%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO561+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 : n008.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 09:52:56 AM UTC 2026
% Result : Theorem 6.52s 1.96s
% Output : Refutation 8.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 97 ( 10 unt; 2 def)
% Number of atoms : 299 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 321 ( 119 ~; 113 |; 72 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 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 : 457 ( 0 sgn 433 !; 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(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(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)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X4)
& circle(X3,X0,X6,X10)
& coll(X7,X3,X5)
& circle(X3,X0,X7,X11)
& coll(X8,X0,X2)
& coll(X8,X6,X7)
& coll(X9,X0,X1)
& coll(X9,X6,X7) )
=> eqangle(X0,X9,X9,X8,X9,X8,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL214022) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( circle(X3,X0,X1,X2)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X4)
& circle(X3,X0,X6,X10)
& coll(X7,X3,X5)
& circle(X3,X0,X7,X11)
& coll(X8,X0,X2)
& coll(X8,X6,X7)
& coll(X9,X0,X1)
& coll(X9,X6,X7) )
=> eqangle(X0,X9,X9,X8,X9,X8,X8,X0) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f108,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(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f108]) ).
fof(f120,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(f121,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(flattening,[],[f120]) ).
fof(f123,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(f125,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(f126,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(f127,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,[],[f126]) ).
fof(f148,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(f149,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(f150,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f41]) ).
fof(f151,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(f152,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,[],[f151]) ).
fof(f153,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(f154,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,[],[f153]) ).
fof(f155,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(f156,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,[],[f155]) ).
fof(f180,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(f181,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(flattening,[],[f180]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X0,X9,X9,X8,X9,X8,X8,X0)
& circle(X3,X0,X1,X2)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X4)
& circle(X3,X0,X6,X10)
& coll(X7,X3,X5)
& circle(X3,X0,X7,X11)
& coll(X8,X0,X2)
& coll(X8,X6,X7)
& coll(X9,X0,X1)
& coll(X9,X6,X7) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ eqangle(X0,X9,X9,X8,X9,X8,X8,X0)
& circle(X3,X0,X1,X2)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X4)
& circle(X3,X0,X6,X10)
& coll(X7,X3,X5)
& circle(X3,X0,X7,X11)
& coll(X8,X0,X2)
& coll(X8,X6,X7)
& coll(X9,X0,X1)
& coll(X9,X6,X7) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( ~ eqangle(sK20,sK29,sK29,sK28,sK29,sK28,sK28,sK20)
& circle(sK23,sK20,sK21,sK22)
& perp(sK24,sK23,sK20,sK22)
& coll(sK24,sK20,sK22)
& perp(sK25,sK23,sK20,sK21)
& coll(sK25,sK20,sK21)
& coll(sK26,sK23,sK24)
& circle(sK23,sK20,sK26,sK30)
& coll(sK27,sK23,sK25)
& circle(sK23,sK20,sK27,sK31)
& coll(sK28,sK20,sK22)
& coll(sK28,sK26,sK27)
& coll(sK29,sK20,sK21)
& coll(sK29,sK26,sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25),skolemize(X6,sK26),skolemize(X7,sK27),skolemize(X8,sK28),skolemize(X9,sK29),skolemize(X10,sK30),skolemize(X11,sK31)],[f250]) ).
fof(f278,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f279,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,[],[f109]) ).
fof(f287,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f121]) ).
fof(f289,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,[],[f123]) ).
fof(f291,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,[],[f125]) ).
fof(f292,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,[],[f127]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f310,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f149]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f312,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,[],[f152]) ).
fof(f313,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f314,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| cong(X0,X1,X3,X4) ),
inference(cnf_transformation,[],[f156]) ).
fof(f327,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f393,plain,
perp(sK25,sK23,sK20,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f397,plain,
~ eqangle(sK20,sK29,sK29,sK28,sK29,sK28,sK28,sK20),
inference(cnf_transformation,[],[f270]) ).
