%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO558+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 : n008.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 09:52:55 AM UTC 2026
% Result : Theorem 6.78s 1.97s
% Output : Refutation 8.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 98 ( 8 unt; 2 def)
% Number of atoms : 277 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 299 ( 120 ~; 114 |; 47 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 426 ( 0 sgn 400 !; 26 ?)
% 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] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X9)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& circle(X6,X0,X1,X5)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X8,X11) )
=> perp(X5,X8,X8,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012018) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X9)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& circle(X6,X0,X1,X5)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X8,X11) )
=> perp(X5,X8,X8,X3) ),
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] :
( ~ perp(X5,X8,X8,X3)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X9)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& circle(X6,X0,X1,X5)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X8,X11) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ perp(X5,X8,X8,X3)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X9)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& circle(X6,X0,X1,X5)
& circle(X7,X2,X4,X5)
& circle(X6,X0,X8,X10)
& circle(X7,X2,X8,X11) ),
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(sK25,sK28,sK28,sK23)
& circle(sK23,sK20,sK21,sK22)
& circle(sK23,sK20,sK24,sK29)
& coll(sK25,sK20,sK22)
& coll(sK25,sK21,sK24)
& circle(sK26,sK20,sK21,sK25)
& circle(sK27,sK22,sK24,sK25)
& circle(sK26,sK20,sK28,sK30)
& circle(sK27,sK22,sK28,sK31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31]),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)],[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(f391,plain,
circle(sK23,sK20,sK21,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f392,plain,
~ perp(sK25,sK28,sK28,sK23),
inference(cnf_transformation,[],[f270]) ).
fof(f393,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(f394,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,[],[f393]) ).
fof(f408,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5) ),
inference(resolution,[],[f289,f310]) ).
fof(f411,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X0,X1)
| para(X2,X3,X2,X3) ),
inference(resolution,[],[f408,f309]) ).
fof(f415,definition,
( spl32_1
<=> ! [X2,X3] : para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
fof(f416,plain,
( ! [X2,X3] : para(X2,X3,X2,X3)
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f418,definition,
( spl32_2
<=> ! [X0,X1] : ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl32_2])],[avatar_definition]) ).
fof(f419,plain,
( ! [X0,X1] : ~ para(X0,X1,X0,X1)
| ~ spl32_2 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f420,plain,
( spl32_1
| spl32_2 ),
inference(avatar_split_clause,[],[f411,f418,f415]) ).
fof(f434,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(f437,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X1)
| cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1) ),
inference(resolution,[],[f434,f312]) ).
fof(f448,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f434]) ).
fof(f452,plain,
! [X2,X3,X0,X1] :
( perp(X0,X1,sK11(X0,X2,X3,X1),X0)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f278,f370]) ).
fof(f459,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(f464,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f459,f452]) ).
fof(f465,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3) ),
inference(duplicate_literal_removal,[],[f464]) ).
fof(f466,plain,
( ! [X2,X3,X0,X1] : ~ circle(X1,X0,X2,X3)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f465,f419]) ).
fof(f467,plain,
( $false
| ~ spl32_2 ),
inference(resolution,[],[f466,f391]) ).
fof(f478,plain,
~ spl32_2,
inference(avatar_contradiction_clause,[],[f467]) ).
fof(f479,plain,
( ! [X2,X0,X1] :
( cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1) )
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f437,f416]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f448,f416]) ).
fof(f484,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f481,f479]) ).
fof(f490,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl32_1 ),
inference(resolution,[],[f484,f287]) ).
fof(f494,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f490,f484]) ).
fof(f500,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl32_1 ),
inference(resolution,[],[f494,f394]) ).
fof(f504,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f500,f494]) ).
fof(f506,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f504,f494]) ).
fof(f507,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl32_1 ),
inference(resolution,[],[f506,f327]) ).
fof(f508,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f507,f506]) ).
fof(f509,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl32_1 ),
inference(resolution,[],[f508,f279]) ).
fof(f510,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl32_1 ),
inference(resolution,[],[f508,f278]) ).
fof(f512,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ para(X0,X1,X2,X2)
| perp(X0,X1,X3,X4) )
| ~ spl32_1 ),
inference(resolution,[],[f508,f280]) ).
fof(f514,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f509,f510]) ).
fof(f521,plain,
( ! [X2,X3,X0,X1] : perp(X0,X1,X2,X3)
| ~ spl32_1 ),
inference(resolution,[],[f512,f514]) ).
fof(f522,plain,
( $false
| ~ spl32_1 ),
inference(resolution,[],[f521,f392]) ).
fof(f528,plain,
~ spl32_1,
inference(avatar_contradiction_clause,[],[f522]) ).
cnf(s1,plain,
( spl32_1
| spl32_2 ),
inference(sat_conversion,[],[f420]) ).
cnf(s7,plain,
~ spl32_2,
inference(sat_conversion,[],[f478]) ).
cnf(s8,plain,
~ spl32_1,
inference(sat_conversion,[],[f528]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s7,s8]) ).
fof(f529,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO558+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 08:31:25 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 6.78/1.96 % (924752)Detected formulas, will run a generic FOF schedule.
