%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO611+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 : n004.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 09:53:03 AM UTC 2026
% Result : Theorem 6.74s 2.05s
% Output : Refutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 19
% Syntax : Number of formulae : 128 ( 15 unt; 2 def)
% Number of atoms : 330 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 342 ( 140 ~; 136 |; 46 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 436 ( 0 sgn 416 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X2,X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD5) ).
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(f14,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X1,X0,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
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(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(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X8)
& perp(X5,X4,X0,X2)
& coll(X5,X0,X2)
& perp(X6,X4,X0,X1)
& coll(X6,X0,X1)
& circle(X3,X4,X7,X9)
& coll(X7,X4,X6) )
=> para(X6,X5,X7,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL618073) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X8)
& perp(X5,X4,X0,X2)
& coll(X5,X0,X2)
& perp(X6,X4,X0,X1)
& coll(X6,X0,X1)
& circle(X3,X4,X7,X9)
& coll(X7,X4,X6) )
=> para(X6,X5,X7,X2) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ para(X6,X5,X7,X2)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X8)
& perp(X5,X4,X0,X2)
& coll(X5,X0,X2)
& perp(X6,X4,X0,X1)
& coll(X6,X0,X1)
& circle(X3,X4,X7,X9)
& coll(X7,X4,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ para(X6,X5,X7,X2)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X8)
& perp(X5,X4,X0,X2)
& coll(X5,X0,X2)
& perp(X6,X4,X0,X1)
& coll(X6,X0,X1)
& circle(X3,X4,X7,X9)
& coll(X7,X4,X6) ),
inference(flattening,[],[f98]) ).
fof(f113,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(f114,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(f117,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(f118,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f117]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f5]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f156,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(f164,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(f165,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,[],[f164]) ).
fof(f166,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(f167,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,[],[f166]) ).
fof(f168,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(f169,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,[],[f168]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f41]) ).
fof(f171,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(f172,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(flattening,[],[f171]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f16]) ).
fof(f174,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f14]) ).
fof(f211,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(f212,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(flattening,[],[f211]) ).
fof(f220,plain,
( ~ para(sK6,sK5,sK7,sK2)
& circle(sK3,sK0,sK1,sK2)
& circle(sK3,sK0,sK4,sK8)
& perp(sK5,sK4,sK0,sK2)
& coll(sK5,sK0,sK2)
& perp(sK6,sK4,sK0,sK1)
& coll(sK6,sK0,sK1)
& circle(sK3,sK4,sK7,sK9)
& coll(sK7,sK4,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8),skolemize(X9,sK9)],[f99]) ).
fof(f244,plain,
perp(sK5,sK4,sK0,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f247,plain,
~ para(sK6,sK5,sK7,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f257,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f113]) ).
fof(f258,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f114]) ).
fof(f260,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,[],[f118]) ).
fof(f262,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f263,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f275,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
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,[],[f156]) ).
fof(f295,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) ),
inference(cnf_transformation,[],[f165]) ).
fof(f296,plain,
! [X2,X3,X0,X1] :
( ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f167]) ).
fof(f297,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,[],[f169]) ).
fof(f298,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f299,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f172]) ).
fof(f300,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f173]) ).
fof(f301,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f174]) ).
fof(f302,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f175]) ).
fof(f330,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f212]) ).
fof(f336,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK5,sK4)
| para(X0,X1,sK0,sK2) ),
inference(resolution,[],[f244,f260]) ).
fof(f338,plain,
perp(sK0,sK2,sK5,sK4),
inference(resolution,[],[f275,f244]) ).
fof(f342,plain,
para(sK0,sK2,sK0,sK2),
inference(resolution,[],[f338,f336]) ).
fof(f416,plain,
para(sK0,sK2,sK2,sK0),
inference(resolution,[],[f263,f342]) ).
fof(f420,plain,
para(sK2,sK0,sK0,sK2),
inference(resolution,[],[f416,f262]) ).
fof(f424,plain,
para(sK2,sK0,sK2,sK0),
inference(resolution,[],[f420,f263]) ).
fof(f433,plain,
! [X0,X1] : eqangle(sK2,sK0,X0,X1,sK2,sK0,X0,X1),
inference(resolution,[],[f424,f257]) ).
fof(f446,plain,
! [X0,X1] : eqangle(X0,X1,sK2,sK0,X0,X1,sK2,sK0),
inference(resolution,[],[f433,f289]) ).
fof(f449,plain,
! [X0] :
( cyclic(sK0,X0,sK2,sK2)
| coll(sK2,sK2,sK0) ),
inference(resolution,[],[f433,f297]) ).
fof(f451,definition,
( spl28_5
<=> coll(sK2,sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl28_5])],[avatar_definition]) ).
