%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO656+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 : n012.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 09:53:10 AM UTC 2026
% Result : Theorem 4.07s 1.18s
% Output : Refutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 104 ( 10 unt; 3 def)
% Number of atoms : 260 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 276 ( 120 ~; 114 |; 22 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 4 prp; 0-8 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 374 ( 0 sgn 362 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( para(X0,X1,X2,X3)
=> para(X0,X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
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(f11,axiom,
! [X0,X1,X2] :
( midp(X2,X1,X0)
=> midp(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD11) ).
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(f64,axiom,
! [X0,X1,X2,X3,X4] :
( ( midp(X4,X0,X1)
& midp(X4,X2,X3) )
=> para(X0,X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD63) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5] :
( ( midp(X3,X1,X0)
& eqangle(X4,X3,X3,X0,X4,X3,X3,X2)
& eqangle(X5,X3,X3,X1,X5,X3,X3,X2) )
=> para(X4,X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE02314) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( midp(X3,X1,X0)
& eqangle(X4,X3,X3,X0,X4,X3,X3,X2)
& eqangle(X5,X3,X3,X1,X5,X3,X3,X2) )
=> para(X4,X5,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f4]) ).
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(f112,plain,
! [X0,X1,X2] :
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
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(f191,plain,
! [X0,X1,X2,X3,X4] :
( para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| ~ midp(X4,X2,X3) ),
inference(ennf_transformation,[],[f64]) ).
fof(f192,plain,
! [X0,X1,X2,X3,X4] :
( para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1)
| ~ midp(X4,X2,X3) ),
inference(flattening,[],[f191]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ para(X4,X5,X0,X1)
& midp(X3,X1,X0)
& eqangle(X4,X3,X3,X0,X4,X3,X3,X2)
& eqangle(X5,X3,X3,X1,X5,X3,X3,X2) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ para(X4,X5,X0,X1)
& midp(X3,X1,X0)
& eqangle(X4,X3,X3,X0,X4,X3,X3,X2)
& eqangle(X5,X3,X3,X1,X5,X3,X3,X2) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( ~ para(sK24,sK25,sK20,sK21)
& midp(sK23,sK21,sK20)
& eqangle(sK24,sK23,sK23,sK20,sK24,sK23,sK23,sK22)
& eqangle(sK25,sK23,sK23,sK21,sK25,sK23,sK23,sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25)],[f250]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X2,X3)
| para(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f102]) ).
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(f281,plain,
! [X2,X0,X1] :
( ~ midp(X2,X1,X0)
| midp(X2,X0,X1) ),
inference(cnf_transformation,[],[f112]) ).
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(f334,plain,
! [X2,X3,X0,X1,X4] :
( ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1)
| para(X0,X2,X1,X3) ),
inference(cnf_transformation,[],[f192]) ).
fof(f386,plain,
midp(sK23,sK21,sK20),
inference(cnf_transformation,[],[f270]) ).
fof(f387,plain,
~ para(sK24,sK25,sK20,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f388,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(f389,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,[],[f388]) ).
fof(f405,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f310,f291]) ).
fof(f407,plain,
! [X2,X3,X0,X1,X4,X5] :
( eqangle(X4,X5,X0,X1,X4,X5,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f310,f289]) ).
fof(f423,plain,
! [X2,X3,X0,X1] :
( ~ para(X0,X1,X0,X1)
| para(X2,X3,X2,X3) ),
inference(resolution,[],[f407,f309]) ).
fof(f429,definition,
( spl26_1
<=> ! [X2,X3] : para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f430,plain,
( ! [X2,X3] : para(X2,X3,X2,X3)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f432,definition,
( spl26_2
<=> ! [X0,X1] : ~ para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f433,plain,
( ! [X0,X1] : ~ para(X0,X1,X0,X1)
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f434,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f423,f432,f429]) ).
fof(f445,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f405]) ).
fof(f451,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f405]) ).