% 6.78/1.96 % (924759)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=1025748113:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.78/1.96 % (924762)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3420234524:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.78/1.96 % (924761)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=66370700:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.78/1.96 % (924758)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=4212476948:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.78/1.96 % (924763)dis-21_1_sil=8000:lcm=predicate:random_seed=2480862333: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)
% 6.78/1.96 % (924757)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=3152122943:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.78/1.96 % (924760)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3915160979:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.78/1.96 % (924760)Refutation not found, incomplete strategy
% 6.78/1.96 % (924760)------------------------------
% 6.78/1.96 % (924760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924760)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924760)Termination reason: Refutation not found, incomplete strategy
% 6.78/1.96 % (924760)Time elapsed: 0.010 s
% 6.78/1.96 % (924760)Peak memory usage: 88 MB
% 6.78/1.96 % (924760)Instructions burned: 17 (million)
% 6.78/1.96 % (924761)Instruction limit reached!
% 6.78/1.96 % (924761)------------------------------
% 6.78/1.96 % (924761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924761)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924761)Termination reason: Instruction limit
% 6.78/1.96 % (924761)Termination phase: Saturation
% 6.78/1.96 % (924761)Time elapsed: 0.069 s
% 6.78/1.96 % (924761)Peak memory usage: 88 MB
% 6.78/1.96 % (924761)Instructions burned: 119 (million)
% 6.78/1.96 % (924763)Instruction limit reached!
% 6.78/1.96 % (924763)------------------------------
% 6.78/1.96 % (924763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924763)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924763)Termination reason: Instruction limit
% 6.78/1.96 % (924763)Termination phase: Saturation
% 6.78/1.96 % (924763)Time elapsed: 0.075 s
% 6.78/1.96 % (924763)Peak memory usage: 89 MB
% 6.78/1.96 % (924763)Instructions burned: 130 (million)
% 6.78/1.96 % (924762)Instruction limit reached!
% 6.78/1.96 % (924762)------------------------------
% 6.78/1.96 % (924762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924762)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924762)Termination reason: Instruction limit
% 6.78/1.96 % (924762)Termination phase: Saturation
% 6.78/1.96 % (924762)Time elapsed: 0.089 s
% 6.78/1.96 % (924762)Peak memory usage: 90 MB
% 6.78/1.96 % (924762)Instructions burned: 139 (million)
% 6.78/1.96 % (924771)lrs+10_1_sil=8000:sp=occurrence:random_seed=4165482686:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.78/1.96 % (924772)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1343433156:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.78/1.96 % (924773)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3895077879:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.78/1.96 % (924760)------------------------------
% 6.78/1.96 % (924760)------------------------------
% 6.78/1.96 % (924772)Instruction limit reached!
% 6.78/1.96 % (924772)------------------------------
% 6.78/1.96 % (924772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924772)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924772)Termination reason: Instruction limit
% 6.78/1.96 % (924772)Termination phase: Saturation
% 6.78/1.96 % (924772)Time elapsed: 0.081 s
% 6.78/1.96 % (924772)Peak memory usage: 89 MB
% 6.78/1.96 % (924772)Instructions burned: 158 (million)
% 6.78/1.96 % (924771)Instruction limit reached!
% 6.78/1.96 % (924771)------------------------------
% 6.78/1.96 % (924771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924771)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924771)Termination reason: Instruction limit
% 6.78/1.96 % (924771)Termination phase: Saturation
% 6.78/1.96 % (924771)Time elapsed: 0.179 s
% 6.78/1.96 % (924771)Peak memory usage: 92 MB
% 6.78/1.96 % (924771)Instructions burned: 286 (million)
% 6.78/1.96 % (924773)Instruction limit reached!
