%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO556+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 09:54:43 AM UTC 2026
% Result : Theorem 2.00s 0.88s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 22
% Syntax : Number of formulae : 130 ( 14 unt; 2 def)
% Number of atoms : 376 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 402 ( 156 ~; 151 |; 72 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 564 ( 0 sgn 539 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( para(X0,X1,X2,X3)
& para(X2,X3,X4,X5) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD6) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD10) ).
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/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',ruleD19) ).
fof(f20,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
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/Axioms/GEO012+0.ax',ruleD21) ).
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/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',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/Axioms/GEO012+0.ax',ruleD43) ).
fof(f49,axiom,
! [X0,X1,X2,X3,X4] :
( ( circle(X3,X0,X1,X2)
& perp(X3,X0,X0,X4) )
=> eqangle(X0,X4,X0,X1,X2,X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD48) ).
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/Axioms/GEO012+0.ax',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/sandbox/benchmark/Axioms/GEO012+0.ax',ruleD57) ).
fof(f90,axiom,
! [X0,X1,X2,X3] :
? [X4] :
( ( perp(X0,X2,X2,X1)
& cyclic(X0,X1,X2,X3) )
=> circle(X4,X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO012+0.ax',ruleX14) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ( coll(X3,X0,X1)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X1,X2)
& coll(X5,X1,X2)
& perp(X6,X1,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X0,X1,X2)
& coll(X7,X1,X2)
& perp(X8,X5,X0,X2)
& coll(X8,X0,X2)
& perp(X9,X4,X1,X2)
& coll(X9,X1,X2)
& coll(X10,X5,X8)
& coll(X10,X4,X9) )
=> perp(X2,X10,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012016) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ( coll(X3,X0,X1)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X1,X2)
& coll(X5,X1,X2)
& perp(X6,X1,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X0,X1,X2)
& coll(X7,X1,X2)
& perp(X8,X5,X0,X2)
& coll(X8,X0,X2)
& perp(X9,X4,X1,X2)
& coll(X9,X1,X2)
& coll(X10,X5,X8)
& coll(X10,X4,X9) )
=> perp(X2,X10,X4,X5) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ para(X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f6]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ para(X2,X3,X4,X5) ),
inference(flattening,[],[f104]) ).
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(f110,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(f111,plain,
! [X0,X1,X2,X3,X4,X5] :
( perp(X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f110]) ).
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(f122,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(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(f124,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f20]) ).
fof(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(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(f164,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
| ~ circle(X3,X0,X1,X2)
| ~ perp(X3,X0,X0,X4) ),
inference(ennf_transformation,[],[f49]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4] :
( eqangle(X0,X4,X0,X1,X2,X0,X2,X1)
| ~ circle(X3,X0,X1,X2)
| ~ perp(X3,X0,X0,X4) ),
inference(flattening,[],[f164]) ).
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(f182,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(f183,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,[],[f182]) ).
fof(f239,plain,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X4,X0,X1,X2)
| ~ perp(X0,X2,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f90]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
? [X4] :
( circle(X4,X0,X1,X2)
| ~ perp(X0,X2,X2,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(flattening,[],[f239]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ perp(X2,X10,X4,X5)
& coll(X3,X0,X1)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X1,X2)
& coll(X5,X1,X2)
& perp(X6,X1,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X0,X1,X2)
& coll(X7,X1,X2)
& perp(X8,X5,X0,X2)
& coll(X8,X0,X2)
& perp(X9,X4,X1,X2)
& coll(X9,X1,X2)
& coll(X10,X5,X8)
& coll(X10,X4,X9) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ perp(X2,X10,X4,X5)
& coll(X3,X0,X1)
& perp(X4,X3,X0,X2)
& coll(X4,X0,X2)
& perp(X5,X3,X1,X2)
& coll(X5,X1,X2)
& perp(X6,X1,X0,X2)
& coll(X6,X0,X2)
& perp(X7,X0,X1,X2)
& coll(X7,X1,X2)
& perp(X8,X5,X0,X2)
& coll(X8,X0,X2)
& perp(X9,X4,X1,X2)
& coll(X9,X1,X2)
& coll(X10,X5,X8)
& coll(X10,X4,X9) ),
inference(flattening,[],[f249]) ).
