%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO298+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 : n008.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 09:52:22 AM UTC 2026
% Result : Theorem 5.01s 1.61s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 116 ( 52 unt; 4 def)
% Number of atoms : 498 ( 149 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 670 ( 288 ~; 279 |; 96 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 18 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 128 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( rR(vd1201,vd1185,vd1187)
| rR(vd1187,vd1185,vd1201) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(321)') ).
fof(f2,negated_conjecture,
~ ( rR(vd1201,vd1185,vd1187)
| rR(vd1187,vd1185,vd1201) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
vd1201 != vd1187,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(320, 1251, 0)') ).
fof(f4,axiom,
~ rR(vd1185,vd1201,vd1187),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','neg(neg(319))') ).
fof(f6,axiom,
! [X0,X1,X2,X3,X4] :
( ( X3 = X4
& ron(X2,X3)
& ron(X1,X3)
& ron(X0,X3)
& rline(X4)
& X1 != X2
& X0 != X2
& X0 != X1
& ? [X5] :
( X2 = X5
& rpoint(X5) )
& ? [X6] :
( X1 = X6
& rpoint(X6) )
& ? [X7] :
( X0 = X7
& rpoint(X7) ) )
=> ( rR(X1,X0,X2)
| rR(X0,X1,X2)
| rR(X2,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))') ).
fof(f7,axiom,
rS(vd1201,vd1187,vd1197),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(comma_conjunct2(comma_conjunct2(plural(271))), 1214, 0)') ).
fof(f8,axiom,
ron(vd1187,vd1232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(s3(plural(315)), 0)') ).
fof(f10,axiom,
? [X0] :
( vd1201 = X0
& rpoint(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(s3(plural(271)))') ).
fof(f11,axiom,
rline(vd1197),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(269, 0)') ).
fof(f12,axiom,
( ~ ? [X0] :
( ron(vd1187,X0)
& ron(vd1186,X0)
& ron(vd1185,X0)
& rline(X0) )
& vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
& vf(vd1178,vd1180) = vf(vd1185,vd1187)
& vf(vd1178,vd1179) = vf(vd1185,vd1186)
& ? [X1] :
( vd1187 = X1
& rpoint(X1) )
& ? [X2] :
( vd1186 = X2
& rpoint(X2) )
& ? [X3] :
( vd1185 = X3
& rpoint(X3) )
& vd1179 != vd1180
& vd1178 != vd1180
& vd1178 != vd1179
& ? [X4] :
( vd1180 = X4
& rpoint(X4) )
& ? [X5] :
( vd1179 = X5
& rpoint(X5) )
& ? [X6] :
( vd1178 = X6
& rpoint(X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))') ).
fof(f14,axiom,
ron(vd1201,vd1232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(s2(plural(315)), 0)') ).
fof(f18,axiom,
ron(vd1199,vd1197),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(conjunct1(conjunct2(comma_conjunct2(plural(271)))), 0)') ).
fof(f27,axiom,
? [X0] :
( vd1199 = X0
& rpoint(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(s1(plural(271)))') ).
fof(f29,axiom,
ron(vd1185,vd1232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(s1(plural(315)), 0)') ).
fof(f43,axiom,
rline(vd1232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(293, 0)') ).
fof(f45,axiom,
vd1199 = vd1185,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(291, 1230, 0)') ).
fof(f57,axiom,
~ ron(vd1187,vd1197),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','neg(neg(270))') ).
fof(f61,axiom,
! [X0,X1,X2,X3] :
( ( rS(X0,X1,X2)
& X2 = X3
& rline(X3)
& ? [X4] :
( X1 = X4
& rpoint(X4) )
& ? [X5] :
( X0 = X5
& rpoint(X5) ) )
=> ~ ron(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))') ).
