%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO548+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:52:54 AM UTC 2026
% Result : Theorem 4.82s 1.90s
% Output : Refutation 4.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 97 ( 10 unt; 2 def)
% Number of atoms : 299 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 321 ( 119 ~; 113 |; 72 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 461 ( 0 sgn 435 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X0,X1,X2,X3)
& perp(X2,X3,X4,X5) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4) )
=> cyclic(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD17) ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
fof(f21,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X0,X1,X4,X5,X2,X3,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
fof(f22,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
& eqangle(X4,X5,X6,X7,X8,X9,X10,X11) )
=> eqangle(X0,X1,X2,X3,X8,X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
fof(f41,axiom,
! [X0,X1,X2,X3] :
( cyclic(X0,X1,X2,X3)
=> eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
fof(f42,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& ~ coll(X2,X3,X0) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42a) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
& coll(X2,X3,X1) )
=> cyclic(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
fof(f44,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( cyclic(X0,X1,X2,X3)
& cyclic(X0,X1,X2,X4)
& cyclic(X0,X1,X2,X5)
& eqangle(X2,X0,X2,X1,X5,X3,X5,X4) )
=> cong(X0,X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD43) ).
fof(f57,axiom,
! [X0,X1,X2,X3] :
( ( cong(X0,X2,X1,X2)
& cong(X0,X3,X1,X3) )
=> perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& perp(X5,X4,X0,X1)
& coll(X5,X0,X1)
& perp(X6,X4,X0,X2)
& coll(X6,X0,X2)
& circle(X3,X0,X7,X12)
& perp(X8,X7,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X7,X0,X2)
& coll(X9,X0,X2)
& coll(X10,X8,X9)
& coll(X10,X5,X6) )
=> eqangle(X4,X0,X0,X7,X9,X10,X10,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012008) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ( circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& perp(X5,X4,X0,X1)
& coll(X5,X0,X1)
& perp(X6,X4,X0,X2)
& coll(X6,X0,X2)
& circle(X3,X0,X7,X12)
& perp(X8,X7,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X7,X0,X2)
& coll(X9,X0,X2)
& coll(X10,X8,X9)
& coll(X10,X5,X6) )
=> eqangle(X4,X0,X0,X7,X9,X10,X10,X6) ),
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,X7,X8,X9,X10,X11,X12] :
( ~ eqangle(X4,X0,X0,X7,X9,X10,X10,X6)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& perp(X5,X4,X0,X1)
& coll(X5,X0,X1)
& perp(X6,X4,X0,X2)
& coll(X6,X0,X2)
& circle(X3,X0,X7,X12)
& perp(X8,X7,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X7,X0,X2)
& coll(X9,X0,X2)
& coll(X10,X8,X9)
& coll(X10,X5,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ~ eqangle(X4,X0,X0,X7,X9,X10,X10,X6)
& circle(X3,X0,X1,X2)
& circle(X3,X0,X4,X11)
& perp(X5,X4,X0,X1)
& coll(X5,X0,X1)
& perp(X6,X4,X0,X2)
& coll(X6,X0,X2)
& circle(X3,X0,X7,X12)
& perp(X8,X7,X0,X1)
& coll(X8,X0,X1)
& perp(X9,X7,X0,X2)
& coll(X9,X0,X2)
& coll(X10,X8,X9)
& coll(X10,X5,X6) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( ~ eqangle(sK24,sK20,sK20,sK27,sK29,sK30,sK30,sK26)
& circle(sK23,sK20,sK21,sK22)
& circle(sK23,sK20,sK24,sK31)
& perp(sK25,sK24,sK20,sK21)
& coll(sK25,sK20,sK21)
& perp(sK26,sK24,sK20,sK22)
& coll(sK26,sK20,sK22)
& circle(sK23,sK20,sK27,sK32)
& perp(sK28,sK27,sK20,sK21)
& coll(sK28,sK20,sK21)
& perp(sK29,sK27,sK20,sK22)
& coll(sK29,sK20,sK22)
& coll(sK30,sK28,sK29)
& coll(sK30,sK25,sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32]),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),skolemize(X10,sK30),skolemize(X11,sK31),skolemize(X12,sK32)],[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(f387,plain,
perp(sK29,sK27,sK20,sK22),
inference(cnf_transformation,[],[f270]) ).
fof(f397,plain,
~ eqangle(sK24,sK20,sK20,sK27,sK29,sK30,sK30,sK26),
inference(cnf_transformation,[],[f270]) ).
fof(f399,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X0,X1,X2,X3,X8,X9,X6,X7)
| ~ para(X4,X5,X8,X9) ),
inference(resolution,[],[f292,f310]) ).
fof(f400,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ para(X6,X7,X4,X5)
| eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X0,X1,X6,X7) ),
inference(resolution,[],[f399,f310]) ).
