%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO277+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:52:19 AM UTC 2026
% Result : Theorem 2.98s 1.60s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 128 ( 28 unt; 2 def)
% Number of atoms : 569 ( 139 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 813 ( 372 ~; 376 |; 53 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 218 ( 0 sgn 203 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ron(vd1085,X0)
& ron(vd1089,X0)
& rline(X0) )
=> X0 = vd1099 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(theu(the(230), 1), imp(the(230)))') ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ron(vd1085,X0)
& ron(vd1089,X0)
& rline(X0) )
=> X0 = vd1099 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( ron(vd1085,vd1099)
& ron(vd1089,vd1099)
& rline(vd1099) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), pred(the(230), 0)))') ).
fof(f9,axiom,
rpoint(vd1089),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(226, 0)') ).
fof(f10,axiom,
vd1085 = vd1086,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(225, 4)') ).
fof(f11,axiom,
rpoint(vd1086),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(225, 1)') ).
fof(f14,axiom,
vf(vd1089,vd1085) = vf(vd1089,vd1080),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(226, 1090, 0)') ).
fof(f16,axiom,
vd1085 != vd1080,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(225), 1087, 0)') ).
fof(f24,axiom,
? [X0] :
( vd1080 = X0
& rpoint(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(s1(plural(224)))') ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( ( rinside(X0,X2)
& X2 = X3
& rcircle(X3)
& X0 = X1
& rpoint(X1) )
=> ~ ron(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))') ).
fof(f38,axiom,
! [X0,X1,X2,X3] :
( ( ron(X1,X3)
& ron(X1,X2)
& ron(X0,X3)
& ron(X0,X2)
& ? [X4] :
( X3 = X4
& rline(X4) )
& ? [X5] :
( X2 = X5
& rline(X5) )
& X0 != X1
& ? [X6] :
( X1 = X6
& rpoint(X6) )
& ? [X7] :
( X0 = X7
& rpoint(X7) ) )
=> X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))') ).
fof(f41,axiom,
! [X0,X1] :
( rcenter(X0,X1)
=> rinside(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))') ).
fof(f43,axiom,
! [X0,X1] :
( ( X0 != X1
& ? [X2] :
( X1 = X2
& rpoint(X2) )
& ? [X3] :
( X0 = X3
& rpoint(X3) ) )
=> ? [X4] :
( ron(X1,X4)
& rcenter(X0,X4)
& rcircle(X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
fof(f121,axiom,
! [X0,X1,X2,X3] :
( ( ron(X1,X3)
& rcenter(X2,X3)
& ? [X4] :
( X1 = X4
& rpoint(X4) )
& ? [X5] :
( X0 = X5
& rpoint(X5) ) )
=> ( rless(vf(X2,X0),vf(X2,X1))
<=> rinside(X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))') ).
fof(f130,plain,
? [X0] :
( vd1099 != X0
& ron(vd1085,X0)
& ron(vd1089,X0)
& rline(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f131,plain,
? [X0] :
( vd1099 != X0
& ron(vd1085,X0)
& ron(vd1089,X0)
& rline(X0) ),
inference(flattening,[],[f130]) ).
fof(f148,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ ron(X1,X3)
| ~ ron(X1,X2)
| ~ ron(X0,X3)
| ~ ron(X0,X2)
| ! [X4] :
( X3 != X4
| ~ rline(X4) )
| ! [X5] :
( X2 != X5
| ~ rline(X5) )
| X0 = X1
| ! [X6] :
( X1 != X6
| ~ rpoint(X6) )
| ! [X7] :
( X0 != X7
| ~ rpoint(X7) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ ron(X1,X3)
| ~ ron(X1,X2)
| ~ ron(X0,X3)
| ~ ron(X0,X2)
| ! [X4] :
( X3 != X4
| ~ rline(X4) )
| ! [X5] :
( X2 != X5
| ~ rline(X5) )
| X0 = X1
| ! [X6] :
( X1 != X6
| ~ rpoint(X6) )
| ! [X7] :
( X0 != X7
| ~ rpoint(X7) ) ),
inference(flattening,[],[f148]) ).