fof(f93,axiom,
! [X0,X1,X2] :
( ( rR(X1,X0,X2)
& ? [X3] :
( X2 = X3
& rpoint(X3) )
& ? [X4] :
( X1 = X4
& rpoint(X4) )
& ? [X5] :
( X0 = X5
& rpoint(X5) ) )
=> ( ~ rR(X0,X1,X2)
& X0 != X2
& X0 != X1
& rR(X1,X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))') ).
fof(f160,plain,
( ~ rR(vd1201,vd1185,vd1187)
& ~ rR(vd1187,vd1185,vd1201) ),
inference(ennf_transformation,[],[f2]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ( ~ rR(X0,X1,X2)
& X0 != X2
& X0 != X1
& rR(X1,X2,X0) )
| ~ rR(X1,X0,X2)
| ! [X3] :
( X2 != X3
| ~ rpoint(X3) )
| ! [X4] :
( X1 != X4
| ~ rpoint(X4) )
| ! [X5] :
( X0 != X5
| ~ rpoint(X5) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ( ~ rR(X0,X1,X2)
& X0 != X2
& X0 != X1
& rR(X1,X2,X0) )
| ~ rR(X1,X0,X2)
| ! [X3] :
( X2 != X3
| ~ rpoint(X3) )
| ! [X4] :
( X1 != X4
| ~ rpoint(X4) )
| ! [X5] :
( X0 != X5
| ~ rpoint(X5) ) ),
inference(flattening,[],[f187]) ).
fof(f219,plain,
! [X0,X1,X2,X3,X4] :
( rR(X1,X0,X2)
| rR(X0,X1,X2)
| rR(X2,X0,X1)
| X3 != X4
| ~ ron(X2,X3)
| ~ ron(X1,X3)
| ~ ron(X0,X3)
| ~ rline(X4)
| X1 = X2
| X0 = X2
| X0 = X1
| ! [X5] :
( X2 != X5
| ~ rpoint(X5) )
| ! [X6] :
( X1 != X6
| ~ rpoint(X6) )
| ! [X7] :
( X0 != X7
| ~ rpoint(X7) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f220,plain,
! [X0,X1,X2,X3,X4] :
( rR(X1,X0,X2)
| rR(X0,X1,X2)
| rR(X2,X0,X1)
| X3 != X4
| ~ ron(X2,X3)
| ~ ron(X1,X3)
| ~ ron(X0,X3)
| ~ rline(X4)
| X1 = X2
| X0 = X2
| X0 = X1
| ! [X5] :
( X2 != X5
| ~ rpoint(X5) )
| ! [X6] :
( X1 != X6
| ~ rpoint(X6) )
| ! [X7] :
( X0 != X7
| ~ rpoint(X7) ) ),
inference(flattening,[],[f219]) ).
fof(f221,plain,
( ! [X0] :
( ~ ron(vd1187,X0)
| ~ ron(vd1186,X0)
| ~ ron(vd1185,X0)
| ~ rline(X0) )
& vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
& vf(vd1178,vd1180) = vf(vd1185,vd1187)
& vf(vd1178,vd1179) = vf(vd1185,vd1186)
& ? [X1] :
( vd1187 = X1
& rpoint(X1) )
& ? [X2] :
( vd1186 = X2
& rpoint(X2) )
& ? [X3] :
( vd1185 = X3
& rpoint(X3) )
& vd1179 != vd1180
& vd1178 != vd1180
& vd1178 != vd1179
& ? [X4] :
( vd1180 = X4
& rpoint(X4) )
& ? [X5] :
( vd1179 = X5
& rpoint(X5) )
& ? [X6] :
( vd1178 = X6
& rpoint(X6) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f272,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ~ rS(X0,X1,X2)
| X2 != X3
| ~ rline(X3)
| ! [X4] :
( X1 != X4
| ~ rpoint(X4) )
| ! [X5] :
( X0 != X5
| ~ rpoint(X5) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f273,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ~ rS(X0,X1,X2)
| X2 != X3
| ~ rline(X3)
| ! [X4] :
( X1 != X4
| ~ rpoint(X4) )
| ! [X5] :
( X0 != X5
| ~ rpoint(X5) ) ),
inference(flattening,[],[f272]) ).