fof(f401,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(f404,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,[],[f401]) ).
fof(f412,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(f431,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(f446,plain,
! [X2,X3,X0,X1] :
( para(X0,X1,X0,X1)
| ~ para(X2,X3,X2,X3) ),
inference(resolution,[],[f309,f412]) ).
fof(f449,definition,
( spl33_1
<=> ! [X2,X3] : ~ para(X2,X3,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl33_1])],[avatar_definition]) ).
fof(f450,plain,
( ! [X2,X3] : ~ para(X2,X3,X2,X3)
| ~ spl33_1 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f452,definition,
( spl33_2
<=> ! [X0,X1] : para(X0,X1,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl33_2])],[avatar_definition]) ).
fof(f453,plain,
( ! [X0,X1] : para(X0,X1,X0,X1)
| ~ spl33_2 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f454,plain,
( spl33_1
| spl33_2 ),
inference(avatar_split_clause,[],[f446,f452,f449]) ).
fof(f461,plain,
perp(sK20,sK22,sK29,sK27),
inference(resolution,[],[f278,f387]) ).
fof(f467,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f313,f431]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ coll(X1,X2,X0) )
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f467,f453]) ).
fof(f475,plain,
! [X0,X1] :
( ~ perp(X0,X1,sK29,sK27)
| para(X0,X1,sK20,sK22) ),
inference(resolution,[],[f279,f387]) ).
fof(f481,plain,
! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| coll(X1,X2,X0)
| ~ para(X1,X0,X1,X0) ),
inference(resolution,[],[f312,f431]) ).
fof(f485,plain,
( ! [X2,X0,X1] :
( cyclic(X0,X0,X1,X2)
| ~ para(X1,X0,X1,X0) )
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f481,f471]) ).
fof(f488,plain,
( ! [X2,X0,X1] : cyclic(X0,X0,X1,X2)
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f485,f453]) ).
fof(f489,plain,
( ! [X2,X3,X0,X1] :
( ~ cyclic(X0,X0,X1,X2)
| cyclic(X0,X1,X2,X3) )
| ~ spl33_2 ),
inference(resolution,[],[f488,f287]) ).
fof(f495,plain,
( ! [X2,X3,X0,X1] : cyclic(X0,X1,X2,X3)
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f489,f488]) ).
fof(f498,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| ~ cyclic(X0,X1,X2,X1)
| cong(X0,X1,X0,X1) )
| ~ spl33_2 ),
inference(resolution,[],[f495,f404]) ).
fof(f501,plain,
( ! [X2,X0,X1] :
( ~ cyclic(X0,X1,X2,X0)
| cong(X0,X1,X0,X1) )
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f498,f495]) ).
fof(f503,plain,
( ! [X0,X1] : cong(X0,X1,X0,X1)
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f501,f495]) ).
fof(f504,plain,
( ! [X2,X0,X1] :
( ~ cong(X0,X1,X0,X1)
| perp(X0,X0,X1,X2) )
| ~ spl33_2 ),
inference(resolution,[],[f503,f327]) ).
fof(f505,plain,
( ! [X2,X0,X1] : perp(X0,X0,X1,X2)
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f504,f503]) ).
fof(f506,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ perp(X0,X1,X2,X2)
| para(X0,X1,X3,X4) )
| ~ spl33_2 ),
inference(resolution,[],[f505,f279]) ).
fof(f507,plain,
( ! [X2,X0,X1] : perp(X0,X1,X2,X2)
| ~ spl33_2 ),
inference(resolution,[],[f505,f278]) ).
fof(f513,plain,
( ! [X3,X0,X1,X4] : para(X0,X1,X3,X4)
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f506,f507]) ).
fof(f514,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ para(X0,X1,X6,X7) )
| ~ spl33_2 ),
inference(resolution,[],[f513,f400]) ).
fof(f515,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X2,X3)
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f514,f513]) ).
fof(f519,plain,
( ! [X2,X3,X0,X1,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X4,X5)
| ~ spl33_2 ),
inference(resolution,[],[f515,f291]) ).
fof(f536,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ para(X6,X7,X4,X5) )
| ~ spl33_2 ),
inference(resolution,[],[f519,f399]) ).
fof(f540,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ spl33_2 ),
inference(forward_subsumption_resolution,[],[f536,f513]) ).
fof(f553,plain,
( $false
| ~ spl33_2 ),
inference(resolution,[],[f540,f397]) ).
fof(f554,plain,
~ spl33_2,
inference(avatar_contradiction_clause,[],[f553]) ).
fof(f558,plain,
para(sK20,sK22,sK20,sK22),
inference(resolution,[],[f461,f475]) ).
fof(f562,plain,
( $false
| ~ spl33_1 ),
inference(forward_subsumption_resolution,[],[f558,f450]) ).
fof(f563,plain,
~ spl33_1,
inference(avatar_contradiction_clause,[],[f562]) ).
cnf(s1,plain,
( spl33_1
| spl33_2 ),
inference(sat_conversion,[],[f454]) ).
cnf(s2,plain,
~ spl33_2,
inference(sat_conversion,[],[f554]) ).
cnf(s3,plain,
~ spl33_1,
inference(sat_conversion,[],[f563]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f564,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO548+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 08:30:41 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.82/1.90 % (201723)Detected formulas, will run a generic FOF schedule.
