%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO544+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 : n009.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 09:52:53 AM UTC 2026
% Result : Theorem 6.44s 1.95s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 8 unt; 2 def)
% Number of atoms : 282 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 305 ( 121 ~; 114 |; 52 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 422 ( 0 sgn 398 !; 24 ?)
% 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] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& midp(X5,X2,X1)
& midp(X6,X0,X4)
& midp(X7,X6,X5)
& coll(X3,X7,X8)
& cong(X3,X7,X3,X8)
& coll(X9,X0,X4)
& coll(X9,X1,X2) )
=> perp(X6,X8,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012004) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& midp(X5,X2,X1)
& midp(X6,X0,X4)
& midp(X7,X6,X5)
& coll(X3,X7,X8)
& cong(X3,X7,X3,X8)
& coll(X9,X0,X4)
& coll(X9,X1,X2) )
=> perp(X6,X8,X1,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(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] :
( ~ perp(X6,X8,X1,X2)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& midp(X5,X2,X1)
& midp(X6,X0,X4)
& midp(X7,X6,X5)
& coll(X3,X7,X8)
& cong(X3,X7,X3,X8)
& coll(X9,X0,X4)
& coll(X9,X1,X2) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ perp(X6,X8,X1,X2)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& midp(X5,X2,X1)
& midp(X6,X0,X4)
& midp(X7,X6,X5)
& coll(X3,X7,X8)
& cong(X3,X7,X3,X8)
& coll(X9,X0,X4)
& coll(X9,X1,X2) ),
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,sK28,sK21,sK22)
& circle(sK23,sK20,sK21,sK22)
& circle(sK23,sK20,sK24,sK30)
& midp(sK25,sK22,sK21)
& midp(sK26,sK20,sK24)
& midp(sK27,sK26,sK25)
& coll(sK23,sK27,sK28)
& cong(sK23,sK27,sK23,sK28)
& coll(sK29,sK20,sK24)
& coll(sK29,sK21,sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30]),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)],[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(f392,plain,
circle(sK23,sK20,sK21,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f393,plain,
~ perp(sK26,sK28,sK21,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f394,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(f395,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,[],[f394]) ).
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(f428,plain,
! [X2,X3,X0,X1] :
( perp(X0,X1,sK11(X0,X2,X3,X1),X0)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f278,f370]) ).
fof(f437,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ para(X2,X3,X2,X3) ),
inference(resolution,[],[f309,f403]) ).
fof(f439,definition,
( spl31_1
<=> ! [X2,X3] : ~ para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
fof(f440,plain,
( ! [X2,X3] : ~ para(X2,X3,X2,X3)
| ~ spl31_1 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f442,definition,
( spl31_2
<=> ! [X0,X1] : para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
fof(f443,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl31_2 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f444,plain,
( spl31_1
| spl31_2 ),
inference(avatar_split_clause,[],[f437,f442,f439]) ).
fof(f449,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f418]) ).
fof(f452,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f449,f443]) ).
fof(f459,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f418]) ).
fof(f462,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) )
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f459,f452]) ).
fof(f465,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f462,f443]) ).
fof(f467,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl31_2 ),
inference(resolution,[],[f465,f287]) ).
fof(f471,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f467,f465]) ).
fof(f474,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl31_2 ),
inference(resolution,[],[f471,f395]) ).
fof(f478,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f474,f471]) ).
fof(f480,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f478,f471]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl31_2 ),
inference(resolution,[],[f480,f327]) ).
fof(f482,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f481,f480]) ).
fof(f483,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl31_2 ),
inference(resolution,[],[f482,f278]) ).
fof(f485,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ para(X0,X1,X2,X2)
| perp(X0,X1,X3,X4) )
| ~ spl31_2 ),
inference(resolution,[],[f482,f280]) ).
fof(f512,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(f515,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl31_2 ),
inference(resolution,[],[f279,f482]) ).
fof(f516,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f515,f483]) ).
fof(f517,plain,
( ! [X2,X3,X0,X1] : perp(X0,X1,X2,X3)
| ~ spl31_2 ),
inference(resolution,[],[f516,f485]) ).
fof(f520,plain,
( $false
| ~ spl31_2 ),
inference(resolution,[],[f517,f393]) ).
fof(f525,plain,
~ spl31_2,
inference(avatar_contradiction_clause,[],[f520]) ).
fof(f527,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f512,f428]) ).
fof(f528,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3) ),
inference(duplicate_literal_removal,[],[f527]) ).
fof(f529,plain,
( ! [X2,X3,X0,X1] : ~ circle(X1,X0,X2,X3)
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f528,f440]) ).
fof(f530,plain,
( $false
| ~ spl31_1 ),
inference(resolution,[],[f529,f392]) ).
fof(f533,plain,
~ spl31_1,
inference(avatar_contradiction_clause,[],[f530]) ).
cnf(s1,plain,
( spl31_1
| spl31_2 ),
inference(sat_conversion,[],[f444]) ).
cnf(s2,plain,
~ spl31_2,
inference(sat_conversion,[],[f525]) ).
cnf(s4,plain,
~ spl31_1,
inference(sat_conversion,[],[f533]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f534,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO544+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 08:28:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 6.44/1.95 % (1720732)Detected formulas, will run a generic FOF schedule.