fof(f348,plain,
( vd1201 = sK1
& rpoint(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f10]) ).
fof(f367,plain,
( ! [X0] :
( ~ ron(vd1187,X0)
| ~ ron(vd1186,X0)
| ~ ron(vd1185,X0)
| ~ rline(X0) )
& vangle(vd1179,vd1178,vd1180) = vangle(vd1186,vd1185,vd1187)
& vf(vd1178,vd1180) = vf(vd1185,vd1187)
& vf(vd1178,vd1179) = vf(vd1185,vd1186)
& vd1187 = sK12
& rpoint(sK12)
& vd1186 = sK13
& rpoint(sK13)
& vd1185 = sK14
& rpoint(sK14)
& vd1179 != vd1180
& vd1178 != vd1180
& vd1178 != vd1179
& vd1180 = sK15
& rpoint(sK15)
& vd1179 = sK16
& rpoint(sK16)
& vd1178 = sK17
& rpoint(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16,sK17]),skolemize(X1,sK12),skolemize(X2,sK13),skolemize(X3,sK14),skolemize(X4,sK15),skolemize(X5,sK16),skolemize(X6,sK17)],[f221]) ).
fof(f385,plain,
( vd1199 = sK28
& rpoint(sK28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X0,sK28)],[f27]) ).
fof(f419,plain,
~ rR(vd1187,vd1185,vd1201),
inference(cnf_transformation,[],[f160]) ).
fof(f420,plain,
~ rR(vd1201,vd1185,vd1187),
inference(cnf_transformation,[],[f160]) ).
fof(f434,plain,
ron(vd1201,vd1232),
inference(cnf_transformation,[],[f14]) ).
fof(f435,plain,
rpoint(sK1),
inference(cnf_transformation,[],[f348]) ).
fof(f436,plain,
vd1201 = sK1,
inference(cnf_transformation,[],[f348]) ).
fof(f437,plain,
rS(vd1201,vd1187,vd1197),
inference(cnf_transformation,[],[f7]) ).
fof(f439,plain,
~ rR(vd1185,vd1201,vd1187),
inference(cnf_transformation,[],[f4]) ).
fof(f440,plain,
vd1201 != vd1187,
inference(cnf_transformation,[],[f3]) ).
fof(f470,plain,
! [X2,X3,X0,X1,X4,X5] :
( rR(X1,X2,X0)
| ~ rR(X1,X0,X2)
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(cnf_transformation,[],[f188]) ).
fof(f511,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rR(X1,X0,X2)
| rR(X0,X1,X2)
| rR(X2,X0,X1)
| X3 != X4
| ~ ron(X2,X3)
| ~ ron(X1,X3)
| ~ ron(X0,X3)
| ~ rline(X4)
| X1 = X2
| X0 = X2
| X0 = X1
| X2 != X5
| ~ rpoint(X5)
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(cnf_transformation,[],[f220]) ).
fof(f513,plain,
vd1185 = vd1199,
inference(cnf_transformation,[],[f45]) ).
fof(f516,plain,
ron(vd1185,vd1232),
inference(cnf_transformation,[],[f29]) ).
fof(f531,plain,
rpoint(sK12),
inference(cnf_transformation,[],[f367]) ).
fof(f532,plain,
vd1187 = sK12,
inference(cnf_transformation,[],[f367]) ).
fof(f538,plain,
~ ron(vd1187,vd1197),
inference(cnf_transformation,[],[f57]) ).
fof(f540,plain,
ron(vd1187,vd1232),
inference(cnf_transformation,[],[f8]) ).
fof(f585,plain,
rpoint(sK28),
inference(cnf_transformation,[],[f385]) ).