% 4.82/1.90 % (201732)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3887667517:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.82/1.90 % (201729)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=946135430:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.82/1.90 % (201734)dis-21_1_sil=8000:lcm=predicate:random_seed=4153682235: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)
% 4.82/1.90 % (201733)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=85304623:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.82/1.90 % (201728)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=1622068645:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.82/1.90 % (201730)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=135236647:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.82/1.90 % (201732)Instruction limit reached!
% 4.82/1.90 % (201732)------------------------------
% 4.82/1.90 % (201732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201732)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201732)Termination reason: Instruction limit
% 4.82/1.90 % (201732)Termination phase: Saturation
% 4.82/1.90 % (201732)Time elapsed: 0.038 s
% 4.82/1.90 % (201732)Peak memory usage: 89 MB
% 4.82/1.90 % (201732)Instructions burned: 122 (million)
% 4.82/1.90 % (201731)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2636200058:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.82/1.90 % (201731)Refutation not found, incomplete strategy
% 4.82/1.90 % (201731)------------------------------
% 4.82/1.90 % (201731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201731)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201731)Termination reason: Refutation not found, incomplete strategy
% 4.82/1.90 % (201731)Time elapsed: 0.039 s
% 4.82/1.90 % (201731)Peak memory usage: 89 MB
% 4.82/1.90 % (201731)Instructions burned: 73 (million)
% 4.82/1.90 % (201734)Instruction limit reached!
% 4.82/1.90 % (201734)------------------------------
% 4.82/1.90 % (201734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201734)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201734)Termination reason: Instruction limit
% 4.82/1.90 % (201734)Termination phase: Saturation
% 4.82/1.90 % (201734)Time elapsed: 0.076 s
% 4.82/1.90 % (201734)Peak memory usage: 89 MB
% 4.82/1.90 % (201734)Instructions burned: 131 (million)
% 4.82/1.90 % (201741)lrs+10_1_sil=8000:sp=occurrence:random_seed=2897161185:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.82/1.90 % (201733)Instruction limit reached!
% 4.82/1.90 % (201733)------------------------------
% 4.82/1.90 % (201733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201733)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201733)Termination reason: Instruction limit
% 4.82/1.90 % (201733)Termination phase: Saturation
% 4.82/1.90 % (201733)Time elapsed: 0.094 s
% 4.82/1.90 % (201733)Peak memory usage: 90 MB
% 4.82/1.90 % (201733)Instructions burned: 139 (million)
% 4.82/1.90 % (201741)Instruction limit reached!
% 4.82/1.90 % (201741)------------------------------
% 4.82/1.90 % (201741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201741)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201741)Termination reason: Instruction limit
% 4.82/1.90 % (201741)Termination phase: Saturation
% 4.82/1.90 % (201741)Time elapsed: 0.100 s
% 4.82/1.90 % (201741)Peak memory usage: 93 MB
% 4.82/1.90 % (201741)Instructions burned: 287 (million)
% 4.82/1.90 % (201743)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2460068842:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.82/1.90 % (201745)lrs+1011_1_sil=32000:sp=occurrence:random_seed=749047435:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.82/1.90 % (201746)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=3586975403:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.82/1.90 % (201743)Instruction limit reached!
% 4.82/1.90 % (201743)------------------------------
% 4.82/1.90 % (201743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201743)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201743)Termination reason: Instruction limit
% 4.82/1.90 % (201743)Termination phase: Saturation
% 4.82/1.90 % (201743)Time elapsed: 0.081 s
% 4.82/1.90 % (201743)Peak memory usage: 89 MB
% 4.82/1.90 % (201743)Instructions burned: 159 (million)
% 4.82/1.90 % (201731)------------------------------
% 4.82/1.90 % (201731)------------------------------
% 4.82/1.90 % (201746)Instruction limit reached!
% 4.82/1.90 % (201746)------------------------------
% 4.82/1.90 % (201746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201746)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201746)Termination reason: Instruction limit
% 4.82/1.90 % (201746)Termination phase: Saturation
% 4.82/1.90 % (201746)Time elapsed: 0.075 s
% 4.82/1.90 % (201746)Peak memory usage: 91 MB
% 4.82/1.90 % (201746)Instructions burned: 250 (million)
% 4.82/1.90 % (201750)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2692017617:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.82/1.90 % (201745)Instruction limit reached!
