%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO625+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 : n004.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 09:53:05 AM UTC 2026
% Result : Theorem 6.81s 1.95s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of formulae : 102 ( 8 unt; 2 def)
% Number of atoms : 291 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 315 ( 126 ~; 119 |; 52 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 3 prp; 0-8 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 484 ( 0 sgn 462 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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/sandbox2/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/sandbox2/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/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(f87,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X3,X0,X1,X2)
=> perp(X4,X0,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX11) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( eqangle(X3,X0,X0,X1,X3,X0,X0,X2)
& eqangle(X3,X1,X1,X2,X3,X1,X1,X0)
& eqangle(X3,X2,X2,X0,X3,X2,X2,X1)
& midp(X4,X1,X0)
& midp(X5,X2,X1)
& midp(X6,X0,X2)
& midp(X7,X3,X1)
& midp(X8,X2,X3)
& circle(X9,X7,X5,X8) )
=> eqangle(X6,X5,X5,X9,X9,X5,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL8110989) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( eqangle(X3,X0,X0,X1,X3,X0,X0,X2)
& eqangle(X3,X1,X1,X2,X3,X1,X1,X0)
& eqangle(X3,X2,X2,X0,X3,X2,X2,X1)
& midp(X4,X1,X0)
& midp(X5,X2,X1)
& midp(X6,X0,X2)
& midp(X7,X3,X1)
& midp(X8,X2,X3)
& circle(X9,X7,X5,X8) )
=> eqangle(X6,X5,X5,X9,X9,X5,X5,X4) ),
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(f234,plain,
! [X0,X1,X2,X3] :
? [X4] :
( perp(X4,X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(ennf_transformation,[],[f87]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ eqangle(X6,X5,X5,X9,X9,X5,X5,X4)
& eqangle(X3,X0,X0,X1,X3,X0,X0,X2)
& eqangle(X3,X1,X1,X2,X3,X1,X1,X0)
& eqangle(X3,X2,X2,X0,X3,X2,X2,X1)
& midp(X4,X1,X0)
& midp(X5,X2,X1)
& midp(X6,X0,X2)
& midp(X7,X3,X1)
& midp(X8,X2,X3)
& circle(X9,X7,X5,X8) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ eqangle(X6,X5,X5,X9,X9,X5,X5,X4)
& eqangle(X3,X0,X0,X1,X3,X0,X0,X2)
& eqangle(X3,X1,X1,X2,X3,X1,X1,X0)
& eqangle(X3,X2,X2,X0,X3,X2,X2,X1)
& midp(X4,X1,X0)
& midp(X5,X2,X1)
& midp(X6,X0,X2)
& midp(X7,X3,X1)
& midp(X8,X2,X3)
& circle(X9,X7,X5,X8) ),
inference(flattening,[],[f249]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( perp(sK11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X4,sK11(X0,X1,X2,X3))],[f234]) ).
fof(f270,plain,
( ~ eqangle(sK26,sK25,sK25,sK29,sK29,sK25,sK25,sK24)
& eqangle(sK23,sK20,sK20,sK21,sK23,sK20,sK20,sK22)
& eqangle(sK23,sK21,sK21,sK22,sK23,sK21,sK21,sK20)
& eqangle(sK23,sK22,sK22,sK20,sK23,sK22,sK22,sK21)
& midp(sK24,sK21,sK20)
& midp(sK25,sK22,sK21)
& midp(sK26,sK20,sK22)
& midp(sK27,sK23,sK21)
& midp(sK28,sK22,sK23)
& circle(sK29,sK27,sK25,sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29]),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)],[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(f370,plain,
! [X2,X3,X0,X1] :
( perp(sK11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f262]) ).
fof(f384,plain,
circle(sK29,sK27,sK25,sK28),
inference(cnf_transformation,[],[f270]) ).
fof(f393,plain,
~ eqangle(sK26,sK25,sK25,sK29,sK29,sK25,sK25,sK24),
inference(cnf_transformation,[],[f270]) ).
fof(f395,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(f396,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,[],[f395]) ).
