%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO630+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 : n018.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 09:53:06 AM UTC 2026
% Result : Theorem 5.55s 1.60s
% Output : Refutation 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 20
% Syntax : Number of formulae : 118 ( 11 unt; 2 def)
% Number of atoms : 340 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 357 ( 135 ~; 132 |; 69 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 12 con; 0-0 aty)
% Number of variables : 437 ( 0 sgn 413 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD7) ).
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(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(f58,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X2,X1,X2)
& cong(X0,X3,X1,X3)
& cyclic(X0,X1,X2,X3) )
=> perp(X2,X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD57) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& circle(X3,X4,X5,X11)
& coll(X5,X4,X3)
& perp(X6,X5,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X4,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X4,X0,X2)
& coll(X9,X0,X2) )
=> perp(X8,X9,X7,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110993) ).
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,X10)
& circle(X3,X4,X5,X11)
& coll(X5,X4,X3)
& perp(X6,X5,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X4,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X4,X0,X2)
& coll(X9,X0,X2) )
=> perp(X8,X9,X7,X6) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ perp(X8,X9,X7,X6)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& circle(X3,X4,X5,X11)
& coll(X5,X4,X3)
& perp(X6,X5,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X4,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X4,X0,X2)
& coll(X9,X0,X2) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ perp(X8,X9,X7,X6)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& circle(X3,X4,X5,X11)
& coll(X5,X4,X3)
& perp(X6,X5,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X4,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X4,X0,X2)
& coll(X9,X0,X2) ),
inference(flattening,[],[f98]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f7]) ).
fof(f137,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(f141,plain,
! [X0,X1,X2,X3] :
( perp(X2,X0,X0,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f58]) ).
fof(f142,plain,
! [X0,X1,X2,X3] :
( perp(X2,X0,X0,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(flattening,[],[f141]) ).
fof(f145,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(f146,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,[],[f145]) ).
fof(f147,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(f148,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,[],[f147]) ).
fof(f149,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(f150,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,[],[f149]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f41]) ).
fof(f152,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(f153,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(flattening,[],[f152]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f16]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f14]) ).
fof(f170,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(f171,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(f172,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(f173,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f172]) ).
fof(f174,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(f175,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f174]) ).
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,
( ~ perp(sK8,sK9,sK7,sK6)
& circle(sK3,sK0,sK1,sK2)
& circle(sK3,sK0,sK4,sK10)
& circle(sK3,sK4,sK5,sK11)
& coll(sK5,sK4,sK3)
& perp(sK6,sK5,sK0,sK2)
& coll(sK6,sK0,sK2)
& perp(sK7,sK5,sK0,sK1)
& coll(sK7,sK0,sK1)
& perp(sK8,sK4,sK0,sK1)
& coll(sK8,sK0,sK1)
& perp(sK9,sK4,sK0,sK2)
& coll(sK9,sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11]),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),skolemize(X10,sK10),skolemize(X11,sK11)],[f99]) ).
fof(f244,plain,
perp(sK7,sK5,sK0,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f251,plain,
~ perp(sK8,sK9,sK7,sK6),
inference(cnf_transformation,[],[f220]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f267,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f115]) ).
fof(f280,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,[],[f137]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X2,X0,X0,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f286,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,[],[f146]) ).
fof(f287,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,[],[f148]) ).
fof(f288,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,[],[f150]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f290,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f153]) ).
fof(f291,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f154]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f155]) ).
fof(f293,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f156]) ).
fof(f304,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f170]) ).
fof(f305,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f171]) ).
fof(f306,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,[],[f173]) ).
fof(f307,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,[],[f175]) ).
fof(f334,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(f341,plain,
perp(sK0,sK1,sK7,sK5),
inference(resolution,[],[f244,f266]) ).
fof(f342,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK7,sK5)
| para(X0,X1,sK0,sK1) ),
inference(resolution,[],[f244,f307]) ).
fof(f348,plain,
para(sK0,sK1,sK0,sK1),
inference(resolution,[],[f342,f341]) ).
fof(f349,plain,
! [X0,X1] : eqangle(sK0,sK1,X0,X1,sK0,sK1,X0,X1),
inference(resolution,[],[f348,f304]) ).
fof(f394,plain,
! [X0] :
( cyclic(sK1,X0,sK0,sK0)
| coll(sK0,sK0,sK1) ),
inference(resolution,[],[f349,f288]) ).