fof(f586,plain,
vd1199 = sK28,
inference(cnf_transformation,[],[f385]) ).
fof(f587,plain,
ron(vd1199,vd1197),
inference(cnf_transformation,[],[f18]) ).
fof(f616,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ron(X0,X2)
| ~ rS(X0,X1,X2)
| X2 != X3
| ~ rline(X3)
| X1 != X4
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(cnf_transformation,[],[f273]) ).
fof(f618,plain,
rline(vd1197),
inference(cnf_transformation,[],[f11]) ).
fof(f635,plain,
rline(vd1232),
inference(cnf_transformation,[],[f43]) ).
fof(f701,plain,
vd1185 = sK28,
inference(definition_unfolding,[],[f513,f586]) ).
fof(f702,plain,
~ rR(sK1,sK28,sK12),
inference(definition_unfolding,[],[f420,f436,f701,f532]) ).
fof(f703,plain,
~ rR(sK12,sK28,sK1),
inference(definition_unfolding,[],[f419,f532,f701,f436]) ).
fof(f717,plain,
ron(sK1,vd1232),
inference(definition_unfolding,[],[f434,f436]) ).
fof(f718,plain,
rS(sK1,sK12,vd1197),
inference(definition_unfolding,[],[f437,f436,f532]) ).
fof(f720,plain,
~ rR(sK28,sK1,sK12),
inference(definition_unfolding,[],[f439,f701,f436,f532]) ).
fof(f721,plain,
sK1 != sK12,
inference(definition_unfolding,[],[f440,f436,f532]) ).
fof(f730,plain,
ron(sK28,vd1232),
inference(definition_unfolding,[],[f516,f701]) ).
fof(f741,plain,
~ ron(sK12,vd1197),
inference(definition_unfolding,[],[f538,f532]) ).
fof(f743,plain,
ron(sK12,vd1232),
inference(definition_unfolding,[],[f540,f532]) ).
fof(f750,plain,
ron(sK28,vd1197),
inference(definition_unfolding,[],[f587,f586]) ).
fof(f884,plain,
! [X3,X0,X1,X4,X5] :
( rR(X1,X3,X0)
| ~ rR(X1,X0,X3)
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f470]) ).
fof(f885,plain,
! [X3,X0,X4,X5] :
( rR(X4,X3,X0)
| ~ rR(X4,X0,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f884]) ).
fof(f886,plain,
! [X3,X4,X5] :
( rR(X4,X3,X5)
| ~ rR(X4,X5,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f885]) ).
fof(f987,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( rR(X1,X0,X2)
| rR(X0,X1,X2)
| rR(X2,X0,X1)
| ~ ron(X2,X4)
| ~ ron(X1,X4)
| ~ ron(X0,X4)
| ~ rline(X4)
| X1 = X2
| X0 = X2
| X0 = X1
| X2 != X5
| ~ rpoint(X5)
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f511]) ).
fof(f988,plain,
! [X0,X1,X6,X7,X4,X5] :
( rR(X1,X0,X5)
| rR(X0,X1,X5)
| rR(X5,X0,X1)
| ~ ron(X5,X4)
| ~ ron(X1,X4)
| ~ ron(X0,X4)
| ~ rline(X4)
| X1 = X5
| X0 = X5
| X0 = X1
| ~ rpoint(X5)
| X1 != X6
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f987]) ).
fof(f989,plain,
! [X0,X6,X7,X4,X5] :
( rR(X6,X0,X5)
| rR(X0,X6,X5)
| rR(X5,X0,X6)
| ~ ron(X5,X4)
| ~ ron(X6,X4)
| ~ ron(X0,X4)
| ~ rline(X4)
| X5 = X6
| X0 = X5
| X0 = X6
| ~ rpoint(X5)
| ~ rpoint(X6)
| X0 != X7
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f988]) ).