fof(f402,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(f417,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(f428,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(f434,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,[],[f428,f310]) ).
fof(f441,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f417]) ).
fof(f448,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ para(X2,X3,X2,X3) ),
inference(resolution,[],[f309,f402]) ).
fof(f451,definition,
( spl30_1
<=> ! [X2,X3] : ~ para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl30_1])],[avatar_definition]) ).
fof(f452,plain,
( ! [X2,X3] : ~ para(X2,X3,X2,X3)
| ~ spl30_1 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f454,definition,
( spl30_2
<=> ! [X0,X1] : para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f455,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl30_2 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f456,plain,
( spl30_1
| spl30_2 ),
inference(avatar_split_clause,[],[f448,f454,f451]) ).
fof(f461,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f417]) ).
fof(f465,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) ),
inference(forward_subsumption_resolution,[],[f461,f441]) ).
fof(f468,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f465,f455]) ).
fof(f470,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl30_2 ),
inference(resolution,[],[f468,f287]) ).
fof(f474,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f470,f468]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl30_2 ),
inference(resolution,[],[f474,f396]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f477,f474]) ).
fof(f483,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f481,f474]) ).
fof(f484,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl30_2 ),
inference(resolution,[],[f483,f327]) ).
fof(f485,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f484,f483]) ).
fof(f503,plain,
! [X2,X3,X0,X1] :
( perp(X0,X1,sK11(X0,X2,X3,X1),X0)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f278,f370]) ).
fof(f504,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl30_2 ),
inference(resolution,[],[f278,f485]) ).
fof(f511,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X0,X1,sK11(X2,X3,X4,X5),X2)
| para(X0,X1,X2,X5)
| ~ circle(X5,X2,X3,X4) ),
inference(resolution,[],[f279,f370]) ).
fof(f513,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl30_2 ),
inference(resolution,[],[f279,f485]) ).
fof(f516,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f513,f504]) ).
fof(f517,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X0,X1,X6,X7) )
| ~ spl30_2 ),
inference(resolution,[],[f516,f434]) ).
fof(f520,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f517,f516]) ).
fof(f526,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ spl30_2 ),
inference(resolution,[],[f520,f291]) ).
fof(f539,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ para(X6,X7,X4,X5) )
| ~ spl30_2 ),
inference(resolution,[],[f526,f428]) ).
fof(f547,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f539,f516]) ).
fof(f560,plain,
( $false
| ~ spl30_2 ),
inference(resolution,[],[f547,f393]) ).
fof(f561,plain,
~ spl30_2,
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f567,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3)
| ~ circle(X1,X0,X2,X3) ),
inference(resolution,[],[f511,f503]) ).
fof(f568,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ circle(X1,X0,X2,X3) ),
inference(duplicate_literal_removal,[],[f567]) ).
fof(f569,plain,
( ! [X2,X3,X0,X1] : ~ circle(X1,X0,X2,X3)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f568,f452]) ).
fof(f570,plain,
( $false
| ~ spl30_1 ),
inference(resolution,[],[f569,f384]) ).
fof(f571,plain,
~ spl30_1,
inference(avatar_contradiction_clause,[],[f570]) ).
cnf(s1,plain,
( spl30_1
| spl30_2 ),
inference(sat_conversion,[],[f456]) ).
cnf(s2,plain,
~ spl30_2,
inference(sat_conversion,[],[f561]) ).
cnf(s3,plain,
~ spl30_1,
inference(sat_conversion,[],[f571]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f572,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO625+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 08:39:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 6.81/1.95 % (3207104)Detected formulas, will run a generic FOF schedule.
% 6.81/1.95 % (3207111)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=4201640944:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.81/1.95 % (3207115)dis-21_1_sil=8000:lcm=predicate:random_seed=1975335805: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)
% 6.81/1.95 % (3207112)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=278803590:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.81/1.95 % (3207113)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4240072918:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.81/1.95 % (3207110)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=3749980381:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.81/1.95 % (3207109)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=508547052:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.81/1.95 % (3207114)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1143691292:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.81/1.95 % (3207112)Instruction limit reached!