fof(f396,definition,
( spl30_1
<=> coll(sK0,sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl30_1])],[avatar_definition]) ).
fof(f397,plain,
( coll(sK0,sK0,sK1)
| ~ spl30_1 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f399,definition,
( spl30_2
<=> ! [X0] : cyclic(sK1,X0,sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f400,plain,
( ! [X0] : cyclic(sK1,X0,sK0,sK0)
| ~ spl30_2 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f401,plain,
( spl30_1
| spl30_2 ),
inference(avatar_split_clause,[],[f394,f399,f396]) ).
fof(f419,plain,
! [X0,X1] : eqangle(X0,X1,sK0,sK1,X0,X1,sK0,sK1),
inference(resolution,[],[f280,f349]) ).
fof(f430,plain,
( ! [X0] : cyclic(X0,sK1,sK0,sK0)
| ~ spl30_2 ),
inference(resolution,[],[f291,f400]) ).
fof(f481,plain,
( ! [X0] : cyclic(X0,sK0,sK1,sK0)
| ~ spl30_2 ),
inference(resolution,[],[f430,f292]) ).
fof(f498,plain,
( ! [X0] : cyclic(X0,sK0,sK0,sK1)
| ~ spl30_2 ),
inference(resolution,[],[f481,f293]) ).
fof(f506,plain,
( ! [X0] : cyclic(sK0,X0,sK0,sK1)
| ~ spl30_2 ),
inference(resolution,[],[f498,f291]) ).
fof(f527,plain,
( ! [X0] : cyclic(sK0,sK0,X0,sK1)
| ~ spl30_2 ),
inference(resolution,[],[f506,f292]) ).
fof(f533,plain,
( ! [X0] : cyclic(sK0,sK0,sK1,X0)
| ~ spl30_2 ),
inference(resolution,[],[f527,f293]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ cyclic(sK0,sK0,sK1,X0)
| cyclic(sK0,sK1,X0,X1) )
| ~ spl30_2 ),
inference(resolution,[],[f533,f290]) ).
fof(f545,plain,
( ! [X0,X1] : cyclic(sK0,sK1,X0,X1)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f544,f533]) ).
fof(f553,plain,
( ! [X2,X0,X1] :
( ~ cyclic(sK0,sK1,X0,X1)
| cyclic(sK1,X0,X1,X2) )
| ~ spl30_2 ),
inference(resolution,[],[f545,f290]) ).
fof(f554,plain,
( ! [X2,X0,X1] : cyclic(sK1,X0,X1,X2)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f553,f545]) ).
fof(f563,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(sK1,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl30_2 ),
inference(resolution,[],[f554,f290]) ).
fof(f565,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f563,f554]) ).
fof(f571,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl30_2 ),
inference(resolution,[],[f565,f289]) ).
fof(f572,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) )
| ~ spl30_2 ),
inference(resolution,[],[f565,f286]) ).
fof(f577,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) )
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f572,f565]) ).
fof(f578,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f577,f565]) ).
fof(f580,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl30_2 ),
inference(resolution,[],[f571,f305]) ).
fof(f601,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3)
| ~ spl30_2 ),
inference(resolution,[],[f580,f304]) ).
fof(f637,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl30_2 ),
inference(resolution,[],[f578,f601]) ).
fof(f638,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X1,X0,X0,X2)
| ~ cyclic(X0,X0,X1,X2) )
| ~ spl30_2 ),
inference(resolution,[],[f637,f284]) ).
fof(f639,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl30_2 ),
inference(resolution,[],[f637,f334]) ).
fof(f645,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f639,f637]) ).
fof(f646,plain,
( ! [X2,X0,X1] :
( perp(X1,X0,X0,X2)
| ~ cyclic(X0,X0,X1,X2) )
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f638,f637]) ).
fof(f647,plain,
( ! [X2,X0,X1] : perp(X1,X0,X0,X2)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f646,f565]) ).
fof(f651,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ para(X0,X1,X2,X2)
| perp(X0,X1,X3,X4) )
| ~ spl30_2 ),
inference(resolution,[],[f645,f306]) ).
fof(f657,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X0)
| ~ spl30_2 ),
inference(resolution,[],[f647,f266]) ).
fof(f658,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X3)
| para(X0,X1,X3,X4) )
| ~ spl30_2 ),
inference(resolution,[],[f647,f307]) ).
