%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO597+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 : n015.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 09:53:01 AM UTC 2026
% Result : Theorem 6.40s 1.96s
% Output : Refutation 8.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 112 ( 11 unt; 2 def)
% Number of atoms : 278 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 288 ( 122 ~; 119 |; 27 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 438 ( 0 sgn 422 !; 16 ?)
% 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(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(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(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(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(f87,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX11) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( circle(X3,X0,X1,X2)
& midp(X4,X1,X0)
& coll(X5,X3,X4)
& circle(X3,X0,X5,X6) )
=> eqangle(X0,X2,X2,X5,X5,X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416059) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( circle(X3,X0,X1,X2)
& midp(X4,X1,X0)
& coll(X5,X3,X4)
& circle(X3,X0,X5,X6) )
=> eqangle(X0,X2,X2,X5,X5,X2,X2,X1) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ eqangle(X0,X2,X2,X5,X5,X2,X2,X1)
& circle(X3,X0,X1,X2)
& midp(X4,X1,X0)
& coll(X5,X3,X4)
& circle(X3,X0,X5,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ eqangle(X0,X2,X2,X5,X5,X2,X2,X1)
& circle(X3,X0,X1,X2)
& midp(X4,X1,X0)
& coll(X5,X3,X4)
& circle(X3,X0,X5,X6) ),
inference(flattening,[],[f98]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
? [X4] :
( perp(X4,X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(ennf_transformation,[],[f87]) ).
fof(f146,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(f147,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,[],[f146]) ).
fof(f150,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(f151,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(f162,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f175,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(f179,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(f180,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f179]) ).
fof(f191,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(f192,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(flattening,[],[f191]) ).
fof(f206,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(f207,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,[],[f206]) ).
fof(f208,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(f209,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,[],[f208]) ).
fof(f210,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(f211,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,[],[f210]) ).
fof(f212,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f41]) ).
fof(f213,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(f214,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(flattening,[],[f213]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f16]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f15]) ).
fof(f217,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f14]) ).
fof(f220,plain,
( ~ eqangle(sK0,sK2,sK2,sK5,sK5,sK2,sK2,sK1)
& circle(sK3,sK0,sK1,sK2)
& midp(sK4,sK1,sK0)
& coll(sK5,sK3,sK4)
& circle(sK3,sK0,sK5,sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f99]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( perp(sK13(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X4,sK13(X0,X1,X2,X3))],[f133]) ).
fof(f242,plain,
circle(sK3,sK0,sK1,sK2),
inference(cnf_transformation,[],[f220]) ).
fof(f243,plain,
~ eqangle(sK0,sK2,sK2,sK5,sK5,sK2,sK2,sK1),
inference(cnf_transformation,[],[f220]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( perp(sK13(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f228]) ).
fof(f273,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,[],[f147]) ).
fof(f276,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,[],[f150]) ).
fof(f277,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,[],[f151]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f162]) ).
fof(f300,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f175]) ).
fof(f303,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,[],[f180]) ).
fof(f313,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f192]) ).
fof(f323,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,[],[f207]) ).
fof(f324,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,[],[f209]) ).
fof(f325,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,[],[f211]) ).
fof(f326,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f327,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f214]) ).
fof(f328,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f215]) ).
fof(f329,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f216]) ).
fof(f330,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f217]) ).
fof(f332,plain,
! [X2,X3,X0,X1] :
( ~ circle(X1,X0,X2,X3)
| perp(X0,X1,sK13(X0,X2,X3,X1),X0) ),
inference(resolution,[],[f289,f266]) ).
fof(f336,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X0,X1,sK13(X2,X3,X4,X5),X2)
| para(X0,X1,X2,X5)
| ~ circle(X5,X2,X3,X4) ),
inference(resolution,[],[f303,f266]) ).
fof(f340,plain,
perp(sK0,sK3,sK13(sK0,sK1,sK2,sK3),sK0),
inference(resolution,[],[f332,f242]) ).
fof(f342,plain,
( para(sK0,sK3,sK0,sK3)
| ~ circle(sK3,sK0,sK1,sK2) ),
inference(resolution,[],[f340,f336]) ).
fof(f346,plain,
para(sK0,sK3,sK0,sK3),
inference(forward_subsumption_resolution,[],[f342,f242]) ).
fof(f347,plain,
! [X0,X1] : eqangle(sK0,sK3,X0,X1,sK0,sK3,X0,X1),
inference(resolution,[],[f346,f300]) ).
fof(f353,plain,
! [X0,X1] : eqangle(X0,X1,sK0,sK3,X0,X1,sK0,sK3),
inference(resolution,[],[f347,f276]) ).
fof(f358,plain,
! [X0] :
( cyclic(sK3,X0,sK0,sK0)
| coll(sK0,sK0,sK3) ),
inference(resolution,[],[f347,f325]) ).
