%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO642+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:53:08 AM UTC 2026
% Result : Theorem 4.21s 1.53s
% Output : Refutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 8 unt; 2 def)
% Number of atoms : 302 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 325 ( 121 ~; 114 |; 72 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ruleX11) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ( midp(X2,X1,X0)
& circle(X2,X0,X9,X10)
& circle(X2,X0,X3,X11)
& circle(X2,X0,X4,X12)
& circle(X3,X1,X13,X14)
& circle(X2,X0,X5,X15)
& circle(X3,X1,X5,X16)
& coll(X6,X1,X4)
& coll(X6,X0,X5)
& coll(X7,X0,X3)
& coll(X7,X1,X4)
& coll(X8,X0,X5)
& coll(X8,X3,X4) )
=> perp(X7,X8,X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL81109108) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ( midp(X2,X1,X0)
& circle(X2,X0,X9,X10)
& circle(X2,X0,X3,X11)
& circle(X2,X0,X4,X12)
& circle(X3,X1,X13,X14)
& circle(X2,X0,X5,X15)
& circle(X3,X1,X5,X16)
& coll(X6,X1,X4)
& coll(X6,X0,X5)
& coll(X7,X0,X3)
& coll(X7,X1,X4)
& coll(X8,X0,X5)
& coll(X8,X3,X4) )
=> perp(X7,X8,X0,X5) ),
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(X7,X8,X0,X5)
& midp(X2,X1,X0)
& circle(X2,X0,X9,X10)
& circle(X2,X0,X3,X11)
& circle(X2,X0,X4,X12)
& circle(X3,X1,X13,X14)
& circle(X2,X0,X5,X15)
& circle(X3,X1,X5,X16)
& coll(X6,X1,X4)
& coll(X6,X0,X5)
& coll(X7,X0,X3)
& coll(X7,X1,X4)
& coll(X8,X0,X5)
& coll(X8,X3,X4) ),
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(X7,X8,X0,X5)
& midp(X2,X1,X0)
& circle(X2,X0,X9,X10)
& circle(X2,X0,X3,X11)
& circle(X2,X0,X4,X12)
& circle(X3,X1,X13,X14)
& circle(X2,X0,X5,X15)
& circle(X3,X1,X5,X16)
& coll(X6,X1,X4)
& coll(X6,X0,X5)
& coll(X7,X0,X3)
& coll(X7,X1,X4)
& coll(X8,X0,X5)
& coll(X8,X3,X4) ),
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(sK27,sK28,sK20,sK25)
& midp(sK22,sK21,sK20)
& circle(sK22,sK20,sK29,sK30)
& circle(sK22,sK20,sK23,sK31)
& circle(sK22,sK20,sK24,sK32)
& circle(sK23,sK21,sK33,sK34)
& circle(sK22,sK20,sK25,sK35)
& circle(sK23,sK21,sK25,sK36)
& coll(sK26,sK21,sK24)
& coll(sK26,sK20,sK25)
& coll(sK27,sK20,sK23)
& coll(sK27,sK21,sK24)
& coll(sK28,sK20,sK25)
& coll(sK28,sK23,sK24) ),
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(f394,plain,
circle(sK22,sK20,sK23,sK31),
inference(cnf_transformation,[],[f270]) ).
fof(f397,plain,
~ perp(sK27,sK28,sK20,sK25),
inference(cnf_transformation,[],[f270]) ).
fof(f398,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(f399,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,[],[f398]) ).
fof(f407,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(f422,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(f435,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ para(X2,X3,X2,X3) ),
inference(resolution,[],[f309,f407]) ).
fof(f437,definition,
( spl37_1
<=> ! [X2,X3] : ~ para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl37_1])],[avatar_definition]) ).
fof(f438,plain,
( ! [X2,X3] : ~ para(X2,X3,X2,X3)
| ~ spl37_1 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f440,definition,
( spl37_2
<=> ! [X0,X1] : para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl37_2])],[avatar_definition]) ).
fof(f441,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl37_2 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f442,plain,
( spl37_1
| spl37_2 ),
inference(avatar_split_clause,[],[f435,f440,f437]) ).
fof(f443,plain,
! [X2,X3,X0,X1] :
( perp(X1,X0,sK11(X1,X2,X3,X0),X1)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[],[f370,f278]) ).
fof(f449,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f422]) ).
fof(f452,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f449,f441]) ).
fof(f459,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f422]) ).
