%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO650+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 : n017.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 09:53:09 AM UTC 2026
% Result : Theorem 8.79s 2.17s
% Output : Refutation 9.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 10 unt; 2 def)
% Number of atoms : 264 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 280 ( 102 ~; 96 |; 66 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 347 ( 0 sgn 327 !; 20 ?)
% 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(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] :
( ( midp(X7,X0,X1)
& perp(X0,X1,X7,X3)
& midp(X8,X0,X2)
& perp(X0,X2,X8,X3)
& midp(X9,X1,X2)
& perp(X1,X2,X9,X3)
& perp(X2,X3,X2,X4)
& perp(X1,X3,X1,X4)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X5)
& coll(X6,X0,X2) )
=> para(X6,X4,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE02211) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( midp(X7,X0,X1)
& perp(X0,X1,X7,X3)
& midp(X8,X0,X2)
& perp(X0,X2,X8,X3)
& midp(X9,X1,X2)
& perp(X1,X2,X9,X3)
& perp(X2,X3,X2,X4)
& perp(X1,X3,X1,X4)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X5)
& coll(X6,X0,X2) )
=> para(X6,X4,X0,X1) ),
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(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] :
( ~ para(X6,X4,X0,X1)
& midp(X7,X0,X1)
& perp(X0,X1,X7,X3)
& midp(X8,X0,X2)
& perp(X0,X2,X8,X3)
& midp(X9,X1,X2)
& perp(X1,X2,X9,X3)
& perp(X2,X3,X2,X4)
& perp(X1,X3,X1,X4)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X5)
& coll(X6,X0,X2) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ para(X6,X4,X0,X1)
& midp(X7,X0,X1)
& perp(X0,X1,X7,X3)
& midp(X8,X0,X2)
& perp(X0,X2,X8,X3)
& midp(X9,X1,X2)
& perp(X1,X2,X9,X3)
& perp(X2,X3,X2,X4)
& perp(X1,X3,X1,X4)
& perp(X5,X3,X0,X1)
& coll(X5,X0,X1)
& coll(X6,X3,X5)
& coll(X6,X0,X2) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( ~ para(sK26,sK24,sK20,sK21)
& midp(sK27,sK20,sK21)
& perp(sK20,sK21,sK27,sK23)
& midp(sK28,sK20,sK22)
& perp(sK20,sK22,sK28,sK23)
& midp(sK29,sK21,sK22)
& perp(sK21,sK22,sK29,sK23)
& perp(sK22,sK23,sK22,sK24)
& perp(sK21,sK23,sK21,sK24)
& perp(sK25,sK23,sK20,sK21)
& coll(sK25,sK20,sK21)
& coll(sK26,sK23,sK25)
& coll(sK26,sK20,sK22) ),
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(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(f392,plain,
perp(sK20,sK22,sK28,sK23),
inference(cnf_transformation,[],[f270]) ).
fof(f396,plain,
~ para(sK26,sK24,sK20,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f397,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(f398,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,[],[f397]) ).
fof(f418,plain,
perp(sK28,sK23,sK20,sK22),
inference(resolution,[],[f392,f278]) ).
fof(f420,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK20,sK22)
| para(X0,X1,sK28,sK23) ),
inference(resolution,[],[f392,f279]) ).
fof(f431,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(f433,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X0,X1)
| para(X2,X3,X2,X3) ),
inference(resolution,[],[f431,f309]) ).
fof(f437,definition,
( spl30_1
<=> ! [X2,X3] : para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl30_1])],[avatar_definition]) ).
fof(f438,plain,
( ! [X2,X3] : para(X2,X3,X2,X3)
| ~ spl30_1 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f440,definition,
( spl30_2
<=> ! [X0,X1] : ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl30_2])],[avatar_definition]) ).
fof(f441,plain,
( ! [X0,X1] : ~ para(X0,X1,X0,X1)
| ~ spl30_2 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f442,plain,
( spl30_1
| spl30_2 ),
inference(avatar_split_clause,[],[f433,f440,f437]) ).
fof(f455,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(f464,plain,
para(sK28,sK23,sK28,sK23),
inference(resolution,[],[f418,f420]) ).
fof(f468,plain,
( $false
| ~ spl30_2 ),
inference(forward_subsumption_resolution,[],[f464,f441]) ).
fof(f469,plain,
~ spl30_2,
inference(avatar_contradiction_clause,[],[f468]) ).
fof(f474,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f455]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f474,f438]) ).
fof(f492,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f455]) ).
fof(f495,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) )
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f492,f477]) ).
fof(f498,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f495,f438]) ).
fof(f500,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl30_1 ),
inference(resolution,[],[f498,f287]) ).
fof(f504,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f500,f498]) ).
fof(f507,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl30_1 ),
inference(resolution,[],[f504,f398]) ).
