%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO600+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 : n011.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 5.20s 1.81s
% Output : Refutation 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 96 ( 8 unt; 2 def)
% Number of atoms : 298 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 316 ( 114 ~; 108 |; 76 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 24 ( 24 usr; 23 con; 0-4 aty)
% Number of variables : 449 ( 0 sgn 401 !; 48 ?)
% 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(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(f67,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
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,X17,X18,X19,X20,X21,X22] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& midp(X5,X2,X4)
& midp(X6,X0,X4)
& circle(X5,X4,X12,X13)
& circle(X6,X4,X14,X15)
& circle(X5,X4,X7,X16)
& circle(X6,X4,X7,X17)
& coll(X8,X0,X1)
& circle(X6,X4,X8,X18)
& midp(X9,X1,X4)
& circle(X9,X1,X19,X20)
& circle(X5,X4,X10,X21)
& circle(X9,X1,X10,X22) )
=> coll(X8,X7,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618062) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X20,X21,X22] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& midp(X5,X2,X4)
& midp(X6,X0,X4)
& circle(X5,X4,X12,X13)
& circle(X6,X4,X14,X15)
& circle(X5,X4,X7,X16)
& circle(X6,X4,X7,X17)
& coll(X8,X0,X1)
& circle(X6,X4,X8,X18)
& midp(X9,X1,X4)
& circle(X9,X1,X19,X20)
& circle(X5,X4,X10,X21)
& circle(X9,X1,X10,X22) )
=> coll(X8,X7,X10) ),
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(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(f197,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f67]) ).
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,X17,X18,X19,X20,X21,X22] :
( ~ coll(X8,X7,X10)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& midp(X5,X2,X4)
& midp(X6,X0,X4)
& circle(X5,X4,X12,X13)
& circle(X6,X4,X14,X15)
& circle(X5,X4,X7,X16)
& circle(X6,X4,X7,X17)
& coll(X8,X0,X1)
& circle(X6,X4,X8,X18)
& midp(X9,X1,X4)
& circle(X9,X1,X19,X20)
& circle(X5,X4,X10,X21)
& circle(X9,X1,X10,X22) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17,X18,X19,X20,X21,X22] :
( ~ coll(X8,X7,X10)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& midp(X5,X2,X4)
& midp(X6,X0,X4)
& circle(X5,X4,X12,X13)
& circle(X6,X4,X14,X15)
& circle(X5,X4,X7,X16)
& circle(X6,X4,X7,X17)
& coll(X8,X0,X1)
& circle(X6,X4,X8,X18)
& midp(X9,X1,X4)
& circle(X9,X1,X19,X20)
& circle(X5,X4,X10,X21)
& circle(X9,X1,X10,X22) ),
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,
( ~ coll(sK28,sK27,sK30)
& circle(sK23,sK20,sK21,sK22)
& circle(sK23,sK20,sK24,sK31)
& midp(sK25,sK22,sK24)
& midp(sK26,sK20,sK24)
& circle(sK25,sK24,sK32,sK33)
& circle(sK26,sK24,sK34,sK35)
& circle(sK25,sK24,sK27,sK36)
& circle(sK26,sK24,sK27,sK37)
& coll(sK28,sK20,sK21)
& circle(sK26,sK24,sK28,sK38)
& midp(sK29,sK21,sK24)
& circle(sK29,sK21,sK39,sK40)
& circle(sK25,sK24,sK30,sK41)
& circle(sK29,sK21,sK30,sK42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35,sK36,sK37,sK38,sK39,sK40,sK41,sK42]),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),skolemize(X17,sK37),skolemize(X18,sK38),skolemize(X19,sK39),skolemize(X20,sK40),skolemize(X21,sK41),skolemize(X22,sK42)],[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(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(f337,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f197]) ).