% 4.82/1.90 % (201745)------------------------------
% 4.82/1.90 % (201745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201745)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201745)Termination reason: Instruction limit
% 4.82/1.90 % (201745)Termination phase: Saturation
% 4.82/1.90 % (201745)Time elapsed: 0.217 s
% 4.82/1.90 % (201745)Peak memory usage: 92 MB
% 4.82/1.90 % (201745)Instructions burned: 326 (million)
% 4.82/1.90 % (201751)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4261729977:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.82/1.90 % (201752)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=350358580:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 4.82/1.90 % (201752)Instruction limit reached!
% 4.82/1.90 % (201752)------------------------------
% 4.82/1.90 % (201752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201752)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201752)Termination reason: Instruction limit
% 4.82/1.90 % (201752)Termination phase: Saturation
% 4.82/1.90 % (201752)Time elapsed: 0.035 s
% 4.82/1.90 % (201752)Peak memory usage: 90 MB
% 4.82/1.90 % (201752)Instructions burned: 113 (million)
% 4.82/1.90 % (201757)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1531719005:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 4.82/1.90 % (201756)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2146135147:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.82/1.90 % (201750)Instruction limit reached!
% 4.82/1.90 % (201750)------------------------------
% 4.82/1.90 % (201750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201750)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201750)Termination reason: Instruction limit
% 4.82/1.90 % (201750)Termination phase: Saturation
% 4.82/1.90 % (201750)Time elapsed: 0.170 s
% 4.82/1.90 % (201750)Peak memory usage: 89 MB
% 4.82/1.90 % (201750)Instructions burned: 296 (million)
% 4.82/1.90 % (201757)Instruction limit reached!
% 4.82/1.90 % (201757)------------------------------
% 4.82/1.90 % (201757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201757)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201757)Termination reason: Instruction limit
% 4.82/1.90 % (201757)Termination phase: Saturation
% 4.82/1.90 % (201757)Time elapsed: 0.033 s
% 4.82/1.90 % (201757)Peak memory usage: 89 MB
% 4.82/1.90 % (201757)Instructions burned: 117 (million)
% 4.82/1.90 % (201756)Instruction limit reached!
% 4.82/1.90 % (201756)------------------------------
% 4.82/1.90 % (201756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201756)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201756)Termination reason: Instruction limit
% 4.82/1.90 % (201756)Termination phase: Saturation
% 4.82/1.90 % (201756)Time elapsed: 0.069 s
% 4.82/1.90 % (201756)Peak memory usage: 89 MB
% 4.82/1.90 % (201756)Instructions burned: 127 (million)
% 4.82/1.90 % (201728)First to succeed.
% 4.82/1.90 % (201728)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-201723"
% 4.82/1.90 % (201761)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2287905685:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 4.82/1.90 % (201729)Also succeeded, but the first one will report.
% 4.82/1.90 % (201760)lrs+10_1_sil=8000:sp=occurrence:random_seed=1187596546:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 4.82/1.90 % (201762)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1977305178:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 4.82/1.90 % (201761)Instruction limit reached!
% 4.82/1.90 % (201761)------------------------------
% 4.82/1.90 % (201761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.90 % (201761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.90 % (201761)CaDiCaL version: 2.1.3
% 4.82/1.90 % (201761)Termination reason: Instruction limit
% 4.82/1.90 % (201761)Termination phase: Saturation
% 4.82/1.90 % (201761)Time elapsed: 0.133 s
% 4.82/1.90 % (201761)Peak memory usage: 91 MB
% 4.82/1.90 % (201761)Instructions burned: 438 (million)
% 4.82/1.90 % (201766)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3266596000:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2990 on theBenchmark for (2990ds/134Mi)
% 4.82/1.90 % (201728)Refutation found. Thanks to Tanya!
% 4.82/1.90 % SZS status Theorem for theBenchmark
% 4.82/1.90 % SZS output start Proof for theBenchmark
% See solution above
% 4.82/1.99 % (201728)------------------------------
% 4.82/1.99 % (201728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.82/1.99 % (201728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.82/1.99 % (201728)CaDiCaL version: 2.1.3
% 4.82/1.99 % (201728)Termination reason: Refutation
% 4.82/1.99 % (201728)Time elapsed: 0.660 s
% 4.82/1.99 % (201728)Peak memory usage: 130 MB
% 4.82/1.99 % (201728)Instructions burned: 989 (million)
% 4.82/1.99 % (201728)------------------------------
% 4.82/1.99 % (201728)------------------------------
% 4.82/1.99 % (201723)Success in time 1.065 s
% 4.82/1.99 % Vampire exiting
%------------------------------------------------------------------------------