fof(f240,plain,
! [X0,X1,X2,X3] :
( ( rless(vf(X2,X0),vf(X2,X1))
<=> rinside(X0,X3) )
| ~ ron(X1,X3)
| ~ rcenter(X2,X3)
| ! [X4] :
( X1 != X4
| ~ rpoint(X4) )
| ! [X5] :
( X0 != X5
| ~ rpoint(X5) ) ),
inference(ennf_transformation,[],[f121]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( ( rless(vf(X2,X0),vf(X2,X1))
<=> rinside(X0,X3) )
| ~ ron(X1,X3)
| ~ rcenter(X2,X3)
| ! [X4] :
( X1 != X4
| ~ rpoint(X4) )
| ! [X5] :
( X0 != X5
| ~ rpoint(X5) ) ),
inference(flattening,[],[f240]) ).
fof(f281,plain,
! [X0,X1] :
( ? [X4] :
( ron(X1,X4)
& rcenter(X0,X4)
& rcircle(X4) )
| X0 = X1
| ! [X2] :
( X1 != X2
| ~ rpoint(X2) )
| ! [X3] :
( X0 != X3
| ~ rpoint(X3) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f282,plain,
! [X0,X1] :
( ? [X4] :
( ron(X1,X4)
& rcenter(X0,X4)
& rcircle(X4) )
| X0 = X1
| ! [X2] :
( X1 != X2
| ~ rpoint(X2) )
| ! [X3] :
( X0 != X3
| ~ rpoint(X3) ) ),
inference(flattening,[],[f281]) ).
fof(f285,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ~ rinside(X0,X2)
| X2 != X3
| ~ rcircle(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f286,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ~ rinside(X0,X2)
| X2 != X3
| ~ rcircle(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(flattening,[],[f285]) ).
fof(f291,plain,
! [X0,X1] :
( rinside(X0,X1)
| ~ rcenter(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f294,plain,
( vd1099 != sK1
& ron(vd1085,sK1)
& ron(vd1089,sK1)
& rline(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f131]) ).
fof(f332,plain,
( vd1080 = sK29
& rpoint(sK29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(X0,sK29)],[f24]) ).
fof(f334,plain,
! [X0,X1,X2,X3] :
( ( ( rless(vf(X2,X0),vf(X2,X1))
| ~ rinside(X0,X3) )
& ( rinside(X0,X3)
| ~ rless(vf(X2,X0),vf(X2,X1)) ) )
| ~ ron(X1,X3)
| ~ rcenter(X2,X3)
| ! [X4] :
( X1 != X4
| ~ rpoint(X4) )
| ! [X5] :
( X0 != X5
| ~ rpoint(X5) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f358,plain,
! [X0,X1] :
( ? [X2] :
( ron(X1,X2)
& rcenter(X0,X2)
& rcircle(X2) )
| X0 = X1
| ! [X3] :
( X1 != X3
| ~ rpoint(X3) )
| ! [X4] :
( X0 != X4
| ~ rpoint(X4) ) ),
inference(rectify,[],[f282]) ).
fof(f359,plain,
! [X0,X1] :
( ( ron(X1,sK44(X0,X1))
& rcenter(X0,sK44(X0,X1))
& rcircle(sK44(X0,X1)) )
| X0 = X1
| ! [X3] :
( X1 != X3
| ~ rpoint(X3) )
| ! [X4] :
( X0 != X4
| ~ rpoint(X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(X2,sK44(X0,X1))],[f358]) ).
fof(f362,plain,
rline(sK1),
inference(cnf_transformation,[],[f294]) ).
fof(f363,plain,
ron(vd1089,sK1),
inference(cnf_transformation,[],[f294]) ).
fof(f364,plain,
ron(vd1085,sK1),
inference(cnf_transformation,[],[f294]) ).
fof(f365,plain,
vd1099 != sK1,
inference(cnf_transformation,[],[f294]) ).
fof(f393,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( X2 = X3
| ~ ron(X1,X3)
| ~ ron(X1,X2)
| ~ ron(X0,X3)
| ~ ron(X0,X2)
| X3 != X4
| ~ rline(X4)
| X2 != X5
| ~ rline(X5)
| X0 = X1
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(cnf_transformation,[],[f149]) ).
fof(f397,plain,
vd1085 != vd1080,
inference(cnf_transformation,[],[f16]) ).
fof(f399,plain,
vf(vd1089,vd1080) = vf(vd1089,vd1085),
inference(cnf_transformation,[],[f14]) ).
fof(f401,plain,
vd1085 = vd1086,
inference(cnf_transformation,[],[f10]) ).
