%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO584+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 09:52:59 AM UTC 2026
% Result : Theorem 4.42s 1.57s
% Output : Refutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 113 ( 13 unt; 2 def)
% Number of atoms : 313 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 313 ( 113 ~; 118 |; 62 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 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 : 516 ( 0 sgn 492 !; 24 ?)
% 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(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(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(f18,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X1,X0,X2,X3,X4,X5,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD18) ).
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(f22,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
& eqangle(X4,X5,X6,X7,X8,X9,X10,X11) )
=> eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
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,X10,X11] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& circle(X3,X0,X5,X11)
& perp(X6,X5,X1,X2)
& coll(X6,X1,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X5,X0,X4)
& coll(X8,X0,X4)
& perp(X9,X5,X2,X4)
& coll(X9,X2,X4) )
=> eqangle(X5,X7,X7,X8,X5,X6,X6,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416046) ).
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,X0,X5,X11)
& perp(X6,X5,X1,X2)
& coll(X6,X1,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X5,X0,X4)
& coll(X8,X0,X4)
& perp(X9,X5,X2,X4)
& coll(X9,X2,X4) )
=> eqangle(X5,X7,X7,X8,X5,X6,X6,X9) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X5,X7,X7,X8,X5,X6,X6,X9)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& circle(X3,X0,X5,X11)
& perp(X6,X5,X1,X2)
& coll(X6,X1,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X5,X0,X4)
& coll(X8,X0,X4)
& perp(X9,X5,X2,X4)
& coll(X9,X2,X4) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X5,X7,X7,X8,X5,X6,X6,X9)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X10)
& circle(X3,X0,X5,X11)
& perp(X6,X5,X1,X2)
& coll(X6,X1,X2)
& perp(X7,X5,X0,X1)
& coll(X7,X0,X1)
& perp(X8,X5,X0,X4)
& coll(X8,X0,X4)
& perp(X9,X5,X2,X4)
& coll(X9,X2,X4) ),
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(f133,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11) ),
inference(ennf_transformation,[],[f22]) ).
fof(f134,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11) ),
inference(flattening,[],[f133]) ).
fof(f135,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(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(f138,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f18]) ).
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(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(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,
( ~ eqangle(sK5,sK7,sK7,sK8,sK5,sK6,sK6,sK9)
& circle(sK3,sK0,sK1,sK2)
& circle(sK3,sK0,sK4,sK10)
& circle(sK3,sK0,sK5,sK11)
& perp(sK6,sK5,sK1,sK2)
& coll(sK6,sK1,sK2)
& perp(sK7,sK5,sK0,sK1)
& coll(sK7,sK0,sK1)
& perp(sK8,sK5,sK0,sK4)
& coll(sK8,sK0,sK4)
& perp(sK9,sK5,sK2,sK4)
& coll(sK9,sK2,sK4) ),
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(f240,plain,
perp(sK9,sK5,sK2,sK4),
inference(cnf_transformation,[],[f220]) ).
fof(f250,plain,
~ eqangle(sK5,sK7,sK7,sK8,sK5,sK6,sK6,sK9),
inference(cnf_transformation,[],[f220]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f276,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
inference(cnf_transformation,[],[f134]) ).
fof(f277,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,[],[f135]) ).
fof(f279,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(f280,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X1,X0,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f138]) ).
fof(f285,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(f286,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(f287,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(f288,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f289,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(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f155]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f156]) ).
fof(f303,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(f304,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)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f175]) ).
fof(f333,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(f342,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK9,sK5)
| para(X0,X1,sK2,sK4) ),
inference(resolution,[],[f240,f306]) ).
fof(f346,plain,
perp(sK2,sK4,sK9,sK5),
inference(resolution,[],[f265,f240]) ).
fof(f421,plain,
para(sK2,sK4,sK2,sK4),
inference(resolution,[],[f346,f342]) ).
fof(f425,plain,
! [X0,X1] : eqangle(sK2,sK4,X0,X1,sK2,sK4,X0,X1),
inference(resolution,[],[f421,f303]) ).
fof(f427,plain,
! [X0,X1] : eqangle(X0,X1,sK2,sK4,X0,X1,sK2,sK4),
inference(resolution,[],[f425,f279]) ).
fof(f516,plain,
! [X0,X1] : para(X0,X1,X0,X1),
inference(resolution,[],[f427,f304]) ).