fof(f360,definition,
( spl25_1
<=> coll(sK0,sK0,sK3) ),
introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition]) ).
fof(f361,plain,
( coll(sK0,sK0,sK3)
| ~ spl25_1 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f363,definition,
( spl25_2
<=> ! [X0] : cyclic(sK3,X0,sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).
fof(f364,plain,
( ! [X0] : cyclic(sK3,X0,sK0,sK0)
| ~ spl25_2 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( spl25_1
| spl25_2 ),
inference(avatar_split_clause,[],[f358,f363,f360]) ).
fof(f367,plain,
( ! [X0,X1] :
( ~ cyclic(sK3,X0,sK0,X1)
| cyclic(X0,sK0,X1,sK0) )
| ~ spl25_2 ),
inference(resolution,[],[f364,f327]) ).
fof(f372,plain,
( ! [X0] : cyclic(X0,sK0,sK0,sK0)
| ~ spl25_2 ),
inference(resolution,[],[f367,f364]) ).
fof(f375,plain,
( ! [X0] : cyclic(sK0,X0,sK0,sK0)
| ~ spl25_2 ),
inference(resolution,[],[f372,f328]) ).
fof(f381,plain,
( ! [X0] : cyclic(sK0,sK0,X0,sK0)
| ~ spl25_2 ),
inference(resolution,[],[f375,f329]) ).
fof(f390,plain,
( ! [X0] : cyclic(sK0,sK0,sK0,X0)
| ~ spl25_2 ),
inference(resolution,[],[f381,f330]) ).
fof(f400,plain,
( ! [X0,X1] :
( ~ cyclic(sK0,sK0,sK0,X0)
| cyclic(sK0,sK0,X0,X1) )
| ~ spl25_2 ),
inference(resolution,[],[f390,f327]) ).
fof(f403,plain,
( ! [X0,X1] : cyclic(sK0,sK0,X0,X1)
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f400,f390]) ).
fof(f409,plain,
( ! [X2,X0,X1] :
( ~ cyclic(sK0,sK0,X0,X1)
| cyclic(sK0,X0,X1,X2) )
| ~ spl25_2 ),
inference(resolution,[],[f403,f327]) ).
fof(f412,plain,
( ! [X2,X0,X1] : cyclic(sK0,X0,X1,X2)
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f409,f403]) ).
fof(f418,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(sK0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl25_2 ),
inference(resolution,[],[f412,f327]) ).
fof(f421,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f418,f412]) ).
fof(f426,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl25_2 ),
inference(resolution,[],[f421,f326]) ).
fof(f428,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) )
| ~ spl25_2 ),
inference(resolution,[],[f421,f323]) ).
fof(f430,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) )
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f428,f421]) ).
fof(f431,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f430,f421]) ).
fof(f432,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X1,X2,X3,X0,X3,X2)
| ~ spl25_2 ),
inference(resolution,[],[f426,f277]) ).
fof(f474,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl25_2 ),
inference(resolution,[],[f431,f432]) ).
fof(f476,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl25_2 ),
inference(resolution,[],[f474,f313]) ).
fof(f481,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f476,f474]) ).
fof(f482,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl25_2 ),
inference(resolution,[],[f481,f303]) ).
fof(f484,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl25_2 ),
inference(resolution,[],[f481,f289]) ).
fof(f486,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl25_2 ),
inference(forward_subsumption_resolution,[],[f482,f484]) ).
fof(f488,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ spl25_2 ),
inference(resolution,[],[f486,f300]) ).
fof(f490,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X0,X1,X4,X5)
| ~ spl25_2 ),
inference(resolution,[],[f488,f276]) ).
fof(f519,plain,
( $false
| ~ spl25_2 ),
inference(unit_resulting_resolution,[],[f273,f243,f488,f490]) ).
fof(f530,plain,
~ spl25_2,
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f531,plain,
( ! [X0] :
( ~ eqangle(sK0,X0,sK0,sK3,sK0,X0,sK0,sK3)
| cyclic(X0,sK3,sK0,sK0) )
| ~ spl25_1 ),
inference(resolution,[],[f361,f324]) ).
fof(f532,plain,
( ! [X0] : cyclic(X0,sK3,sK0,sK0)
| ~ spl25_1 ),
inference(forward_subsumption_resolution,[],[f531,f353]) ).
fof(f535,plain,
( ! [X0] : cyclic(sK3,X0,sK0,sK0)
| ~ spl25_1 ),
inference(resolution,[],[f532,f328]) ).
fof(f539,plain,
( spl25_2
| ~ spl25_1 ),
inference(avatar_split_clause,[],[f535,f360,f363]) ).
cnf(s1,plain,
( spl25_1
| spl25_2 ),
inference(sat_conversion,[],[f365]) ).