% 6.81/1.95 % (3207112)------------------------------
% 6.81/1.95 % (3207112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207112)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207112)Termination reason: Instruction limit
% 6.81/1.95 % (3207112)Termination phase: Saturation
% 6.81/1.95 % (3207112)Time elapsed: 0.063 s
% 6.81/1.95 % (3207112)Peak memory usage: 89 MB
% 6.81/1.95 % (3207112)Instructions burned: 110 (million)
% 6.81/1.95 % (3207113)Instruction limit reached!
% 6.81/1.95 % (3207113)------------------------------
% 6.81/1.95 % (3207113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207113)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207113)Termination reason: Instruction limit
% 6.81/1.95 % (3207113)Termination phase: Saturation
% 6.81/1.95 % (3207113)Time elapsed: 0.068 s
% 6.81/1.95 % (3207113)Peak memory usage: 88 MB
% 6.81/1.95 % (3207113)Instructions burned: 120 (million)
% 6.81/1.95 % (3207115)Instruction limit reached!
% 6.81/1.95 % (3207115)------------------------------
% 6.81/1.95 % (3207115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207115)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207115)Termination reason: Instruction limit
% 6.81/1.95 % (3207115)Termination phase: Saturation
% 6.81/1.95 % (3207115)Time elapsed: 0.072 s
% 6.81/1.95 % (3207115)Peak memory usage: 89 MB
% 6.81/1.95 % (3207115)Instructions burned: 130 (million)
% 6.81/1.95 % (3207114)Instruction limit reached!
% 6.81/1.95 % (3207114)------------------------------
% 6.81/1.95 % (3207114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207114)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207114)Termination reason: Instruction limit
% 6.81/1.95 % (3207114)Termination phase: Saturation
% 6.81/1.95 % (3207114)Time elapsed: 0.082 s
% 6.81/1.95 % (3207114)Peak memory usage: 90 MB
% 6.81/1.95 % (3207114)Instructions burned: 140 (million)
% 6.81/1.95 % (3207123)lrs+10_1_sil=8000:sp=occurrence:random_seed=1632564980:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.81/1.95 % (3207124)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4263554274:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.81/1.95 % (3207125)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1114846673:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.81/1.95 % (3207126)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=3131288965:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.81/1.95 % (3207124)Instruction limit reached!
% 6.81/1.95 % (3207124)------------------------------
% 6.81/1.95 % (3207124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207124)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207124)Termination reason: Instruction limit
% 6.81/1.95 % (3207124)Termination phase: Saturation
% 6.81/1.95 % (3207124)Time elapsed: 0.078 s
% 6.81/1.95 % (3207124)Peak memory usage: 91 MB
% 6.81/1.95 % (3207124)Instructions burned: 157 (million)
% 6.81/1.95 % (3207126)Instruction limit reached!
% 6.81/1.95 % (3207126)------------------------------
% 6.81/1.95 % (3207126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207126)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207126)Termination reason: Instruction limit
% 6.81/1.95 % (3207126)Termination phase: Saturation
% 6.81/1.95 % (3207126)Time elapsed: 0.131 s
% 6.81/1.95 % (3207126)Peak memory usage: 91 MB
% 6.81/1.95 % (3207126)Instructions burned: 250 (million)
% 6.81/1.95 % (3207123)Instruction limit reached!
% 6.81/1.95 % (3207123)------------------------------
% 6.81/1.95 % (3207123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207123)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207123)Termination reason: Instruction limit
% 6.81/1.95 % (3207123)Termination phase: Saturation
% 6.81/1.95 % (3207123)Time elapsed: 0.179 s
% 6.81/1.95 % (3207123)Peak memory usage: 92 MB
% 6.81/1.95 % (3207123)Instructions burned: 285 (million)
% 6.81/1.95 % (3207125)Instruction limit reached!