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(f397,plain,
circle(sK23,sK20,sK21,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f398,plain,
~ coll(sK28,sK27,sK30),
inference(cnf_transformation,[],[f270]) ).
fof(f399,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(f400,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,[],[f399]) ).
fof(f417,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(f421,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X0,X1)
| para(X2,X3,X2,X3) ),
inference(resolution,[],[f417,f309]) ).
fof(f425,definition,
( spl43_1
<=> ! [X2,X3] : para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl43_1])],[avatar_definition]) ).
fof(f426,plain,
( ! [X2,X3] : para(X2,X3,X2,X3)
| ~ spl43_1 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f428,definition,
( spl43_2
<=> ! [X0,X1] : ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl43_2])],[avatar_definition]) ).
fof(f429,plain,
( ! [X0,X1] : ~ para(X0,X1,X0,X1)
| ~ spl43_2 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f430,plain,
( spl43_1
| spl43_2 ),
inference(avatar_split_clause,[],[f421,f428,f425]) ).
fof(f445,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(f448,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X1)
| cyclic(X1,X1,X0,X2)
| ~ coll(X0,X2,X1) ),
inference(resolution,[],[f445,f313]) ).
fof(f449,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X1)
| cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1) ),
inference(resolution,[],[f445,f312]) ).
fof(f457,plain,
! [X2,X3,X0,X1] :
( perp(X0,X1,sK11(X0,X2,X3,X1),X0)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f278,f370]) ).
fof(f458,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(f487,plain,
! [X2,X3,X0,X1] :
( ~ circle(X0,X1,X2,X3)
| para(X1,X0,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[],[f457,f458]) ).
fof(f491,plain,
! [X2,X3,X0,X1] :
( ~ circle(X0,X1,X2,X3)
| para(X1,X0,X1,X0) ),
inference(duplicate_literal_removal,[],[f487]) ).
fof(f492,plain,
( ! [X2,X3,X0,X1] : ~ circle(X0,X1,X2,X3)
| ~ spl43_2 ),
inference(forward_subsumption_resolution,[],[f491,f429]) ).
fof(f493,plain,
( $false
| ~ spl43_2 ),
inference(resolution,[],[f492,f397]) ).
fof(f512,plain,
~ spl43_2,
inference(avatar_contradiction_clause,[],[f493]) ).
fof(f513,plain,
( ! [X2,X0,X1] :
( cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1) )
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f449,f426]) ).
fof(f514,plain,
( ! [X2,X0,X1] :
( cyclic(X1,X1,X0,X2)
| ~ coll(X0,X2,X1) )
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f448,f426]) ).
fof(f515,plain,
( ! [X2,X0,X1] : cyclic(X1,X1,X0,X2)
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f514,f513]) ).
fof(f520,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl43_1 ),
inference(resolution,[],[f515,f287]) ).
fof(f524,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f520,f515]) ).
fof(f530,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl43_1 ),
inference(resolution,[],[f524,f400]) ).
fof(f534,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f530,f524]) ).
fof(f536,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f534,f524]) ).
fof(f537,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl43_1 ),
inference(resolution,[],[f536,f327]) ).
fof(f539,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f537,f536]) ).
fof(f540,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl43_1 ),
inference(resolution,[],[f539,f279]) ).
fof(f541,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl43_1 ),
inference(resolution,[],[f539,f278]) ).
fof(f544,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl43_1 ),
inference(forward_subsumption_resolution,[],[f540,f541]) ).
fof(f545,plain,
( ! [X2,X0,X1] : coll(X0,X1,X2)
| ~ spl43_1 ),
inference(resolution,[],[f544,f337]) ).
fof(f548,plain,
( $false
| ~ spl43_1 ),
inference(resolution,[],[f545,f398]) ).
fof(f552,plain,
~ spl43_1,
inference(avatar_contradiction_clause,[],[f548]) ).
cnf(s1,plain,
( spl43_1
| spl43_2 ),
inference(sat_conversion,[],[f430]) ).
cnf(s11,plain,
~ spl43_2,
inference(sat_conversion,[],[f512]) ).
cnf(s12,plain,
~ spl43_1,
inference(sat_conversion,[],[f552]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s11,s12]) ).
fof(f553,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO600+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 08:37:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 5.20/1.81 % (2100128)Detected formulas, will run a generic FOF schedule.
% 5.20/1.81 % (2100137)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3640223778:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.20/1.81 % (2100137)Instruction limit reached!