fof(f520,definition,
( spl26_8
<=> midp(sK23,sK20,sK21) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
fof(f521,plain,
( midp(sK23,sK20,sK21)
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f522,plain,
( ~ midp(sK23,sK20,sK21)
| spl26_8 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f547,plain,
! [X0,X1] :
( para(X0,sK21,X1,sK20)
| ~ midp(sK23,X0,X1) ),
inference(resolution,[],[f334,f386]) ).
fof(f551,plain,
! [X0,X1] :
( para(X0,sK21,sK20,X1)
| ~ midp(sK23,X0,X1) ),
inference(resolution,[],[f547,f274]) ).
fof(f554,plain,
( ~ midp(sK23,sK20,sK21)
| ~ spl26_2 ),
inference(resolution,[],[f551,f433]) ).
fof(f571,plain,
midp(sK23,sK20,sK21),
inference(resolution,[],[f281,f386]) ).
fof(f572,plain,
( $false
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f571,f522]) ).
fof(f573,plain,
spl26_8,
inference(avatar_contradiction_clause,[],[f572]) ).
fof(f574,plain,
( $false
| ~ spl26_2
| ~ spl26_8 ),
inference(forward_subsumption_resolution,[],[f554,f521]) ).
fof(f575,plain,
( ~ spl26_2
| ~ spl26_8 ),
inference(avatar_contradiction_clause,[],[f574]) ).
fof(f577,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0) )
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f445,f430]) ).
fof(f581,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f451,f430]) ).
fof(f584,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f581,f577]) ).
fof(f600,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl26_1 ),
inference(resolution,[],[f584,f287]) ).
fof(f608,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f600,f584]) ).
fof(f614,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl26_1 ),
inference(resolution,[],[f608,f389]) ).
fof(f620,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f614,f608]) ).
fof(f622,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f620,f608]) ).
fof(f623,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl26_1 ),
inference(resolution,[],[f622,f327]) ).
fof(f630,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl26_1 ),
inference(forward_subsumption_resolution,[],[f623,f622]) ).
fof(f632,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl26_1 ),
inference(resolution,[],[f630,f278]) ).
fof(f634,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl26_1 ),
inference(resolution,[],[f630,f279]) ).
fof(f655,plain,
( ! [X2,X3,X0,X1] : para(X0,X1,X2,X3)
| ~ spl26_1 ),
inference(resolution,[],[f632,f634]) ).
fof(f656,plain,
( $false
| ~ spl26_1 ),
inference(resolution,[],[f655,f387]) ).
fof(f663,plain,
~ spl26_1,
inference(avatar_contradiction_clause,[],[f656]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f434]) ).
cnf(s6,plain,
spl26_8,
inference(sat_conversion,[],[f573]) ).
cnf(s7,plain,
( ~ spl26_2
| ~ spl26_8 ),
inference(sat_conversion,[],[f575]) ).
cnf(s8,plain,
~ spl26_1,
inference(sat_conversion,[],[f663]) ).
cnf(s9,plain,
~ spl26_2,
inference(rat,[],[s7,s6]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
fof(f664,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO656+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 08:44:05 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 Running first-order theorem proving
% 0.07/0.34 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
% 4.07/1.18 % (2069737)Detected formulas, will run a generic FOF schedule.
% 4.07/1.18 % (2069742)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=1555696648:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.07/1.18 % (2069744)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=1868903912:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.07/1.18 % (2069746)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2519066196:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.07/1.18 % (2069745)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=846636258:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.07/1.18 % (2069747)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1214598610:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.07/1.18 % (2069748)dis-21_1_sil=8000:lcm=predicate:random_seed=607716631:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.07/1.18 % (2069743)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=1500419962:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.07/1.18 % (2069745)Instruction limit reached!
% 4.07/1.18 % (2069745)------------------------------
% 4.07/1.18 % (2069745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069745)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069745)Termination reason: Instruction limit
% 4.07/1.18 % (2069745)Termination phase: Saturation
% 4.07/1.18 % (2069745)Time elapsed: 0.037 s
% 4.07/1.18 % (2069745)Peak memory usage: 89 MB
% 4.07/1.18 % (2069745)Instructions burned: 110 (million)
% 4.07/1.18 % (2069746)Instruction limit reached!
