%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO613+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 : n016.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 09:53:04 AM UTC 2026
% Result : Theorem 6.67s 1.98s
% Output : Refutation 8.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of formulae : 100 ( 8 unt; 2 def)
% Number of atoms : 295 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 323 ( 128 ~; 121 |; 57 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 17 ( 17 usr; 16 con; 0-4 aty)
% Number of variables : 501 ( 0 sgn 467 !; 34 ?)
% 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(f22,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
& eqangle(X4,X5,X6,X7,X8,X9,X10,X11) )
=> eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
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(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] :
( ( circle(X0,X1,X8,X9)
& circle(X2,X1,X10,X11)
& circle(X0,X1,X3,X12)
& circle(X2,X1,X3,X13)
& midp(X4,X3,X1)
& circle(X0,X1,X5,X14)
& circle(X2,X1,X6,X15)
& coll(X6,X1,X5)
& coll(X7,X0,X5)
& coll(X7,X2,X6) )
=> eqangle(X5,X3,X3,X6,X0,X7,X7,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618075y) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ( circle(X0,X1,X8,X9)
& circle(X2,X1,X10,X11)
& circle(X0,X1,X3,X12)
& circle(X2,X1,X3,X13)
& midp(X4,X3,X1)
& circle(X0,X1,X5,X14)
& circle(X2,X1,X6,X15)
& coll(X6,X1,X5)
& coll(X7,X0,X5)
& coll(X7,X2,X6) )
=> eqangle(X5,X3,X3,X6,X0,X7,X7,X2) ),
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(f126,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11) ),
inference(flattening,[],[f126]) ).
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(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] :
( ~ eqangle(X5,X3,X3,X6,X0,X7,X7,X2)
& circle(X0,X1,X8,X9)
& circle(X2,X1,X10,X11)
& circle(X0,X1,X3,X12)
& circle(X2,X1,X3,X13)
& midp(X4,X3,X1)
& circle(X0,X1,X5,X14)
& circle(X2,X1,X6,X15)
& coll(X6,X1,X5)
& coll(X7,X0,X5)
& coll(X7,X2,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ~ eqangle(X5,X3,X3,X6,X0,X7,X7,X2)
& circle(X0,X1,X8,X9)
& circle(X2,X1,X10,X11)
& circle(X0,X1,X3,X12)
& circle(X2,X1,X3,X13)
& midp(X4,X3,X1)
& circle(X0,X1,X5,X14)
& circle(X2,X1,X6,X15)
& coll(X6,X1,X5)
& coll(X7,X0,X5)
& coll(X7,X2,X6) ),
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,
( ~ eqangle(sK25,sK23,sK23,sK26,sK20,sK27,sK27,sK22)
& circle(sK20,sK21,sK28,sK29)
& circle(sK22,sK21,sK30,sK31)
& circle(sK20,sK21,sK23,sK32)
& circle(sK22,sK21,sK23,sK33)
& midp(sK24,sK23,sK21)
& circle(sK20,sK21,sK25,sK34)
& circle(sK22,sK21,sK26,sK35)
& coll(sK26,sK21,sK25)
& coll(sK27,sK20,sK25)
& coll(sK27,sK22,sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35]),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)],[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(f292,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(cnf_transformation,[],[f127]) ).
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(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(f390,plain,
circle(sK22,sK21,sK23,sK33),
inference(cnf_transformation,[],[f270]) ).
fof(f394,plain,
~ eqangle(sK25,sK23,sK23,sK26,sK20,sK27,sK27,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X1,X3,X0,X3)
| ~ cyclic(X1,X3,X0,X2)
| ~ para(X0,X1,X0,X2)
| ~ cyclic(X1,X3,X0,X0)
| cong(X1,X3,X2,X3) ),
inference(resolution,[],[f310,f314]) ).
fof(f403,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(f418,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(f429,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X6,X7)
| ~ para(X4,X5,X8,X9) ),
inference(resolution,[],[f292,f310]) ).
fof(f435,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ para(X6,X7,X4,X5)
| eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X0,X1,X6,X7) ),
inference(resolution,[],[f429,f310]) ).
fof(f443,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ para(X2,X3,X2,X3) ),
inference(resolution,[],[f309,f403]) ).