fof(f402,plain,
rline(vd1099),
inference(cnf_transformation,[],[f3]) ).
fof(f403,plain,
ron(vd1089,vd1099),
inference(cnf_transformation,[],[f3]) ).
fof(f404,plain,
ron(vd1085,vd1099),
inference(cnf_transformation,[],[f3]) ).
fof(f455,plain,
rpoint(vd1089),
inference(cnf_transformation,[],[f9]) ).
fof(f498,plain,
rpoint(sK29),
inference(cnf_transformation,[],[f332]) ).
fof(f499,plain,
vd1080 = sK29,
inference(cnf_transformation,[],[f332]) ).
fof(f509,plain,
! [X2,X3,X0,X1,X4,X5] :
( rinside(X0,X3)
| ~ rless(vf(X2,X0),vf(X2,X1))
| ~ ron(X1,X3)
| ~ rcenter(X2,X3)
| X1 != X4
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(cnf_transformation,[],[f334]) ).
fof(f510,plain,
! [X2,X3,X0,X1,X4,X5] :
( rless(vf(X2,X0),vf(X2,X1))
| ~ rinside(X0,X3)
| ~ ron(X1,X3)
| ~ rcenter(X2,X3)
| X1 != X4
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(cnf_transformation,[],[f334]) ).
fof(f534,plain,
rpoint(vd1086),
inference(cnf_transformation,[],[f11]) ).
fof(f578,plain,
! [X3,X0,X1,X4] :
( rcircle(sK44(X0,X1))
| X0 = X1
| X1 != X3
| ~ rpoint(X3)
| X0 != X4
| ~ rpoint(X4) ),
inference(cnf_transformation,[],[f359]) ).
fof(f579,plain,
! [X3,X0,X1,X4] :
( rcenter(X0,sK44(X0,X1))
| X0 = X1
| X1 != X3
| ~ rpoint(X3)
| X0 != X4
| ~ rpoint(X4) ),
inference(cnf_transformation,[],[f359]) ).
fof(f580,plain,
! [X3,X0,X1,X4] :
( ron(X1,sK44(X0,X1))
| X0 = X1
| X1 != X3
| ~ rpoint(X3)
| X0 != X4
| ~ rpoint(X4) ),
inference(cnf_transformation,[],[f359]) ).
fof(f583,plain,
! [X2,X3,X0,X1] :
( ~ ron(X0,X2)
| ~ rinside(X0,X2)
| X2 != X3
| ~ rcircle(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(cnf_transformation,[],[f286]) ).
fof(f592,plain,
! [X0,X1] :
( rinside(X0,X1)
| ~ rcenter(X0,X1) ),
inference(cnf_transformation,[],[f291]) ).
fof(f593,plain,
ron(vd1086,sK1),
inference(definition_unfolding,[],[f364,f401]) ).
fof(f594,plain,
vd1086 != sK29,
inference(definition_unfolding,[],[f397,f401,f499]) ).
fof(f596,plain,
vf(vd1089,sK29) = vf(vd1089,vd1086),
inference(definition_unfolding,[],[f399,f499,f401]) ).
fof(f598,plain,
ron(vd1086,vd1099),
inference(definition_unfolding,[],[f404,f401]) ).
fof(f683,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( X2 = X4
| ~ ron(X1,X4)
| ~ ron(X1,X2)
| ~ ron(X0,X4)
| ~ ron(X0,X2)
| ~ rline(X4)
| X2 != X5
| ~ rline(X5)
| X0 = X1
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f393]) ).
fof(f684,plain,
! [X0,X1,X6,X7,X4,X5] :
( X4 = X5
| ~ ron(X1,X4)
| ~ ron(X1,X5)
| ~ ron(X0,X4)
| ~ ron(X0,X5)
| ~ rline(X4)
| ~ rline(X5)
| X0 = X1
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f683]) ).
fof(f685,plain,
! [X0,X6,X7,X4,X5] :
( X4 = X5
| ~ ron(X6,X4)
| ~ ron(X6,X5)
| ~ ron(X0,X4)
| ~ ron(X0,X5)
| ~ rline(X4)
| ~ rline(X5)
| X0 = X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f684]) ).
