%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO635+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 : n007.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 09:53:07 AM UTC 2026
% Result : Theorem 4.45s 1.56s
% Output : Refutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 19
% Syntax : Number of formulae : 108 ( 12 unt; 2 def)
% Number of atoms : 283 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 295 ( 120 ~; 117 |; 38 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 423 ( 0 sgn 405 !; 18 ?)
% 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(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(f20,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD20) ).
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(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] :
( ( circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& circle(X3,X0,X5,X7)
& eqangle(X0,X2,X2,X4,X5,X2,X2,X1)
& circle(X3,X2,X6,X8)
& coll(X6,X2,X4) )
=> para(X0,X1,X6,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110998) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& circle(X3,X0,X5,X7)
& eqangle(X0,X2,X2,X4,X5,X2,X2,X1)
& circle(X3,X2,X6,X8)
& coll(X6,X2,X4) )
=> para(X0,X1,X6,X5) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ para(X0,X1,X6,X5)
& circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& circle(X3,X0,X5,X7)
& eqangle(X0,X2,X2,X4,X5,X2,X2,X1)
& circle(X3,X2,X6,X8)
& coll(X6,X2,X4) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ para(X0,X1,X6,X5)
& circle(X3,X0,X1,X2)
& coll(X4,X0,X1)
& circle(X3,X0,X5,X7)
& eqangle(X0,X2,X2,X4,X5,X2,X2,X1)
& circle(X3,X2,X6,X8)
& coll(X6,X2,X4) ),
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(f122,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f140,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(f141,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,[],[f140]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f20]) ).
fof(f144,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(f160,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(f161,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,[],[f160]) ).
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(f220,plain,
( ~ para(sK0,sK1,sK6,sK5)
& circle(sK3,sK0,sK1,sK2)
& coll(sK4,sK0,sK1)
& circle(sK3,sK0,sK5,sK7)
& eqangle(sK0,sK2,sK2,sK4,sK5,sK2,sK2,sK1)
& circle(sK3,sK2,sK6,sK8)
& coll(sK6,sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),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)],[f99]) ).
fof(f241,plain,
eqangle(sK0,sK2,sK2,sK4,sK5,sK2,sK2,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f245,plain,
~ para(sK0,sK1,sK6,sK5),
inference(cnf_transformation,[],[f220]) ).
fof(f255,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(f256,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(f258,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(f261,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f271,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,[],[f141]) ).
fof(f273,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f143]) ).
fof(f274,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,[],[f144]) ).
fof(f291,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,[],[f161]) ).
fof(f293,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(f294,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(f295,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(f296,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f170]) ).
fof(f297,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(f298,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f173]) ).
fof(f299,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f174]) ).
fof(f300,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f175]) ).
fof(f335,plain,
eqangle(sK5,sK2,sK2,sK1,sK0,sK2,sK2,sK4),
inference(resolution,[],[f273,f241]) ).
fof(f347,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X0,X1,X2,X3,sK0,sK2,sK2,sK4)
| eqangle(X0,X1,X2,X3,sK5,sK2,sK2,sK1) ),
inference(resolution,[],[f271,f241]) ).
fof(f468,plain,
eqangle(sK5,sK2,sK2,sK1,sK5,sK2,sK2,sK1),
inference(resolution,[],[f347,f335]) ).
fof(f469,plain,
para(sK5,sK2,sK5,sK2),
inference(resolution,[],[f468,f256]) ).
fof(f480,plain,
! [X0,X1] : eqangle(sK5,sK2,X0,X1,sK5,sK2,X0,X1),
inference(resolution,[],[f469,f255]) ).
fof(f504,plain,
! [X0,X1] : eqangle(X0,X1,sK5,sK2,X0,X1,sK5,sK2),
inference(resolution,[],[f480,f274]) ).
fof(f507,plain,
! [X0] :
( cyclic(sK2,X0,sK5,sK5)
| coll(sK5,sK5,sK2) ),
inference(resolution,[],[f480,f295]) ).