fof(f446,definition,
( spl36_1
<=> ! [X2,X3] : ~ para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl36_1])],[avatar_definition]) ).
fof(f447,plain,
( ! [X2,X3] : ~ para(X2,X3,X2,X3)
| ~ spl36_1 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f449,definition,
( spl36_2
<=> ! [X0,X1] : para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl36_2])],[avatar_definition]) ).
fof(f450,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl36_2 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f451,plain,
( spl36_1
| spl36_2 ),
inference(avatar_split_clause,[],[f443,f449,f446]) ).
fof(f456,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f418]) ).
fof(f460,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f456,f450]) ).
fof(f480,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f418]) ).
fof(f484,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) )
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f480,f460]) ).
fof(f489,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f484,f450]) ).
fof(f502,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl36_2 ),
inference(resolution,[],[f489,f287]) ).
fof(f508,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f502,f489]) ).
fof(f515,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ para(X2,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X2)
| cong(X0,X1,X3,X1) )
| ~ spl36_2 ),
inference(resolution,[],[f508,f395]) ).
fof(f516,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ para(X2,X0,X2,X3)
| cong(X0,X1,X3,X1) )
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f515,f508]) ).
fof(f517,plain,
( ! [X2,X3,X0,X1] :
( ~ para(X2,X0,X2,X3)
| cong(X0,X1,X3,X1) )
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f516,f508]) ).
fof(f526,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl36_2 ),
inference(resolution,[],[f517,f450]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl36_2 ),
inference(resolution,[],[f526,f327]) ).
fof(f528,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f527,f526]) ).
fof(f551,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(f552,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl36_2 ),
inference(resolution,[],[f279,f528]) ).
fof(f557,plain,
! [X2,X3,X0,X1] :
( perp(X0,X1,sK11(X0,X2,X3,X1),X0)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f278,f370]) ).
fof(f558,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl36_2 ),
inference(resolution,[],[f278,f528]) ).
fof(f570,plain,
( ! [X2,X3,X0,X1] : para(X0,X1,X2,X3)
| ~ spl36_2 ),
inference(resolution,[],[f552,f558]) ).
fof(f571,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X0,X1,X6,X7) )
| ~ spl36_2 ),
inference(resolution,[],[f570,f435]) ).
fof(f575,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f571,f570]) ).
fof(f581,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ spl36_2 ),
inference(resolution,[],[f575,f291]) ).
fof(f589,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ para(X6,X7,X4,X5) )
| ~ spl36_2 ),
inference(resolution,[],[f581,f429]) ).
fof(f597,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f589,f570]) ).
fof(f600,plain,
( $false
| ~ spl36_2 ),
inference(resolution,[],[f597,f394]) ).
fof(f611,plain,
~ spl36_2,
inference(avatar_contradiction_clause,[],[f600]) ).
fof(f615,plain,
! [X2,X3,X0,X1] :
( ~ circle(X0,X1,X2,X3)
| para(X1,X0,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[],[f557,f551]) ).
fof(f619,plain,
! [X2,X3,X0,X1] :
( ~ circle(X0,X1,X2,X3)
| para(X1,X0,X1,X0) ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f620,plain,
( ! [X2,X3,X0,X1] : ~ circle(X0,X1,X2,X3)
| ~ spl36_1 ),
inference(forward_subsumption_resolution,[],[f619,f447]) ).
fof(f621,plain,
( $false
| ~ spl36_1 ),
inference(resolution,[],[f620,f390]) ).
fof(f632,plain,
~ spl36_1,
inference(avatar_contradiction_clause,[],[f621]) ).
cnf(s1,plain,
( spl36_1
| spl36_2 ),
inference(sat_conversion,[],[f451]) ).
cnf(s2,plain,
~ spl36_2,
inference(sat_conversion,[],[f611]) ).
cnf(s8,plain,
~ spl36_1,
inference(sat_conversion,[],[f632]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s2,s8]) ).
fof(f633,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO613+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 08:43:17 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 6.67/1.98 % (2327179)Detected formulas, will run a generic FOF schedule.
% 6.67/1.98 % (2327189)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1415045980:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.67/1.98 % (2327185)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=2273054761:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.67/1.98 % (2327184)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=1505047839:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.67/1.98 % (2327186)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=4081711974:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.67/1.98 % (2327187)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=253525405:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.67/1.98 % (2327188)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=529074004:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.67/1.98 % (2327189)Instruction limit reached!
