cnf(s10,plain,
( spl20_15
| spl20_16 ),
inference(sat_conversion,[],[f530]) ).
cnf(s28,plain,
~ spl20_7,
inference(sat_conversion,[],[f863]) ).
cnf(s44,plain,
~ spl20_15,
inference(sat_conversion,[],[f1051]) ).
cnf(s54,plain,
( ~ spl20_6
| ~ spl20_16
| spl20_58
| spl20_59 ),
inference(sat_conversion,[],[f1212]) ).
cnf(s83,plain,
( ~ spl20_2
| ~ spl20_6
| ~ spl20_16
| ~ spl20_59 ),
inference(sat_conversion,[],[f1989]) ).
cnf(s89,plain,
~ spl20_58,
inference(sat_conversion,[],[f2055]) ).
cnf(s95,plain,
( ~ spl20_6
| ~ spl20_16
| spl20_59 ),
inference(rat,[],[s54,s89]) ).
cnf(s100,plain,
spl20_16,
inference(rat,[],[s10,s44]) ).
cnf(s104,plain,
spl20_6,
inference(rat,[],[s5,s28]) ).
cnf(s105,plain,
spl20_59,
inference(rat,[],[s95,s100,s104]) ).
cnf(s107,plain,
~ spl20_2,
inference(rat,[],[s83,s104,s100,s105]) ).
cnf(s109,plain,
~ spl20_3,
inference(rat,[],[s2,s107]) ).
cnf(s110,plain,
spl20_1,
inference(rat,[],[s3,s109]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s1,s107,s110]) ).
fof(f2064,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO009+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 22:21:56 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % (975845)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (975855)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1509715243:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (975851)% WARNING: option uhcvi not known.
% 0.11/0.45 % (975850)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=124483224_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (975852)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3709275459:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (975853)dis+10_1_sil=32000:sp=arity:random_seed=2097592707:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (975854)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1365520722:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (975856)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1849999271:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (975851)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3166879598:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % Detected minimum model sizes of [4]
% 0.11/0.45 % Detected maximum model sizes of [max]
% 0.11/0.45 % TRYING [4]
% 0.11/0.45 % (975855) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-975845-975855"...
% 0.11/0.45 % (975855)...printing done.
% 0.11/0.45 % (975855)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (975855)------------------------------
% 0.11/0.46 % (975855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (975855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (975855)CaDiCaL version: 2.1.3
% 0.11/0.46 % (975855)Termination reason: Refutation
% 0.11/0.46 % (975855)Time elapsed: 0.021 s
% 0.11/0.46 % (975855)Peak memory usage: 13 MB
% 0.11/0.46 % (975855)Instructions burned: 53 (million)
% 0.11/0.46 % (975845)Success in time 0.049 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------