% 6.78/1.96 % (924773)------------------------------
% 6.78/1.96 % (924773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924773)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924773)Termination reason: Instruction limit
% 6.78/1.96 % (924773)Termination phase: Saturation
% 6.78/1.96 % (924773)Time elapsed: 0.174 s
% 6.78/1.96 % (924773)Peak memory usage: 90 MB
% 6.78/1.96 % (924773)Instructions burned: 326 (million)
% 6.78/1.96 % (924777)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=2477071620:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.78/1.96 % (924778)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3418810398:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.78/1.96 % (924779)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3633063534:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.78/1.96 % (924777)Instruction limit reached!
% 6.78/1.96 % (924777)------------------------------
% 6.78/1.96 % (924777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924777)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924777)Termination reason: Instruction limit
% 6.78/1.96 % (924777)Termination phase: Saturation
% 6.78/1.96 % (924777)Time elapsed: 0.140 s
% 6.78/1.96 % (924777)Peak memory usage: 90 MB
% 6.78/1.96 % (924777)Instructions burned: 249 (million)
% 6.78/1.96 % (924780)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2457517130:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.78/1.96 % (924780)Instruction limit reached!
% 6.78/1.96 % (924780)------------------------------
% 6.78/1.96 % (924780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.96 % (924780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.96 % (924780)CaDiCaL version: 2.1.3
% 6.78/1.96 % (924780)Termination reason: Instruction limit
% 6.78/1.96 % (924780)Termination phase: Saturation
% 6.78/1.96 % (924780)Time elapsed: 0.064 s
% 6.78/1.96 % (924780)Peak memory usage: 90 MB
% 6.78/1.96 % (924780)Instructions burned: 113 (million)
% 6.78/1.96 % (924778)Instruction limit reached!
% 6.78/1.96 % (924778)------------------------------
% 6.78/1.97 % (924778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.97 % (924778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.97 % (924778)CaDiCaL version: 2.1.3
% 6.78/1.97 % (924778)Termination reason: Instruction limit
% 6.78/1.97 % (924778)Termination phase: Saturation
% 6.78/1.97 % (924778)Time elapsed: 0.167 s
% 6.78/1.97 % (924778)Peak memory usage: 89 MB
% 6.78/1.97 % (924778)Instructions burned: 294 (million)
% 6.78/1.97 % (924757)First to succeed.
% 6.78/1.97 % (924757)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-924752"
% 6.78/1.97 % (924758)Also succeeded, but the first one will report.
% 6.78/1.97 % (924785)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=699886047:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 6.78/1.97 % (924785)Instruction limit reached!
% 6.78/1.97 % (924785)------------------------------
% 6.78/1.97 % (924785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.97 % (924785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.97 % (924785)CaDiCaL version: 2.1.3
% 6.78/1.97 % (924785)Termination reason: Instruction limit
% 6.78/1.97 % (924785)Termination phase: Saturation
% 6.78/1.97 % (924785)Time elapsed: 0.069 s
% 6.78/1.97 % (924785)Peak memory usage: 89 MB
% 6.78/1.97 % (924785)Instructions burned: 128 (million)
% 6.78/1.97 % (924786)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2154170888:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.78/1.97 % (924787)lrs+10_1_sil=8000:sp=occurrence:random_seed=2388020195:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.78/1.97 % (924786)Instruction limit reached!
% 6.78/1.97 % (924786)------------------------------
% 6.78/1.97 % (924786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/1.97 % (924786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/1.97 % (924786)CaDiCaL version: 2.1.3
% 6.78/1.97 % (924786)Termination reason: Instruction limit
% 6.78/1.97 % (924786)Termination phase: Saturation
% 6.78/1.97 % (924786)Time elapsed: 0.062 s
% 6.78/1.97 % (924786)Peak memory usage: 89 MB
% 6.78/1.97 % (924786)Instructions burned: 115 (million)
% 6.78/1.97 % (924757)Refutation found. Thanks to Tanya!
% 6.78/1.97 % SZS status Theorem for theBenchmark
% 6.78/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 8.24/2.08 % (924757)------------------------------
% 8.24/2.08 % (924757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.24/2.08 % (924757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.24/2.08 % (924757)CaDiCaL version: 2.1.3
% 8.24/2.08 % (924757)Termination reason: Refutation
% 8.24/2.08 % (924757)Time elapsed: 0.651 s
% 8.24/2.08 % (924757)Peak memory usage: 131 MB
% 8.24/2.08 % (924757)Instructions burned: 986 (million)
% 8.24/2.08 % (924757)------------------------------
% 8.24/2.08 % (924757)------------------------------
% 8.24/2.08 % (924752)Success in time 1.092 s
% 8.24/2.08 % Vampire exiting
%------------------------------------------------------------------------------