fof(f518,plain,
! [X2,X3,X0,X1] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[],[f516,f303]) ).
fof(f526,plain,
! [X2,X0,X1] :
( cyclic(X0,X1,X2,X2)
| coll(X2,X2,X0) ),
inference(resolution,[],[f518,f287]) ).
fof(f543,plain,
! [X2,X0,X1] :
( cyclic(X1,X0,X2,X0)
| coll(X0,X0,X1) ),
inference(resolution,[],[f526,f291]) ).
fof(f548,plain,
! [X2,X0,X1] :
( cyclic(X1,X0,X0,X2)
| coll(X0,X0,X1) ),
inference(resolution,[],[f543,f292]) ).
fof(f558,plain,
! [X2,X3,X0,X1] :
( coll(X0,X0,X1)
| ~ cyclic(X1,X0,X0,X2)
| cyclic(X0,X0,X2,X3) ),
inference(resolution,[],[f548,f289]) ).
fof(f560,plain,
! [X2,X3,X0,X1] :
( coll(X0,X0,X1)
| cyclic(X0,X0,X2,X3) ),
inference(forward_subsumption_resolution,[],[f558,f548]) ).
fof(f568,plain,
! [X2,X3,X0,X1,X4] :
( coll(X0,X0,X1)
| ~ cyclic(X0,X0,X2,X3)
| cyclic(X0,X2,X3,X4) ),
inference(resolution,[],[f560,f289]) ).
fof(f570,plain,
! [X2,X3,X0,X1,X4] :
( coll(X0,X0,X1)
| cyclic(X0,X2,X3,X4) ),
inference(forward_subsumption_resolution,[],[f568,f560]) ).
fof(f579,plain,
! [X2,X3,X0,X1,X4,X5] :
( coll(X0,X0,X1)
| ~ cyclic(X0,X2,X3,X4)
| cyclic(X2,X3,X4,X5) ),
inference(resolution,[],[f570,f289]) ).
fof(f581,plain,
! [X2,X3,X0,X1,X4,X5] :
( coll(X0,X0,X1)
| cyclic(X2,X3,X4,X5) ),
inference(forward_subsumption_resolution,[],[f579,f570]) ).
fof(f585,definition,
( spl30_9
<=> ! [X4,X5,X2,X3] : cyclic(X2,X3,X4,X5) ),
introduced(definition,[new_symbols(definition,[spl30_9])],[avatar_definition]) ).
fof(f586,plain,
( ! [X2,X3,X4,X5] : cyclic(X2,X3,X4,X5)
| ~ spl30_9 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f588,definition,
( spl30_10
<=> ! [X0,X1] : coll(X0,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl30_10])],[avatar_definition]) ).
fof(f589,plain,
( ! [X0,X1] : coll(X0,X0,X1)
| ~ spl30_10 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f590,plain,
( spl30_9
| spl30_10 ),
inference(avatar_split_clause,[],[f581,f588,f585]) ).
fof(f592,plain,
( ! [X2,X0,X1] :
( ~ eqangle(X0,X1,X0,X2,X0,X1,X0,X2)
| cyclic(X1,X2,X0,X0) )
| ~ spl30_10 ),
inference(resolution,[],[f589,f286]) ).
fof(f593,plain,
( ! [X2,X0,X1] : cyclic(X1,X2,X0,X0)
| ~ spl30_10 ),
inference(forward_subsumption_resolution,[],[f592,f518]) ).
fof(f595,plain,
( ! [X2,X0,X1] : cyclic(X0,X1,X2,X1)
| ~ spl30_10 ),
inference(resolution,[],[f593,f291]) ).
fof(f600,plain,
( ! [X2,X0,X1] : cyclic(X0,X1,X1,X2)
| ~ spl30_10 ),
inference(resolution,[],[f595,f292]) ).
fof(f610,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X1,X2)
| cyclic(X1,X1,X2,X3) )
| ~ spl30_10 ),
inference(resolution,[],[f600,f289]) ).
fof(f612,plain,
( ! [X2,X3,X1] : cyclic(X1,X1,X2,X3)
| ~ spl30_10 ),
inference(forward_subsumption_resolution,[],[f610,f600]) ).
fof(f619,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl30_10 ),
inference(resolution,[],[f612,f289]) ).