fof(f990,plain,
! [X6,X7,X4,X5] :
( rR(X7,X6,X5)
| rR(X6,X7,X5)
| rR(X5,X7,X6)
| ~ ron(X5,X4)
| ~ ron(X6,X4)
| ~ ron(X7,X4)
| ~ rline(X4)
| X5 = X6
| X5 = X7
| X6 = X7
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f989]) ).
fof(f1193,plain,
! [X3,X0,X1,X4,X5] :
( ~ ron(X0,X3)
| ~ rS(X0,X1,X3)
| ~ rline(X3)
| X1 != X4
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f616]) ).
fof(f1194,plain,
! [X3,X0,X4,X5] :
( ~ ron(X0,X3)
| ~ rS(X0,X4,X3)
| ~ rline(X3)
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f1193]) ).
fof(f1195,plain,
! [X3,X4,X5] :
( ~ rS(X5,X4,X3)
| ~ ron(X5,X3)
| ~ rline(X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f1194]) ).
fof(f1400,plain,
! [X0] :
( rR(sK28,sK1,sK12)
| rR(sK12,sK1,sK28)
| ~ ron(sK12,X0)
| ~ ron(sK28,X0)
| ~ ron(sK1,X0)
| ~ rline(X0)
| sK12 = sK28
| sK1 = sK12
| sK1 = sK28
| ~ rpoint(sK12)
| ~ rpoint(sK28)
| ~ rpoint(sK1) ),
inference(resolution,[],[f702,f990]) ).
fof(f1409,plain,
! [X0] :
( rR(sK12,sK1,sK28)
| ~ ron(sK12,X0)
| ~ ron(sK28,X0)
| ~ ron(sK1,X0)
| ~ rline(X0)
| sK12 = sK28
| sK1 = sK12
| sK1 = sK28
| ~ rpoint(sK12)
| ~ rpoint(sK28)
| ~ rpoint(sK1) ),
inference(forward_subsumption_resolution,[],[f1400,f720]) ).
fof(f1414,plain,
! [X0] :
( rR(sK12,sK1,sK28)
| ~ ron(sK12,X0)
| ~ ron(sK28,X0)
| ~ ron(sK1,X0)
| ~ rline(X0)
| sK12 = sK28
| sK1 = sK28
| ~ rpoint(sK12)
| ~ rpoint(sK28)
| ~ rpoint(sK1) ),
inference(forward_subsumption_resolution,[],[f1409,f721]) ).
fof(f1419,plain,
! [X0] :
( rR(sK12,sK1,sK28)
| ~ ron(sK12,X0)
| ~ ron(sK28,X0)
| ~ ron(sK1,X0)
| ~ rline(X0)
| sK12 = sK28
| sK1 = sK28
| ~ rpoint(sK28)
| ~ rpoint(sK1) ),
inference(forward_subsumption_resolution,[],[f1414,f531]) ).
fof(f1421,definition,
( spl54_1
<=> ! [X1] :
( ~ ron(sK12,X1)
| ~ rline(X1)
| ~ ron(sK1,X1)
| ~ ron(sK28,X1) ) ),
introduced(definition,[new_symbols(definition,[spl54_1])],[avatar_definition]) ).
fof(f1422,plain,
( ! [X1] :
( ~ ron(sK28,X1)
| ~ rline(X1)
| ~ ron(sK1,X1)
| ~ ron(sK12,X1) )
| ~ spl54_1 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1427,definition,
( spl54_3
<=> sK12 = sK28 ),
introduced(definition,[new_symbols(definition,[spl54_3])],[avatar_definition]) ).
fof(f1429,plain,
( sK12 = sK28
| ~ spl54_3 ),
inference(avatar_component_clause,[],[f1427]) ).
fof(f1431,plain,
! [X0] :
( rR(sK12,sK1,sK28)
| ~ ron(sK12,X0)
| ~ ron(sK28,X0)
| ~ ron(sK1,X0)
| ~ rline(X0)
| sK12 = sK28
| sK1 = sK28
| ~ rpoint(sK1) ),
inference(forward_subsumption_resolution,[],[f1419,f585]) ).