fof(f509,definition,
( spl27_10
<=> coll(sK5,sK5,sK2) ),
introduced(definition,[new_symbols(definition,[spl27_10])],[avatar_definition]) ).
fof(f510,plain,
( coll(sK5,sK5,sK2)
| ~ spl27_10 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f512,definition,
( spl27_11
<=> ! [X0] : cyclic(sK2,X0,sK5,sK5) ),
introduced(definition,[new_symbols(definition,[spl27_11])],[avatar_definition]) ).
fof(f513,plain,
( ! [X0] : cyclic(sK2,X0,sK5,sK5)
| ~ spl27_11 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f514,plain,
( spl27_10
| spl27_11 ),
inference(avatar_split_clause,[],[f507,f512,f509]) ).
fof(f536,plain,
( ! [X0,X1] :
( ~ cyclic(sK2,X0,sK5,X1)
| cyclic(X0,sK5,X1,sK5) )
| ~ spl27_11 ),
inference(resolution,[],[f513,f297]) ).
fof(f544,plain,
( ! [X0] : cyclic(X0,sK5,sK5,sK5)
| ~ spl27_11 ),
inference(resolution,[],[f536,f513]) ).
fof(f548,plain,
( ! [X0] : cyclic(sK5,X0,sK5,sK5)
| ~ spl27_11 ),
inference(resolution,[],[f544,f298]) ).
fof(f554,plain,
( ! [X0] : cyclic(sK5,sK5,X0,sK5)
| ~ spl27_11 ),
inference(resolution,[],[f548,f299]) ).
fof(f559,plain,
( ! [X0] : cyclic(sK5,sK5,sK5,X0)
| ~ spl27_11 ),
inference(resolution,[],[f554,f300]) ).
fof(f569,plain,
( ! [X0,X1] :
( ~ cyclic(sK5,sK5,sK5,X0)
| cyclic(sK5,sK5,X0,X1) )
| ~ spl27_11 ),
inference(resolution,[],[f559,f297]) ).
fof(f572,plain,
( ! [X0,X1] : cyclic(sK5,sK5,X0,X1)
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f569,f559]) ).
fof(f578,plain,
( ! [X2,X0,X1] :
( ~ cyclic(sK5,sK5,X0,X1)
| cyclic(sK5,X0,X1,X2) )
| ~ spl27_11 ),
inference(resolution,[],[f572,f297]) ).
fof(f581,plain,
( ! [X2,X0,X1] : cyclic(sK5,X0,X1,X2)
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f578,f572]) ).
fof(f587,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(sK5,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl27_11 ),
inference(resolution,[],[f581,f297]) ).
fof(f590,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f587,f581]) ).
fof(f595,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl27_11 ),
inference(resolution,[],[f590,f296]) ).
fof(f597,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) )
| ~ spl27_11 ),
inference(resolution,[],[f590,f293]) ).
fof(f599,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) )
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f597,f590]) ).
fof(f600,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f599,f590]) ).
fof(f608,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl27_11 ),
inference(resolution,[],[f595,f256]) ).
fof(f621,plain,
( ! [X0,X1] : para(X0,X1,X1,X0)
| ~ spl27_11 ),
inference(resolution,[],[f608,f261]) ).
fof(f632,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X2,X3,X1,X0,X2,X3)
| ~ spl27_11 ),
inference(resolution,[],[f621,f255]) ).
fof(f652,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl27_11 ),
inference(resolution,[],[f600,f632]) ).
fof(f654,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X1,X0,X0,X2)
| ~ cyclic(X0,X0,X1,X2) )
| ~ spl27_11 ),
inference(resolution,[],[f652,f291]) ).
fof(f662,plain,
( ! [X2,X0,X1] :
( perp(X1,X0,X0,X2)
| ~ cyclic(X0,X0,X1,X2) )
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f654,f652]) ).
fof(f663,plain,
( ! [X2,X0,X1] : perp(X1,X0,X0,X2)
| ~ spl27_11 ),
inference(forward_subsumption_resolution,[],[f662,f590]) ).
fof(f669,plain,
( $false
| ~ spl27_11 ),
inference(unit_resulting_resolution,[],[f258,f245,f663,f663]) ).