% 6.44/1.95 % (1720743)dis-21_1_sil=8000:lcm=predicate:random_seed=2844159051: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)
% 6.44/1.95 % (1720743)Instruction limit reached!
% 6.44/1.95 % (1720743)------------------------------
% 6.44/1.95 % (1720743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720743)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720743)Termination reason: Instruction limit
% 6.44/1.95 % (1720743)Termination phase: Saturation
% 6.44/1.95 % (1720743)Time elapsed: 0.041 s
% 6.44/1.95 % (1720737)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=4275766607:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.44/1.95 % (1720741)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2984140203:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.44/1.95 % (1720740)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3740338920:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.44/1.95 % (1720739)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=275486302:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.44/1.95 % (1720738)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=1243641109:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.44/1.95 % (1720743)Peak memory usage: 89 MB
% 6.44/1.95 % (1720743)Instructions burned: 131 (million)
% 6.44/1.95 % (1720742)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3415314961:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.44/1.95 % (1720740)Instruction limit reached!
% 6.44/1.95 % (1720740)------------------------------
% 6.44/1.95 % (1720740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720740)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720740)Termination reason: Instruction limit
% 6.44/1.95 % (1720740)Termination phase: Saturation
% 6.44/1.95 % (1720740)Time elapsed: 0.068 s
% 6.44/1.95 % (1720740)Peak memory usage: 90 MB
% 6.44/1.95 % (1720740)Instructions burned: 109 (million)
% 6.44/1.95 % (1720741)Instruction limit reached!
% 6.44/1.95 % (1720741)------------------------------
% 6.44/1.95 % (1720741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720741)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720741)Termination reason: Instruction limit
% 6.44/1.95 % (1720741)Termination phase: Saturation
% 6.44/1.95 % (1720741)Time elapsed: 0.069 s
% 6.44/1.95 % (1720741)Peak memory usage: 88 MB
% 6.44/1.95 % (1720741)Instructions burned: 120 (million)
% 6.44/1.95 % (1720742)Instruction limit reached!
% 6.44/1.95 % (1720742)------------------------------
% 6.44/1.95 % (1720742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720742)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720742)Termination reason: Instruction limit
% 6.44/1.95 % (1720742)Termination phase: Saturation
% 6.44/1.95 % (1720742)Time elapsed: 0.096 s
% 6.44/1.95 % (1720742)Peak memory usage: 90 MB
% 6.44/1.95 % (1720742)Instructions burned: 140 (million)
% 6.44/1.95 % (1720751)lrs+10_1_sil=8000:sp=occurrence:random_seed=2141086208:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.44/1.95 % (1720751)Instruction limit reached!
% 6.44/1.95 % (1720751)------------------------------
% 6.44/1.95 % (1720751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720751)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720751)Termination reason: Instruction limit
% 6.44/1.95 % (1720751)Termination phase: Saturation
% 6.44/1.95 % (1720751)Time elapsed: 0.102 s
% 6.44/1.95 % (1720751)Peak memory usage: 93 MB
% 6.44/1.95 % (1720751)Instructions burned: 287 (million)
% 6.44/1.95 % (1720753)lrs+1011_1_sil=32000:sp=occurrence:random_seed=106159362:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.44/1.95 % (1720752)lrs+10_1_sil=32000:urr=on:br=off:random_seed=972326144:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.44/1.95 % (1720754)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=1903633861:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.44/1.95 % (1720752)Instruction limit reached!
% 6.44/1.95 % (1720752)------------------------------
% 6.44/1.95 % (1720752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720752)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720752)Termination reason: Instruction limit
% 6.44/1.95 % (1720752)Termination phase: Saturation
% 6.44/1.95 % (1720752)Time elapsed: 0.085 s
% 6.44/1.95 % (1720752)Peak memory usage: 91 MB
% 6.44/1.95 % (1720752)Instructions burned: 159 (million)
% 6.44/1.95 % (1720758)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2703845561:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.44/1.95 % (1720754)Instruction limit reached!