cnf(s3,plain,
~ spl25_2,
inference(sat_conversion,[],[f530]) ).
cnf(s4,plain,
( ~ spl25_1
| spl25_2 ),
inference(sat_conversion,[],[f539]) ).
cnf(s5,plain,
~ spl25_1,
inference(rat,[],[s4,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
fof(f540,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO597+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.40 % Computer : n015.cluster.edu
% 0.07/0.40 % Model : x86_64 x86_64
% 0.07/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.40 % Memory : 8046.5625MB
% 0.07/0.40 % OS : Linux 6.8.0-71-generic
% 0.07/0.40 % CPULimit : 300
% 0.07/0.40 % WCLimit : 300
% 0.07/0.40 % DateTime : Sun Sep 27 08:39:30 UTC 2026
% 0.07/0.41 % CPUTime :
% 0.07/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.44 Running first-order theorem proving
% 0.07/0.44 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
% 6.40/1.96 % (1351050)Detected formulas, will run a generic FOF schedule.
% 6.40/1.96 % (1351058)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2927201234:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.40/1.96 % (1351058)Refutation not found, incomplete strategy
% 6.40/1.96 % (1351058)------------------------------
% 6.40/1.96 % (1351058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351058)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351058)Termination reason: Refutation not found, incomplete strategy
% 6.40/1.96 % (1351058)Time elapsed: 0.006 s
% 6.40/1.96 % (1351058)Peak memory usage: 88 MB
% 6.40/1.96 % (1351058)Instructions burned: 19 (million)
% 6.40/1.96 % (1351056)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=2537201707:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.40/1.96 % (1351055)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=2278300350:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.40/1.96 % (1351057)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=1264233973:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.40/1.96 % (1351059)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1080494503:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.40/1.96 % (1351061)dis-21_1_sil=8000:lcm=predicate:random_seed=591617363: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)
% 6.40/1.96 % (1351060)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1106746955:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.40/1.96 % (1351059)Instruction limit reached!
% 6.40/1.96 % (1351059)------------------------------
% 6.40/1.96 % (1351059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351059)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351059)Termination reason: Instruction limit
% 6.40/1.96 % (1351059)Termination phase: Saturation
% 6.40/1.96 % (1351059)Time elapsed: 0.068 s
% 6.40/1.96 % (1351059)Peak memory usage: 88 MB
% 6.40/1.96 % (1351059)Instructions burned: 119 (million)
% 6.40/1.96 % (1351061)Instruction limit reached!
% 6.40/1.96 % (1351061)------------------------------
% 6.40/1.96 % (1351061)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351061)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351061)Termination reason: Instruction limit
% 6.40/1.96 % (1351061)Termination phase: Saturation
% 6.40/1.96 % (1351061)Time elapsed: 0.078 s
% 6.40/1.96 % (1351061)Peak memory usage: 89 MB
% 6.40/1.96 % (1351061)Instructions burned: 130 (million)
% 6.40/1.96 % (1351060)Instruction limit reached!
% 6.40/1.96 % (1351060)------------------------------
% 6.40/1.96 % (1351060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351060)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351060)Termination reason: Instruction limit
% 6.40/1.96 % (1351060)Termination phase: Saturation
% 6.40/1.96 % (1351060)Time elapsed: 0.085 s
% 6.40/1.96 % (1351060)Peak memory usage: 90 MB
% 6.40/1.96 % (1351060)Instructions burned: 139 (million)
% 6.40/1.96 % (1351058)------------------------------
% 6.40/1.96 % (1351058)------------------------------
% 6.40/1.96 % (1351069)lrs+10_1_sil=8000:sp=occurrence:random_seed=4251673745:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.40/1.96 % (1351070)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3459973134:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.40/1.96 % (1351072)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=1106161320:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.40/1.96 % (1351071)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1120894758:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.40/1.96 % (1351070)Instruction limit reached!
% 6.40/1.96 % (1351070)------------------------------
% 6.40/1.96 % (1351070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351070)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351070)Termination reason: Instruction limit
% 6.40/1.96 % (1351070)Termination phase: Saturation
% 6.40/1.96 % (1351070)Time elapsed: 0.081 s
% 6.40/1.96 % (1351070)Peak memory usage: 90 MB
% 6.40/1.96 % (1351070)Instructions burned: 159 (million)
% 6.40/1.96 % (1351072)Instruction limit reached!
% 6.40/1.96 % (1351072)------------------------------
% 6.40/1.96 % (1351072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351072)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351072)Termination reason: Instruction limit
% 6.40/1.96 % (1351072)Termination phase: Saturation
% 6.40/1.96 % (1351072)Time elapsed: 0.073 s
% 6.40/1.96 % (1351072)Peak memory usage: 91 MB
% 6.40/1.96 % (1351072)Instructions burned: 250 (million)
% 6.40/1.96 % (1351078)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=39399485:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.40/1.96 % (1351069)Instruction limit reached!