fof(f256,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| ~ para(X2,X3,X4,X5)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f105]) ).
fof(f258,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f259,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f109]) ).
fof(f260,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5)
| perp(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f111]) ).
fof(f267,plain,
! [X2,X3,X0,X1,X4] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| cyclic(X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f121]) ).
fof(f268,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,[],[f122]) ).
fof(f269,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(f270,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f124]) ).
fof(f271,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(f289,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(f290,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(f291,plain,
! [X2,X3,X0,X1] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| coll(X2,X3,X0)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f152]) ).
fof(f293,plain,
! [X2,X3,X0,X1] :
( ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ coll(X2,X3,X1)
| cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f154]) ).
fof(f294,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3)
| cong(X0,X1,X3,X4) ),
inference(cnf_transformation,[],[f156]) ).
fof(f299,plain,
! [X2,X3,X0,X1,X4] :
( ~ circle(X3,X0,X1,X2)
| ~ perp(X3,X0,X0,X4)
| eqangle(X0,X4,X0,X1,X2,X0,X2,X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f307,plain,
! [X2,X3,X0,X1] :
( ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3)
| perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f181]) ).
fof(f308,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2)
| perp(X2,X0,X0,X3) ),
inference(cnf_transformation,[],[f183]) ).
fof(f356,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ perp(X0,X2,X2,X1)
| circle(sK15(X0,X1,X2,X3),X0,X1,X2) ),
inference(cnf_transformation,[],[f240]) ).
fof(f369,plain,
perp(sK28,sK25,sK20,sK22),
inference(cnf_transformation,[],[f250]) ).
fof(f373,plain,
perp(sK26,sK21,sK20,sK22),
inference(cnf_transformation,[],[f250]) ).
fof(f379,plain,
~ perp(sK22,sK30,sK24,sK25),
inference(cnf_transformation,[],[f250]) ).
fof(f526,plain,
perp(sK20,sK22,sK26,sK21),
inference(resolution,[],[f258,f373]) ).
fof(f528,plain,
perp(sK20,sK22,sK28,sK25),
inference(resolution,[],[f258,f369]) ).
fof(f781,plain,
! [X0,X1] :
( ~ perp(sK20,sK22,X0,X1)
| para(sK26,sK21,X0,X1) ),
inference(resolution,[],[f259,f373]) ).
fof(f783,plain,
! [X0,X1] :
( ~ perp(sK20,sK22,X0,X1)
| para(sK28,sK25,X0,X1) ),
inference(resolution,[],[f259,f369]) ).
fof(f973,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X1,X0,X4,X5) ),
inference(resolution,[],[f268,f290]) ).
fof(f1004,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X2,X1,X0,X3)
| eqangle(X0,X1,X0,X2,X3,X1,X3,X2) ),
inference(resolution,[],[f269,f291]) ).
fof(f1015,definition,
( spl31_1
<=> ! [X2,X3] : para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
fof(f1016,plain,
( ! [X2,X3] : para(X2,X3,X2,X3)
| ~ spl31_1 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1018,definition,
( spl31_2
<=> ! [X0,X1] : ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
fof(f1019,plain,
( ! [X0,X1] : ~ para(X0,X1,X0,X1)
| ~ spl31_2 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f1532,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X5,X4,X0,X1) ),
inference(resolution,[],[f270,f973]) ).
fof(f1585,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f271,f290]) ).
fof(f1741,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X3,X2,X4,X5,X1,X0,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f1532,f268]) ).
fof(f2232,plain,
para(sK26,sK21,sK28,sK25),
inference(resolution,[],[f781,f528]) ).
fof(f2328,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X1,X0,X4,X5,X3,X2,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f1741,f270]) ).
fof(f2507,plain,
para(sK28,sK25,sK26,sK21),
inference(resolution,[],[f783,f526]) ).
fof(f2732,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X4,X5,X1,X0,X4,X5,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f2328,f269]) ).
fof(f3129,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X0,X1)
| para(X2,X3,X2,X3) ),
inference(resolution,[],[f2732,f289]) ).