fof(f399,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X6,X7)
| ~ para(X4,X5,X8,X9) ),
inference(resolution,[],[f292,f310]) ).
fof(f400,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ para(X6,X7,X4,X5)
| eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X0,X1,X6,X7) ),
inference(resolution,[],[f399,f310]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X0,X1) ),
inference(resolution,[],[f311,f314]) ).
fof(f404,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) ),
inference(duplicate_literal_removal,[],[f401]) ).
fof(f412,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5) ),
inference(resolution,[],[f289,f310]) ).
fof(f431,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f291,f310]) ).
fof(f446,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ para(X2,X3,X2,X3) ),
inference(resolution,[],[f309,f412]) ).
fof(f449,definition,
( spl32_1
<=> ! [X2,X3] : ~ para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition]) ).
fof(f450,plain,
( ! [X2,X3] : ~ para(X2,X3,X2,X3)
| ~ spl32_1 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f452,definition,
( spl32_2
<=> ! [X0,X1] : para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl32_2])],[avatar_definition]) ).
fof(f453,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl32_2 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f454,plain,
( spl32_1
| spl32_2 ),
inference(avatar_split_clause,[],[f446,f452,f449]) ).
fof(f459,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f431]) ).
fof(f463,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f459,f453]) ).
fof(f468,plain,
perp(sK20,sK21,sK25,sK23),
inference(resolution,[],[f278,f393]) ).
fof(f473,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f431]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) )
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f473,f463]) ).
fof(f480,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f477,f453]) ).
fof(f481,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl32_2 ),
inference(resolution,[],[f480,f287]) ).
fof(f487,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f481,f480]) ).
fof(f490,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl32_2 ),
inference(resolution,[],[f487,f404]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f490,f487]) ).
fof(f495,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f493,f487]) ).
fof(f496,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl32_2 ),
inference(resolution,[],[f495,f327]) ).
fof(f497,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f496,f495]) ).
fof(f498,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl32_2 ),
inference(resolution,[],[f497,f278]) ).
fof(f504,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK25,sK23)
| para(X0,X1,sK20,sK21) ),
inference(resolution,[],[f279,f393]) ).
fof(f506,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl32_2 ),
inference(resolution,[],[f279,f497]) ).
fof(f508,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f506,f498]) ).
fof(f509,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X0,X1,X6,X7) )
| ~ spl32_2 ),
inference(resolution,[],[f508,f400]) ).
fof(f511,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f509,f508]) ).
fof(f515,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ spl32_2 ),
inference(resolution,[],[f511,f291]) ).
fof(f529,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ para(X6,X7,X4,X5) )
| ~ spl32_2 ),
inference(resolution,[],[f515,f399]) ).
fof(f533,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ spl32_2 ),
inference(forward_subsumption_resolution,[],[f529,f508]) ).
fof(f546,plain,
( $false
| ~ spl32_2 ),
inference(resolution,[],[f533,f397]) ).
fof(f547,plain,
~ spl32_2,
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f551,plain,
para(sK20,sK21,sK20,sK21),
inference(resolution,[],[f468,f504]) ).
fof(f555,plain,
( $false
| ~ spl32_1 ),
inference(forward_subsumption_resolution,[],[f551,f450]) ).
fof(f556,plain,
~ spl32_1,
inference(avatar_contradiction_clause,[],[f555]) ).
cnf(s1,plain,
( spl32_1
| spl32_2 ),
inference(sat_conversion,[],[f454]) ).
cnf(s2,plain,
~ spl32_2,
inference(sat_conversion,[],[f547]) ).
cnf(s3,plain,
~ spl32_1,
inference(sat_conversion,[],[f556]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f557,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO561+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 08:31:39 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 6.52/1.96 % (925178)Detected formulas, will run a generic FOF schedule.