% 4.07/1.18 % (2069746)------------------------------
% 4.07/1.18 % (2069746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069746)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069746)Termination reason: Instruction limit
% 4.07/1.18 % (2069746)Termination phase: Saturation
% 4.07/1.18 % (2069746)Time elapsed: 0.038 s
% 4.07/1.18 % (2069746)Peak memory usage: 88 MB
% 4.07/1.18 % (2069746)Instructions burned: 121 (million)
% 4.07/1.18 % (2069748)Instruction limit reached!
% 4.07/1.18 % (2069748)------------------------------
% 4.07/1.18 % (2069748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069748)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069748)Termination reason: Instruction limit
% 4.07/1.18 % (2069748)Termination phase: Saturation
% 4.07/1.18 % (2069748)Time elapsed: 0.040 s
% 4.07/1.18 % (2069748)Peak memory usage: 89 MB
% 4.07/1.18 % (2069748)Instructions burned: 129 (million)
% 4.07/1.18 % (2069747)Instruction limit reached!
% 4.07/1.18 % (2069747)------------------------------
% 4.07/1.18 % (2069747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069747)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069747)Termination reason: Instruction limit
% 4.07/1.18 % (2069747)Termination phase: Saturation
% 4.07/1.18 % (2069747)Time elapsed: 0.051 s
% 4.07/1.18 % (2069747)Peak memory usage: 90 MB
% 4.07/1.18 % (2069747)Instructions burned: 140 (million)
% 4.07/1.18 % (2069758)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4202458029:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 4.07/1.18 % (2069756)lrs+10_1_sil=8000:sp=occurrence:random_seed=354516409:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.07/1.18 % (2069757)lrs+10_1_sil=32000:urr=on:br=off:random_seed=969608092:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 4.07/1.18 % (2069759)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=3050451457:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 4.07/1.18 % (2069757)Instruction limit reached!
% 4.07/1.18 % (2069757)------------------------------
% 4.07/1.18 % (2069757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069757)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069757)Termination reason: Instruction limit
% 4.07/1.18 % (2069757)Termination phase: Saturation
% 4.07/1.18 % (2069757)Time elapsed: 0.046 s
% 4.07/1.18 % (2069757)Peak memory usage: 90 MB
% 4.07/1.18 % (2069757)Instructions burned: 160 (million)
% 4.07/1.18 % (2069759)Instruction limit reached!
% 4.07/1.18 % (2069759)------------------------------
% 4.07/1.18 % (2069759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069759)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069759)Termination reason: Instruction limit
% 4.07/1.18 % (2069759)Termination phase: Saturation
% 4.07/1.18 % (2069759)Time elapsed: 0.073 s
% 4.07/1.18 % (2069759)Peak memory usage: 90 MB
% 4.07/1.18 % (2069759)Instructions burned: 248 (million)
% 4.07/1.18 % (2069756)Instruction limit reached!
% 4.07/1.18 % (2069756)------------------------------
% 4.07/1.18 % (2069756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069756)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069756)Termination reason: Instruction limit
% 4.07/1.18 % (2069756)Termination phase: Saturation
% 4.07/1.18 % (2069756)Time elapsed: 0.095 s
% 4.07/1.18 % (2069756)Peak memory usage: 91 MB
% 4.07/1.18 % (2069756)Instructions burned: 285 (million)
% 4.07/1.18 % (2069758)Instruction limit reached!
% 4.07/1.18 % (2069758)------------------------------
% 4.07/1.18 % (2069758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069758)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069758)Termination reason: Instruction limit
% 4.07/1.18 % (2069758)Termination phase: Saturation
% 4.07/1.18 % (2069758)Time elapsed: 0.113 s
% 4.07/1.18 % (2069758)Peak memory usage: 91 MB
% 4.07/1.18 % (2069758)Instructions burned: 327 (million)
% 4.07/1.18 % (2069764)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3082904639:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2997 on theBenchmark for (2997ds/294Mi)
% 4.07/1.18 % (2069765)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2358952033:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 4.07/1.18 % (2069766)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4143281738:cts=off:i=113:fsr=off:ss=included:sgt=4_2996 on theBenchmark for (2996ds/113Mi)
% 4.07/1.18 % (2069767)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=769732441:i=127:av=off:fsr=off:sup=off_2996 on theBenchmark for (2996ds/127Mi)
% 4.07/1.18 % (2069764)Instruction limit reached!