fof(f1432,plain,
! [X0] :
( rR(sK12,sK1,sK28)
| ~ ron(sK12,X0)
| ~ ron(sK28,X0)
| ~ ron(sK1,X0)
| ~ rline(X0)
| sK12 = sK28
| sK1 = sK28 ),
inference(forward_subsumption_resolution,[],[f1431,f435]) ).
fof(f1434,definition,
( spl54_4
<=> sK1 = sK28 ),
introduced(definition,[new_symbols(definition,[spl54_4])],[avatar_definition]) ).
fof(f1436,plain,
( sK1 = sK28
| ~ spl54_4 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f1438,definition,
( spl54_5
<=> rR(sK12,sK1,sK28) ),
introduced(definition,[new_symbols(definition,[spl54_5])],[avatar_definition]) ).
fof(f1440,plain,
( rR(sK12,sK1,sK28)
| ~ spl54_5 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f1441,plain,
( spl54_4
| spl54_3
| spl54_1
| spl54_5 ),
inference(avatar_split_clause,[],[f1432,f1438,f1421,f1427,f1434]) ).
fof(f1446,plain,
( ~ rR(sK12,sK1,sK28)
| ~ rpoint(sK28)
| ~ rpoint(sK12)
| ~ rpoint(sK1) ),
inference(resolution,[],[f703,f886]) ).
fof(f1449,plain,
( ~ rR(sK12,sK1,sK28)
| ~ rpoint(sK12)
| ~ rpoint(sK1) ),
inference(forward_subsumption_resolution,[],[f1446,f585]) ).
fof(f1453,plain,
( ~ rR(sK12,sK1,sK28)
| ~ rpoint(sK1) ),
inference(forward_subsumption_resolution,[],[f1449,f531]) ).
fof(f1457,plain,
~ rR(sK12,sK1,sK28),
inference(forward_subsumption_resolution,[],[f1453,f435]) ).
fof(f1486,plain,
( ~ ron(sK28,vd1197)
| ~ spl54_3 ),
inference(superposition,[],[f741,f1429]) ).
fof(f1489,plain,
( $false
| ~ spl54_3 ),
inference(forward_subsumption_resolution,[],[f1486,f750]) ).
fof(f1490,plain,
~ spl54_3,
inference(avatar_contradiction_clause,[],[f1489]) ).
fof(f1511,plain,
( rS(sK28,sK12,vd1197)
| ~ spl54_4 ),
inference(superposition,[],[f718,f1436]) ).
fof(f1638,plain,
( ~ ron(sK28,vd1197)
| ~ rline(vd1197)
| ~ rpoint(sK12)
| ~ rpoint(sK28)
| ~ spl54_4 ),
inference(resolution,[],[f1511,f1195]) ).
fof(f1642,plain,
( ~ rline(vd1197)
| ~ rpoint(sK12)
| ~ rpoint(sK28)
| ~ spl54_4 ),
inference(forward_subsumption_resolution,[],[f1638,f750]) ).
fof(f1644,plain,
( ~ rpoint(sK12)
| ~ rpoint(sK28)
| ~ spl54_4 ),
inference(forward_subsumption_resolution,[],[f1642,f618]) ).
fof(f1646,plain,
( ~ rpoint(sK28)
| ~ spl54_4 ),
inference(forward_subsumption_resolution,[],[f1644,f531]) ).
fof(f1647,plain,
( $false
| ~ spl54_4 ),
inference(forward_subsumption_resolution,[],[f1646,f585]) ).
fof(f1648,plain,
~ spl54_4,
inference(avatar_contradiction_clause,[],[f1647]) ).
fof(f1651,plain,
( $false
| ~ spl54_5 ),
inference(forward_subsumption_resolution,[],[f1457,f1440]) ).