fof(f686,plain,
! [X6,X7,X4,X5] :
( ~ ron(X7,X5)
| ~ ron(X6,X4)
| ~ ron(X6,X5)
| ~ ron(X7,X4)
| X4 = X5
| ~ rline(X4)
| ~ rline(X5)
| X6 = X7
| ~ rpoint(X6)
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f685]) ).
fof(f1002,plain,
! [X2,X3,X0,X4,X5] :
( rless(vf(X2,X0),vf(X2,X4))
| ~ rinside(X0,X3)
| ~ ron(X4,X3)
| ~ rcenter(X2,X3)
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f510]) ).
fof(f1003,plain,
! [X2,X3,X4,X5] :
( rless(vf(X2,X5),vf(X2,X4))
| ~ rinside(X5,X3)
| ~ ron(X4,X3)
| ~ rcenter(X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f1002]) ).
fof(f1004,plain,
! [X2,X3,X0,X4,X5] :
( rinside(X0,X3)
| ~ rless(vf(X2,X0),vf(X2,X4))
| ~ ron(X4,X3)
| ~ rcenter(X2,X3)
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f509]) ).
fof(f1005,plain,
! [X2,X3,X4,X5] :
( ~ rless(vf(X2,X5),vf(X2,X4))
| rinside(X5,X3)
| ~ ron(X4,X3)
| ~ rcenter(X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f1004]) ).
fof(f1192,plain,
! [X3,X0,X4] :
( ron(X3,sK44(X0,X3))
| X0 = X3
| ~ rpoint(X3)
| X0 != X4
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f580]) ).
fof(f1193,plain,
! [X3,X4] :
( ron(X3,sK44(X4,X3))
| X3 = X4
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f1192]) ).
fof(f1194,plain,
! [X3,X0,X4] :
( rcenter(X0,sK44(X0,X3))
| X0 = X3
| ~ rpoint(X3)
| X0 != X4
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f579]) ).
fof(f1195,plain,
! [X3,X4] :
( rcenter(X4,sK44(X4,X3))
| X3 = X4
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f1194]) ).
fof(f1196,plain,
! [X3,X0,X4] :
( rcircle(sK44(X0,X3))
| X0 = X3
| ~ rpoint(X3)
| X0 != X4
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f578]) ).
fof(f1197,plain,
! [X3,X4] :
( rcircle(sK44(X4,X3))
| X3 = X4
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f1196]) ).
fof(f1200,plain,
! [X3,X0,X1] :
( ~ ron(X0,X3)
| ~ rinside(X0,X3)
| ~ rcircle(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f583]) ).
fof(f1201,plain,
! [X3,X1] :
( ~ rinside(X1,X3)
| ~ ron(X1,X3)
| ~ rcircle(X3)
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f1200]) ).
fof(f1210,plain,
! [X0,X1] :
( ~ ron(X0,X1)
| ~ ron(X0,sK1)
| ~ ron(vd1089,X1)
| sK1 = X1
| ~ rline(X1)
| ~ rline(sK1)
| vd1089 = X0
| ~ rpoint(X0)
| ~ rpoint(vd1089) ),
inference(resolution,[],[f363,f686]) ).
fof(f1211,plain,
! [X0,X1] :
( ~ ron(X0,X1)
| ~ ron(X0,sK1)
| ~ ron(vd1089,X1)
| sK1 = X1
| ~ rline(X1)
| vd1089 = X0
| ~ rpoint(X0)
| ~ rpoint(vd1089) ),
inference(forward_subsumption_resolution,[],[f1210,f362]) ).
fof(f1212,plain,
! [X0,X1] :
( ~ ron(vd1089,X1)
| ~ ron(X0,sK1)
| ~ ron(X0,X1)
| sK1 = X1
| ~ rline(X1)
| vd1089 = X0
| ~ rpoint(X0) ),
inference(forward_subsumption_resolution,[],[f1211,f455]) ).
fof(f1216,plain,
! [X0] :
( ~ ron(X0,sK1)
| ~ ron(X0,vd1099)
| vd1099 = sK1
| ~ rline(vd1099)
| vd1089 = X0
| ~ rpoint(X0) ),
inference(resolution,[],[f1212,f403]) ).
fof(f1227,plain,
! [X0] :
( ~ ron(X0,sK1)
| ~ ron(X0,vd1099)
| ~ rline(vd1099)
| vd1089 = X0
| ~ rpoint(X0) ),
inference(forward_subsumption_resolution,[],[f1216,f365]) ).