% 5.20/1.81 % (2100137)------------------------------
% 5.20/1.81 % (2100137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100137)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100137)Termination reason: Instruction limit
% 5.20/1.81 % (2100137)Termination phase: Saturation
% 5.20/1.81 % (2100137)Time elapsed: 0.038 s
% 5.20/1.81 % (2100137)Peak memory usage: 88 MB
% 5.20/1.81 % (2100137)Instructions burned: 122 (million)
% 5.20/1.81 % (2100134)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=1957866702:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.20/1.81 % (2100136)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=372894638:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.20/1.81 % (2100139)dis-21_1_sil=8000:lcm=predicate:random_seed=2595355951: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)
% 5.20/1.81 % (2100133)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=2843063951:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.20/1.81 % (2100135)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=2411256004:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.20/1.81 % (2100138)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=467013031:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.20/1.81 % (2100136)Refutation not found, incomplete strategy
% 5.20/1.81 % (2100136)------------------------------
% 5.20/1.81 % (2100136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100136)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100136)Termination reason: Refutation not found, incomplete strategy
% 5.20/1.81 % (2100136)Time elapsed: 0.042 s
% 5.20/1.81 % (2100136)Peak memory usage: 88 MB
% 5.20/1.81 % (2100136)Instructions burned: 77 (million)
% 5.20/1.81 % (2100139)Instruction limit reached!
% 5.20/1.81 % (2100139)------------------------------
% 5.20/1.81 % (2100139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100139)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100139)Termination reason: Instruction limit
% 5.20/1.81 % (2100139)Termination phase: Saturation
% 5.20/1.81 % (2100139)Time elapsed: 0.075 s
% 5.20/1.81 % (2100139)Peak memory usage: 90 MB
% 5.20/1.81 % (2100139)Instructions burned: 129 (million)
% 5.20/1.81 % (2100138)Instruction limit reached!
% 5.20/1.81 % (2100138)------------------------------
% 5.20/1.81 % (2100138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100138)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100138)Termination reason: Instruction limit
% 5.20/1.81 % (2100138)Termination phase: Saturation
% 5.20/1.81 % (2100138)Time elapsed: 0.094 s
% 5.20/1.81 % (2100138)Peak memory usage: 90 MB
% 5.20/1.81 % (2100138)Instructions burned: 140 (million)
% 5.20/1.81 % (2100141)lrs+10_1_sil=8000:sp=occurrence:random_seed=3732029471:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.20/1.81 % (2100141)Instruction limit reached!
% 5.20/1.81 % (2100141)------------------------------
% 5.20/1.81 % (2100141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100141)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100141)Termination reason: Instruction limit
% 5.20/1.81 % (2100141)Termination phase: Saturation
% 5.20/1.81 % (2100141)Time elapsed: 0.099 s
% 5.20/1.81 % (2100141)Peak memory usage: 93 MB
% 5.20/1.81 % (2100141)Instructions burned: 286 (million)
% 5.20/1.81 % (2100148)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3554007297:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.20/1.81 % (2100149)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1104248739:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.20/1.81 % (2100136)------------------------------
% 5.20/1.81 % (2100136)------------------------------
% 5.20/1.81 % (2100148)Instruction limit reached!
% 5.20/1.81 % (2100148)------------------------------
% 5.20/1.81 % (2100148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100148)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100148)Termination reason: Instruction limit
% 5.20/1.81 % (2100148)Termination phase: Saturation
% 5.20/1.81 % (2100148)Time elapsed: 0.081 s
% 5.20/1.81 % (2100148)Peak memory usage: 91 MB
% 5.20/1.81 % (2100148)Instructions burned: 159 (million)
% 5.20/1.81 % (2100151)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=1463749160:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.20/1.81 % (2100149)Instruction limit reached!
% 5.20/1.81 % (2100149)------------------------------
% 5.20/1.81 % (2100149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100149)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100149)Termination reason: Instruction limit
% 5.20/1.81 % (2100149)Termination phase: Saturation
% 5.20/1.81 % (2100149)Time elapsed: 0.114 s
% 5.20/1.81 % (2100149)Peak memory usage: 88 MB
% 5.20/1.81 % (2100149)Instructions burned: 326 (million)
% 5.20/1.81 % (2100151)Instruction limit reached!