% 6.40/1.96 % (1351069)------------------------------
% 6.40/1.96 % (1351069)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351069)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351069)Termination reason: Instruction limit
% 6.40/1.96 % (1351069)Termination phase: Saturation
% 6.40/1.96 % (1351069)Time elapsed: 0.187 s
% 6.40/1.96 % (1351069)Peak memory usage: 92 MB
% 6.40/1.96 % (1351069)Instructions burned: 286 (million)
% 6.40/1.96 % (1351077)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3084341685:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.40/1.96 % (1351071)Instruction limit reached!
% 6.40/1.96 % (1351071)------------------------------
% 6.40/1.96 % (1351071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351071)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351071)Termination reason: Instruction limit
% 6.40/1.96 % (1351071)Termination phase: Saturation
% 6.40/1.96 % (1351071)Time elapsed: 0.197 s
% 6.40/1.96 % (1351071)Peak memory usage: 91 MB
% 6.40/1.96 % (1351071)Instructions burned: 325 (million)
% 6.40/1.96 % (1351080)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=502234950:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.40/1.96 % (1351082)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2125002249:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.40/1.96 % (1351080)Instruction limit reached!
% 6.40/1.96 % (1351080)------------------------------
% 6.40/1.96 % (1351080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351080)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351080)Termination reason: Instruction limit
% 6.40/1.96 % (1351080)Termination phase: Saturation
% 6.40/1.96 % (1351080)Time elapsed: 0.068 s
% 6.40/1.96 % (1351080)Peak memory usage: 89 MB
% 6.40/1.96 % (1351080)Instructions burned: 114 (million)
% 6.40/1.96 % (1351077)Instruction limit reached!
% 6.40/1.96 % (1351077)------------------------------
% 6.40/1.96 % (1351077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351077)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351077)Termination reason: Instruction limit
% 6.40/1.96 % (1351077)Termination phase: Saturation
% 6.40/1.96 % (1351077)Time elapsed: 0.165 s
% 6.40/1.96 % (1351077)Peak memory usage: 89 MB
% 6.40/1.96 % (1351077)Instructions burned: 295 (million)
% 6.40/1.96 % (1351082)Instruction limit reached!
% 6.40/1.96 % (1351082)------------------------------
% 6.40/1.96 % (1351082)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351082)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351082)Termination reason: Instruction limit
% 6.40/1.96 % (1351082)Termination phase: Saturation
% 6.40/1.96 % (1351082)Time elapsed: 0.071 s
% 6.40/1.96 % (1351082)Peak memory usage: 89 MB
% 6.40/1.96 % (1351082)Instructions burned: 128 (million)
% 6.40/1.96 % (1351056)First to succeed.
% 6.40/1.96 % (1351056)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1351050"
% 6.40/1.96 % (1351055)Also succeeded, but the first one will report.
% 6.40/1.96 % (1351086)lrs+10_1_sil=8000:sp=occurrence:random_seed=2119544968:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.40/1.96 % (1351085)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=226046529:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.40/1.96 % (1351078)Also succeeded, but the first one will report.
% 6.40/1.96 % (1351087)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=417645732:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.40/1.96 % (1351085)Instruction limit reached!
% 6.40/1.96 % (1351085)------------------------------
% 6.40/1.96 % (1351085)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.96 % (1351085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.96 % (1351085)CaDiCaL version: 2.1.3
% 6.40/1.96 % (1351085)Termination reason: Instruction limit
% 6.40/1.96 % (1351085)Termination phase: Saturation
% 6.40/1.96 % (1351085)Time elapsed: 0.066 s
% 6.40/1.96 % (1351085)Peak memory usage: 89 MB
% 6.40/1.96 % (1351085)Instructions burned: 115 (million)
% 6.40/1.96 % (1351091)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3004781255:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.40/1.96 % (1351056)Refutation found. Thanks to Tanya!
% 6.40/1.96 % SZS status Theorem for theBenchmark
% 6.40/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 8.22/2.17 % (1351056)------------------------------
% 8.22/2.17 % (1351056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.22/2.17 % (1351056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.22/2.17 % (1351056)CaDiCaL version: 2.1.3
% 8.22/2.17 % (1351056)Termination reason: Refutation
% 8.22/2.17 % (1351056)Time elapsed: 0.664 s
% 8.22/2.17 % (1351056)Peak memory usage: 131 MB
% 8.22/2.17 % (1351056)Instructions burned: 998 (million)
% 8.22/2.17 % (1351056)------------------------------
% 8.22/2.17 % (1351056)------------------------------
% 8.22/2.17 % (1351050)Success in time 1.083 s
% 8.22/2.17 % Vampire exiting
%------------------------------------------------------------------------------