% 6.44/1.95 % (1720754)------------------------------
% 6.44/1.95 % (1720754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720754)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720754)Termination reason: Instruction limit
% 6.44/1.95 % (1720754)Termination phase: Saturation
% 6.44/1.95 % (1720754)Time elapsed: 0.132 s
% 6.44/1.95 % (1720754)Peak memory usage: 92 MB
% 6.44/1.95 % (1720754)Instructions burned: 249 (million)
% 6.44/1.95 % (1720758)Instruction limit reached!
% 6.44/1.95 % (1720758)------------------------------
% 6.44/1.95 % (1720758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720758)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720758)Termination reason: Instruction limit
% 6.44/1.95 % (1720758)Termination phase: Saturation
% 6.44/1.95 % (1720758)Time elapsed: 0.090 s
% 6.44/1.95 % (1720758)Peak memory usage: 89 MB
% 6.44/1.95 % (1720758)Instructions burned: 294 (million)
% 6.44/1.95 % (1720753)Instruction limit reached!
% 6.44/1.95 % (1720753)------------------------------
% 6.44/1.95 % (1720753)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720753)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720753)Termination reason: Instruction limit
% 6.44/1.95 % (1720753)Termination phase: Saturation
% 6.44/1.95 % (1720753)Time elapsed: 0.207 s
% 6.44/1.95 % (1720753)Peak memory usage: 91 MB
% 6.44/1.95 % (1720753)Instructions burned: 325 (million)
% 6.44/1.95 % (1720760)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3398439015:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.44/1.95 % (1720762)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3993253736:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.44/1.95 % (1720763)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1651936645:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.44/1.95 % (1720763)Instruction limit reached!
% 6.44/1.95 % (1720763)------------------------------
% 6.44/1.95 % (1720763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720763)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720763)Termination reason: Instruction limit
% 6.44/1.95 % (1720763)Termination phase: Saturation
% 6.44/1.95 % (1720763)Time elapsed: 0.038 s
% 6.44/1.95 % (1720763)Peak memory usage: 89 MB
% 6.44/1.95 % (1720763)Instructions burned: 131 (million)
% 6.44/1.95 % (1720764)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1534331831:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 6.44/1.95 % (1720762)Instruction limit reached!
% 6.44/1.95 % (1720762)------------------------------
% 6.44/1.95 % (1720762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720762)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720762)Termination reason: Instruction limit
% 6.44/1.95 % (1720762)Termination phase: Saturation
% 6.44/1.95 % (1720762)Time elapsed: 0.068 s
% 6.44/1.95 % (1720762)Peak memory usage: 89 MB
% 6.44/1.95 % (1720762)Instructions burned: 113 (million)
% 6.44/1.95 % (1720764)Instruction limit reached!
% 6.44/1.95 % (1720764)------------------------------
% 6.44/1.95 % (1720764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.44/1.95 % (1720764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.44/1.95 % (1720764)CaDiCaL version: 2.1.3
% 6.44/1.95 % (1720764)Termination reason: Instruction limit
% 6.44/1.95 % (1720764)Termination phase: Saturation
% 6.44/1.95 % (1720764)Time elapsed: 0.066 s
% 6.44/1.95 % (1720764)Peak memory usage: 89 MB
% 6.44/1.95 % (1720764)Instructions burned: 115 (million)
% 6.44/1.95 % (1720737)First to succeed.
% 6.44/1.95 % (1720737)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1720732"
% 6.44/1.95 % (1720768)lrs+10_1_sil=8000:sp=occurrence:random_seed=1697257951:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.44/1.95 % (1720770)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=578448343:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.44/1.95 % (1720738)Also succeeded, but the first one will report.
% 6.44/1.95 % (1720771)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1441627405:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.44/1.95 % (1720737)Refutation found. Thanks to Tanya!
% 6.44/1.95 % SZS status Theorem for theBenchmark
% 6.44/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/2.14 % (1720737)------------------------------
% 0.16/2.14 % (1720737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (1720737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (1720737)CaDiCaL version: 2.1.3
% 0.16/2.14 % (1720737)Termination reason: Refutation
% 0.16/2.14 % (1720737)Time elapsed: 0.661 s
% 0.16/2.14 % (1720737)Peak memory usage: 131 MB
% 0.16/2.14 % (1720737)Instructions burned: 981 (million)
% 0.16/2.14 % (1720737)------------------------------
% 0.16/2.14 % (1720737)------------------------------
% 0.16/2.14 % (1720732)Success in time 1.1 s
% 0.16/2.14 % Vampire exiting
%------------------------------------------------------------------------------