fof(f452,plain,
( coll(sK2,sK2,sK0)
| ~ spl28_5 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f454,definition,
( spl28_6
<=> ! [X0] : cyclic(sK0,X0,sK2,sK2) ),
introduced(definition,[new_symbols(definition,[spl28_6])],[avatar_definition]) ).
fof(f455,plain,
( ! [X0] : cyclic(sK0,X0,sK2,sK2)
| ~ spl28_6 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f456,plain,
( spl28_5
| spl28_6 ),
inference(avatar_split_clause,[],[f449,f454,f451]) ).
fof(f457,plain,
( ! [X0] :
( ~ eqangle(sK2,X0,sK2,sK0,sK2,X0,sK2,sK0)
| cyclic(X0,sK0,sK2,sK2) )
| ~ spl28_5 ),
inference(resolution,[],[f452,f296]) ).
fof(f458,plain,
( ! [X0] : cyclic(X0,sK0,sK2,sK2)
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f457,f446]) ).
fof(f460,plain,
( ! [X0] : cyclic(X0,sK2,sK0,sK2)
| ~ spl28_5 ),
inference(resolution,[],[f458,f301]) ).
fof(f470,plain,
( ! [X0,X1] :
( ~ cyclic(sK0,X0,sK2,X1)
| cyclic(X0,sK2,X1,sK2) )
| ~ spl28_6 ),
inference(resolution,[],[f455,f299]) ).
fof(f472,plain,
( ! [X0] : cyclic(X0,sK2,sK2,sK0)
| ~ spl28_5 ),
inference(resolution,[],[f460,f302]) ).
fof(f480,plain,
( ! [X0] : cyclic(sK2,X0,sK2,sK0)
| ~ spl28_5 ),
inference(resolution,[],[f472,f300]) ).
fof(f507,plain,
( ! [X0] : cyclic(sK2,sK2,X0,sK0)
| ~ spl28_5 ),
inference(resolution,[],[f480,f301]) ).
fof(f512,plain,
( ! [X0] : cyclic(sK2,sK2,sK0,X0)
| ~ spl28_5 ),
inference(resolution,[],[f507,f302]) ).
fof(f522,plain,
( ! [X0,X1] :
( ~ cyclic(sK2,sK2,sK0,X0)
| cyclic(sK2,sK0,X0,X1) )
| ~ spl28_5 ),
inference(resolution,[],[f512,f299]) ).
fof(f525,plain,
( ! [X0,X1] : cyclic(sK2,sK0,X0,X1)
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f522,f512]) ).
fof(f531,plain,
( ! [X2,X0,X1] :
( ~ cyclic(sK2,sK0,X0,X1)
| cyclic(sK0,X0,X1,X2) )
| ~ spl28_5 ),
inference(resolution,[],[f525,f299]) ).
fof(f534,plain,
( ! [X2,X0,X1] : cyclic(sK0,X0,X1,X2)
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f531,f525]) ).
fof(f540,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(sK0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl28_5 ),
inference(resolution,[],[f534,f299]) ).
fof(f543,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f540,f534]) ).
fof(f548,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl28_5 ),
inference(resolution,[],[f543,f298]) ).
fof(f550,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
| ~ spl28_5 ),
inference(resolution,[],[f543,f295]) ).
fof(f551,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f550,f543]) ).
fof(f552,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f551,f543]) ).
fof(f553,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl28_5 ),
inference(resolution,[],[f548,f258]) ).
fof(f567,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3)
| ~ spl28_5 ),
inference(resolution,[],[f553,f257]) ).
fof(f604,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl28_5 ),
inference(resolution,[],[f552,f567]) ).
fof(f605,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl28_5 ),
inference(resolution,[],[f604,f330]) ).
fof(f609,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f605,f604]) ).
fof(f611,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl28_5 ),
inference(resolution,[],[f609,f275]) ).
fof(f615,plain,
( $false
| ~ spl28_5 ),
inference(unit_resulting_resolution,[],[f260,f247,f609,f611]) ).
fof(f619,plain,
~ spl28_5,
inference(avatar_contradiction_clause,[],[f615]) ).
fof(f632,plain,
( ! [X0] : cyclic(X0,sK2,sK2,sK2)
| ~ spl28_6 ),
inference(resolution,[],[f470,f455]) ).
fof(f637,plain,
( ! [X0] : cyclic(sK2,X0,sK2,sK2)
| ~ spl28_6 ),
inference(resolution,[],[f632,f300]) ).
fof(f643,plain,
( ! [X0] : cyclic(sK2,sK2,X0,sK2)
| ~ spl28_6 ),
inference(resolution,[],[f637,f301]) ).
fof(f648,plain,
( ! [X0] : cyclic(sK2,sK2,sK2,X0)
| ~ spl28_6 ),
inference(resolution,[],[f643,f302]) ).
