%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO552+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:52:55 AM UTC 2026
% Result : Theorem 4.55s 1.53s
% Output : Refutation 5.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 20
% Syntax : Number of formulae : 119 ( 11 unt; 2 def)
% Number of atoms : 312 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 329 ( 136 ~; 133 |; 39 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 424 ( 0 sgn 408 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ruleD10) ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD14) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X0,X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD15) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> cyclic(X1,X0,X2,X3) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ruleD57) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( circle(X3,X0,X1,X2)
& perp(X0,X2,X1,X4)
& circle(X3,X0,X4,X7)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& midp(X6,X1,X0) )
=> perp(X6,X5,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012012) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( circle(X3,X0,X1,X2)
& perp(X0,X2,X1,X4)
& circle(X3,X0,X4,X7)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& midp(X6,X1,X0) )
=> perp(X6,X5,X2,X4) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ perp(X6,X5,X2,X4)
& circle(X3,X0,X1,X2)
& perp(X0,X2,X1,X4)
& circle(X3,X0,X4,X7)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& midp(X6,X1,X0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f99,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ perp(X6,X5,X2,X4)
& circle(X3,X0,X1,X2)
& perp(X0,X2,X1,X4)
& circle(X3,X0,X4,X7)
& coll(X5,X0,X2)
& coll(X5,X1,X4)
& midp(X6,X1,X0) ),
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(f162,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(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(f176,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(f177,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(f178,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f177]) ).
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(f184,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f4]) ).
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(f202,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(f203,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,[],[f202]) ).
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,
( ~ perp(sK6,sK5,sK2,sK4)
& circle(sK3,sK0,sK1,sK2)
& perp(sK0,sK2,sK1,sK4)
& circle(sK3,sK0,sK4,sK7)
& coll(sK5,sK0,sK2)
& coll(sK5,sK1,sK4)
& midp(sK6,sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f99]) ).
fof(f243,plain,
perp(sK0,sK2,sK1,sK4),
inference(cnf_transformation,[],[f220]) ).
fof(f245,plain,
~ perp(sK6,sK5,sK2,sK4),
inference(cnf_transformation,[],[f220]) ).
fof(f260,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f291,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,[],[f162]) ).
fof(f302,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] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f176]) ).
fof(f304,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,[],[f178]) ).
fof(f305,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(f308,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f184]) ).
fof(f315,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] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X2,X0,X0,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f203]) ).
fof(f325,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(f326,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(f327,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(f328,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f329,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(f330,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X0,X2,X3) ),
inference(cnf_transformation,[],[f215]) ).
fof(f331,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f216]) ).
fof(f332,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| cyclic(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f217]) ).
fof(f335,plain,
perp(sK1,sK4,sK0,sK2),
inference(resolution,[],[f260,f243]) ).
fof(f343,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK0,sK2)
| para(X0,X1,sK1,sK4) ),
inference(resolution,[],[f305,f243]) ).
fof(f346,plain,
para(sK1,sK4,sK1,sK4),
inference(resolution,[],[f343,f335]) ).
fof(f347,plain,
! [X0,X1] : eqangle(sK1,sK4,X0,X1,sK1,sK4,X0,X1),
inference(resolution,[],[f346,f302]) ).
fof(f350,plain,
! [X0] :
( cyclic(sK4,X0,sK1,sK1)
| coll(sK1,sK1,sK4) ),
inference(resolution,[],[f347,f327]) ).
fof(f353,plain,
! [X0,X1] : eqangle(X0,X1,sK1,sK4,X0,X1,sK1,sK4),
inference(resolution,[],[f347,f291]) ).
fof(f357,definition,
( spl26_1
<=> coll(sK1,sK1,sK4) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f358,plain,
( coll(sK1,sK1,sK4)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f360,definition,
( spl26_2
<=> ! [X0] : cyclic(sK4,X0,sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f361,plain,
( ! [X0] : cyclic(sK4,X0,sK1,sK1)
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f362,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f350,f360,f357]) ).
