%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO603+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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:53:02 AM UTC 2026
% Result : Theorem 4.62s 1.53s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 19
% Syntax : Number of formulae : 115 ( 11 unt; 2 def)
% Number of atoms : 303 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 329 ( 141 ~; 136 |; 32 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 442 ( 0 sgn 426 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD5) ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( para(X0,X1,X2,X3)
& para(X2,X3,X4,X5) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD6) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X0,X1,X2,X3)
& perp(X2,X3,X4,X5) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4) )
=> cyclic(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& ~ coll(X2,X3,X0) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42a) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& coll(X2,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X5)
& eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
=> cong(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD43) ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X2,X1,X2)
& cong(X0,X3,X1,X3) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
fof(f67,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
fof(f87,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX11) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& para(X1,X2,X5,X4)
& coll(X5,X0,X2)
& circle(X6,X0,X4,X5) )
=> coll(X0,X6,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618065) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& para(X1,X2,X5,X4)
& coll(X5,X0,X2)
& circle(X6,X0,X4,X5) )
=> coll(X0,X6,X3) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f5]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ para(X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f6]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ para(X2,X3,X4,X5) ),
inference(flattening,[],[f104]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f108]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(ennf_transformation,[],[f17]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(flattening,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f19]) ).
fof(f125,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f21]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f39]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f40]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f41]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| coll(X2,X3,X0) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ coll(X2,X3,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ coll(X2,X3,X1) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) ),
inference(ennf_transformation,[],[f44]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) ),
inference(flattening,[],[f155]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(flattening,[],[f180]) ).
fof(f197,plain,
! [X0,X1,X2] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
? [X4] :
( perp(X4,X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(ennf_transformation,[],[f87]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ coll(X0,X6,X3)
& circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& para(X1,X2,X5,X4)
& coll(X5,X0,X2)
& circle(X6,X0,X4,X5) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ coll(X0,X6,X3)
& circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& para(X1,X2,X5,X4)
& coll(X5,X0,X2)
& circle(X6,X0,X4,X5) ),
inference(flattening,[],[f249]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( perp(sK11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X2,X3))],[f234]) ).
fof(f270,plain,
( ~ coll(sK20,sK26,sK23)
& circle(sK23,sK20,sK21,sK22)
& coll(sK24,sK20,sK21)
& para(sK21,sK22,sK25,sK24)
& coll(sK25,sK20,sK22)
& circle(sK26,sK20,sK24,sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25),skolemize(X6,sK26)],[f250]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f275,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f276,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f105]) ).
fof(f279,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f109]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f121]) ).
fof(f289,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(cnf_transformation,[],[f123]) ).
fof(f291,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
inference(cnf_transformation,[],[f125]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f310,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f149]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f312,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f313,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f314,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| cong(X0,X1,X3,X4) ),
inference(cnf_transformation,[],[f156]) ).
fof(f327,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f337,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f197]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( perp(sK11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f262]) ).
fof(f386,plain,
para(sK21,sK22,sK25,sK24),
inference(cnf_transformation,[],[f270]) ).
fof(f388,plain,
circle(sK23,sK20,sK21,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f389,plain,
~ coll(sK20,sK26,sK23),
inference(cnf_transformation,[],[f270]) ).
fof(f390,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(f391,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(f392,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,[],[f391]) ).
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(f412,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X0,X1)
| para(X2,X3,X2,X3) ),
inference(resolution,[],[f407,f309]) ).
fof(f416,definition,
( spl27_1
<=> ! [X2,X3] : para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f417,plain,
( ! [X2,X3] : para(X2,X3,X2,X3)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f419,definition,
( spl27_2
<=> ! [X0,X1] : ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f420,plain,
( ! [X0,X1] : ~ para(X0,X1,X0,X1)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f421,plain,
( spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f412,f419,f416]) ).
fof(f435,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(f439,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X1)
| cyclic(X1,X1,X0,X2)
| ~ coll(X0,X2,X1) ),
inference(resolution,[],[f435,f313]) ).
fof(f440,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X1)
| cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1) ),
inference(resolution,[],[f435,f312]) ).
fof(f449,plain,
para(sK25,sK24,sK21,sK22),
inference(resolution,[],[f275,f386]) ).
fof(f453,plain,
! [X0,X1] :
( ~ para(X0,X1,sK21,sK22)
| para(X0,X1,sK25,sK24) ),
inference(resolution,[],[f276,f386]) ).
fof(f456,plain,
para(sK25,sK24,sK25,sK24),
inference(resolution,[],[f453,f449]) ).
fof(f457,plain,
( $false
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f456,f420]) ).
fof(f458,plain,
~ spl27_2,
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f459,plain,
( ! [X2,X0,X1] :
( cyclic(X1,X1,X0,X2)
| coll(X0,X2,X1) )
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f440,f417]) ).