fof(f658,plain,
( ! [X0,X1] :
( ~ cyclic(sK2,sK2,sK2,X0)
| cyclic(sK2,sK2,X0,X1) )
| ~ spl28_6 ),
inference(resolution,[],[f648,f299]) ).
fof(f661,plain,
( ! [X0,X1] : cyclic(sK2,sK2,X0,X1)
| ~ spl28_6 ),
inference(forward_subsumption_resolution,[],[f658,f648]) ).
fof(f667,plain,
( ! [X2,X0,X1] :
( ~ cyclic(sK2,sK2,X0,X1)
| cyclic(sK2,X0,X1,X2) )
| ~ spl28_6 ),
inference(resolution,[],[f661,f299]) ).
fof(f670,plain,
( ! [X2,X0,X1] : cyclic(sK2,X0,X1,X2)
| ~ spl28_6 ),
inference(forward_subsumption_resolution,[],[f667,f661]) ).
fof(f676,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(sK2,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl28_6 ),
inference(resolution,[],[f670,f299]) ).
fof(f679,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl28_6 ),
inference(forward_subsumption_resolution,[],[f676,f670]) ).
fof(f684,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl28_6 ),
inference(resolution,[],[f679,f298]) ).
fof(f686,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
| ~ spl28_6 ),
inference(resolution,[],[f679,f295]) ).
fof(f688,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
| ~ spl28_6 ),
inference(forward_subsumption_resolution,[],[f686,f679]) ).
fof(f689,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl28_6 ),
inference(forward_subsumption_resolution,[],[f688,f679]) ).
fof(f697,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl28_6 ),
inference(resolution,[],[f684,f258]) ).
fof(f711,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3)
| ~ spl28_6 ),
inference(resolution,[],[f697,f257]) ).
fof(f742,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl28_6 ),
inference(resolution,[],[f689,f711]) ).
fof(f743,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl28_6 ),
inference(resolution,[],[f742,f330]) ).
fof(f749,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl28_6 ),
inference(forward_subsumption_resolution,[],[f743,f742]) ).
fof(f751,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl28_6 ),
inference(resolution,[],[f749,f275]) ).
fof(f760,plain,
( $false
| ~ spl28_6 ),
inference(unit_resulting_resolution,[],[f260,f247,f749,f751]) ).
fof(f764,plain,
~ spl28_6,
inference(avatar_contradiction_clause,[],[f760]) ).
cnf(s4,plain,
( spl28_5
| spl28_6 ),
inference(sat_conversion,[],[f456]) ).
cnf(s6,plain,
~ spl28_5,
inference(sat_conversion,[],[f619]) ).
cnf(s7,plain,
~ spl28_6,
inference(sat_conversion,[],[f764]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s4,s7,s6]) ).
fof(f765,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO611+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n004.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 08:38:22 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 6.74/2.05 % (3203432)Detected formulas, will run a generic FOF schedule.
% 6.74/2.05 % (3203539)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=3223508562:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.74/2.05 % (3203538)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=2617041168:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.74/2.05 % (3203540)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=2049776266:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.74/2.05 % (3203541)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1860848388:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.74/2.05 % (3203544)dis-21_1_sil=8000:lcm=predicate:random_seed=1663211831: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)
% 6.74/2.05 % (3203542)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2721712465:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.74/2.05 % (3203543)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=303958051:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.74/2.05 % (3203542)Instruction limit reached!
% 6.74/2.05 % (3203542)------------------------------
% 6.74/2.05 % (3203542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203542)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203542)Termination reason: Instruction limit
% 6.74/2.05 % (3203542)Termination phase: Saturation
% 6.74/2.05 % (3203542)Time elapsed: 0.081 s
% 6.74/2.05 % (3203542)Peak memory usage: 88 MB
% 6.74/2.05 % (3203542)Instructions burned: 120 (million)
% 6.74/2.05 % (3203544)Instruction limit reached!
% 6.74/2.05 % (3203544)------------------------------
% 6.74/2.05 % (3203544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203544)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203544)Termination reason: Instruction limit
% 6.74/2.05 % (3203544)Termination phase: Saturation
% 6.74/2.05 % (3203544)Time elapsed: 0.088 s
% 6.74/2.05 % (3203544)Peak memory usage: 89 MB
% 6.74/2.05 % (3203544)Instructions burned: 130 (million)
% 6.74/2.05 % (3203541)Instruction limit reached!
% 6.74/2.05 % (3203541)------------------------------
% 6.74/2.05 % (3203541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203541)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203541)Termination reason: Instruction limit
% 6.74/2.05 % (3203541)Termination phase: Saturation
% 6.74/2.05 % (3203541)Time elapsed: 0.091 s
% 6.74/2.05 % (3203541)Peak memory usage: 89 MB
% 6.74/2.05 % (3203541)Instructions burned: 109 (million)
% 6.74/2.05 % (3203543)Instruction limit reached!