% 6.52/1.96 % (925187)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3366193310:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.52/1.96 % (925183)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=355044462:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.52/1.96 % (925189)dis-21_1_sil=8000:lcm=predicate:random_seed=2514211686: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)
% 6.52/1.96 % (925188)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2185233546:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.52/1.96 % (925185)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=2958554618:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.52/1.96 % (925186)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1876529008:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.52/1.96 % (925184)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=2009727006:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.52/1.96 % (925187)Instruction limit reached!
% 6.52/1.96 % (925187)------------------------------
% 6.52/1.96 % (925187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925187)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925187)Termination reason: Instruction limit
% 6.52/1.96 % (925187)Termination phase: Saturation
% 6.52/1.96 % (925187)Time elapsed: 0.038 s
% 6.52/1.96 % (925187)Peak memory usage: 89 MB
% 6.52/1.96 % (925187)Instructions burned: 123 (million)
% 6.52/1.96 % (925186)Instruction limit reached!
% 6.52/1.96 % (925186)------------------------------
% 6.52/1.96 % (925186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925186)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925186)Termination reason: Instruction limit
% 6.52/1.96 % (925186)Termination phase: Saturation
% 6.52/1.96 % (925186)Time elapsed: 0.061 s
% 6.52/1.96 % (925186)Peak memory usage: 89 MB
% 6.52/1.96 % (925186)Instructions burned: 111 (million)
% 6.52/1.96 % (925189)Instruction limit reached!
% 6.52/1.96 % (925189)------------------------------
% 6.52/1.96 % (925189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925189)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925189)Termination reason: Instruction limit
% 6.52/1.96 % (925189)Termination phase: Saturation
% 6.52/1.96 % (925189)Time elapsed: 0.076 s
% 6.52/1.96 % (925189)Peak memory usage: 89 MB
% 6.52/1.96 % (925189)Instructions burned: 130 (million)
% 6.52/1.96 % (925188)Instruction limit reached!
% 6.52/1.96 % (925188)------------------------------
% 6.52/1.96 % (925188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925188)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925188)Termination reason: Instruction limit
% 6.52/1.96 % (925188)Termination phase: Saturation
% 6.52/1.96 % (925188)Time elapsed: 0.089 s
% 6.52/1.96 % (925188)Peak memory usage: 90 MB
% 6.52/1.96 % (925188)Instructions burned: 140 (million)
% 6.52/1.96 % (925197)lrs+10_1_sil=8000:sp=occurrence:random_seed=61388631:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.52/1.96 % (925199)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3100842303:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.52/1.96 % (925198)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2914538725:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.52/1.96 % (925197)Instruction limit reached!
% 6.52/1.96 % (925197)------------------------------
% 6.52/1.96 % (925197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925197)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925197)Termination reason: Instruction limit
% 6.52/1.96 % (925197)Termination phase: Saturation
% 6.52/1.96 % (925197)Time elapsed: 0.100 s
% 6.52/1.96 % (925197)Peak memory usage: 93 MB
% 6.52/1.96 % (925197)Instructions burned: 287 (million)
% 6.52/1.96 % (925200)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=3509722527:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.52/1.96 % (925198)Instruction limit reached!
% 6.52/1.96 % (925198)------------------------------
% 6.52/1.96 % (925198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925198)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925198)Termination reason: Instruction limit
% 6.52/1.96 % (925198)Termination phase: Saturation
% 6.52/1.96 % (925198)Time elapsed: 0.081 s
% 6.52/1.96 % (925198)Peak memory usage: 89 MB
% 6.52/1.96 % (925198)Instructions burned: 157 (million)
% 6.52/1.96 % (925204)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2032797040:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.52/1.96 % (925200)Instruction limit reached!
% 6.52/1.96 % (925200)------------------------------
% 6.52/1.96 % (925200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925200)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925200)Termination reason: Instruction limit
% 6.52/1.96 % (925200)Termination phase: Saturation
% 6.52/1.96 % (925200)Time elapsed: 0.140 s
% 6.52/1.96 % (925200)Peak memory usage: 91 MB
% 6.52/1.96 % (925200)Instructions burned: 248 (million)
% 6.52/1.96 % (925199)Instruction limit reached!
