%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO560+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 : 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 09:52:56 AM UTC 2026
% Result : Theorem 6.34s 1.90s
% Output : Refutation 7.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 103 ( 10 unt; 2 def)
% Number of atoms : 294 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 324 ( 133 ~; 127 |; 47 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-8 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 461 ( 0 sgn 447 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X0,X1,X2,X3)
& perp(X2,X3,X4,X5) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4) )
=> cyclic(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD17) ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD19) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD21) ).
fof(f22,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
& eqangle(X4,X5,X6,X7,X8,X9,X10,X11) )
=> eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD41) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& ~ coll(X2,X3,X0) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42a) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& coll(X2,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X5)
& eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
=> cong(X0,X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X2,X1,X2)
& cong(X0,X3,X1,X3) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( perp(X3,X0,X1,X2)
& coll(X3,X1,X2)
& perp(X4,X1,X0,X2)
& coll(X4,X0,X2)
& coll(X5,X0,X3)
& coll(X5,X1,X4)
& perp(X6,X5,X0,X1)
& coll(X6,X0,X1) )
=> eqangle(X4,X6,X6,X5,X5,X6,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012020) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( perp(X3,X0,X1,X2)
& coll(X3,X1,X2)
& perp(X4,X1,X0,X2)
& coll(X4,X0,X2)
& coll(X5,X0,X3)
& coll(X5,X1,X4)
& perp(X6,X5,X0,X1)
& coll(X6,X0,X1) )
=> eqangle(X4,X6,X6,X5,X5,X6,X6,X3) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X4,X5)
| ~ perp(X0,X1,X2,X3)
| ~ perp(X2,X3,X4,X5) ),
inference(flattening,[],[f108]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(ennf_transformation,[],[f17]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4] :
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4) ),
inference(flattening,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f19]) ).
fof(f125,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(ennf_transformation,[],[f21]) ).
fof(f126,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11) ),
inference(flattening,[],[f126]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f39]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f40]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f41]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| coll(X2,X3,X0) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ coll(X2,X3,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ coll(X2,X3,X1) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) ),
inference(ennf_transformation,[],[f44]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5] :
( cong(X0,X1,X3,X4)
| ~ cyclic(X0,X1,X2,X3)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4) ),
inference(flattening,[],[f155]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
| ~ cong(X0,X2,X1,X2)
| ~ cong(X0,X3,X1,X3) ),
inference(flattening,[],[f180]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ eqangle(X4,X6,X6,X5,X5,X6,X6,X3)
& perp(X3,X0,X1,X2)
& coll(X3,X1,X2)
& perp(X4,X1,X0,X2)
& coll(X4,X0,X2)
& coll(X5,X0,X3)
& coll(X5,X1,X4)
& perp(X6,X5,X0,X1)
& coll(X6,X0,X1) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ eqangle(X4,X6,X6,X5,X5,X6,X6,X3)
& perp(X3,X0,X1,X2)
& coll(X3,X1,X2)
& perp(X4,X1,X0,X2)
& coll(X4,X0,X2)
& coll(X5,X0,X3)
& coll(X5,X1,X4)
& perp(X6,X5,X0,X1)
& coll(X6,X0,X1) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( ~ eqangle(sK24,sK26,sK26,sK25,sK25,sK26,sK26,sK23)
& perp(sK23,sK20,sK21,sK22)
& coll(sK23,sK21,sK22)
& perp(sK24,sK21,sK20,sK22)
& coll(sK24,sK20,sK22)
& coll(sK25,sK20,sK23)
& coll(sK25,sK21,sK24)
& perp(sK26,sK25,sK20,sK21)
& coll(sK26,sK20,sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25),skolemize(X6,sK26)],[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(f385,plain,
perp(sK26,sK25,sK20,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f392,plain,
~ eqangle(sK24,sK26,sK26,sK25,sK25,sK26,sK26,sK23),
inference(cnf_transformation,[],[f270]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( ~ cyclic(X1,X3,X0,X3)
| ~ cyclic(X1,X3,X0,X2)
| ~ para(X0,X1,X0,X2)
| ~ cyclic(X1,X3,X0,X0)
| cong(X1,X3,X2,X3) ),
inference(resolution,[],[f310,f314]) ).
fof(f394,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X4,X5,X6,X7,X0,X1,X8,X9)
| ~ para(X0,X1,X2,X3)
| eqangle(X4,X5,X6,X7,X2,X3,X8,X9) ),
inference(resolution,[],[f310,f292]) ).
fof(f395,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ para(X4,X5,X0,X1)
| eqangle(X4,X5,X6,X7,X2,X3,X6,X7)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[],[f394,f310]) ).