fof(f621,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl30_10 ),
inference(forward_subsumption_resolution,[],[f619,f612]) ).
fof(f623,plain,
( spl30_9
| ~ spl30_10 ),
inference(avatar_split_clause,[],[f621,f588,f585]) ).
fof(f628,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_9 ),
inference(resolution,[],[f586,f285]) ).
fof(f630,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl30_9 ),
inference(resolution,[],[f586,f288]) ).
fof(f631,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_9 ),
inference(forward_subsumption_resolution,[],[f628,f586]) ).
fof(f632,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl30_9 ),
inference(forward_subsumption_resolution,[],[f631,f586]) ).
fof(f633,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X1,X2,X3,X0,X3,X2)
| ~ spl30_9 ),
inference(resolution,[],[f630,f280]) ).
fof(f858,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl30_9 ),
inference(resolution,[],[f632,f633]) ).
fof(f860,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl30_9 ),
inference(resolution,[],[f858,f333]) ).
fof(f865,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl30_9 ),
inference(forward_subsumption_resolution,[],[f860,f858]) ).
fof(f867,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl30_9 ),
inference(resolution,[],[f865,f265]) ).
fof(f868,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl30_9 ),
inference(resolution,[],[f865,f306]) ).
fof(f895,plain,
( ! [X2,X3,X0,X1] : para(X0,X1,X2,X3)
| ~ spl30_9 ),
inference(resolution,[],[f868,f867]) ).
fof(f896,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ spl30_9 ),
inference(resolution,[],[f895,f303]) ).
fof(f902,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ spl30_9 ),
inference(resolution,[],[f896,f277]) ).
fof(f952,plain,
( $false
| ~ spl30_9 ),
inference(unit_resulting_resolution,[],[f276,f250,f896,f902]) ).
fof(f961,plain,
~ spl30_9,
inference(avatar_contradiction_clause,[],[f952]) ).
cnf(s8,plain,
( spl30_9
| spl30_10 ),
inference(sat_conversion,[],[f590]) ).
cnf(s9,plain,
( spl30_9
| ~ spl30_10 ),
inference(sat_conversion,[],[f623]) ).
cnf(s11,plain,
~ spl30_9,
inference(sat_conversion,[],[f961]) ).
cnf(s12,plain,
~ spl30_10,
inference(rat,[],[s9,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s8,s12,s11]) ).
fof(f962,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO584+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 08:36:23 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.42/1.57 % (2032269)Detected formulas, will run a generic FOF schedule.
% 4.42/1.57 % (2032275)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=752203292:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.42/1.57 % (2032279)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2649754235:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.42/1.57 % (2032278)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3301547791:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.42/1.57 % (2032277)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3740248725:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.42/1.57 % (2032274)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=3057454268:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.42/1.57 % (2032276)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=2726924194:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.42/1.57 % (2032280)dis-21_1_sil=8000:lcm=predicate:random_seed=3694613245: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)
% 4.42/1.57 % (2032277)Refutation not found, incomplete strategy
% 4.42/1.57 % (2032277)------------------------------
% 4.42/1.57 % (2032277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.57 % (2032277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.57 % (2032277)CaDiCaL version: 2.1.3
% 4.42/1.57 % (2032277)Termination reason: Refutation not found, incomplete strategy
% 4.42/1.57 % (2032277)Time elapsed: 0.039 s
% 4.42/1.57 % (2032277)Peak memory usage: 89 MB
% 4.42/1.57 % (2032277)Instructions burned: 72 (million)
% 4.42/1.57 % (2032278)Instruction limit reached!
% 4.42/1.57 % (2032278)------------------------------
% 4.42/1.57 % (2032278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.57 % (2032278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.57 % (2032278)CaDiCaL version: 2.1.3
% 4.42/1.57 % (2032278)Termination reason: Instruction limit
% 4.42/1.57 % (2032278)Termination phase: Saturation
% 4.42/1.57 % (2032278)Time elapsed: 0.069 s
% 4.42/1.57 % (2032278)Peak memory usage: 89 MB
% 4.42/1.57 % (2032278)Instructions burned: 120 (million)
% 4.42/1.57 % (2032280)Instruction limit reached!