% 6.52/1.96 % (925199)------------------------------
% 6.52/1.96 % (925199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925199)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925199)Termination reason: Instruction limit
% 6.52/1.96 % (925199)Termination phase: Saturation
% 6.52/1.96 % (925199)Time elapsed: 0.218 s
% 6.52/1.96 % (925199)Peak memory usage: 92 MB
% 6.52/1.96 % (925199)Instructions burned: 325 (million)
% 6.52/1.96 % (925204)Instruction limit reached!
% 6.52/1.96 % (925204)------------------------------
% 6.52/1.96 % (925204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925204)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925204)Termination reason: Instruction limit
% 6.52/1.96 % (925204)Termination phase: Saturation
% 6.52/1.96 % (925204)Time elapsed: 0.090 s
% 6.52/1.96 % (925204)Peak memory usage: 89 MB
% 6.52/1.96 % (925204)Instructions burned: 295 (million)
% 6.52/1.96 % (925206)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3976755115:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.52/1.96 % (925208)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1672363859:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.52/1.96 % (925211)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3122270730:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.52/1.96 % (925211)Instruction limit reached!
% 6.52/1.96 % (925211)------------------------------
% 6.52/1.96 % (925211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925211)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925211)Termination reason: Instruction limit
% 6.52/1.96 % (925211)Termination phase: Saturation
% 6.52/1.96 % (925211)Time elapsed: 0.033 s
% 6.52/1.96 % (925211)Peak memory usage: 89 MB
% 6.52/1.96 % (925211)Instructions burned: 118 (million)
% 6.52/1.96 % (925209)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2058833964:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.52/1.96 % (925208)Instruction limit reached!
% 6.52/1.96 % (925208)------------------------------
% 6.52/1.96 % (925208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925208)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925208)Termination reason: Instruction limit
% 6.52/1.96 % (925208)Termination phase: Saturation
% 6.52/1.96 % (925208)Time elapsed: 0.066 s
% 6.52/1.96 % (925208)Peak memory usage: 89 MB
% 6.52/1.96 % (925208)Instructions burned: 113 (million)
% 6.52/1.96 % (925183)First to succeed.
% 6.52/1.96 % (925183)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-925178"
% 6.52/1.96 % (925209)Instruction limit reached!
% 6.52/1.96 % (925209)------------------------------
% 6.52/1.96 % (925209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.96 % (925209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.96 % (925209)CaDiCaL version: 2.1.3
% 6.52/1.96 % (925209)Termination reason: Instruction limit
% 6.52/1.96 % (925209)Termination phase: Saturation
% 6.52/1.96 % (925209)Time elapsed: 0.071 s
% 6.52/1.96 % (925209)Peak memory usage: 89 MB
% 6.52/1.96 % (925209)Instructions burned: 129 (million)
% 6.52/1.96 % (925184)Also succeeded, but the first one will report.
% 6.52/1.96 % (925215)lrs+10_1_sil=8000:sp=occurrence:random_seed=3229592549:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.52/1.96 % (925216)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3284521363:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.52/1.96 % (925217)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1846694556:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.52/1.96 % (925183)Refutation found. Thanks to Tanya!
% 6.52/1.96 % SZS status Theorem for theBenchmark
% 6.52/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 8.29/2.08 % (925183)------------------------------
% 8.29/2.08 % (925183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.29/2.08 % (925183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.29/2.08 % (925183)CaDiCaL version: 2.1.3
% 8.29/2.08 % (925183)Termination reason: Refutation
% 8.29/2.08 % (925183)Time elapsed: 0.660 s
% 8.29/2.08 % (925183)Peak memory usage: 130 MB
% 8.29/2.08 % (925183)Instructions burned: 986 (million)
% 8.29/2.08 % (925183)------------------------------
% 8.29/2.08 % (925183)------------------------------
% 8.29/2.08 % (925178)Success in time 1.101 s
% 8.29/2.08 % Vampire exiting
%------------------------------------------------------------------------------