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(f419,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(f429,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(f436,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,[],[f429]) ).
fof(f440,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f419]) ).
fof(f447,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ para(X2,X3,X2,X3) ),
inference(resolution,[],[f309,f402]) ).
fof(f450,definition,
( spl27_1
<=> ! [X2,X3] : ~ para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f451,plain,
( ! [X2,X3] : ~ para(X2,X3,X2,X3)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f453,definition,
( spl27_2
<=> ! [X0,X1] : para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f454,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f455,plain,
( spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f447,f453,f450]) ).
fof(f457,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK26,sK25)
| para(X0,X1,sK20,sK21) ),
inference(resolution,[],[f279,f385]) ).
fof(f463,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f419]) ).
fof(f467,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) ),
inference(forward_subsumption_resolution,[],[f463,f440]) ).
fof(f470,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f467,f454]) ).
fof(f471,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl27_2 ),
inference(resolution,[],[f470,f287]) ).
fof(f477,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f471,f470]) ).
fof(f480,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl27_2 ),
inference(resolution,[],[f477,f436]) ).
fof(f481,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ para(X2,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X2)
| cong(X0,X1,X3,X1) )
| ~ spl27_2 ),
inference(resolution,[],[f477,f393]) ).
fof(f482,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X1,X2,X3)
| ~ para(X2,X0,X2,X3)
| cong(X0,X1,X3,X1) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f481,f477]) ).
fof(f483,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f480,f477]) ).
fof(f484,plain,
( ! [X2,X3,X0,X1] :
( ~ para(X2,X0,X2,X3)
| cong(X0,X1,X3,X1) )
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f482,f477]) ).
fof(f485,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f483,f477]) ).
fof(f486,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl27_2 ),
inference(resolution,[],[f485,f327]) ).
fof(f487,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f486,f485]) ).
fof(f488,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl27_2 ),
inference(resolution,[],[f487,f279]) ).
fof(f492,plain,
( ! [X2,X0,X1] : para(X0,X0,X1,X2)
| ~ spl27_2 ),
inference(resolution,[],[f488,f487]) ).
fof(f495,plain,
( ! [X2,X0,X1] : cong(X0,X1,X2,X1)
| ~ spl27_2 ),
inference(resolution,[],[f484,f492]) ).
fof(f496,plain,
( ! [X2,X3,X0,X1] :
( ~ cong(X0,X1,X2,X1)
| perp(X0,X2,X1,X3) )
| ~ spl27_2 ),
inference(resolution,[],[f495,f327]) ).
fof(f497,plain,
( ! [X2,X3,X0,X1] : perp(X0,X2,X1,X3)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f496,f495]) ).
fof(f499,plain,
( ! [X2,X3,X0,X1] : para(X0,X1,X2,X3)
| ~ spl27_2 ),
inference(resolution,[],[f497,f488]) ).
fof(f503,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X6,X7,X4,X5) )
| ~ spl27_2 ),
inference(resolution,[],[f499,f395]) ).
fof(f505,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f503,f499]) ).
fof(f509,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ spl27_2 ),
inference(resolution,[],[f505,f291]) ).
fof(f523,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X4,X5,X6,X7,X2,X3,X0,X1) )
| ~ spl27_2 ),
inference(resolution,[],[f509,f394]) ).
fof(f527,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : eqangle(X4,X5,X6,X7,X2,X3,X0,X1)
| ~ spl27_2 ),
inference(forward_subsumption_resolution,[],[f523,f499]) ).
fof(f540,plain,
( $false
| ~ spl27_2 ),
inference(resolution,[],[f527,f392]) ).
fof(f541,plain,
~ spl27_2,
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f548,plain,
perp(sK20,sK21,sK26,sK25),
inference(resolution,[],[f278,f385]) ).
fof(f551,plain,
para(sK20,sK21,sK20,sK21),
inference(resolution,[],[f548,f457]) ).
fof(f555,plain,
( $false
| ~ spl27_1 ),
inference(forward_subsumption_resolution,[],[f551,f451]) ).
fof(f556,plain,
~ spl27_1,
inference(avatar_contradiction_clause,[],[f555]) ).
cnf(s1,plain,
( spl27_1
| spl27_2 ),
inference(sat_conversion,[],[f455]) ).
cnf(s2,plain,
~ spl27_2,
inference(sat_conversion,[],[f541]) ).
cnf(s3,plain,
~ spl27_1,
inference(sat_conversion,[],[f556]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f557,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO560+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 08:31:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.34/1.90 % (3198850)Detected formulas, will run a generic FOF schedule.