fof(f366,plain,
( ! [X0] : cyclic(X0,sK4,sK1,sK1)
| ~ spl26_2 ),
inference(resolution,[],[f330,f361]) ).
fof(f383,plain,
( ! [X0] : cyclic(X0,sK1,sK4,sK1)
| ~ spl26_2 ),
inference(resolution,[],[f366,f331]) ).
fof(f397,plain,
( ! [X0] : cyclic(X0,sK1,sK1,sK4)
| ~ spl26_2 ),
inference(resolution,[],[f383,f332]) ).
fof(f405,plain,
( ! [X0] : cyclic(sK1,X0,sK1,sK4)
| ~ spl26_2 ),
inference(resolution,[],[f397,f330]) ).
fof(f431,plain,
( ! [X0] : cyclic(sK1,sK1,X0,sK4)
| ~ spl26_2 ),
inference(resolution,[],[f405,f331]) ).
fof(f436,plain,
( ! [X0] : cyclic(sK1,sK1,sK4,X0)
| ~ spl26_2 ),
inference(resolution,[],[f431,f332]) ).
fof(f447,plain,
( ! [X0,X1] :
( ~ cyclic(sK1,sK1,sK4,X0)
| cyclic(sK1,sK4,X0,X1) )
| ~ spl26_2 ),
inference(resolution,[],[f436,f329]) ).
fof(f448,plain,
( ! [X0,X1] : cyclic(sK1,sK4,X0,X1)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f447,f436]) ).
fof(f456,plain,
( ! [X2,X0,X1] :
( ~ cyclic(sK1,sK4,X0,X1)
| cyclic(sK4,X0,X1,X2) )
| ~ spl26_2 ),
inference(resolution,[],[f448,f329]) ).
fof(f457,plain,
( ! [X2,X0,X1] : cyclic(sK4,X0,X1,X2)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f456,f448]) ).
fof(f467,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(sK4,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl26_2 ),
inference(resolution,[],[f457,f329]) ).
fof(f468,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f467,f457]) ).
fof(f475,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl26_2 ),
inference(resolution,[],[f468,f328]) ).
fof(f476,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) )
| ~ spl26_2 ),
inference(resolution,[],[f468,f325]) ).
fof(f480,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) )
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f476,f468]) ).
fof(f481,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f480,f468]) ).
fof(f492,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl26_2 ),
inference(resolution,[],[f475,f303]) ).
fof(f500,plain,
( ! [X0,X1] : para(X0,X1,X1,X0)
| ~ spl26_2 ),
inference(resolution,[],[f492,f308]) ).
fof(f504,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X2,X3,X0,X1,X2,X3)
| ~ spl26_2 ),
inference(resolution,[],[f492,f302]) ).
fof(f539,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl26_2 ),
inference(resolution,[],[f481,f504]) ).
fof(f540,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X1,X0,X0,X2)
| ~ cyclic(X0,X0,X1,X2) )
| ~ spl26_2 ),
inference(resolution,[],[f539,f323]) ).
fof(f541,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl26_2 ),
inference(resolution,[],[f539,f315]) ).
fof(f547,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f541,f539]) ).
fof(f548,plain,
( ! [X2,X0,X1] :
( perp(X1,X0,X0,X2)
| ~ cyclic(X0,X0,X1,X2) )
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f540,f539]) ).
fof(f549,plain,
( ! [X2,X0,X1] : perp(X1,X0,X0,X2)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f548,f468]) ).
fof(f550,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl26_2 ),
inference(resolution,[],[f547,f305]) ).
fof(f552,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl26_2 ),
inference(resolution,[],[f547,f260]) ).
fof(f555,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f550,f552]) ).
fof(f559,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ para(X0,X1,X2,X3)
| perp(X0,X1,X3,X4) )
| ~ spl26_2 ),
inference(resolution,[],[f549,f304]) ).