% 4.07/1.18 % (2069764)------------------------------
% 4.07/1.18 % (2069764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069764)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069764)Termination reason: Instruction limit
% 4.07/1.18 % (2069764)Termination phase: Saturation
% 4.07/1.18 % (2069764)Time elapsed: 0.085 s
% 4.07/1.18 % (2069764)Peak memory usage: 89 MB
% 4.07/1.18 % (2069764)Instructions burned: 298 (million)
% 4.07/1.18 % (2069766)Instruction limit reached!
% 4.07/1.18 % (2069766)------------------------------
% 4.07/1.18 % (2069766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069766)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069766)Termination reason: Instruction limit
% 4.07/1.18 % (2069766)Termination phase: Saturation
% 4.07/1.18 % (2069766)Time elapsed: 0.036 s
% 4.07/1.18 % (2069766)Peak memory usage: 89 MB
% 4.07/1.18 % (2069766)Instructions burned: 115 (million)
% 4.07/1.18 % (2069767)Instruction limit reached!
% 4.07/1.18 % (2069767)------------------------------
% 4.07/1.18 % (2069767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069767)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069767)Termination reason: Instruction limit
% 4.07/1.18 % (2069767)Termination phase: Saturation
% 4.07/1.18 % (2069767)Time elapsed: 0.038 s
% 4.07/1.18 % (2069767)Peak memory usage: 89 MB
% 4.07/1.18 % (2069767)Instructions burned: 129 (million)
% 4.07/1.18 % (2069742)First to succeed.
% 4.07/1.18 % (2069742)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2069737"
% 4.07/1.18 % (2069772)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4057888884:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2995 on theBenchmark for (2995ds/114Mi)
% 4.07/1.18 % (2069773)lrs+10_1_sil=8000:sp=occurrence:random_seed=146788990:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2995 on theBenchmark for (2995ds/907Mi)
% 4.07/1.18 % (2069774)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3263373651:i=437:sd=1:aac=none:ss=included_2995 on theBenchmark for (2995ds/437Mi)
% 4.07/1.18 % (2069772)Instruction limit reached!
% 4.07/1.18 % (2069772)------------------------------
% 4.07/1.18 % (2069772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.18 % (2069772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.18 % (2069772)CaDiCaL version: 2.1.3
% 4.07/1.18 % (2069772)Termination reason: Instruction limit
% 4.07/1.18 % (2069772)Termination phase: Saturation
% 4.07/1.18 % (2069772)Time elapsed: 0.035 s
% 4.07/1.18 % (2069772)Peak memory usage: 89 MB
% 4.07/1.18 % (2069772)Instructions burned: 116 (million)
% 4.07/1.18 % (2069742)Refutation found. Thanks to Tanya!
% 4.07/1.18 % SZS status Theorem for theBenchmark
% 4.07/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 4.71/1.28 % (2069742)------------------------------
% 4.71/1.28 % (2069742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.71/1.28 % (2069742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.71/1.28 % (2069742)CaDiCaL version: 2.1.3
% 4.71/1.28 % (2069742)Termination reason: Refutation
% 4.71/1.28 % (2069742)Time elapsed: 0.385 s
% 4.71/1.28 % (2069742)Peak memory usage: 129 MB
% 4.71/1.28 % (2069742)Instructions burned: 1017 (million)
% 4.71/1.28 % (2069742)------------------------------
% 4.71/1.28 % (2069742)------------------------------
% 4.71/1.28 % (2069737)Success in time 0.648 s
% 4.71/1.28 % Vampire exiting
%------------------------------------------------------------------------------