% 6.74/2.05 % (3203543)------------------------------
% 6.74/2.05 % (3203543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203543)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203543)Termination reason: Instruction limit
% 6.74/2.05 % (3203543)Termination phase: Saturation
% 6.74/2.05 % (3203543)Time elapsed: 0.135 s
% 6.74/2.05 % (3203543)Peak memory usage: 90 MB
% 6.74/2.05 % (3203543)Instructions burned: 139 (million)
% 6.74/2.05 % (3203579)lrs+10_1_sil=8000:sp=occurrence:random_seed=737211043:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.74/2.05 % (3203581)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1664350392:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.74/2.05 % (3203582)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=2157665853:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.74/2.05 % (3203580)lrs+10_1_sil=32000:urr=on:br=off:random_seed=298951869:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.74/2.05 % (3203580)Instruction limit reached!
% 6.74/2.05 % (3203580)------------------------------
% 6.74/2.05 % (3203580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203580)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203580)Termination reason: Instruction limit
% 6.74/2.05 % (3203580)Termination phase: Saturation
% 6.74/2.05 % (3203580)Time elapsed: 0.150 s
% 6.74/2.05 % (3203580)Peak memory usage: 90 MB
% 6.74/2.05 % (3203580)Instructions burned: 158 (million)
% 6.74/2.05 % (3203582)Instruction limit reached!
% 6.74/2.05 % (3203582)------------------------------
% 6.74/2.05 % (3203582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203582)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203582)Termination reason: Instruction limit
% 6.74/2.05 % (3203582)Termination phase: Saturation
% 6.74/2.05 % (3203582)Time elapsed: 0.222 s
% 6.74/2.05 % (3203582)Peak memory usage: 90 MB
% 6.74/2.05 % (3203582)Instructions burned: 248 (million)
% 6.74/2.05 % (3203539)First to succeed.
% 6.74/2.05 % (3203539)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3203432"
% 6.74/2.05 % (3203579)Instruction limit reached!
% 6.74/2.05 % (3203579)------------------------------
% 6.74/2.05 % (3203579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203579)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203579)Termination reason: Instruction limit
% 6.74/2.05 % (3203579)Termination phase: Saturation
% 6.74/2.05 % (3203579)Time elapsed: 0.302 s
% 6.74/2.05 % (3203579)Peak memory usage: 92 MB
% 6.74/2.05 % (3203579)Instructions burned: 285 (million)
% 6.74/2.05 % (3203581)Instruction limit reached!
% 6.74/2.05 % (3203581)------------------------------
% 6.74/2.05 % (3203581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203581)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203581)Termination reason: Instruction limit
% 6.74/2.05 % (3203581)Termination phase: Saturation
% 6.74/2.05 % (3203581)Time elapsed: 0.358 s
% 6.74/2.05 % (3203581)Peak memory usage: 92 MB
% 6.74/2.05 % (3203581)Instructions burned: 326 (million)
% 6.74/2.05 % (3203599)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3930963458:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 6.74/2.05 % (3203600)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=50448066:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 6.74/2.05 % (3203599)Instruction limit reached!
% 6.74/2.05 % (3203599)------------------------------
% 6.74/2.05 % (3203599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.74/2.05 % (3203599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.74/2.05 % (3203599)CaDiCaL version: 2.1.3
% 6.74/2.05 % (3203599)Termination reason: Instruction limit
% 6.74/2.05 % (3203599)Termination phase: Saturation
% 6.74/2.05 % (3203599)Time elapsed: 0.144 s
% 6.74/2.05 % (3203599)Peak memory usage: 89 MB
% 6.74/2.05 % (3203599)Instructions burned: 296 (million)
% 6.74/2.05 % (3203601)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3391957748:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 6.74/2.05 % (3203604)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1986054923:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 6.74/2.05 % (3203539)Refutation found. Thanks to Tanya!
% 6.74/2.05 % SZS status Theorem for theBenchmark
% 6.74/2.05 % SZS output start Proof for theBenchmark
% See solution above
% 8.76/2.25 % (3203539)------------------------------
% 8.76/2.25 % (3203539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.76/2.25 % (3203539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.76/2.25 % (3203539)CaDiCaL version: 2.1.3
% 8.76/2.25 % (3203539)Termination reason: Refutation
% 8.76/2.25 % (3203539)Time elapsed: 0.638 s
% 8.76/2.25 % (3203539)Peak memory usage: 131 MB
% 8.76/2.25 % (3203539)Instructions burned: 1050 (million)
% 8.76/2.25 % (3203539)------------------------------
% 8.76/2.25 % (3203539)------------------------------
% 8.76/2.25 % (3203432)Success in time 1.176 s
% 8.76/2.25 % Vampire exiting
%------------------------------------------------------------------------------