fof(f462,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) )
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f459,f452]) ).
fof(f465,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f462,f441]) ).
fof(f469,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl37_2 ),
inference(resolution,[],[f465,f287]) ).
fof(f475,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f469,f465]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl37_2 ),
inference(resolution,[],[f475,f399]) ).
fof(f484,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f481,f475]) ).
fof(f486,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f484,f475]) ).
fof(f487,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl37_2 ),
inference(resolution,[],[f486,f327]) ).
fof(f488,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f487,f486]) ).
fof(f489,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl37_2 ),
inference(resolution,[],[f488,f278]) ).
fof(f502,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ para(X0,X1,X2,X2)
| perp(X0,X1,X3,X4) )
| ~ spl37_2 ),
inference(resolution,[],[f280,f488]) ).
fof(f576,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(f577,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl37_2 ),
inference(resolution,[],[f279,f488]) ).
fof(f579,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl37_2 ),
inference(forward_subsumption_resolution,[],[f577,f489]) ).
fof(f583,plain,
( ! [X2,X3,X0,X1] : perp(X0,X1,X2,X3)
| ~ spl37_2 ),
inference(resolution,[],[f579,f502]) ).
fof(f586,plain,
( $false
| ~ spl37_2 ),
inference(resolution,[],[f583,f397]) ).
fof(f591,plain,
~ spl37_2,
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f595,plain,
! [X2,X3,X0,X1] :
( ~ circle(X0,X1,X2,X3)
| para(X1,X0,X1,X0)
| ~ circle(X0,X1,X2,X3) ),
inference(resolution,[],[f443,f576]) ).
fof(f600,plain,
! [X2,X3,X0,X1] :
( ~ circle(X0,X1,X2,X3)
| para(X1,X0,X1,X0) ),
inference(duplicate_literal_removal,[],[f595]) ).
fof(f601,plain,
( ! [X2,X3,X0,X1] : ~ circle(X0,X1,X2,X3)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f600,f438]) ).
fof(f602,plain,
( $false
| ~ spl37_1 ),
inference(resolution,[],[f601,f394]) ).
fof(f613,plain,
~ spl37_1,
inference(avatar_contradiction_clause,[],[f602]) ).
cnf(s1,plain,
( spl37_1
| spl37_2 ),
inference(sat_conversion,[],[f442]) ).
cnf(s2,plain,
~ spl37_2,
inference(sat_conversion,[],[f591]) ).
cnf(s8,plain,
~ spl37_1,
inference(sat_conversion,[],[f613]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s2,s8]) ).
fof(f614,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO642+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 08:47:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.21/1.53 % (2329764)Detected formulas, will run a generic FOF schedule.
% 4.21/1.53 % (2329769)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=1249044130:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.21/1.53 % (2329775)dis-21_1_sil=8000:lcm=predicate:random_seed=2773952904: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)
% 4.21/1.53 % (2329772)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3647206368:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.21/1.53 % (2329773)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1957994119:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.21/1.53 % (2329770)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=2949078248:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.21/1.53 % (2329771)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=1759280724:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.21/1.53 % (2329774)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2547043275:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.21/1.53 % (2329772)Refutation not found, incomplete strategy
% 4.21/1.53 % (2329772)------------------------------
% 4.21/1.53 % (2329772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.53 % (2329772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.53 % (2329772)CaDiCaL version: 2.1.3
% 4.21/1.53 % (2329772)Termination reason: Refutation not found, incomplete strategy
% 4.21/1.53 % (2329772)Time elapsed: 0.058 s
% 4.21/1.53 % (2329772)Peak memory usage: 89 MB
% 4.21/1.53 % (2329772)Instructions burned: 109 (million)
% 4.21/1.53 % (2329773)Instruction limit reached!
% 4.21/1.53 % (2329773)------------------------------
% 4.21/1.53 % (2329773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.53 % (2329773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.53 % (2329773)CaDiCaL version: 2.1.3
% 4.21/1.53 % (2329773)Termination reason: Instruction limit
% 4.21/1.53 % (2329773)Termination phase: Saturation
% 4.21/1.53 % (2329773)Time elapsed: 0.068 s
% 4.21/1.53 % (2329773)Peak memory usage: 88 MB
% 4.21/1.53 % (2329773)Instructions burned: 119 (million)
% 4.21/1.53 % (2329775)Instruction limit reached!