fof(f1652,plain,
~ spl54_5,
inference(avatar_contradiction_clause,[],[f1651]) ).
fof(f1838,plain,
( ~ rline(vd1232)
| ~ ron(sK1,vd1232)
| ~ ron(sK12,vd1232)
| ~ spl54_1 ),
inference(resolution,[],[f1422,f730]) ).
fof(f1854,plain,
( ~ ron(sK1,vd1232)
| ~ ron(sK12,vd1232)
| ~ spl54_1 ),
inference(forward_subsumption_resolution,[],[f1838,f635]) ).
fof(f1857,plain,
( ~ ron(sK12,vd1232)
| ~ spl54_1 ),
inference(forward_subsumption_resolution,[],[f1854,f717]) ).
fof(f1860,plain,
( $false
| ~ spl54_1 ),
inference(forward_subsumption_resolution,[],[f1857,f743]) ).
fof(f1861,plain,
~ spl54_1,
inference(avatar_contradiction_clause,[],[f1860]) ).
cnf(s2,plain,
( spl54_1
| spl54_3
| spl54_4
| spl54_5 ),
inference(sat_conversion,[],[f1441]) ).
cnf(s4,plain,
~ spl54_3,
inference(sat_conversion,[],[f1490]) ).
cnf(s7,plain,
~ spl54_4,
inference(sat_conversion,[],[f1648]) ).
cnf(s8,plain,
~ spl54_5,
inference(sat_conversion,[],[f1652]) ).
cnf(s22,plain,
~ spl54_1,
inference(sat_conversion,[],[f1861]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s2,s8,s7,s4,s22]) ).
fof(f1862,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO298+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.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 08:02:24 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
% 5.01/1.61 % (904661)Detected formulas, will run a generic FOF schedule.
% 5.01/1.61 % (904669)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=600694412:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.01/1.61 % (904669)Refutation not found, incomplete strategy
% 5.01/1.61 % (904669)------------------------------
% 5.01/1.61 % (904669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904669)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904669)Termination reason: Refutation not found, incomplete strategy
% 5.01/1.61 % (904669)Time elapsed: 0.002 s
% 5.01/1.61 % (904669)Peak memory usage: 88 MB
% 5.01/1.61 % (904669)Instructions burned: 2 (million)
% 5.01/1.61 % (904670)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3850718287:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.01/1.61 % (904672)dis-21_1_sil=8000:lcm=predicate:random_seed=2174652614: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)
% 5.01/1.61 % (904666)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=3095022091:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.01/1.61 % (904668)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=1980694173:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.01/1.61 % (904671)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2873974855:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.01/1.61 % (904667)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=2873529875:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.01/1.61 % (904670)Instruction limit reached!
% 5.01/1.61 % (904670)------------------------------
% 5.01/1.61 % (904670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904670)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904670)Termination reason: Instruction limit
% 5.01/1.61 % (904670)Termination phase: Saturation
% 5.01/1.61 % (904670)Time elapsed: 0.068 s
% 5.01/1.61 % (904670)Peak memory usage: 88 MB
% 5.01/1.61 % (904670)Instructions burned: 120 (million)
% 5.01/1.61 % (904672)Instruction limit reached!
% 5.01/1.61 % (904672)------------------------------
% 5.01/1.61 % (904672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904672)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904672)Termination reason: Instruction limit
% 5.01/1.61 % (904672)Termination phase: Saturation
% 5.01/1.61 % (904672)Time elapsed: 0.072 s
% 5.01/1.61 % (904672)Peak memory usage: 90 MB
% 5.01/1.61 % (904672)Instructions burned: 130 (million)
% 5.01/1.61 % (904671)Instruction limit reached!