fof(f561,plain,
( ! [X3,X0,X1,X4] : perp(X0,X1,X3,X4)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f559,f555]) ).
fof(f567,plain,
( $false
| ~ spl26_2 ),
inference(unit_resulting_resolution,[],[f304,f245,f500,f561]) ).
fof(f580,plain,
~ spl26_2,
inference(avatar_contradiction_clause,[],[f567]) ).
fof(f581,plain,
( ! [X0] :
( ~ eqangle(sK1,X0,sK1,sK4,sK1,X0,sK1,sK4)
| cyclic(X0,sK4,sK1,sK1) )
| ~ spl26_1 ),
inference(resolution,[],[f358,f326]) ).
fof(f582,plain,
( ! [X0] : cyclic(X0,sK4,sK1,sK1)
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f581,f353]) ).
fof(f585,plain,
( ! [X0] : cyclic(sK4,X0,sK1,sK1)
| ~ spl26_1 ),
inference(resolution,[],[f582,f330]) ).
fof(f589,plain,
( spl26_2
| ~ spl26_1 ),
inference(avatar_split_clause,[],[f585,f357,f360]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f362]) ).
cnf(s8,plain,
~ spl26_2,
inference(sat_conversion,[],[f580]) ).
cnf(s9,plain,
( ~ spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f589]) ).
cnf(s10,plain,
~ spl26_1,
inference(rat,[],[s9,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s8,s10]) ).
fof(f590,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO552+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 08:29:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.55/1.53 % (2687782)Detected formulas, will run a generic FOF schedule.
% 4.55/1.53 % (2687788)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=1695177655:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.55/1.53 % (2687793)dis-21_1_sil=8000:lcm=predicate:random_seed=3619848237: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)
% 4.55/1.53 % (2687787)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=3797557256:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.55/1.53 % (2687790)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2269983904:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.55/1.53 % (2687791)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3287037958:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.55/1.53 % (2687792)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2799393008:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.55/1.53 % (2687789)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=1138829815:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.55/1.53 % (2687790)Refutation not found, incomplete strategy
% 4.55/1.53 % (2687790)------------------------------
% 4.55/1.53 % (2687790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.53 % (2687790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.53 % (2687790)CaDiCaL version: 2.1.3
% 4.55/1.53 % (2687790)Termination reason: Refutation not found, incomplete strategy
% 4.55/1.53 % (2687790)Time elapsed: 0.019 s
% 4.55/1.53 % (2687790)Peak memory usage: 88 MB
% 4.55/1.53 % (2687790)Instructions burned: 32 (million)
% 4.55/1.53 % (2687792)Instruction limit reached!
% 4.55/1.53 % (2687792)------------------------------
% 4.55/1.53 % (2687792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.53 % (2687792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.53 % (2687792)CaDiCaL version: 2.1.3
% 4.55/1.53 % (2687792)Termination reason: Instruction limit
% 4.55/1.53 % (2687792)Termination phase: Saturation
% 4.55/1.53 % (2687792)Time elapsed: 0.053 s
% 4.55/1.53 % (2687792)Peak memory usage: 88 MB
% 4.55/1.53 % (2687792)Instructions burned: 142 (million)
% 4.55/1.53 % (2687791)Instruction limit reached!
% 4.55/1.53 % (2687791)------------------------------
% 4.55/1.53 % (2687791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.53 % (2687791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.53 % (2687791)CaDiCaL version: 2.1.3
% 4.55/1.53 % (2687791)Termination reason: Instruction limit
% 4.55/1.53 % (2687791)Termination phase: Saturation
% 4.55/1.53 % (2687791)Time elapsed: 0.069 s
% 4.55/1.53 % (2687791)Peak memory usage: 88 MB
% 4.55/1.53 % (2687791)Instructions burned: 120 (million)
% 4.55/1.53 % (2687793)Instruction limit reached!