% 6.67/1.98 % (2327189)------------------------------
% 6.67/1.98 % (2327189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327189)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327189)Termination reason: Instruction limit
% 6.67/1.98 % (2327189)Termination phase: Saturation
% 6.67/1.98 % (2327189)Time elapsed: 0.044 s
% 6.67/1.98 % (2327189)Peak memory usage: 89 MB
% 6.67/1.98 % (2327189)Instructions burned: 140 (million)
% 6.67/1.98 % (2327190)dis-21_1_sil=8000:lcm=predicate:random_seed=2765658452: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)
% 6.67/1.98 % (2327187)Refutation not found, incomplete strategy
% 6.67/1.98 % (2327187)------------------------------
% 6.67/1.98 % (2327187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327187)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327187)Termination reason: Refutation not found, incomplete strategy
% 6.67/1.98 % (2327187)Time elapsed: 0.042 s
% 6.67/1.98 % (2327187)Peak memory usage: 88 MB
% 6.67/1.98 % (2327187)Instructions burned: 77 (million)
% 6.67/1.98 % (2327188)Instruction limit reached!
% 6.67/1.98 % (2327188)------------------------------
% 6.67/1.98 % (2327188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327188)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327188)Termination reason: Instruction limit
% 6.67/1.98 % (2327188)Termination phase: Saturation
% 6.67/1.98 % (2327188)Time elapsed: 0.069 s
% 6.67/1.98 % (2327188)Peak memory usage: 89 MB
% 6.67/1.98 % (2327188)Instructions burned: 120 (million)
% 6.67/1.98 % (2327190)Instruction limit reached!
% 6.67/1.98 % (2327190)------------------------------
% 6.67/1.98 % (2327190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327190)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327190)Termination reason: Instruction limit
% 6.67/1.98 % (2327190)Termination phase: Saturation
% 6.67/1.98 % (2327190)Time elapsed: 0.075 s
% 6.67/1.98 % (2327190)Peak memory usage: 89 MB
% 6.67/1.98 % (2327190)Instructions burned: 129 (million)
% 6.67/1.98 % (2327197)lrs+10_1_sil=8000:sp=occurrence:random_seed=705751081:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.67/1.98 % (2327199)lrs+10_1_sil=32000:urr=on:br=off:random_seed=705750440:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.67/1.98 % (2327197)Instruction limit reached!
% 6.67/1.98 % (2327197)------------------------------
% 6.67/1.98 % (2327197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327197)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327197)Termination reason: Instruction limit
% 6.67/1.98 % (2327197)Termination phase: Saturation
% 6.67/1.98 % (2327197)Time elapsed: 0.101 s
% 6.67/1.98 % (2327197)Peak memory usage: 93 MB
% 6.67/1.98 % (2327197)Instructions burned: 287 (million)
% 6.67/1.98 % (2327200)lrs+1011_1_sil=32000:sp=occurrence:random_seed=345418259:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.67/1.98 % (2327187)------------------------------
% 6.67/1.98 % (2327187)------------------------------
% 6.67/1.98 % (2327199)Instruction limit reached!
% 6.67/1.98 % (2327199)------------------------------
% 6.67/1.98 % (2327199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327199)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327199)Termination reason: Instruction limit
% 6.67/1.98 % (2327199)Termination phase: Saturation
% 6.67/1.98 % (2327199)Time elapsed: 0.082 s
% 6.67/1.98 % (2327199)Peak memory usage: 90 MB
% 6.67/1.98 % (2327199)Instructions burned: 159 (million)
% 6.67/1.98 % (2327204)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=2856944707:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.67/1.98 % (2327204)Instruction limit reached!
% 6.67/1.98 % (2327204)------------------------------
% 6.67/1.98 % (2327204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327204)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327204)Termination reason: Instruction limit
% 6.67/1.98 % (2327204)Termination phase: Saturation
% 6.67/1.98 % (2327204)Time elapsed: 0.076 s
% 6.67/1.98 % (2327204)Peak memory usage: 90 MB
% 6.67/1.98 % (2327204)Instructions burned: 250 (million)
% 6.67/1.98 % (2327207)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2568119220:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.67/1.98 % (2327206)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=154436028:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.67/1.98 % (2327200)Instruction limit reached!