% 5.01/1.61 % (904671)------------------------------
% 5.01/1.61 % (904671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904671)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904671)Termination reason: Instruction limit
% 5.01/1.61 % (904671)Termination phase: Saturation
% 5.01/1.61 % (904671)Time elapsed: 0.089 s
% 5.01/1.61 % (904671)Peak memory usage: 90 MB
% 5.01/1.61 % (904671)Instructions burned: 141 (million)
% 5.01/1.61 % (904669)------------------------------
% 5.01/1.61 % (904669)------------------------------
% 5.01/1.61 % (904680)lrs+10_1_sil=8000:sp=occurrence:random_seed=4273832942:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.01/1.61 % (904681)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3262674621:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.01/1.61 % (904681)Refutation not found, incomplete strategy
% 5.01/1.61 % (904681)------------------------------
% 5.01/1.61 % (904681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904681)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904681)Termination reason: Refutation not found, incomplete strategy
% 5.01/1.61 % (904681)Time elapsed: 0.004 s
% 5.01/1.61 % (904681)Peak memory usage: 89 MB
% 5.01/1.61 % (904681)Instructions burned: 4 (million)
% 5.01/1.61 % (904683)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=2028262137:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.01/1.61 % (904682)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1065440958:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.01/1.61 % (904682)Refutation not found, incomplete strategy
% 5.01/1.61 % (904682)------------------------------
% 5.01/1.61 % (904682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904682)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904682)Termination reason: Refutation not found, incomplete strategy
% 5.01/1.61 % (904682)Time elapsed: 0.004 s
% 5.01/1.61 % (904682)Peak memory usage: 89 MB
% 5.01/1.61 % (904682)Instructions burned: 4 (million)
% 5.01/1.61 % (904683)Instruction limit reached!
% 5.01/1.61 % (904683)------------------------------
% 5.01/1.61 % (904683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904683)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904683)Termination reason: Instruction limit
% 5.01/1.61 % (904683)Termination phase: Saturation
% 5.01/1.61 % (904683)Time elapsed: 0.063 s
% 5.01/1.61 % (904683)Peak memory usage: 91 MB
% 5.01/1.61 % (904683)Instructions burned: 250 (million)
% 5.01/1.61 % (904680)Instruction limit reached!
% 5.01/1.61 % (904680)------------------------------
% 5.01/1.61 % (904680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.01/1.61 % (904680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.01/1.61 % (904680)CaDiCaL version: 2.1.3
% 5.01/1.61 % (904680)Termination reason: Instruction limit
% 5.01/1.61 % (904680)Termination phase: Saturation
% 5.01/1.61 % (904680)Time elapsed: 0.152 s
% 5.01/1.61 % (904680)Peak memory usage: 91 MB
% 5.01/1.61 % (904680)Instructions burned: 285 (million)
% 5.01/1.61 % (904688)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2316019873:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.01/1.61 % (904688)First to succeed.
% 5.01/1.61 % (904688)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-904661"
% 5.01/1.61 % (904681)------------------------------
% 5.01/1.61 % (904681)------------------------------
% 5.01/1.61 % (904682)------------------------------
% 5.01/1.61 % (904682)------------------------------
% 5.01/1.61 % (904689)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=363753854:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.01/1.61 % (904688)Refutation found. Thanks to Tanya!
% 5.01/1.61 % SZS status Theorem for theBenchmark
% 5.01/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.80 % (904688)------------------------------
% 0.15/1.80 % (904688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.80 % (904688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.80 % (904688)CaDiCaL version: 2.1.3
% 0.15/1.80 % (904688)Termination reason: Refutation
% 0.15/1.80 % (904688)Time elapsed: 0.017 s
% 0.15/1.80 % (904688)Peak memory usage: 90 MB
% 0.15/1.80 % (904688)Instructions burned: 55 (million)
% 0.15/1.80 % (904688)------------------------------
% 0.15/1.80 % (904688)------------------------------
% 0.15/1.80 % (904661)Success in time 0.77 s
% 0.15/1.80 % Vampire exiting
%------------------------------------------------------------------------------