fof(f675,plain,
~ spl27_11,
inference(avatar_contradiction_clause,[],[f669]) ).
fof(f694,plain,
( ! [X0] :
( ~ eqangle(sK5,X0,sK5,sK2,sK5,X0,sK5,sK2)
| cyclic(X0,sK2,sK5,sK5) )
| ~ spl27_10 ),
inference(resolution,[],[f510,f294]) ).
fof(f695,plain,
( ! [X0] : cyclic(X0,sK2,sK5,sK5)
| ~ spl27_10 ),
inference(forward_subsumption_resolution,[],[f694,f504]) ).
fof(f698,plain,
( ! [X0] : cyclic(sK2,X0,sK5,sK5)
| ~ spl27_10 ),
inference(resolution,[],[f695,f298]) ).
fof(f702,plain,
( spl27_11
| ~ spl27_10 ),
inference(avatar_split_clause,[],[f698,f509,f512]) ).
cnf(s9,plain,
( spl27_10
| spl27_11 ),
inference(sat_conversion,[],[f514]) ).
cnf(s15,plain,
~ spl27_11,
inference(sat_conversion,[],[f675]) ).
cnf(s16,plain,
( ~ spl27_10
| spl27_11 ),
inference(sat_conversion,[],[f702]) ).
cnf(s17,plain,
~ spl27_10,
inference(rat,[],[s16,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s9,s15,s17]) ).
fof(f703,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO635+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 08:39:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 4.45/1.56 % (1110074)Detected formulas, will run a generic FOF schedule.
% 4.45/1.56 % (1110080)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=3887707182:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.45/1.56 % (1110081)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=866496668:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.45/1.56 % (1110084)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1026921394:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.45/1.56 % (1110083)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4111945028:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.45/1.56 % (1110082)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=325671247:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.45/1.56 % (1110079)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=1457428454:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.45/1.56 % (1110085)dis-21_1_sil=8000:lcm=predicate:random_seed=4212750252: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)
% 4.45/1.56 % (1110083)Instruction limit reached!
% 4.45/1.56 % (1110083)------------------------------
% 4.45/1.56 % (1110083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110083)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110083)Termination reason: Instruction limit
% 4.45/1.56 % (1110083)Termination phase: Saturation
% 4.45/1.56 % (1110083)Time elapsed: 0.067 s
% 4.45/1.56 % (1110083)Peak memory usage: 88 MB
% 4.45/1.56 % (1110083)Instructions burned: 119 (million)
% 4.45/1.56 % (1110082)Instruction limit reached!
% 4.45/1.56 % (1110082)------------------------------
% 4.45/1.56 % (1110082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110082)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110082)Termination reason: Instruction limit
% 4.45/1.56 % (1110082)Termination phase: Saturation
% 4.45/1.56 % (1110082)Time elapsed: 0.067 s
% 4.45/1.56 % (1110082)Peak memory usage: 89 MB
% 4.45/1.56 % (1110082)Instructions burned: 109 (million)
% 4.45/1.56 % (1110085)Instruction limit reached!
% 4.45/1.56 % (1110085)------------------------------
% 4.45/1.56 % (1110085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110085)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110085)Termination reason: Instruction limit
% 4.45/1.56 % (1110085)Termination phase: Saturation
% 4.45/1.56 % (1110085)Time elapsed: 0.073 s
% 4.45/1.56 % (1110085)Peak memory usage: 89 MB
% 4.45/1.56 % (1110085)Instructions burned: 130 (million)
% 4.45/1.56 % (1110084)Instruction limit reached!
% 4.45/1.56 % (1110084)------------------------------
% 4.45/1.56 % (1110084)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110084)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110084)Termination reason: Instruction limit
% 4.45/1.56 % (1110084)Termination phase: Saturation
% 4.45/1.56 % (1110084)Time elapsed: 0.094 s
% 4.45/1.56 % (1110084)Peak memory usage: 90 MB
% 4.45/1.56 % (1110084)Instructions burned: 139 (million)
% 4.45/1.56 % (1110093)lrs+10_1_sil=8000:sp=occurrence:random_seed=1804407556:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.45/1.56 % (1110094)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1977545063:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.45/1.56 % (1110095)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2477128821:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.45/1.56 % (1110096)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=2124395907:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.45/1.56 % (1110094)Instruction limit reached!
