%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO602+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:53:02 AM UTC 2026
% Result : Theorem 4.69s 1.91s
% Output : Refutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 8 unt; 2 def)
% Number of atoms : 292 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 314 ( 120 ~; 114 |; 62 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 18 ( 18 usr; 17 con; 0-4 aty)
% Number of variables : 446 ( 0 sgn 410 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X0,X1,X2,X3)
& perp(X2,X3,X4,X5) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f10,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( para(X0,X1,X2,X3)
& perp(X2,X3,X4,X5) )
=> perp(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD10) ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4) )
=> cyclic(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& ~ coll(X2,X3,X0) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42a) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& coll(X2,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X5)
& eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
=> cong(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD43) ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X2,X1,X2)
& cong(X0,X3,X1,X3) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
fof(f87,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX11) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ( circle(X1,X2,X8,X9)
& circle(X0,X2,X10,X11)
& circle(X1,X2,X3,X12)
& circle(X0,X2,X3,X13)
& coll(X4,X0,X1)
& coll(X4,X2,X3)
& circle(X1,X2,X5,X14)
& circle(X0,X2,X6,X15)
& coll(X6,X2,X5)
& coll(X7,X3,X5)
& circle(X0,X2,X7,X16) )
=> perp(X6,X7,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618064) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ( circle(X1,X2,X8,X9)
& circle(X0,X2,X10,X11)
& circle(X1,X2,X3,X12)
& circle(X0,X2,X3,X13)
& coll(X4,X0,X1)
& coll(X4,X2,X3)
& circle(X1,X2,X5,X14)
& circle(X0,X2,X6,X15)
& coll(X6,X2,X5)
& coll(X7,X3,X5)
& circle(X0,X2,X7,X16) )
=> perp(X6,X7,X5,X1) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f10]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f110]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(ennf_transformation,[],[f17]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(flattening,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f19]) ).
fof(f125,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f21]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f39]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f40]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f41]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| coll(X2,X3,X0) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ coll(X2,X3,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ coll(X2,X3,X1) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) ),
inference(ennf_transformation,[],[f44]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) ),
inference(flattening,[],[f155]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(flattening,[],[f180]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
? [X4] :
( perp(X4,X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(ennf_transformation,[],[f87]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ~ perp(X6,X7,X5,X1)
& circle(X1,X2,X8,X9)
& circle(X0,X2,X10,X11)
& circle(X1,X2,X3,X12)
& circle(X0,X2,X3,X13)
& coll(X4,X0,X1)
& coll(X4,X2,X3)
& circle(X1,X2,X5,X14)
& circle(X0,X2,X6,X15)
& coll(X6,X2,X5)
& coll(X7,X3,X5)
& circle(X0,X2,X7,X16) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ~ perp(X6,X7,X5,X1)
& circle(X1,X2,X8,X9)
& circle(X0,X2,X10,X11)
& circle(X1,X2,X3,X12)
& circle(X0,X2,X3,X13)
& coll(X4,X0,X1)
& coll(X4,X2,X3)
& circle(X1,X2,X5,X14)
& circle(X0,X2,X6,X15)
& coll(X6,X2,X5)
& coll(X7,X3,X5)
& circle(X0,X2,X7,X16) ),
inference(flattening,[],[f249]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( perp(sK11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X2,X3))],[f234]) ).
fof(f270,plain,
( ~ perp(sK26,sK27,sK25,sK21)
& circle(sK21,sK22,sK28,sK29)
& circle(sK20,sK22,sK30,sK31)
& circle(sK21,sK22,sK23,sK32)
& circle(sK20,sK22,sK23,sK33)
& coll(sK24,sK20,sK21)
& coll(sK24,sK22,sK23)
& circle(sK21,sK22,sK25,sK34)
& circle(sK20,sK22,sK26,sK35)
& coll(sK26,sK22,sK25)
& coll(sK27,sK23,sK25)
& circle(sK20,sK22,sK27,sK36) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35,sK36]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25),skolemize(X6,sK26),skolemize(X7,sK27),skolemize(X8,sK28),skolemize(X9,sK29),skolemize(X10,sK30),skolemize(X11,sK31),skolemize(X12,sK32),skolemize(X13,sK33),skolemize(X14,sK34),skolemize(X15,sK35),skolemize(X16,sK36)],[f250]) ).
fof(f278,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f279,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f109]) ).
fof(f280,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| perp(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f111]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f121]) ).