fof(f1236,plain,
! [X0] :
( ~ ron(X0,sK1)
| ~ ron(X0,vd1099)
| vd1089 = X0
| ~ rpoint(X0) ),
inference(forward_subsumption_resolution,[],[f1227,f402]) ).
fof(f1417,definition,
( spl47_29
<=> vd1089 = vd1086 ),
introduced(definition,[new_symbols(definition,[spl47_29])],[avatar_definition]) ).
fof(f1418,plain,
( vd1089 != vd1086
| spl47_29 ),
inference(avatar_component_clause,[],[f1417]) ).
fof(f1419,plain,
( vd1089 = vd1086
| ~ spl47_29 ),
inference(avatar_component_clause,[],[f1417]) ).
fof(f1422,plain,
( ~ ron(vd1086,vd1099)
| vd1089 = vd1086
| ~ rpoint(vd1086) ),
inference(resolution,[],[f1236,f593]) ).
fof(f1459,plain,
( vd1089 = vd1086
| ~ rpoint(vd1086) ),
inference(forward_subsumption_resolution,[],[f1422,f598]) ).
fof(f1460,plain,
( ~ rpoint(vd1086)
| spl47_29 ),
inference(forward_subsumption_resolution,[],[f1459,f1418]) ).
fof(f1461,plain,
( $false
| spl47_29 ),
inference(forward_subsumption_resolution,[],[f1460,f534]) ).
fof(f1462,plain,
spl47_29,
inference(avatar_contradiction_clause,[],[f1461]) ).
fof(f1603,plain,
( vd1089 != sK29
| ~ spl47_29 ),
inference(superposition,[],[f594,f1419]) ).
fof(f1604,plain,
( vf(vd1089,sK29) = vf(vd1089,vd1089)
| ~ spl47_29 ),
inference(superposition,[],[f596,f1419]) ).
fof(f2676,plain,
( ! [X0,X1] :
( rless(vf(vd1089,sK29),vf(vd1089,X0))
| ~ rinside(vd1089,X1)
| ~ ron(X0,X1)
| ~ rcenter(vd1089,X1)
| ~ rpoint(X0)
| ~ rpoint(vd1089) )
| ~ spl47_29 ),
inference(superposition,[],[f1003,f1604]) ).
fof(f2694,plain,
( ! [X0,X1] :
( rless(vf(vd1089,sK29),vf(vd1089,X0))
| ~ ron(X0,X1)
| ~ rcenter(vd1089,X1)
| ~ rpoint(X0)
| ~ rpoint(vd1089) )
| ~ spl47_29 ),
inference(forward_subsumption_resolution,[],[f2676,f592]) ).
fof(f2699,plain,
( ! [X0,X1] :
( rless(vf(vd1089,sK29),vf(vd1089,X0))
| ~ ron(X0,X1)
| ~ rcenter(vd1089,X1)
| ~ rpoint(X0) )
| ~ spl47_29 ),
inference(forward_subsumption_resolution,[],[f2694,f455]) ).
fof(f2735,definition,
( spl47_32
<=> rless(vf(vd1089,sK29),vf(vd1089,sK29)) ),
introduced(definition,[new_symbols(definition,[spl47_32])],[avatar_definition]) ).
fof(f2736,plain,
( ~ rless(vf(vd1089,sK29),vf(vd1089,sK29))
| spl47_32 ),
inference(avatar_component_clause,[],[f2735]) ).
fof(f2737,plain,
( rless(vf(vd1089,sK29),vf(vd1089,sK29))
| ~ spl47_32 ),
inference(avatar_component_clause,[],[f2735]) ).
fof(f2917,plain,
( ! [X0] :
( ~ ron(sK29,X0)
| ~ rcenter(vd1089,X0)
| ~ rpoint(sK29) )
| ~ spl47_29
| spl47_32 ),
inference(resolution,[],[f2736,f2699]) ).
fof(f2929,plain,
( ! [X0] :
( ~ rcenter(vd1089,X0)
| ~ ron(sK29,X0) )
| ~ spl47_29
| spl47_32 ),
inference(forward_subsumption_resolution,[],[f2917,f498]) ).