% 6.81/1.95 % (3207125)------------------------------
% 6.81/1.95 % (3207125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207125)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207125)Termination reason: Instruction limit
% 6.81/1.95 % (3207125)Termination phase: Saturation
% 6.81/1.95 % (3207125)Time elapsed: 0.183 s
% 6.81/1.95 % (3207125)Peak memory usage: 91 MB
% 6.81/1.95 % (3207125)Instructions burned: 325 (million)
% 6.81/1.95 % (3207131)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=453793295:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.81/1.95 % (3207132)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3568689843:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.81/1.95 % (3207133)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1255882206:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.81/1.95 % (3207134)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1155312353:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.81/1.95 % (3207133)Instruction limit reached!
% 6.81/1.95 % (3207133)------------------------------
% 6.81/1.95 % (3207133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207133)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207133)Termination reason: Instruction limit
% 6.81/1.95 % (3207133)Termination phase: Saturation
% 6.81/1.95 % (3207133)Time elapsed: 0.066 s
% 6.81/1.95 % (3207133)Peak memory usage: 90 MB
% 6.81/1.95 % (3207133)Instructions burned: 114 (million)
% 6.81/1.95 % (3207131)Instruction limit reached!
% 6.81/1.95 % (3207131)------------------------------
% 6.81/1.95 % (3207131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207131)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207131)Termination reason: Instruction limit
% 6.81/1.95 % (3207131)Termination phase: Saturation
% 6.81/1.95 % (3207131)Time elapsed: 0.164 s
% 6.81/1.95 % (3207131)Peak memory usage: 89 MB
% 6.81/1.95 % (3207131)Instructions burned: 295 (million)
% 6.81/1.95 % (3207134)Instruction limit reached!
% 6.81/1.95 % (3207134)------------------------------
% 6.81/1.95 % (3207134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207134)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207134)Termination reason: Instruction limit
% 6.81/1.95 % (3207134)Termination phase: Saturation
% 6.81/1.95 % (3207134)Time elapsed: 0.071 s
% 6.81/1.95 % (3207134)Peak memory usage: 89 MB
% 6.81/1.95 % (3207134)Instructions burned: 129 (million)
% 6.81/1.95 % (3207109)First to succeed.
% 6.81/1.95 % (3207109)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3207104"
% 6.81/1.95 % (3207110)Also succeeded, but the first one will report.
% 6.81/1.95 % (3207139)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3179400914:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.81/1.95 % (3207140)lrs+10_1_sil=8000:sp=occurrence:random_seed=1776786045:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.81/1.95 % (3207139)Instruction limit reached!
% 6.81/1.95 % (3207139)------------------------------
% 6.81/1.95 % (3207139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.81/1.95 % (3207139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.81/1.95 % (3207139)CaDiCaL version: 2.1.3
% 6.81/1.95 % (3207139)Termination reason: Instruction limit
% 6.81/1.95 % (3207139)Termination phase: Saturation
% 6.81/1.95 % (3207139)Time elapsed: 0.062 s
% 6.81/1.95 % (3207139)Peak memory usage: 89 MB
% 6.81/1.95 % (3207139)Instructions burned: 115 (million)
% 6.81/1.95 % (3207141)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2782246346:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.81/1.95 % (3207109)Refutation found. Thanks to Tanya!
% 6.81/1.95 % SZS status Theorem for theBenchmark
% 6.81/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/2.14 % (3207109)------------------------------
% 0.18/2.14 % (3207109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/2.14 % (3207109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/2.14 % (3207109)CaDiCaL version: 2.1.3
% 0.18/2.14 % (3207109)Termination reason: Refutation
% 0.18/2.14 % (3207109)Time elapsed: 0.652 s
% 0.18/2.14 % (3207109)Peak memory usage: 129 MB
% 0.18/2.14 % (3207109)Instructions burned: 991 (million)
% 0.18/2.14 % (3207109)------------------------------
% 0.18/2.14 % (3207109)------------------------------
% 0.18/2.14 % (3207104)Success in time 1.09 s
% 0.18/2.14 % Vampire exiting
%------------------------------------------------------------------------------