fof(f460,plain,
( ! [X2,X0,X1] :
( cyclic(X1,X1,X0,X2)
| ~ coll(X0,X2,X1) )
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f439,f417]) ).
fof(f461,plain,
( ! [X2,X0,X1] : cyclic(X1,X1,X0,X2)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f460,f459]) ).
fof(f471,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl27_1 ),
inference(resolution,[],[f461,f287]) ).
fof(f475,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f471,f461]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl27_1 ),
inference(resolution,[],[f475,f392]) ).
fof(f483,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) )
| ~ spl27_1 ),
inference(resolution,[],[f475,f390]) ).
fof(f484,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ para(X2,X0,X2,X3)
| cong(X0,X1,X3,X1) )
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f483,f475]) ).
fof(f485,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f481,f475]) ).
fof(f486,plain,
( ! [X2,X3,X0,X1] :
( ~ para(X2,X0,X2,X3)
| cong(X0,X1,X3,X1) )
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f484,f475]) ).
fof(f487,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f485,f475]) ).
fof(f488,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl27_1 ),
inference(resolution,[],[f487,f327]) ).
fof(f489,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f488,f487]) ).
fof(f513,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(f516,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ circle(X2,X1,X3,X4)
| para(X0,X0,X1,X2) )
| ~ spl27_1 ),
inference(resolution,[],[f513,f489]) ).
fof(f518,plain,
( ! [X0] : para(X0,X0,sK20,sK23)
| ~ spl27_1 ),
inference(resolution,[],[f516,f388]) ).
fof(f530,plain,
( ! [X0] : para(X0,X0,sK23,sK20)
| ~ spl27_1 ),
inference(resolution,[],[f518,f274]) ).
fof(f540,plain,
( ! [X0] : cong(sK23,X0,sK20,X0)
| ~ spl27_1 ),
inference(resolution,[],[f530,f486]) ).
fof(f579,plain,
( ! [X0,X1] :
( ~ cong(sK23,X0,sK20,X0)
| perp(sK23,sK20,X0,X1) )
| ~ spl27_1 ),
inference(resolution,[],[f540,f327]) ).
fof(f580,plain,
( ! [X0,X1] : perp(sK23,sK20,X0,X1)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f579,f540]) ).
fof(f581,plain,
( ! [X2,X3,X0,X1] :
( ~ perp(X0,X1,sK23,sK20)
| para(X0,X1,X2,X3) )
| ~ spl27_1 ),
inference(resolution,[],[f580,f279]) ).
fof(f584,plain,
( ! [X2,X0,X1] : para(X0,X0,X1,X2)
| ~ spl27_1 ),
inference(resolution,[],[f581,f489]) ).
fof(f592,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ para(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl27_1 ),
inference(resolution,[],[f584,f276]) ).
fof(f593,plain,
( ! [X2,X0,X1] : para(X0,X1,X2,X2)
| ~ spl27_1 ),
inference(resolution,[],[f584,f275]) ).
fof(f596,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f592,f593]) ).
fof(f599,plain,
( ! [X2,X0,X1] : coll(X0,X1,X2)
| ~ spl27_1 ),
inference(resolution,[],[f596,f337]) ).
fof(f604,plain,
( $false
| ~ spl27_1 ),
inference(resolution,[],[f599,f389]) ).
fof(f605,plain,
~ spl27_1,
inference(avatar_contradiction_clause,[],[f604]) ).
cnf(s1,plain,
( spl27_1
| spl27_2 ),
inference(sat_conversion,[],[f421]) ).
cnf(s2,plain,
~ spl27_2,
inference(sat_conversion,[],[f458]) ).
cnf(s3,plain,
~ spl27_1,
inference(sat_conversion,[],[f605]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f606,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO603+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 08:37:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 4.62/1.53 % (640725)Detected formulas, will run a generic FOF schedule.
% 4.62/1.53 % (640730)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=2973290518:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.62/1.53 % (640735)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3828131096:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.62/1.53 % (640732)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=2747796925:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.62/1.53 % (640734)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3922639114:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.62/1.53 % (640736)dis-21_1_sil=8000:lcm=predicate:random_seed=2297968292: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)
% 4.62/1.53 % (640731)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=467363452:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.62/1.53 % (640733)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3413756035:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.62/1.53 % (640735)Instruction limit reached!
% 4.62/1.53 % (640735)------------------------------
% 4.62/1.53 % (640735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640735)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640735)Termination reason: Instruction limit
% 4.62/1.53 % (640735)Termination phase: Saturation
% 4.62/1.53 % (640735)Time elapsed: 0.059 s
% 4.62/1.53 % (640735)Peak memory usage: 88 MB
% 4.62/1.53 % (640735)Instructions burned: 139 (million)
% 4.62/1.53 % (640733)Instruction limit reached!