fof(f2936,plain,
( ! [X0] :
( ~ ron(sK29,sK44(vd1089,X0))
| vd1089 = X0
| ~ rpoint(X0)
| ~ rpoint(vd1089) )
| ~ spl47_29
| spl47_32 ),
inference(resolution,[],[f2929,f1195]) ).
fof(f2937,plain,
( ! [X0] :
( ~ ron(sK29,sK44(vd1089,X0))
| vd1089 = X0
| ~ rpoint(X0) )
| ~ spl47_29
| spl47_32 ),
inference(forward_subsumption_resolution,[],[f2936,f455]) ).
fof(f2973,plain,
( vd1089 = sK29
| ~ rpoint(sK29)
| vd1089 = sK29
| ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_29
| spl47_32 ),
inference(resolution,[],[f2937,f1193]) ).
fof(f2974,plain,
( vd1089 = sK29
| ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_29
| spl47_32 ),
inference(duplicate_literal_removal,[],[f2973]) ).
fof(f2975,plain,
( ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_29
| spl47_32 ),
inference(forward_subsumption_resolution,[],[f2974,f1603]) ).
fof(f2976,plain,
( ~ rpoint(vd1089)
| ~ spl47_29
| spl47_32 ),
inference(forward_subsumption_resolution,[],[f2975,f498]) ).
fof(f2977,plain,
( $false
| ~ spl47_29
| spl47_32 ),
inference(forward_subsumption_resolution,[],[f2976,f455]) ).
fof(f2978,plain,
( ~ spl47_29
| spl47_32 ),
inference(avatar_contradiction_clause,[],[f2977]) ).
fof(f2979,plain,
( ! [X0] :
( rinside(sK29,X0)
| ~ ron(sK29,X0)
| ~ rcenter(vd1089,X0)
| ~ rpoint(sK29)
| ~ rpoint(sK29) )
| ~ spl47_32 ),
inference(resolution,[],[f2737,f1005]) ).
fof(f2984,plain,
( ! [X0] :
( rinside(sK29,X0)
| ~ ron(sK29,X0)
| ~ rcenter(vd1089,X0)
| ~ rpoint(sK29) )
| ~ spl47_32 ),
inference(duplicate_literal_removal,[],[f2979]) ).
fof(f2989,plain,
( ! [X0] :
( rinside(sK29,X0)
| ~ ron(sK29,X0)
| ~ rcenter(vd1089,X0) )
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f2984,f498]) ).
fof(f3003,plain,
( ! [X0] :
( ~ ron(sK29,X0)
| ~ rcenter(vd1089,X0)
| ~ ron(sK29,X0)
| ~ rcircle(X0)
| ~ rpoint(sK29) )
| ~ spl47_32 ),
inference(resolution,[],[f2989,f1201]) ).
fof(f3006,plain,
( ! [X0] :
( ~ ron(sK29,X0)
| ~ rcenter(vd1089,X0)
| ~ rcircle(X0)
| ~ rpoint(sK29) )
| ~ spl47_32 ),
inference(duplicate_literal_removal,[],[f3003]) ).
fof(f3009,plain,
( ! [X0] :
( ~ rcenter(vd1089,X0)
| ~ ron(sK29,X0)
| ~ rcircle(X0) )
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3006,f498]) ).
fof(f3039,plain,
( ! [X0] :
( ~ ron(sK29,sK44(vd1089,X0))
| ~ rcircle(sK44(vd1089,X0))
| vd1089 = X0
| ~ rpoint(X0)
| ~ rpoint(vd1089) )
| ~ spl47_32 ),
inference(resolution,[],[f3009,f1195]) ).
fof(f3040,plain,
( ! [X0] :
( ~ ron(sK29,sK44(vd1089,X0))
| ~ rcircle(sK44(vd1089,X0))
| vd1089 = X0
| ~ rpoint(X0) )
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3039,f455]) ).
fof(f3068,plain,
( ~ rcircle(sK44(vd1089,sK29))
| vd1089 = sK29
| ~ rpoint(sK29)
| vd1089 = sK29
| ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_32 ),
inference(resolution,[],[f3040,f1193]) ).
fof(f3069,plain,
( ~ rcircle(sK44(vd1089,sK29))
| vd1089 = sK29
| ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_32 ),
inference(duplicate_literal_removal,[],[f3068]) ).
fof(f3070,plain,
( ~ rcircle(sK44(vd1089,sK29))
| ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_29
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3069,f1603]) ).
