%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO306+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:52:24 AM UTC 2026
% Result : Theorem 2.29s 1.18s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 97 ( 26 unt; 2 def)
% Number of atoms : 543 ( 215 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 788 ( 342 ~; 370 |; 70 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-8 aty)
% Number of variables : 236 ( 0 sgn 228 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
( vf(vd1287,vd1299) = vf(vd1287,X0)
& rR(X0,vd1287,vd1302)
& rpoint(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(352)') ).
fof(f2,negated_conjecture,
~ ? [X0] :
( vf(vd1287,vd1299) = vf(vd1287,X0)
& rR(X0,vd1287,vd1302)
& rpoint(X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
rless(vf(vd1287,vd1299),vf(vd1287,vd1302)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(351, 1305, 0)') ).
fof(f6,axiom,
( vd1302 = vd1303
& rR(vd1289,vd1287,vd1302)
& rpoint(vd1303)
& rR(vd1288,vd1287,vd1299) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))') ).
fof(f10,axiom,
( vf(vd1287,vd1288) = vf(vd1287,vd1289)
& vd1288 != vd1289
& vd1287 != vd1289
& vd1287 != vd1288
& ? [X0] :
( vd1289 = X0
& rpoint(X0) )
& ? [X1] :
( vd1288 = X1
& rpoint(X1) )
& ? [X2] :
( vd1287 = X2
& rpoint(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))') ).
fof(f12,axiom,
vd1299 = vd1300,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(348, 4)') ).
fof(f13,axiom,
rpoint(vd1300),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(348, 1)') ).
fof(f17,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( rless(vf(X4,X6),vf(X0,X2))
& X4 != X6
& X0 != X2
& X6 = X7
& rpoint(X7)
& X4 = X5
& rpoint(X5)
& X2 = X3
& rpoint(X3)
& X0 = X1
& rpoint(X1) )
=> vf(X0,vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7)) = vf(X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 0)') ).
fof(f18,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( rless(vf(X4,X6),vf(X0,X2))
& X4 != X6
& X0 != X2
& X6 = X7
& rpoint(X7)
& X4 = X5
& rpoint(X5)
& X2 = X3
& rpoint(X3)
& X0 = X1
& rpoint(X1) )
=> rR(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7),X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 1)') ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( rless(vf(X4,X6),vf(X0,X2))
& X4 != X6
& X0 != X2
& X6 = X7
& rpoint(X7)
& X4 = X5
& rpoint(X5)
& X2 = X3
& rpoint(X3)
& X0 = X1
& rpoint(X1) )
=> rpoint(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(238), 0), 2)') ).
fof(f49,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/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))') ).
fof(f133,plain,
! [X0] :
( vf(vd1287,vd1299) != vf(vd1287,X0)
| ~ rR(X0,vd1287,vd1302)
| ~ rpoint(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vf(X0,vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7)) = vf(X4,X6)
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f137,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vf(X0,vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7)) = vf(X4,X6)
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( rR(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7),X0,X2)
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f139,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( rR(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7),X0,X2)
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( rpoint(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7))
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( rpoint(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7))
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(flattening,[],[f140]) ).
fof(f196,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,[],[f49]) ).
fof(f197,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,[],[f196]) ).
fof(f346,plain,
( vf(vd1287,vd1288) = vf(vd1287,vd1289)
& vd1288 != vd1289
& vd1287 != vd1289
& vd1287 != vd1288
& vd1289 = sK1
& rpoint(sK1)
& vd1288 = sK2
& rpoint(sK2)
& vd1287 = sK3
& rpoint(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f10]) ).
fof(f422,plain,
! [X0] :
( ~ rpoint(X0)
| ~ rR(X0,vd1287,vd1302)
| vf(vd1287,vd1299) != vf(vd1287,X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f423,plain,
rless(vf(vd1287,vd1299),vf(vd1287,vd1302)),
inference(cnf_transformation,[],[f3]) ).
fof(f426,plain,
rR(vd1288,vd1287,vd1299),
inference(cnf_transformation,[],[f6]) ).