fof(f3669,plain,
! [X2,X0,X1] :
( coll(X0,X1,X2)
| cyclic(X2,X2,X0,X1)
| ~ para(X0,X2,X0,X2) ),
inference(resolution,[],[f292,f1585]) ).
fof(f3754,plain,
( ! [X2,X0,X1] :
( cyclic(X2,X2,X0,X1)
| coll(X0,X1,X2) )
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f3669,f1016]) ).
fof(f4214,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| cyclic(X2,X2,X0,X1)
| ~ para(X0,X2,X0,X2) ),
inference(resolution,[],[f293,f1585]) ).
fof(f4324,plain,
( ! [X2,X0,X1] :
( cyclic(X2,X2,X0,X1)
| ~ para(X0,X2,X0,X2) )
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f4214,f3754]) ).
fof(f4388,plain,
( ! [X2,X0,X1] : cyclic(X2,X2,X0,X1)
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f4324,f1016]) ).
fof(f4426,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X3,X2) )
| ~ spl31_1 ),
inference(resolution,[],[f4388,f267]) ).
fof(f4432,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X3,X2)
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f4426,f4388]) ).
fof(f4554,plain,
( ! [X2,X3,X0,X1] : eqangle(X0,X1,X0,X2,X3,X1,X3,X2)
| ~ spl31_1 ),
inference(resolution,[],[f4432,f1004]) ).
fof(f5303,plain,
! [X0,X1] :
( para(sK26,sK21,X0,X1)
| ~ para(sK28,sK25,X0,X1) ),
inference(resolution,[],[f2232,f256]) ).
fof(f7681,plain,
( ! [X2,X3,X0,X1] :
( ~ perp(X0,X2,X2,X1)
| circle(sK15(X0,X1,X2,X3),X0,X1,X2) )
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f356,f4432]) ).
fof(f7782,plain,
( ! [X2,X3,X0,X1] :
( ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3)
| perp(X2,X0,X0,X3) )
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f308,f4432]) ).
fof(f12936,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| cong(X0,X1,X3,X4) )
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f294,f4432]) ).
fof(f12937,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| cong(X0,X1,X3,X4) )
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f12936,f4432]) ).
fof(f12938,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| cong(X0,X1,X3,X4) )
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f12937,f4432]) ).
fof(f13129,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl31_1 ),
inference(resolution,[],[f12938,f4554]) ).
fof(f13296,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X2,X0,X0,X1) )
| ~ spl31_1 ),
inference(resolution,[],[f13129,f7782]) ).
fof(f13297,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X2,X1) )
| ~ spl31_1 ),
inference(resolution,[],[f13129,f307]) ).
fof(f13364,plain,
( ! [X2,X0,X1] : perp(X0,X0,X2,X1)
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f13297,f13129]) ).
fof(f13365,plain,
( ! [X2,X0,X1] : perp(X2,X0,X0,X1)
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f13296,f13129]) ).
fof(f13693,plain,
( ! [X2,X0,X1] : circle(sK15(X0,X1,X0,X2),X0,X1,X0)
| ~ spl31_1 ),
inference(resolution,[],[f13364,f7681]) ).
fof(f15775,plain,
( ! [X2,X3,X0,X1] :
( ~ perp(sK15(X0,X1,X0,X2),X0,X0,X3)
| eqangle(X0,X3,X0,X1,X0,X0,X0,X1) )
| ~ spl31_1 ),
inference(resolution,[],[f13693,f299]) ).
fof(f15776,plain,
( ! [X3,X0,X1] : eqangle(X0,X3,X0,X1,X0,X0,X0,X1)
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f15775,f13365]) ).
fof(f16375,plain,
( ! [X0,X1] : para(X0,X1,X0,X0)
| ~ spl31_1 ),
inference(resolution,[],[f15776,f289]) ).
fof(f16390,plain,
( ! [X2,X3,X0,X1] :
( ~ perp(X0,X0,X1,X2)
| perp(X0,X3,X1,X2) )
| ~ spl31_1 ),
inference(resolution,[],[f16375,f260]) ).