% 6.67/1.98 % (2327200)------------------------------
% 6.67/1.98 % (2327200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327200)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327200)Termination reason: Instruction limit
% 6.67/1.98 % (2327200)Termination phase: Saturation
% 6.67/1.98 % (2327200)Time elapsed: 0.194 s
% 6.67/1.98 % (2327200)Peak memory usage: 91 MB
% 6.67/1.98 % (2327200)Instructions burned: 325 (million)
% 6.67/1.98 % (2327209)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1289380956:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.67/1.98 % (2327209)Instruction limit reached!
% 6.67/1.98 % (2327209)------------------------------
% 6.67/1.98 % (2327209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327209)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327209)Termination reason: Instruction limit
% 6.67/1.98 % (2327209)Termination phase: Saturation
% 6.67/1.98 % (2327209)Time elapsed: 0.037 s
% 6.67/1.98 % (2327209)Peak memory usage: 89 MB
% 6.67/1.98 % (2327209)Instructions burned: 117 (million)
% 6.67/1.98 % (2327206)Instruction limit reached!
% 6.67/1.98 % (2327206)------------------------------
% 6.67/1.98 % (2327206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327206)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327206)Termination reason: Instruction limit
% 6.67/1.98 % (2327206)Termination phase: Saturation
% 6.67/1.98 % (2327206)Time elapsed: 0.167 s
% 6.67/1.98 % (2327206)Peak memory usage: 89 MB
% 6.67/1.98 % (2327206)Instructions burned: 294 (million)
% 6.67/1.98 % (2327212)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4026210759:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.67/1.98 % (2327184)First to succeed.
% 6.67/1.98 % (2327184)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2327179"
% 6.67/1.98 % (2327212)Instruction limit reached!
% 6.67/1.98 % (2327212)------------------------------
% 6.67/1.98 % (2327212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327212)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327212)Termination reason: Instruction limit
% 6.67/1.98 % (2327212)Termination phase: Saturation
% 6.67/1.98 % (2327212)Time elapsed: 0.073 s
% 6.67/1.98 % (2327212)Peak memory usage: 89 MB
% 6.67/1.98 % (2327212)Instructions burned: 129 (million)
% 6.67/1.98 % (2327214)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=21272406:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.67/1.98 % (2327214)Instruction limit reached!
% 6.67/1.98 % (2327214)------------------------------
% 6.67/1.98 % (2327214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.98 % (2327214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.98 % (2327214)CaDiCaL version: 2.1.3
% 6.67/1.98 % (2327214)Termination reason: Instruction limit
% 6.67/1.98 % (2327214)Termination phase: Saturation
% 6.67/1.98 % (2327214)Time elapsed: 0.035 s
% 6.67/1.98 % (2327214)Peak memory usage: 89 MB
% 6.67/1.98 % (2327214)Instructions burned: 115 (million)
% 6.67/1.98 % (2327185)Also succeeded, but the first one will report.
% 6.67/1.98 % (2327215)lrs+10_1_sil=8000:sp=occurrence:random_seed=1299840233:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.67/1.98 % (2327218)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=888288062:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.67/1.98 % (2327219)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1821225272:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.67/1.98 % (2327184)Refutation found. Thanks to Tanya!
% 6.67/1.98 % SZS status Theorem for theBenchmark
% 6.67/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 8.46/2.18 % (2327184)------------------------------
% 8.46/2.18 % (2327184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.46/2.18 % (2327184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.46/2.18 % (2327184)CaDiCaL version: 2.1.3
% 8.46/2.18 % (2327184)Termination reason: Refutation
% 8.46/2.18 % (2327184)Time elapsed: 0.673 s
% 8.46/2.18 % (2327184)Peak memory usage: 130 MB
% 8.46/2.18 % (2327184)Instructions burned: 1002 (million)
% 8.46/2.18 % (2327184)------------------------------
% 8.46/2.18 % (2327184)------------------------------
% 8.46/2.18 % (2327179)Success in time 1.114 s
% 8.46/2.18 % Vampire exiting
%------------------------------------------------------------------------------