% 4.55/1.53 % (2687793)------------------------------
% 4.55/1.53 % (2687793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.53 % (2687793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.53 % (2687793)CaDiCaL version: 2.1.3
% 4.55/1.53 % (2687793)Termination reason: Instruction limit
% 4.55/1.53 % (2687793)Termination phase: Saturation
% 4.55/1.53 % (2687793)Time elapsed: 0.077 s
% 4.55/1.53 % (2687793)Peak memory usage: 89 MB
% 4.55/1.53 % (2687793)Instructions burned: 129 (million)
% 4.55/1.53 % (2687801)lrs+10_1_sil=8000:sp=occurrence:random_seed=1770898491:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.55/1.53 % (2687802)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3432346930:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.55/1.53 % (2687803)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2029220585:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.55/1.53 % (2687790)------------------------------
% 4.55/1.53 % (2687790)------------------------------
% 4.55/1.53 % (2687802)Instruction limit reached!
% 4.55/1.53 % (2687802)------------------------------
% 4.55/1.53 % (2687802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.53 % (2687802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.53 % (2687802)CaDiCaL version: 2.1.3
% 4.55/1.53 % (2687802)Termination reason: Instruction limit
% 4.55/1.53 % (2687802)Termination phase: Saturation
% 4.55/1.53 % (2687802)Time elapsed: 0.080 s
% 4.55/1.53 % (2687802)Peak memory usage: 90 MB
% 4.55/1.53 % (2687802)Instructions burned: 157 (million)
% 4.55/1.53 % (2687788)First to succeed.
% 4.55/1.53 % (2687788)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2687782"
% 4.55/1.53 % (2687801)Instruction limit reached!
% 4.55/1.53 % (2687801)------------------------------
% 4.55/1.53 % (2687801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.53 % (2687801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.53 % (2687801)CaDiCaL version: 2.1.3
% 4.55/1.53 % (2687801)Termination reason: Instruction limit
% 4.55/1.53 % (2687801)Termination phase: Saturation
% 4.55/1.53 % (2687801)Time elapsed: 0.186 s
% 4.55/1.53 % (2687801)Peak memory usage: 92 MB
% 4.55/1.53 % (2687801)Instructions burned: 285 (million)
% 4.55/1.53 % (2687807)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=1800334450:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.55/1.53 % (2687803)Instruction limit reached!
% 4.55/1.53 % (2687803)------------------------------
% 4.55/1.53 % (2687803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.53 % (2687803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.53 % (2687803)CaDiCaL version: 2.1.3
% 4.55/1.53 % (2687803)Termination reason: Instruction limit
% 4.55/1.53 % (2687803)Termination phase: Saturation
% 4.55/1.53 % (2687803)Time elapsed: 0.196 s
% 4.55/1.53 % (2687803)Peak memory usage: 91 MB
% 4.55/1.53 % (2687803)Instructions burned: 325 (million)
% 4.55/1.53 % (2687808)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2067425673:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.55/1.53 % (2687788)Refutation found. Thanks to Tanya!
% 4.55/1.53 % SZS status Theorem for theBenchmark
% 4.55/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.46/1.73 % (2687788)------------------------------
% 5.46/1.73 % (2687788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.46/1.73 % (2687788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.73 % (2687788)CaDiCaL version: 2.1.3
% 5.46/1.73 % (2687788)Termination reason: Refutation
% 5.46/1.73 % (2687788)Time elapsed: 0.396 s
% 5.46/1.73 % (2687788)Peak memory usage: 130 MB
% 5.46/1.73 % (2687788)Instructions burned: 1009 (million)
% 5.46/1.73 % (2687788)------------------------------
% 5.46/1.73 % (2687788)------------------------------
% 5.46/1.73 % (2687782)Success in time 0.687 s
% 5.46/1.73 % Vampire exiting
%------------------------------------------------------------------------------