fof(f672,plain,
( ! [X2,X0,X1] : perp(X0,X1,X0,X2)
| ~ spl30_2 ),
inference(resolution,[],[f657,f267]) ).
fof(f717,plain,
( ! [X2,X3,X0,X1] : para(X0,X1,X2,X3)
| ~ spl30_2 ),
inference(resolution,[],[f658,f672]) ).
fof(f739,plain,
( $false
| ~ spl30_2 ),
inference(unit_resulting_resolution,[],[f651,f251,f717]) ).
fof(f758,plain,
~ spl30_2,
inference(avatar_contradiction_clause,[],[f739]) ).
fof(f766,plain,
( ! [X0] :
( ~ eqangle(sK0,X0,sK0,sK1,sK0,X0,sK0,sK1)
| cyclic(X0,sK1,sK0,sK0) )
| ~ spl30_1 ),
inference(resolution,[],[f397,f287]) ).
fof(f767,plain,
( ! [X0] : cyclic(X0,sK1,sK0,sK0)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f766,f419]) ).
fof(f770,plain,
( ! [X0] : cyclic(sK1,X0,sK0,sK0)
| ~ spl30_1 ),
inference(resolution,[],[f767,f291]) ).
fof(f775,plain,
( spl30_2
| ~ spl30_1 ),
inference(avatar_split_clause,[],[f770,f396,f399]) ).
cnf(s1,plain,
( spl30_1
| spl30_2 ),
inference(sat_conversion,[],[f401]) ).
cnf(s10,plain,
~ spl30_2,
inference(sat_conversion,[],[f758]) ).
cnf(s11,plain,
( ~ spl30_1
| spl30_2 ),
inference(sat_conversion,[],[f775]) ).
cnf(s12,plain,
~ spl30_1,
inference(rat,[],[s11,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s10,s12]) ).
fof(f776,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO630+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 : n018.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 08:42:39 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
% 4.35/1.60 % (2033950)Detected formulas, will run a generic FOF schedule.
% 4.35/1.60 % (2033956)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=2712936518:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.35/1.60 % (2033957)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=2150068829:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.35/1.60 % (2033960)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3310015478:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.35/1.60 % (2033955)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=1803717537:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.35/1.60 % (2033959)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3651984473:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.35/1.60 % (2033961)dis-21_1_sil=8000:lcm=predicate:random_seed=4148119047: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)
% 4.35/1.60 % (2033958)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1964149712:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.35/1.60 % (2033958)Refutation not found, incomplete strategy
% 4.35/1.60 % (2033958)------------------------------
% 4.35/1.60 % (2033958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.60 % (2033958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.60 % (2033958)CaDiCaL version: 2.1.3
% 4.35/1.60 % (2033958)Termination reason: Refutation not found, incomplete strategy
% 4.35/1.60 % (2033958)Time elapsed: 0.028 s
% 4.35/1.60 % (2033958)Peak memory usage: 88 MB
% 4.35/1.60 % (2033958)Instructions burned: 50 (million)
% 4.35/1.60 % (2033959)Instruction limit reached!
% 4.35/1.60 % (2033959)------------------------------
% 4.35/1.60 % (2033959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.60 % (2033959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.60 % (2033959)CaDiCaL version: 2.1.3
% 4.35/1.60 % (2033959)Termination reason: Instruction limit
% 4.35/1.60 % (2033959)Termination phase: Saturation
% 4.35/1.60 % (2033959)Time elapsed: 0.070 s
% 4.35/1.60 % (2033959)Peak memory usage: 88 MB
% 4.35/1.60 % (2033959)Instructions burned: 119 (million)
% 4.35/1.60 % (2033961)Instruction limit reached!
% 4.35/1.60 % (2033961)------------------------------
% 4.35/1.60 % (2033961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.60 % (2033961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.60 % (2033961)CaDiCaL version: 2.1.3
% 4.35/1.60 % (2033961)Termination reason: Instruction limit
% 4.35/1.60 % (2033961)Termination phase: Saturation
% 4.35/1.60 % (2033961)Time elapsed: 0.077 s
% 4.35/1.60 % (2033961)Peak memory usage: 89 MB
% 4.35/1.60 % (2033961)Instructions burned: 130 (million)
% 4.35/1.60 % (2033960)Instruction limit reached!