fof(f16448,plain,
( ! [X2,X3,X0,X1] : perp(X0,X3,X1,X2)
| ~ spl31_1 ),
inference(forward_subsumption_resolution,[],[f16390,f13364]) ).
fof(f17078,plain,
( $false
| ~ spl31_1 ),
inference(resolution,[],[f16448,f379]) ).
fof(f17099,plain,
~ spl31_1,
inference(avatar_contradiction_clause,[],[f17078]) ).
fof(f17126,plain,
( spl31_1
| spl31_2 ),
inference(avatar_split_clause,[],[f3129,f1018,f1015]) ).
fof(f17209,plain,
( ~ para(sK28,sK25,sK26,sK21)
| ~ spl31_2 ),
inference(resolution,[],[f1019,f5303]) ).
fof(f17216,plain,
( $false
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f17209,f2507]) ).
fof(f17217,plain,
~ spl31_2,
inference(avatar_contradiction_clause,[],[f17216]) ).
cnf(s95,plain,
~ spl31_1,
inference(sat_conversion,[],[f17099]) ).
cnf(s107,plain,
( spl31_1
| spl31_2 ),
inference(sat_conversion,[],[f17126]) ).
cnf(s113,plain,
~ spl31_2,
inference(sat_conversion,[],[f17217]) ).
cnf(s115,plain,
spl31_1,
inference(rat,[],[s107,s113]) ).
cnf(s116,plain,
$false,
inference(rat,[],[s95,s115]) ).
fof(f17218,plain,
$false,
inference(avatar_sat_refutation,[],[s116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO556+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n015.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 08:34:00 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.00/0.87 % (1348440)Will run a generic schedule for satisfiability detection.
% 2.00/0.87 % (1348450)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2904451748:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.00/0.87 % (1348446)% WARNING: option uhcvi not known.
% 2.00/0.87 % (1348445)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4281534668_2999 on theBenchmark for (2999ds/0Mi)
% 2.00/0.87 % (1348446)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3355625287:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.00/0.87 % (1348447)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2399835955:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.00/0.87 % (1348448)dis+10_1_sil=32000:sp=arity:random_seed=3233680387:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.00/0.87 % (1348449)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=909000647:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.00/0.87 % (1348451)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=469960000:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.00/0.87 % TRYING [1]
% 2.00/0.87 % TRYING [2]
% 2.00/0.87 % (1348450)Instruction limit reached!
% 2.00/0.87 % (1348450)------------------------------
% 2.00/0.87 % (1348450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.87 % (1348450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.87 % (1348450)CaDiCaL version: 2.1.3
% 2.00/0.87 % (1348450)Termination reason: Instruction limit
% 2.00/0.87 % (1348450)Termination phase: Saturation
% 2.00/0.87 % (1348450)Time elapsed: 0.045 s
% 2.00/0.87 % (1348450)Peak memory usage: 14 MB
% 2.00/0.87 % (1348450)Instructions burned: 133 (million)
% 2.00/0.87 % TRYING [3]
% 2.00/0.87 % (1348459)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1482830978:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.00/0.87 % (1348449)Instruction limit reached!
% 2.00/0.87 % (1348449)------------------------------
% 2.00/0.87 % (1348449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.87 % (1348449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (1348449)CaDiCaL version: 2.1.3
% 2.00/0.88 % (1348449)Termination reason: Instruction limit
% 2.00/0.88 % (1348449)Termination phase: Saturation
% 2.00/0.88 % (1348449)Time elapsed: 0.066 s
% 2.00/0.88 % (1348449)Peak memory usage: 13 MB
% 2.00/0.88 % (1348449)Instructions burned: 117 (million)
% 2.00/0.88 % (1348448)Instruction limit reached!
% 2.00/0.88 % (1348448)------------------------------
% 2.00/0.88 % (1348448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.88 % (1348448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (1348448)CaDiCaL version: 2.1.3
% 2.00/0.88 % (1348448)Termination reason: Instruction limit
% 2.00/0.88 % (1348448)Termination phase: Saturation
% 2.00/0.88 % (1348448)Time elapsed: 0.066 s
% 2.00/0.88 % (1348448)Peak memory usage: 13 MB
% 2.00/0.88 % (1348448)Instructions burned: 103 (million)
% 2.00/0.88 % TRYING [1]
% 2.00/0.88 % TRYING [2]
% 2.00/0.88 % (1348461)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3609105805:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.00/0.88 % (1348462)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=73976142:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.00/0.88 % (1348451)Instruction limit reached!