% 5.20/1.81 % (2100151)------------------------------
% 5.20/1.81 % (2100151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100151)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100151)Termination reason: Instruction limit
% 5.20/1.81 % (2100151)Termination phase: Saturation
% 5.20/1.81 % (2100151)Time elapsed: 0.071 s
% 5.20/1.81 % (2100151)Peak memory usage: 92 MB
% 5.20/1.81 % (2100151)Instructions burned: 251 (million)
% 5.20/1.81 % (2100154)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2683096289:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.20/1.81 % (2100155)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2037206595:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.20/1.81 % (2100157)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1008854226:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.20/1.81 % (2100158)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3424855626:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.20/1.81 % (2100157)Instruction limit reached!
% 5.20/1.81 % (2100157)------------------------------
% 5.20/1.81 % (2100157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100157)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100157)Termination reason: Instruction limit
% 5.20/1.81 % (2100157)Termination phase: Saturation
% 5.20/1.81 % (2100157)Time elapsed: 0.067 s
% 5.20/1.81 % (2100157)Peak memory usage: 90 MB
% 5.20/1.81 % (2100157)Instructions burned: 114 (million)
% 5.20/1.81 % (2100158)Instruction limit reached!
% 5.20/1.81 % (2100158)------------------------------
% 5.20/1.81 % (2100158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100158)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100158)Termination reason: Instruction limit
% 5.20/1.81 % (2100158)Termination phase: Saturation
% 5.20/1.81 % (2100158)Time elapsed: 0.038 s
% 5.20/1.81 % (2100158)Peak memory usage: 89 MB
% 5.20/1.81 % (2100158)Instructions burned: 131 (million)
% 5.20/1.81 % (2100154)Instruction limit reached!
% 5.20/1.81 % (2100154)------------------------------
% 5.20/1.81 % (2100154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100154)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100154)Termination reason: Instruction limit
% 5.20/1.81 % (2100154)Termination phase: Saturation
% 5.20/1.81 % (2100154)Time elapsed: 0.166 s
% 5.20/1.81 % (2100154)Peak memory usage: 89 MB
% 5.20/1.81 % (2100154)Instructions burned: 295 (million)
% 5.20/1.81 % (2100133)First to succeed.
% 5.20/1.81 % (2100133)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2100128"
% 5.20/1.81 % (2100163)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2368038144:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.20/1.81 % (2100164)lrs+10_1_sil=8000:sp=occurrence:random_seed=3887802408:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.20/1.81 % (2100165)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2630066889:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.20/1.81 % (2100163)Instruction limit reached!
% 5.20/1.81 % (2100163)------------------------------
% 5.20/1.81 % (2100163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.81 % (2100163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.81 % (2100163)CaDiCaL version: 2.1.3
% 5.20/1.81 % (2100163)Termination reason: Instruction limit
% 5.20/1.81 % (2100163)Termination phase: Saturation
% 5.20/1.81 % (2100163)Time elapsed: 0.065 s
% 5.20/1.81 % (2100163)Peak memory usage: 89 MB
% 5.20/1.81 % (2100163)Instructions burned: 115 (million)
% 5.20/1.81 % (2100133)Refutation found. Thanks to Tanya!
% 5.20/1.81 % SZS status Theorem for theBenchmark
% 5.20/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 7.36/2.01 % (2100133)------------------------------
% 7.36/2.01 % (2100133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.36/2.01 % (2100133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.36/2.01 % (2100133)CaDiCaL version: 2.1.3
% 7.36/2.01 % (2100133)Termination reason: Refutation
% 7.36/2.01 % (2100133)Time elapsed: 0.627 s
% 7.36/2.01 % (2100133)Peak memory usage: 130 MB
% 7.36/2.01 % (2100133)Instructions burned: 997 (million)
% 7.36/2.01 % (2100133)------------------------------
% 7.36/2.01 % (2100133)------------------------------
% 7.36/2.01 % (2100128)Success in time 0.967 s
% 7.36/2.01 % Vampire exiting
%------------------------------------------------------------------------------