% 4.62/1.53 % (640733)------------------------------
% 4.62/1.53 % (640733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640733)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640733)Termination reason: Instruction limit
% 4.62/1.53 % (640733)Termination phase: Saturation
% 4.62/1.53 % (640733)Time elapsed: 0.067 s
% 4.62/1.53 % (640733)Peak memory usage: 89 MB
% 4.62/1.53 % (640733)Instructions burned: 110 (million)
% 4.62/1.53 % (640734)Instruction limit reached!
% 4.62/1.53 % (640734)------------------------------
% 4.62/1.53 % (640734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640734)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640734)Termination reason: Instruction limit
% 4.62/1.53 % (640734)Termination phase: Saturation
% 4.62/1.53 % (640734)Time elapsed: 0.068 s
% 4.62/1.53 % (640734)Peak memory usage: 88 MB
% 4.62/1.53 % (640734)Instructions burned: 119 (million)
% 4.62/1.53 % (640736)Instruction limit reached!
% 4.62/1.53 % (640736)------------------------------
% 4.62/1.53 % (640736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640736)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640736)Termination reason: Instruction limit
% 4.62/1.53 % (640736)Termination phase: Saturation
% 4.62/1.53 % (640736)Time elapsed: 0.074 s
% 4.62/1.53 % (640736)Peak memory usage: 89 MB
% 4.62/1.53 % (640736)Instructions burned: 130 (million)
% 4.62/1.53 % (640744)lrs+10_1_sil=8000:sp=occurrence:random_seed=750083428:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.62/1.53 % (640745)lrs+10_1_sil=32000:urr=on:br=off:random_seed=918214448:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.62/1.53 % (640746)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3619642106:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.62/1.53 % (640747)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=1203566957:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.62/1.53 % (640745)Instruction limit reached!
% 4.62/1.53 % (640745)------------------------------
% 4.62/1.53 % (640745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640745)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640745)Termination reason: Instruction limit
% 4.62/1.53 % (640745)Termination phase: Saturation
% 4.62/1.53 % (640745)Time elapsed: 0.080 s
% 4.62/1.53 % (640745)Peak memory usage: 90 MB
% 4.62/1.53 % (640745)Instructions burned: 158 (million)
% 4.62/1.53 % (640730)First to succeed.
% 4.62/1.53 % (640730)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-640725"
% 4.62/1.53 % (640747)Instruction limit reached!
% 4.62/1.53 % (640747)------------------------------
% 4.62/1.53 % (640747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640747)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640747)Termination reason: Instruction limit
% 4.62/1.53 % (640747)Termination phase: Saturation
% 4.62/1.53 % (640747)Time elapsed: 0.134 s
% 4.62/1.53 % (640747)Peak memory usage: 90 MB
% 4.62/1.53 % (640747)Instructions burned: 249 (million)
% 4.62/1.53 % (640744)Instruction limit reached!
% 4.62/1.53 % (640744)------------------------------
% 4.62/1.53 % (640744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640744)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640744)Termination reason: Instruction limit
% 4.62/1.53 % (640744)Termination phase: Saturation
% 4.62/1.53 % (640744)Time elapsed: 0.183 s
% 4.62/1.53 % (640744)Peak memory usage: 92 MB
% 4.62/1.53 % (640744)Instructions burned: 285 (million)
% 4.62/1.53 % (640746)Instruction limit reached!
% 4.62/1.53 % (640746)------------------------------
% 4.62/1.53 % (640746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.62/1.53 % (640746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.62/1.53 % (640746)CaDiCaL version: 2.1.3
% 4.62/1.53 % (640746)Termination reason: Instruction limit
% 4.62/1.53 % (640746)Termination phase: Saturation
% 4.62/1.53 % (640746)Time elapsed: 0.191 s
% 4.62/1.53 % (640746)Peak memory usage: 91 MB
% 4.62/1.53 % (640746)Instructions burned: 326 (million)
% 4.62/1.53 % (640752)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=311531717:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.62/1.53 % (640730)Refutation found. Thanks to Tanya!
% 4.62/1.53 % SZS status Theorem for theBenchmark
% 4.62/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.38/1.72 % (640730)------------------------------
% 5.38/1.72 % (640730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.72 % (640730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.72 % (640730)CaDiCaL version: 2.1.3
% 5.38/1.72 % (640730)Termination reason: Refutation
% 5.38/1.72 % (640730)Time elapsed: 0.383 s
% 5.38/1.72 % (640730)Peak memory usage: 131 MB
% 5.38/1.72 % (640730)Instructions burned: 1001 (million)
% 5.38/1.72 % (640730)------------------------------
% 5.38/1.72 % (640730)------------------------------
% 5.38/1.72 % (640725)Success in time 0.672 s
% 5.38/1.72 % Vampire exiting
%------------------------------------------------------------------------------