% 2.00/0.88 % (1348451)------------------------------
% 2.00/0.88 % (1348451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.88 % (1348451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (1348451)CaDiCaL version: 2.1.3
% 2.00/0.88 % (1348451)Termination reason: Instruction limit
% 2.00/0.88 % (1348451)Termination phase: Saturation
% 2.00/0.88 % (1348451)Time elapsed: 0.088 s
% 2.00/0.88 % (1348451)Peak memory usage: 16 MB
% 2.00/0.88 % (1348451)Instructions burned: 159 (million)
% 2.00/0.88 % (1348465)ott-21_1_sil=16000:fs=off:random_seed=3076825580:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.00/0.88 % TRYING [3]
% 2.00/0.88 % (1348461)Instruction limit reached!
% 2.00/0.88 % (1348461)------------------------------
% 2.00/0.88 % (1348461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.88 % (1348461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (1348461)CaDiCaL version: 2.1.3
% 2.00/0.88 % (1348461)Termination reason: Instruction limit
% 2.00/0.88 % (1348461)Termination phase: Saturation
% 2.00/0.88 % (1348461)Time elapsed: 0.075 s
% 2.00/0.88 % (1348461)Peak memory usage: 14 MB
% 2.00/0.88 % (1348461)Instructions burned: 131 (million)
% 2.00/0.88 % (1348467)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3000510634:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.00/0.88 % (1348465)Instruction limit reached!
% 2.00/0.88 % (1348465)------------------------------
% 2.00/0.88 % (1348465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.88 % (1348465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (1348465)CaDiCaL version: 2.1.3
% 2.00/0.88 % (1348465)Termination reason: Instruction limit
% 2.00/0.88 % (1348465)Termination phase: Saturation
% 2.00/0.88 % (1348465)Time elapsed: 0.095 s
% 2.00/0.88 % (1348465)Peak memory usage: 13 MB
% 2.00/0.88 % (1348465)Instructions burned: 181 (million)
% 2.00/0.88 % (1348469)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3792621857:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.00/0.88 % TRYING [1]
% 2.00/0.88 % TRYING [2]
% 2.00/0.88 % TRYING [3]
% 2.00/0.88 % (1348459)Instruction limit reached!
% 2.00/0.88 % (1348459)------------------------------
% 2.00/0.88 % (1348459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.88 % (1348459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (1348459)CaDiCaL version: 2.1.3
% 2.00/0.88 % (1348459)Termination reason: Instruction limit
% 2.00/0.88 % (1348459)Termination phase: Finite model building constraint generation
% 2.00/0.88 % (1348459)Time elapsed: 0.253 s
% 2.00/0.88 % (1348459)Peak memory usage: 24 MB
% 2.00/0.88 % (1348459)Instructions burned: 717 (million)
% 2.00/0.88 % (1348471)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3620920607:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 2.00/0.88 % (1348462) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1348440-1348462"...
% 2.00/0.88 % (1348462)...printing done.
% 2.00/0.88 % (1348462)Refutation found. Thanks to Tanya!
% 2.00/0.88 % SZS status Theorem for theBenchmark
% 2.00/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.00/0.88 % (1348462)------------------------------
% 2.00/0.88 % (1348462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.00/0.88 % (1348462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.00/0.88 % (1348462)CaDiCaL version: 2.1.3
% 2.00/0.88 % (1348462)Termination reason: Refutation
% 2.00/0.88 % (1348462)Time elapsed: 0.299 s
% 2.00/0.88 % (1348462)Peak memory usage: 17 MB
% 2.00/0.88 % (1348462)Instructions burned: 523 (million)
% 2.00/0.88 % (1348440)Success in time 0.431 s
% 2.00/0.88 % Vampire exiting
%------------------------------------------------------------------------------