% 6.34/1.90 % (3198861)dis-21_1_sil=8000:lcm=predicate:random_seed=2179128525: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)
% 6.34/1.90 % (3198858)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=24465296:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.34/1.90 % (3198856)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=291018193:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.34/1.90 % (3198855)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=2160386906:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.34/1.90 % (3198857)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=2182334758:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.34/1.90 % (3198859)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1425865102:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.34/1.90 % (3198860)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1770325132:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.34/1.90 % (3198861)Instruction limit reached!
% 6.34/1.90 % (3198861)------------------------------
% 6.34/1.90 % (3198861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198861)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198861)Termination reason: Instruction limit
% 6.34/1.90 % (3198861)Termination phase: Saturation
% 6.34/1.90 % (3198861)Time elapsed: 0.038 s
% 6.34/1.90 % (3198861)Peak memory usage: 89 MB
% 6.34/1.90 % (3198861)Instructions burned: 131 (million)
% 6.34/1.90 % (3198858)Refutation not found, incomplete strategy
% 6.34/1.90 % (3198858)------------------------------
% 6.34/1.90 % (3198858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198858)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198858)Termination reason: Refutation not found, incomplete strategy
% 6.34/1.90 % (3198858)Time elapsed: 0.025 s
% 6.34/1.90 % (3198858)Peak memory usage: 88 MB
% 6.34/1.90 % (3198858)Instructions burned: 45 (million)
% 6.34/1.90 % (3198859)Instruction limit reached!
% 6.34/1.90 % (3198859)------------------------------
% 6.34/1.90 % (3198859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198859)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198859)Termination reason: Instruction limit
% 6.34/1.90 % (3198859)Termination phase: Saturation
% 6.34/1.90 % (3198859)Time elapsed: 0.062 s
% 6.34/1.90 % (3198859)Peak memory usage: 88 MB
% 6.34/1.90 % (3198859)Instructions burned: 120 (million)
% 6.34/1.90 % (3198860)Instruction limit reached!
% 6.34/1.90 % (3198860)------------------------------
% 6.34/1.90 % (3198860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198860)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198860)Termination reason: Instruction limit
% 6.34/1.90 % (3198860)Termination phase: Saturation
% 6.34/1.90 % (3198860)Time elapsed: 0.091 s
% 6.34/1.90 % (3198860)Peak memory usage: 89 MB
% 6.34/1.90 % (3198860)Instructions burned: 140 (million)
% 6.34/1.90 % (3198869)lrs+10_1_sil=8000:sp=occurrence:random_seed=2548606082:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.34/1.90 % (3198870)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3025011681:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.34/1.90 % (3198869)Instruction limit reached!
% 6.34/1.90 % (3198869)------------------------------
% 6.34/1.90 % (3198869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198869)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198869)Termination reason: Instruction limit
% 6.34/1.90 % (3198869)Termination phase: Saturation
% 6.34/1.90 % (3198869)Time elapsed: 0.088 s
% 6.34/1.90 % (3198869)Peak memory usage: 93 MB
% 6.34/1.90 % (3198869)Instructions burned: 288 (million)
% 6.34/1.90 % (3198870)Refutation not found, incomplete strategy
% 6.34/1.90 % (3198870)------------------------------
% 6.34/1.90 % (3198870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198870)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198870)Termination reason: Refutation not found, incomplete strategy
% 6.34/1.90 % (3198870)Time elapsed: 0.039 s
% 6.34/1.90 % (3198870)Peak memory usage: 88 MB
% 6.34/1.90 % (3198870)Instructions burned: 79 (million)
% 6.34/1.90 % (3198871)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2426042669:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.34/1.90 % (3198858)------------------------------
% 6.34/1.90 % (3198858)------------------------------
% 6.34/1.90 % (3198874)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=2685259025:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 6.34/1.90 % (3198874)Instruction limit reached!
% 6.34/1.90 % (3198874)------------------------------
% 6.34/1.90 % (3198874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198874)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198874)Termination reason: Instruction limit
% 6.34/1.90 % (3198874)Termination phase: Saturation
% 6.34/1.90 % (3198874)Time elapsed: 0.072 s
% 6.34/1.90 % (3198874)Peak memory usage: 91 MB
% 6.34/1.90 % (3198874)Instructions burned: 249 (million)
% 6.34/1.90 % (3198876)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3164076174:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.34/1.90 % (3198871)Instruction limit reached!