fof(f3071,plain,
( ~ rcircle(sK44(vd1089,sK29))
| ~ rpoint(vd1089)
| ~ spl47_29
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3070,f498]) ).
fof(f3072,plain,
( ~ rcircle(sK44(vd1089,sK29))
| ~ spl47_29
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3071,f455]) ).
fof(f3075,plain,
( vd1089 = sK29
| ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_29
| ~ spl47_32 ),
inference(resolution,[],[f3072,f1197]) ).
fof(f3076,plain,
( ~ rpoint(sK29)
| ~ rpoint(vd1089)
| ~ spl47_29
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3075,f1603]) ).
fof(f3077,plain,
( ~ rpoint(vd1089)
| ~ spl47_29
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3076,f498]) ).
fof(f3078,plain,
( $false
| ~ spl47_29
| ~ spl47_32 ),
inference(forward_subsumption_resolution,[],[f3077,f455]) ).
fof(f3079,plain,
( ~ spl47_29
| ~ spl47_32 ),
inference(avatar_contradiction_clause,[],[f3078]) ).
cnf(s23,plain,
spl47_29,
inference(sat_conversion,[],[f1462]) ).
cnf(s45,plain,
( ~ spl47_29
| spl47_32 ),
inference(sat_conversion,[],[f2978]) ).
cnf(s48,plain,
( ~ spl47_29
| ~ spl47_32 ),
inference(sat_conversion,[],[f3079]) ).
cnf(s50,plain,
~ spl47_32,
inference(rat,[],[s48,s23]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s45,s50,s23]) ).
fof(f3080,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO277+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 % Computer : n003.cluster.edu
% 0.09/0.40 % Model : x86_64 x86_64
% 0.09/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.40 % Memory : 8046.5625MB
% 0.09/0.40 % OS : Linux 6.8.0-71-generic
% 0.09/0.40 % CPULimit : 300
% 0.09/0.40 % WCLimit : 300
% 0.09/0.40 % DateTime : Sun Sep 27 08:00:11 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.44 Running first-order theorem proving
% 0.09/0.44 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
% 2.98/1.60 % (179953)Detected formulas, will run a generic FOF schedule.
% 2.98/1.60 % (179959)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=1503276810:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.98/1.60 % (179958)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=2101855933:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.98/1.60 % (179962)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3121380845:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.98/1.60 % (179961)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3484409570:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.98/1.60 % (179960)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=1537143123:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.98/1.60 % (179963)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2579203830:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.98/1.60 % (179964)dis-21_1_sil=8000:lcm=predicate:random_seed=1454872829: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)
% 2.98/1.60 % (179961)Instruction limit reached!
% 2.98/1.60 % (179961)------------------------------
% 2.98/1.60 % (179961)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179961)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179961)Termination reason: Instruction limit
% 2.98/1.60 % (179961)Termination phase: Saturation
% 2.98/1.60 % (179961)Time elapsed: 0.060 s
% 2.98/1.60 % (179961)Peak memory usage: 89 MB
% 2.98/1.60 % (179961)Instructions burned: 109 (million)
% 2.98/1.60 % (179962)Instruction limit reached!
% 2.98/1.60 % (179962)------------------------------
% 2.98/1.60 % (179962)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179962)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179962)Termination reason: Instruction limit
% 2.98/1.60 % (179962)Termination phase: Saturation
% 2.98/1.60 % (179962)Time elapsed: 0.065 s
% 2.98/1.60 % (179962)Peak memory usage: 88 MB
% 2.98/1.60 % (179962)Instructions burned: 120 (million)
% 2.98/1.60 % (179964)Instruction limit reached!
% 2.98/1.60 % (179964)------------------------------
% 2.98/1.60 % (179964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179964)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179964)Termination reason: Instruction limit
% 2.98/1.60 % (179964)Termination phase: Saturation
% 2.98/1.60 % (179964)Time elapsed: 0.070 s
% 2.98/1.60 % (179964)Peak memory usage: 90 MB
% 2.98/1.60 % (179964)Instructions burned: 130 (million)
% 2.98/1.60 % (179963)Instruction limit reached!