% 4.35/1.60 % (2033960)------------------------------
% 4.35/1.60 % (2033960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.60 % (2033960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.60 % (2033960)CaDiCaL version: 2.1.3
% 5.55/1.60 % (2033960)Termination reason: Instruction limit
% 5.55/1.60 % (2033960)Termination phase: Saturation
% 5.55/1.60 % (2033960)Time elapsed: 0.093 s
% 5.55/1.60 % (2033960)Peak memory usage: 90 MB
% 5.55/1.60 % (2033960)Instructions burned: 140 (million)
% 5.55/1.60 % (2033969)lrs+10_1_sil=8000:sp=occurrence:random_seed=1880546531:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.55/1.60 % (2033970)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3525854329:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.55/1.60 % (2033971)lrs+1011_1_sil=32000:sp=occurrence:random_seed=343271641:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.55/1.60 % (2033958)------------------------------
% 5.55/1.60 % (2033958)------------------------------
% 5.55/1.60 % (2033970)Instruction limit reached!
% 5.55/1.60 % (2033970)------------------------------
% 5.55/1.60 % (2033970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.60 % (2033970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.60 % (2033970)CaDiCaL version: 2.1.3
% 5.55/1.60 % (2033970)Termination reason: Instruction limit
% 5.55/1.60 % (2033970)Termination phase: Saturation
% 5.55/1.60 % (2033970)Time elapsed: 0.079 s
% 5.55/1.60 % (2033970)Peak memory usage: 89 MB
% 5.55/1.60 % (2033970)Instructions burned: 158 (million)
% 5.55/1.60 % (2033969)Instruction limit reached!
% 5.55/1.60 % (2033969)------------------------------
% 5.55/1.60 % (2033969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.60 % (2033969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.60 % (2033969)CaDiCaL version: 2.1.3
% 5.55/1.60 % (2033969)Termination reason: Instruction limit
% 5.55/1.60 % (2033969)Termination phase: Saturation
% 5.55/1.60 % (2033969)Time elapsed: 0.181 s
% 5.55/1.60 % (2033969)Peak memory usage: 93 MB
% 5.55/1.60 % (2033969)Instructions burned: 285 (million)
% 5.55/1.60 % (2033956)First to succeed.
% 5.55/1.60 % (2033956)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2033950"
% 5.55/1.60 % (2033976)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2550812345:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.55/1.60 % (2033975)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=2443199170:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.55/1.60 % (2033971)Instruction limit reached!
% 5.55/1.60 % (2033971)------------------------------
% 5.55/1.60 % (2033971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.60 % (2033971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.60 % (2033971)CaDiCaL version: 2.1.3
% 5.55/1.60 % (2033971)Termination reason: Instruction limit
% 5.55/1.60 % (2033971)Termination phase: Saturation
% 5.55/1.60 % (2033971)Time elapsed: 0.211 s
% 5.55/1.60 % (2033971)Peak memory usage: 92 MB
% 5.55/1.60 % (2033971)Instructions burned: 326 (million)
% 5.55/1.60 % (2033977)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3385602327:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.55/1.60 % (2033975)Instruction limit reached!
% 5.55/1.60 % (2033975)------------------------------
% 5.55/1.60 % (2033975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.60 % (2033975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.60 % (2033975)CaDiCaL version: 2.1.3
% 5.55/1.60 % (2033975)Termination reason: Instruction limit
% 5.55/1.60 % (2033975)Termination phase: Saturation
% 5.55/1.60 % (2033975)Time elapsed: 0.142 s
% 5.55/1.60 % (2033975)Peak memory usage: 90 MB
% 5.55/1.60 % (2033975)Instructions burned: 250 (million)
% 5.55/1.60 % (2033956)Refutation found. Thanks to Tanya!
% 5.55/1.60 % SZS status Theorem for theBenchmark
% 5.55/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.65/1.79 % (2033956)------------------------------
% 5.65/1.79 % (2033956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.65/1.79 % (2033956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.65/1.79 % (2033956)CaDiCaL version: 2.1.3
% 5.65/1.79 % (2033956)Termination reason: Refutation
% 5.65/1.79 % (2033956)Time elapsed: 0.445 s
% 5.65/1.79 % (2033956)Peak memory usage: 131 MB
% 5.65/1.79 % (2033956)Instructions burned: 1050 (million)
% 5.65/1.79 % (2033956)------------------------------
% 5.65/1.79 % (2033956)------------------------------
% 5.65/1.79 % (2033950)Success in time 0.725 s
% 5.65/1.79 % Vampire exiting
%------------------------------------------------------------------------------