% 6.34/1.90 % (3198871)------------------------------
% 6.34/1.90 % (3198871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198871)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198871)Termination reason: Instruction limit
% 6.34/1.90 % (3198871)Termination phase: Saturation
% 6.34/1.90 % (3198871)Time elapsed: 0.192 s
% 6.34/1.90 % (3198871)Peak memory usage: 90 MB
% 6.34/1.90 % (3198871)Instructions burned: 326 (million)
% 6.34/1.90 % (3198870)------------------------------
% 6.34/1.90 % (3198870)------------------------------
% 6.34/1.90 % (3198878)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4022950702:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.34/1.90 % (3198880)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3008396044:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.34/1.90 % (3198876)Instruction limit reached!
% 6.34/1.90 % (3198876)------------------------------
% 6.34/1.90 % (3198876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198876)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198876)Termination reason: Instruction limit
% 6.34/1.90 % (3198876)Termination phase: Saturation
% 6.34/1.90 % (3198876)Time elapsed: 0.168 s
% 6.34/1.90 % (3198876)Peak memory usage: 89 MB
% 6.34/1.90 % (3198876)Instructions burned: 295 (million)
% 6.34/1.90 % (3198882)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=220519893:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.34/1.90 % (3198880)Instruction limit reached!
% 6.34/1.90 % (3198880)------------------------------
% 6.34/1.90 % (3198880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198880)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198880)Termination reason: Instruction limit
% 6.34/1.90 % (3198880)Termination phase: Saturation
% 6.34/1.90 % (3198880)Time elapsed: 0.060 s
% 6.34/1.90 % (3198880)Peak memory usage: 89 MB
% 6.34/1.90 % (3198880)Instructions burned: 113 (million)
% 6.34/1.90 % (3198855)First to succeed.
% 6.34/1.90 % (3198855)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3198850"
% 6.34/1.90 % (3198882)Instruction limit reached!
% 6.34/1.90 % (3198882)------------------------------
% 6.34/1.90 % (3198882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198882)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198882)Termination reason: Instruction limit
% 6.34/1.90 % (3198882)Termination phase: Saturation
% 6.34/1.90 % (3198882)Time elapsed: 0.069 s
% 6.34/1.90 % (3198882)Peak memory usage: 89 MB
% 6.34/1.90 % (3198882)Instructions burned: 127 (million)
% 6.34/1.90 % (3198884)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1033816499:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.34/1.90 % (3198886)lrs+10_1_sil=8000:sp=occurrence:random_seed=726143634:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.34/1.90 % (3198884)Instruction limit reached!
% 6.34/1.90 % (3198884)------------------------------
% 6.34/1.90 % (3198884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.34/1.90 % (3198884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.34/1.90 % (3198884)CaDiCaL version: 2.1.3
% 6.34/1.90 % (3198884)Termination reason: Instruction limit
% 6.34/1.90 % (3198884)Termination phase: Saturation
% 6.34/1.90 % (3198884)Time elapsed: 0.060 s
% 6.34/1.90 % (3198884)Peak memory usage: 89 MB
% 6.34/1.90 % (3198884)Instructions burned: 115 (million)
% 6.34/1.90 % (3198887)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=234436880:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.34/1.90 % (3198890)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3914468818:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.34/1.90 % (3198878)Also succeeded, but the first one will report.
% 6.34/1.90 % (3198855)Refutation found. Thanks to Tanya!
% 6.34/1.90 % SZS status Theorem for theBenchmark
% 6.34/1.90 % SZS output start Proof for theBenchmark
% See solution above
% 7.91/1.99 % (3198855)------------------------------
% 7.91/1.99 % (3198855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.91/1.99 % (3198855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.91/1.99 % (3198855)CaDiCaL version: 2.1.3
% 7.91/1.99 % (3198855)Termination reason: Refutation
% 7.91/1.99 % (3198855)Time elapsed: 0.661 s
% 7.91/1.99 % (3198855)Peak memory usage: 131 MB
% 7.91/1.99 % (3198855)Instructions burned: 992 (million)
% 7.91/1.99 % (3198855)------------------------------
% 7.91/1.99 % (3198855)------------------------------
% 7.91/1.99 % (3198850)Success in time 1.06 s
% 7.91/1.99 % Vampire exiting
%------------------------------------------------------------------------------