fof(f289,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(cnf_transformation,[],[f123]) ).
fof(f291,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(cnf_transformation,[],[f125]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f310,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f149]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f312,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f313,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f314,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| cong(X0,X1,X3,X4) ),
inference(cnf_transformation,[],[f156]) ).
fof(f327,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( perp(sK11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f262]) ).
fof(f388,plain,
circle(sK21,sK22,sK25,sK34),
inference(cnf_transformation,[],[f270]) ).
fof(f395,plain,
~ perp(sK26,sK27,sK25,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X0,X1) ),
inference(resolution,[],[f311,f314]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) ),
inference(duplicate_literal_removal,[],[f396]) ).
fof(f408,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5) ),
inference(resolution,[],[f289,f310]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X0,X1)
| para(X2,X3,X2,X3) ),
inference(resolution,[],[f408,f309]) ).
fof(f414,definition,
( spl37_1
<=> ! [X2,X3] : para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl37_1])],[avatar_definition]) ).
fof(f415,plain,
( ! [X2,X3] : para(X2,X3,X2,X3)
| ~ spl37_1 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f417,definition,
( spl37_2
<=> ! [X0,X1] : ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl37_2])],[avatar_definition]) ).
fof(f418,plain,
( ! [X0,X1] : ~ para(X0,X1,X0,X1)
| ~ spl37_2 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f419,plain,
( spl37_1
| spl37_2 ),
inference(avatar_split_clause,[],[f410,f417,f414]) ).
fof(f432,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f291,f310]) ).
fof(f445,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f432]) ).
fof(f451,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f432]) ).
fof(f455,plain,
! [X2,X3,X0,X1] :
( perp(X0,X1,sK11(X0,X2,X3,X1),X0)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f278,f370]) ).
fof(f474,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X0,X1,sK11(X2,X3,X4,X5),X2)
| para(X0,X1,X2,X5)
| ~ circle(X5,X2,X3,X4) ),
inference(resolution,[],[f279,f370]) ).
fof(f479,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f474,f455]) ).
fof(f480,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3) ),
inference(duplicate_literal_removal,[],[f479]) ).
fof(f481,plain,
( ! [X2,X3,X0,X1] : ~ circle(X1,X0,X2,X3)
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f480,f418]) ).
fof(f482,plain,
( $false
| ~ spl37_2 ),
inference(resolution,[],[f481,f388]) ).
fof(f495,plain,
~ spl37_2,
inference(avatar_contradiction_clause,[],[f482]) ).
fof(f497,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0) )
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f445,f415]) ).
fof(f501,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f451,f415]) ).
fof(f504,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f501,f497]) ).
fof(f511,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl37_1 ),
inference(resolution,[],[f504,f287]) ).
fof(f515,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f511,f504]) ).
fof(f521,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl37_1 ),
inference(resolution,[],[f515,f397]) ).
fof(f525,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f521,f515]) ).
fof(f527,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f525,f515]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl37_1 ),
inference(resolution,[],[f527,f327]) ).
fof(f529,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f528,f527]) ).
fof(f530,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl37_1 ),
inference(resolution,[],[f529,f279]) ).
fof(f531,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl37_1 ),
inference(resolution,[],[f529,f278]) ).
fof(f533,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ para(X0,X1,X2,X2)
| perp(X0,X1,X3,X4) )
| ~ spl37_1 ),
inference(resolution,[],[f529,f280]) ).
fof(f535,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f530,f531]) ).
fof(f544,plain,
( ! [X2,X3,X0,X1] : perp(X0,X1,X2,X3)
| ~ spl37_1 ),
inference(resolution,[],[f533,f535]) ).
fof(f545,plain,
( $false
| ~ spl37_1 ),
inference(resolution,[],[f544,f395]) ).
fof(f551,plain,
~ spl37_1,
inference(avatar_contradiction_clause,[],[f545]) ).
cnf(s1,plain,
( spl37_1
| spl37_2 ),
inference(sat_conversion,[],[f419]) ).
cnf(s8,plain,
~ spl37_2,
inference(sat_conversion,[],[f495]) ).
cnf(s9,plain,
~ spl37_1,
inference(sat_conversion,[],[f551]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9]) ).
fof(f552,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO602+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 08:37:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 4.69/1.91 % (3095547)Detected formulas, will run a generic FOF schedule.