fof(f511,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f507,f504]) ).
fof(f513,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f511,f504]) ).
fof(f514,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl30_1 ),
inference(resolution,[],[f513,f327]) ).
fof(f515,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl30_1 ),
inference(forward_subsumption_resolution,[],[f514,f513]) ).
fof(f516,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl30_1 ),
inference(resolution,[],[f515,f278]) ).
fof(f518,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl30_1 ),
inference(resolution,[],[f515,f279]) ).
fof(f529,plain,
( ! [X2,X3,X0,X1] : para(X0,X1,X2,X3)
| ~ spl30_1 ),
inference(resolution,[],[f516,f518]) ).
fof(f530,plain,
( $false
| ~ spl30_1 ),
inference(resolution,[],[f529,f396]) ).
fof(f531,plain,
~ spl30_1,
inference(avatar_contradiction_clause,[],[f530]) ).
cnf(s1,plain,
( spl30_1
| spl30_2 ),
inference(sat_conversion,[],[f442]) ).
cnf(s2,plain,
~ spl30_2,
inference(sat_conversion,[],[f469]) ).
cnf(s3,plain,
~ spl30_1,
inference(sat_conversion,[],[f531]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f532,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO650+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n017.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 08:39:06 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.79/2.17 % (2241291)Detected formulas, will run a generic FOF schedule.
% 8.79/2.17 % (2241306)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=3050006093:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.79/2.17 % (2241312)dis-21_1_sil=8000:lcm=predicate:random_seed=3826198179: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)
% 8.79/2.17 % (2241308)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=2193703351:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.79/2.17 % (2241311)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=966729716:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.79/2.17 % (2241307)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=2136046230:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.79/2.17 % (2241310)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=286576146:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.79/2.17 % (2241309)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=158335736:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.79/2.17 % (2241312)Instruction limit reached!
% 8.79/2.17 % (2241312)------------------------------
% 8.79/2.17 % (2241312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241312)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241312)Termination reason: Instruction limit
% 8.79/2.17 % (2241312)Termination phase: Saturation
% 8.79/2.17 % (2241312)Time elapsed: 0.123 s
% 8.79/2.17 % (2241312)Peak memory usage: 89 MB
% 8.79/2.17 % (2241312)Instructions burned: 129 (million)
% 8.79/2.17 % (2241309)Instruction limit reached!
% 8.79/2.17 % (2241309)------------------------------
% 8.79/2.17 % (2241309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241309)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241309)Termination reason: Instruction limit
% 8.79/2.17 % (2241309)Termination phase: Saturation
% 8.79/2.17 % (2241309)Time elapsed: 0.117 s
% 8.79/2.17 % (2241309)Peak memory usage: 90 MB
% 8.79/2.17 % (2241309)Instructions burned: 109 (million)
% 8.79/2.17 % (2241310)Instruction limit reached!
% 8.79/2.17 % (2241310)------------------------------
% 8.79/2.17 % (2241310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241310)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241310)Termination reason: Instruction limit
% 8.79/2.17 % (2241310)Termination phase: Saturation
% 8.79/2.17 % (2241310)Time elapsed: 0.120 s
% 8.79/2.17 % (2241310)Peak memory usage: 88 MB
% 8.79/2.17 % (2241310)Instructions burned: 119 (million)
% 8.79/2.17 % (2241311)Instruction limit reached!
% 8.79/2.17 % (2241311)------------------------------
% 8.79/2.17 % (2241311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241311)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241311)Termination reason: Instruction limit
% 8.79/2.17 % (2241311)Termination phase: Saturation
% 8.79/2.17 % (2241311)Time elapsed: 0.151 s
% 8.79/2.17 % (2241311)Peak memory usage: 90 MB
% 8.79/2.17 % (2241311)Instructions burned: 139 (million)
% 8.79/2.17 % (2241326)lrs+10_1_sil=8000:sp=occurrence:random_seed=593505903:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 8.79/2.17 % (2241327)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3573651805:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 8.79/2.17 % (2241328)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4273100067:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 8.79/2.17 % (2241329)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=1025771512:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 8.79/2.17 % (2241327)Instruction limit reached!
% 8.79/2.17 % (2241327)------------------------------
% 8.79/2.17 % (2241327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241327)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241327)Termination reason: Instruction limit
% 8.79/2.17 % (2241327)Termination phase: Saturation
% 8.79/2.17 % (2241327)Time elapsed: 0.138 s
% 8.79/2.17 % (2241327)Peak memory usage: 90 MB
% 8.79/2.17 % (2241327)Instructions burned: 157 (million)
% 8.79/2.17 % (2241329)Instruction limit reached!