% 4.45/1.56 % (1110094)------------------------------
% 4.45/1.56 % (1110094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110094)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110094)Termination reason: Instruction limit
% 4.45/1.56 % (1110094)Termination phase: Saturation
% 4.45/1.56 % (1110094)Time elapsed: 0.084 s
% 4.45/1.56 % (1110094)Peak memory usage: 89 MB
% 4.45/1.56 % (1110094)Instructions burned: 157 (million)
% 4.45/1.56 % (1110096)Instruction limit reached!
% 4.45/1.56 % (1110096)------------------------------
% 4.45/1.56 % (1110096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110096)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110096)Termination reason: Instruction limit
% 4.45/1.56 % (1110096)Termination phase: Saturation
% 4.45/1.56 % (1110096)Time elapsed: 0.138 s
% 4.45/1.56 % (1110096)Peak memory usage: 90 MB
% 4.45/1.56 % (1110096)Instructions burned: 249 (million)
% 4.45/1.56 % (1110093)Instruction limit reached!
% 4.45/1.56 % (1110093)------------------------------
% 4.45/1.56 % (1110093)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110093)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110093)Termination reason: Instruction limit
% 4.45/1.56 % (1110093)Termination phase: Saturation
% 4.45/1.56 % (1110093)Time elapsed: 0.180 s
% 4.45/1.56 % (1110093)Peak memory usage: 92 MB
% 4.45/1.56 % (1110093)Instructions burned: 286 (million)
% 4.45/1.56 % (1110080)First to succeed.
% 4.45/1.56 % (1110095)Instruction limit reached!
% 4.45/1.56 % (1110095)------------------------------
% 4.45/1.56 % (1110095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110095)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110095)Termination reason: Instruction limit
% 4.45/1.56 % (1110095)Termination phase: Saturation
% 4.45/1.56 % (1110095)Time elapsed: 0.194 s
% 4.45/1.56 % (1110095)Peak memory usage: 92 MB
% 4.45/1.56 % (1110095)Instructions burned: 325 (million)
% 4.45/1.56 % (1110080)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1110074"
% 4.45/1.56 % (1110101)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=519343882:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.45/1.56 % (1110102)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4248942913:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.45/1.56 % (1110103)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=346807287:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.45/1.56 % (1110104)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1675887646:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.45/1.56 % (1110103)Instruction limit reached!
% 4.45/1.56 % (1110103)------------------------------
% 4.45/1.56 % (1110103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.45/1.56 % (1110103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.45/1.56 % (1110103)CaDiCaL version: 2.1.3
% 4.45/1.56 % (1110103)Termination reason: Instruction limit
% 4.45/1.56 % (1110103)Termination phase: Saturation
% 4.45/1.56 % (1110103)Time elapsed: 0.066 s
% 4.45/1.56 % (1110103)Peak memory usage: 89 MB
% 4.45/1.56 % (1110103)Instructions burned: 113 (million)
% 4.45/1.56 % (1110080)Refutation found. Thanks to Tanya!
% 4.45/1.56 % SZS status Theorem for theBenchmark
% 4.45/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 5.61/1.76 % (1110080)------------------------------
% 5.61/1.76 % (1110080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.76 % (1110080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.76 % (1110080)CaDiCaL version: 2.1.3
% 5.61/1.76 % (1110080)Termination reason: Refutation
% 5.61/1.76 % (1110080)Time elapsed: 0.451 s
% 5.61/1.76 % (1110080)Peak memory usage: 130 MB
% 5.61/1.76 % (1110080)Instructions burned: 1034 (million)
% 5.61/1.76 % (1110080)------------------------------
% 5.61/1.76 % (1110080)------------------------------
% 5.61/1.76 % (1110074)Success in time 0.714 s
% 5.61/1.76 % Vampire exiting
%------------------------------------------------------------------------------