% 4.42/1.57 % (2032280)------------------------------
% 4.42/1.57 % (2032280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.57 % (2032280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.57 % (2032280)CaDiCaL version: 2.1.3
% 4.42/1.57 % (2032280)Termination reason: Instruction limit
% 4.42/1.57 % (2032280)Termination phase: Saturation
% 4.42/1.57 % (2032280)Time elapsed: 0.075 s
% 4.42/1.57 % (2032280)Peak memory usage: 89 MB
% 4.42/1.57 % (2032280)Instructions burned: 130 (million)
% 4.42/1.57 % (2032279)Instruction limit reached!
% 4.42/1.57 % (2032279)------------------------------
% 4.42/1.57 % (2032279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.57 % (2032279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.57 % (2032279)CaDiCaL version: 2.1.3
% 4.42/1.57 % (2032279)Termination reason: Instruction limit
% 4.42/1.57 % (2032279)Termination phase: Saturation
% 4.42/1.57 % (2032279)Time elapsed: 0.090 s
% 4.42/1.57 % (2032279)Peak memory usage: 90 MB
% 4.42/1.57 % (2032279)Instructions burned: 140 (million)
% 4.42/1.57 % (2032288)lrs+10_1_sil=8000:sp=occurrence:random_seed=1918600855:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.42/1.57 % (2032289)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1573196245:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.42/1.57 % (2032290)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1348551424:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.42/1.57 % (2032277)------------------------------
% 4.42/1.57 % (2032277)------------------------------
% 4.42/1.57 % (2032289)Instruction limit reached!
% 4.42/1.57 % (2032289)------------------------------
% 4.42/1.57 % (2032289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.57 % (2032289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.57 % (2032289)CaDiCaL version: 2.1.3
% 4.42/1.57 % (2032289)Termination reason: Instruction limit
% 4.42/1.57 % (2032289)Termination phase: Saturation
% 4.42/1.57 % (2032289)Time elapsed: 0.080 s
% 4.42/1.57 % (2032289)Peak memory usage: 89 MB
% 4.42/1.57 % (2032289)Instructions burned: 159 (million)
% 4.42/1.57 % (2032275)First to succeed.
% 4.42/1.57 % (2032275)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2032269"
% 4.42/1.57 % (2032288)Instruction limit reached!
% 4.42/1.57 % (2032288)------------------------------
% 4.42/1.57 % (2032288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.57 % (2032288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.57 % (2032288)CaDiCaL version: 2.1.3
% 4.42/1.57 % (2032288)Termination reason: Instruction limit
% 4.42/1.57 % (2032288)Termination phase: Saturation
% 4.42/1.57 % (2032288)Time elapsed: 0.183 s
% 4.42/1.57 % (2032288)Peak memory usage: 93 MB
% 4.42/1.57 % (2032288)Instructions burned: 286 (million)
% 4.42/1.57 % (2032294)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=3678109107:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.42/1.57 % (2032295)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1349826655:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.42/1.57 % (2032290)Instruction limit reached!
% 4.42/1.57 % (2032290)------------------------------
% 4.42/1.57 % (2032290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.42/1.57 % (2032290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.42/1.57 % (2032290)CaDiCaL version: 2.1.3
% 4.42/1.57 % (2032290)Termination reason: Instruction limit
% 4.42/1.57 % (2032290)Termination phase: Saturation
% 4.42/1.57 % (2032290)Time elapsed: 0.215 s
% 4.42/1.57 % (2032290)Peak memory usage: 92 MB
% 4.42/1.57 % (2032290)Instructions burned: 325 (million)
% 4.42/1.57 % (2032296)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3187150276:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.42/1.57 % (2032275)Refutation found. Thanks to Tanya!
% 4.42/1.57 % SZS status Theorem for theBenchmark
% 4.42/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 5.52/1.76 % (2032275)------------------------------
% 5.52/1.76 % (2032275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.76 % (2032275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.76 % (2032275)CaDiCaL version: 2.1.3
% 5.52/1.76 % (2032275)Termination reason: Refutation
% 5.52/1.76 % (2032275)Time elapsed: 0.416 s
% 5.52/1.76 % (2032275)Peak memory usage: 131 MB
% 5.52/1.76 % (2032275)Instructions burned: 1083 (million)
% 5.52/1.76 % (2032275)------------------------------
% 5.52/1.76 % (2032275)------------------------------
% 5.52/1.76 % (2032269)Success in time 0.708 s
% 5.52/1.76 % Vampire exiting
%------------------------------------------------------------------------------