% 8.79/2.17 % (2241329)------------------------------
% 8.79/2.17 % (2241329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241329)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241329)Termination reason: Instruction limit
% 8.79/2.17 % (2241329)Termination phase: Saturation
% 8.79/2.17 % (2241329)Time elapsed: 0.227 s
% 8.79/2.17 % (2241329)Peak memory usage: 91 MB
% 8.79/2.17 % (2241329)Instructions burned: 248 (million)
% 8.79/2.17 % (2241326)Instruction limit reached!
% 8.79/2.17 % (2241326)------------------------------
% 8.79/2.17 % (2241326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241326)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241326)Termination reason: Instruction limit
% 8.79/2.17 % (2241326)Termination phase: Saturation
% 8.79/2.17 % (2241326)Time elapsed: 0.306 s
% 8.79/2.17 % (2241326)Peak memory usage: 92 MB
% 8.79/2.17 % (2241326)Instructions burned: 285 (million)
% 8.79/2.17 % (2241306)First to succeed.
% 8.79/2.17 % (2241306)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2241291"
% 8.79/2.17 % (2241336)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=993760532:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 8.79/2.17 % (2241328)Instruction limit reached!
% 8.79/2.17 % (2241328)------------------------------
% 8.79/2.17 % (2241328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241328)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241328)Termination reason: Instruction limit
% 8.79/2.17 % (2241328)Termination phase: Saturation
% 8.79/2.17 % (2241328)Time elapsed: 0.344 s
% 8.79/2.17 % (2241328)Peak memory usage: 91 MB
% 8.79/2.17 % (2241328)Instructions burned: 325 (million)
% 8.79/2.17 % (2241336)Instruction limit reached!
% 8.79/2.17 % (2241336)------------------------------
% 8.79/2.17 % (2241336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241336)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241336)Termination reason: Instruction limit
% 8.79/2.17 % (2241336)Termination phase: Saturation
% 8.79/2.17 % (2241336)Time elapsed: 0.161 s
% 8.79/2.17 % (2241336)Peak memory usage: 89 MB
% 8.79/2.17 % (2241336)Instructions burned: 294 (million)
% 8.79/2.17 % (2241337)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1086941077:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 8.79/2.17 % (2241338)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=893704033:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 8.79/2.17 % (2241342)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1630067490:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2989 on theBenchmark for (2989ds/114Mi)
% 8.79/2.17 % (2241340)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3650399211:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 8.79/2.17 % (2241342)Instruction limit reached!
% 8.79/2.17 % (2241342)------------------------------
% 8.79/2.17 % (2241342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241342)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241342)Termination reason: Instruction limit
% 8.79/2.17 % (2241342)Termination phase: Saturation
% 8.79/2.17 % (2241342)Time elapsed: 0.036 s
% 8.79/2.17 % (2241342)Peak memory usage: 89 MB
% 8.79/2.17 % (2241342)Instructions burned: 117 (million)
% 8.79/2.17 % (2241338)Instruction limit reached!
% 8.79/2.17 % (2241338)------------------------------
% 8.79/2.17 % (2241338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241338)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241338)Termination reason: Instruction limit
% 8.79/2.17 % (2241338)Termination phase: Saturation
% 8.79/2.17 % (2241338)Time elapsed: 0.112 s
% 8.79/2.17 % (2241338)Peak memory usage: 90 MB
% 8.79/2.17 % (2241338)Instructions burned: 113 (million)
% 8.79/2.17 % (2241340)Instruction limit reached!
% 8.79/2.17 % (2241340)------------------------------
% 8.79/2.17 % (2241340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.17 % (2241340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.17 % (2241340)CaDiCaL version: 2.1.3
% 8.79/2.17 % (2241340)Termination reason: Instruction limit
% 8.79/2.17 % (2241340)Termination phase: Saturation
% 8.79/2.17 % (2241340)Time elapsed: 0.116 s
% 8.79/2.17 % (2241340)Peak memory usage: 89 MB
% 8.79/2.17 % (2241340)Instructions burned: 127 (million)
% 8.79/2.17 % (2241306)Refutation found. Thanks to Tanya!
% 8.79/2.17 % SZS status Theorem for theBenchmark
% 8.79/2.17 % SZS output start Proof for theBenchmark
% See solution above
% 9.55/2.39 % (2241306)------------------------------
% 9.55/2.39 % (2241306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.55/2.39 % (2241306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.55/2.39 % (2241306)CaDiCaL version: 2.1.3
% 9.55/2.39 % (2241306)Termination reason: Refutation
% 9.55/2.39 % (2241306)Time elapsed: 0.704 s
% 9.55/2.39 % (2241306)Peak memory usage: 131 MB
% 9.55/2.39 % (2241306)Instructions burned: 991 (million)
% 9.55/2.39 % (2241306)------------------------------
% 9.55/2.39 % (2241306)------------------------------
% 9.55/2.39 % (2241291)Success in time 1.263 s
% 9.55/2.39 % Vampire exiting
%------------------------------------------------------------------------------