% 4.21/1.53 % (2329775)------------------------------
% 4.21/1.53 % (2329775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.53 % (2329775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.53 % (2329775)CaDiCaL version: 2.1.3
% 4.21/1.53 % (2329775)Termination reason: Instruction limit
% 4.21/1.53 % (2329775)Termination phase: Saturation
% 4.21/1.53 % (2329775)Time elapsed: 0.075 s
% 4.21/1.53 % (2329775)Peak memory usage: 89 MB
% 4.21/1.53 % (2329775)Instructions burned: 129 (million)
% 4.21/1.53 % (2329774)Instruction limit reached!
% 4.21/1.53 % (2329774)------------------------------
% 4.21/1.53 % (2329774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.53 % (2329774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.53 % (2329774)CaDiCaL version: 2.1.3
% 4.21/1.53 % (2329774)Termination reason: Instruction limit
% 4.21/1.53 % (2329774)Termination phase: Saturation
% 4.21/1.53 % (2329774)Time elapsed: 0.093 s
% 4.21/1.53 % (2329774)Peak memory usage: 90 MB
% 4.21/1.53 % (2329774)Instructions burned: 140 (million)
% 4.21/1.53 % (2329784)lrs+10_1_sil=32000:urr=on:br=off:random_seed=604374603:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.21/1.53 % (2329783)lrs+10_1_sil=8000:sp=occurrence:random_seed=3347115922:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.21/1.53 % (2329785)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1387353603:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.21/1.53 % (2329772)------------------------------
% 4.21/1.53 % (2329772)------------------------------
% 4.21/1.53 % (2329784)Instruction limit reached!
% 4.21/1.53 % (2329784)------------------------------
% 4.21/1.53 % (2329784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.53 % (2329784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.53 % (2329784)CaDiCaL version: 2.1.3
% 4.21/1.53 % (2329784)Termination reason: Instruction limit
% 4.21/1.53 % (2329784)Termination phase: Saturation
% 4.21/1.53 % (2329784)Time elapsed: 0.084 s
% 4.21/1.53 % (2329784)Peak memory usage: 89 MB
% 4.21/1.53 % (2329784)Instructions burned: 158 (million)
% 4.21/1.53 % (2329769)First to succeed.
% 4.21/1.53 % (2329769)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2329764"
% 4.21/1.53 % (2329783)Instruction limit reached!
% 4.21/1.53 % (2329783)------------------------------
% 4.21/1.53 % (2329783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.53 % (2329783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.53 % (2329783)CaDiCaL version: 2.1.3
% 4.21/1.53 % (2329783)Termination reason: Instruction limit
% 4.21/1.53 % (2329783)Termination phase: Saturation
% 4.21/1.53 % (2329783)Time elapsed: 0.183 s
% 4.21/1.53 % (2329783)Peak memory usage: 92 MB
% 4.21/1.53 % (2329783)Instructions burned: 286 (million)
% 4.21/1.53 % (2329785)Instruction limit reached!
% 4.21/1.53 % (2329785)------------------------------
% 4.21/1.53 % (2329785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.53 % (2329785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.53 % (2329785)CaDiCaL version: 2.1.3
% 4.21/1.53 % (2329785)Termination reason: Instruction limit
% 4.21/1.53 % (2329785)Termination phase: Saturation
% 4.21/1.53 % (2329785)Time elapsed: 0.208 s
% 4.21/1.53 % (2329785)Peak memory usage: 91 MB
% 4.21/1.53 % (2329785)Instructions burned: 326 (million)
% 4.21/1.53 % (2329790)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2805824604:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.21/1.53 % (2329789)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=1542087158:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.21/1.53 % (2329769)Refutation found. Thanks to Tanya!
% 4.21/1.53 % SZS status Theorem for theBenchmark
% 4.21/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.25/1.63 % (2329769)------------------------------
% 5.25/1.63 % (2329769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/1.63 % (2329769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/1.63 % (2329769)CaDiCaL version: 2.1.3
% 5.25/1.63 % (2329769)Termination reason: Refutation
% 5.25/1.63 % (2329769)Time elapsed: 0.372 s
% 5.25/1.63 % (2329769)Peak memory usage: 130 MB
% 5.25/1.63 % (2329769)Instructions burned: 998 (million)
% 5.25/1.63 % (2329769)------------------------------
% 5.25/1.63 % (2329769)------------------------------
% 5.25/1.63 % (2329764)Success in time 0.667 s
% 5.25/1.63 % Vampire exiting
%------------------------------------------------------------------------------