% 4.69/1.91 % (3095554)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=2744075566:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.69/1.91 % (3095556)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2241730600:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.69/1.91 % (3095553)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=2633505445:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.69/1.91 % (3095552)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=2728074733:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.69/1.91 % (3095555)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1286323444:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.69/1.91 % (3095557)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3124806922:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.69/1.91 % (3095558)dis-21_1_sil=8000:lcm=predicate:random_seed=1778231474: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)
% 4.69/1.91 % (3095555)Refutation not found, incomplete strategy
% 4.69/1.91 % (3095555)------------------------------
% 4.69/1.91 % (3095555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095555)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095555)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.91 % (3095555)Time elapsed: 0.038 s
% 4.69/1.91 % (3095555)Peak memory usage: 88 MB
% 4.69/1.91 % (3095555)Instructions burned: 70 (million)
% 4.69/1.91 % (3095556)Instruction limit reached!
% 4.69/1.91 % (3095556)------------------------------
% 4.69/1.91 % (3095556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095556)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095556)Termination reason: Instruction limit
% 4.69/1.91 % (3095556)Termination phase: Saturation
% 4.69/1.91 % (3095556)Time elapsed: 0.067 s
% 4.69/1.91 % (3095556)Peak memory usage: 88 MB
% 4.69/1.91 % (3095556)Instructions burned: 119 (million)
% 4.69/1.91 % (3095558)Instruction limit reached!
% 4.69/1.91 % (3095558)------------------------------
% 4.69/1.91 % (3095558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095558)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095558)Termination reason: Instruction limit
% 4.69/1.91 % (3095558)Termination phase: Saturation
% 4.69/1.91 % (3095558)Time elapsed: 0.071 s
% 4.69/1.91 % (3095558)Peak memory usage: 89 MB
% 4.69/1.91 % (3095558)Instructions burned: 129 (million)
% 4.69/1.91 % (3095557)Instruction limit reached!
% 4.69/1.91 % (3095557)------------------------------
% 4.69/1.91 % (3095557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095557)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095557)Termination reason: Instruction limit
% 4.69/1.91 % (3095557)Termination phase: Saturation
% 4.69/1.91 % (3095557)Time elapsed: 0.094 s
% 4.69/1.91 % (3095557)Peak memory usage: 90 MB
% 4.69/1.91 % (3095557)Instructions burned: 139 (million)
% 4.69/1.91 % (3095566)lrs+10_1_sil=8000:sp=occurrence:random_seed=4150405393:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.69/1.91 % (3095567)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1564399183:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.69/1.91 % (3095568)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1478219201:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.69/1.91 % (3095555)------------------------------
% 4.69/1.91 % (3095555)------------------------------
% 4.69/1.91 % (3095567)Instruction limit reached!
% 4.69/1.91 % (3095567)------------------------------
% 4.69/1.91 % (3095567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095567)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095567)Termination reason: Instruction limit
% 4.69/1.91 % (3095567)Termination phase: Saturation
% 4.69/1.91 % (3095567)Time elapsed: 0.079 s
% 4.69/1.91 % (3095567)Peak memory usage: 90 MB
% 4.69/1.91 % (3095567)Instructions burned: 157 (million)
% 4.69/1.91 % (3095566)Instruction limit reached!
% 4.69/1.91 % (3095566)------------------------------
% 4.69/1.91 % (3095566)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095566)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095566)Termination reason: Instruction limit
% 4.69/1.91 % (3095566)Termination phase: Saturation
% 4.69/1.91 % (3095566)Time elapsed: 0.180 s
% 4.69/1.91 % (3095566)Peak memory usage: 93 MB
% 4.69/1.91 % (3095566)Instructions burned: 286 (million)
% 4.69/1.91 % (3095568)Instruction limit reached!
% 4.69/1.91 % (3095568)------------------------------
% 4.69/1.91 % (3095568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095568)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095568)Termination reason: Instruction limit
% 4.69/1.91 % (3095568)Termination phase: Saturation
% 4.69/1.91 % (3095568)Time elapsed: 0.182 s
% 4.69/1.91 % (3095568)Peak memory usage: 91 MB
% 4.69/1.91 % (3095568)Instructions burned: 327 (million)
% 4.69/1.91 % (3095573)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1944170071:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.69/1.91 % (3095572)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1578764592:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.69/1.91 % (3095574)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=618607345:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.69/1.91 % (3095577)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1348700954:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.69/1.91 % (3095572)Instruction limit reached!