% 2.98/1.60 % (179963)------------------------------
% 2.98/1.60 % (179963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179963)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179963)Termination reason: Instruction limit
% 2.98/1.60 % (179963)Termination phase: Saturation
% 2.98/1.60 % (179963)Time elapsed: 0.088 s
% 2.98/1.60 % (179963)Peak memory usage: 90 MB
% 2.98/1.60 % (179963)Instructions burned: 140 (million)
% 2.98/1.60 % (179973)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3786556075:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.98/1.60 % (179972)lrs+10_1_sil=8000:sp=occurrence:random_seed=3747150612:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.98/1.60 % (179975)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=3567352718:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 2.98/1.60 % (179974)lrs+1011_1_sil=32000:sp=occurrence:random_seed=784091167:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.98/1.60 % (179973)Instruction limit reached!
% 2.98/1.60 % (179973)------------------------------
% 2.98/1.60 % (179973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179973)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179973)Termination reason: Instruction limit
% 2.98/1.60 % (179973)Termination phase: Saturation
% 2.98/1.60 % (179973)Time elapsed: 0.074 s
% 2.98/1.60 % (179973)Peak memory usage: 89 MB
% 2.98/1.60 % (179973)Instructions burned: 159 (million)
% 2.98/1.60 % (179975)Instruction limit reached!
% 2.98/1.60 % (179975)------------------------------
% 2.98/1.60 % (179975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179975)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179975)Termination reason: Instruction limit
% 2.98/1.60 % (179975)Termination phase: Saturation
% 2.98/1.60 % (179975)Time elapsed: 0.116 s
% 2.98/1.60 % (179975)Peak memory usage: 91 MB
% 2.98/1.60 % (179975)Instructions burned: 250 (million)
% 2.98/1.60 % (179972)Instruction limit reached!
% 2.98/1.60 % (179972)------------------------------
% 2.98/1.60 % (179972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179972)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179972)Termination reason: Instruction limit
% 2.98/1.60 % (179972)Termination phase: Saturation
% 2.98/1.60 % (179972)Time elapsed: 0.161 s
% 2.98/1.60 % (179972)Peak memory usage: 92 MB
% 2.98/1.60 % (179972)Instructions burned: 286 (million)
% 2.98/1.60 % (179980)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4246070918:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 2.98/1.60 % (179974)Instruction limit reached!
% 2.98/1.60 % (179974)------------------------------
% 2.98/1.60 % (179974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179974)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179974)Termination reason: Instruction limit
% 2.98/1.60 % (179974)Termination phase: Saturation
% 2.98/1.60 % (179974)Time elapsed: 0.185 s
% 2.98/1.60 % (179974)Peak memory usage: 91 MB
% 2.98/1.60 % (179974)Instructions burned: 326 (million)
% 2.98/1.60 % (179980)First to succeed.
% 2.98/1.60 % (179980)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-179953"
% 2.98/1.60 % (179981)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3023822004:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 2.98/1.60 % (179982)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1907913805:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 2.98/1.60 % (179982)Instruction limit reached!
% 2.98/1.60 % (179982)------------------------------
% 2.98/1.60 % (179982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.60 % (179982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.60 % (179982)CaDiCaL version: 2.1.3
% 2.98/1.60 % (179982)Termination reason: Instruction limit
% 2.98/1.60 % (179982)Termination phase: Saturation
% 2.98/1.60 % (179982)Time elapsed: 0.060 s
% 2.98/1.60 % (179982)Peak memory usage: 90 MB
% 2.98/1.60 % (179982)Instructions burned: 114 (million)
% 2.98/1.60 % (179984)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2595034263:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 2.98/1.60 % (179959)Also succeeded, but the first one will report.
% 2.98/1.60 % (179980)Refutation found. Thanks to Tanya!
% 2.98/1.60 % SZS status Theorem for theBenchmark
% 2.98/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.80 % (179980)------------------------------
% 0.18/1.80 % (179980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.80 % (179980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.80 % (179980)CaDiCaL version: 2.1.3
% 0.18/1.80 % (179980)Termination reason: Refutation
% 0.18/1.80 % (179980)Time elapsed: 0.050 s
% 0.18/1.80 % (179980)Peak memory usage: 91 MB
% 0.18/1.80 % (179980)Instructions burned: 185 (million)
% 0.18/1.80 % (179980)------------------------------
% 0.18/1.80 % (179980)------------------------------
% 0.18/1.80 % (179953)Success in time 0.721 s
% 0.18/1.80 % Vampire exiting
%------------------------------------------------------------------------------