% 4.69/1.91 % (3095572)------------------------------
% 4.69/1.91 % (3095572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095572)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095572)Termination reason: Instruction limit
% 4.69/1.91 % (3095572)Termination phase: Saturation
% 4.69/1.91 % (3095572)Time elapsed: 0.137 s
% 4.69/1.91 % (3095572)Peak memory usage: 91 MB
% 4.69/1.91 % (3095572)Instructions burned: 248 (million)
% 4.69/1.91 % (3095573)Instruction limit reached!
% 4.69/1.91 % (3095573)------------------------------
% 4.69/1.91 % (3095573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095573)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095573)Termination reason: Instruction limit
% 4.69/1.91 % (3095573)Termination phase: Saturation
% 4.69/1.91 % (3095573)Time elapsed: 0.163 s
% 4.69/1.91 % (3095573)Peak memory usage: 89 MB
% 4.69/1.91 % (3095573)Instructions burned: 294 (million)
% 4.69/1.91 % (3095577)Instruction limit reached!
% 4.69/1.91 % (3095577)------------------------------
% 4.69/1.91 % (3095577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095577)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095577)Termination reason: Instruction limit
% 4.69/1.91 % (3095577)Termination phase: Saturation
% 4.69/1.91 % (3095577)Time elapsed: 0.064 s
% 4.69/1.91 % (3095577)Peak memory usage: 90 MB
% 4.69/1.91 % (3095577)Instructions burned: 114 (million)
% 4.69/1.91 % (3095552)First to succeed.
% 4.69/1.91 % (3095552)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3095547"
% 4.69/1.91 % (3095580)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1864321018:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 4.69/1.91 % (3095581)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3611178374:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 4.69/1.91 % (3095553)Also succeeded, but the first one will report.
% 4.69/1.91 % (3095580)Instruction limit reached!
% 4.69/1.91 % (3095580)------------------------------
% 4.69/1.91 % (3095580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095580)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095580)Termination reason: Instruction limit
% 4.69/1.91 % (3095580)Termination phase: Saturation
% 4.69/1.91 % (3095580)Time elapsed: 0.069 s
% 4.69/1.91 % (3095580)Peak memory usage: 89 MB
% 4.69/1.91 % (3095580)Instructions burned: 128 (million)
% 4.69/1.91 % (3095582)lrs+10_1_sil=8000:sp=occurrence:random_seed=4263871167:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 4.69/1.91 % (3095581)Instruction limit reached!
% 4.69/1.91 % (3095581)------------------------------
% 4.69/1.91 % (3095581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095581)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095581)Termination reason: Instruction limit
% 4.69/1.91 % (3095581)Termination phase: Saturation
% 4.69/1.91 % (3095581)Time elapsed: 0.062 s
% 4.69/1.91 % (3095581)Peak memory usage: 89 MB
% 4.69/1.91 % (3095581)Instructions burned: 115 (million)
% 4.69/1.91 % (3095585)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=349827204:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 4.69/1.91 % (3095585)Refutation not found, incomplete strategy
% 4.69/1.91 % (3095585)------------------------------
% 4.69/1.91 % (3095585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.91 % (3095585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.91 % (3095585)CaDiCaL version: 2.1.3
% 4.69/1.91 % (3095585)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.91 % (3095585)Time elapsed: 0.002 s
% 4.69/1.91 % (3095585)Peak memory usage: 88 MB
% 4.69/1.91 % (3095585)Instructions burned: 2 (million)
% 4.69/1.91 % (3095587)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2391983626:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 4.69/1.91 % (3095552)Refutation found. Thanks to Tanya!
% 4.69/1.91 % SZS status Theorem for theBenchmark
% 4.69/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 8.05/2.10 % (3095552)------------------------------
% 8.05/2.10 % (3095552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.05/2.10 % (3095552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.05/2.10 % (3095552)CaDiCaL version: 2.1.3
% 8.05/2.10 % (3095552)Termination reason: Refutation
% 8.05/2.10 % (3095552)Time elapsed: 0.649 s
% 8.05/2.10 % (3095552)Peak memory usage: 129 MB
% 8.05/2.10 % (3095552)Instructions burned: 991 (million)
% 8.05/2.10 % (3095552)------------------------------
% 8.05/2.10 % (3095552)------------------------------
% 8.05/2.10 % (3095547)Success in time 1.063 s
% 8.05/2.10 % Vampire exiting
%------------------------------------------------------------------------------