fof(f427,plain,
rpoint(vd1303),
inference(cnf_transformation,[],[f6]) ).
fof(f428,plain,
rR(vd1289,vd1287,vd1302),
inference(cnf_transformation,[],[f6]) ).
fof(f429,plain,
vd1302 = vd1303,
inference(cnf_transformation,[],[f6]) ).
fof(f433,plain,
rpoint(sK3),
inference(cnf_transformation,[],[f346]) ).
fof(f434,plain,
vd1287 = sK3,
inference(cnf_transformation,[],[f346]) ).
fof(f435,plain,
rpoint(sK2),
inference(cnf_transformation,[],[f346]) ).
fof(f436,plain,
vd1288 = sK2,
inference(cnf_transformation,[],[f346]) ).
fof(f437,plain,
rpoint(sK1),
inference(cnf_transformation,[],[f346]) ).
fof(f438,plain,
vd1289 = sK1,
inference(cnf_transformation,[],[f346]) ).
fof(f444,plain,
vd1299 = vd1300,
inference(cnf_transformation,[],[f12]) ).
fof(f445,plain,
rpoint(vd1300),
inference(cnf_transformation,[],[f13]) ).
fof(f449,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vf(X4,X6) = vf(X0,vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7))
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f450,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rR(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7),X0,X2)
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f451,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rpoint(vskolem1120(X0,X1,X2,X3,X4,X5,X6,X7))
| ~ rless(vf(X4,X6),vf(X0,X2))
| X4 = X6
| X0 = X2
| X6 != X7
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(cnf_transformation,[],[f141]) ).
fof(f505,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 != X2
| ~ rR(X1,X0,X2)
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4)
| X0 != X5
| ~ rpoint(X5) ),
inference(cnf_transformation,[],[f197]) ).
fof(f697,plain,
! [X2,X3,X0,X1,X7,X4,X5] :
( vf(X4,X7) = vf(X0,vskolem1120(X0,X1,X2,X3,X4,X5,X7,X7))
| ~ rless(vf(X4,X7),vf(X0,X2))
| X4 = X7
| X0 = X2
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f449]) ).
fof(f698,plain,
! [X2,X3,X0,X1,X7,X5] :
( vf(X5,X7) = vf(X0,vskolem1120(X0,X1,X2,X3,X5,X5,X7,X7))
| ~ rless(vf(X5,X7),vf(X0,X2))
| X5 = X7
| X0 = X2
| ~ rpoint(X7)
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f697]) ).
fof(f699,plain,
! [X3,X0,X1,X7,X5] :
( vf(X5,X7) = vf(X0,vskolem1120(X0,X1,X3,X3,X5,X5,X7,X7))
| ~ rless(vf(X5,X7),vf(X0,X3))
| X5 = X7
| X0 = X3
| ~ rpoint(X7)
| ~ rpoint(X5)
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f698]) ).
fof(f700,plain,
! [X3,X1,X7,X5] :
( vf(X5,X7) = vf(X1,vskolem1120(X1,X1,X3,X3,X5,X5,X7,X7))
| ~ rless(vf(X5,X7),vf(X1,X3))
| X5 = X7
| X1 = X3
| ~ rpoint(X7)
| ~ rpoint(X5)
| ~ rpoint(X3)
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f699]) ).
fof(f701,plain,
! [X2,X3,X0,X1,X7,X4,X5] :
( rR(vskolem1120(X0,X1,X2,X3,X4,X5,X7,X7),X0,X2)
| ~ rless(vf(X4,X7),vf(X0,X2))
| X4 = X7
| X0 = X2
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f450]) ).
fof(f702,plain,
! [X2,X3,X0,X1,X7,X5] :
( rR(vskolem1120(X0,X1,X2,X3,X5,X5,X7,X7),X0,X2)
| ~ rless(vf(X5,X7),vf(X0,X2))
| X5 = X7
| X0 = X2
| ~ rpoint(X7)
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f701]) ).
fof(f703,plain,
! [X3,X0,X1,X7,X5] :
( rR(vskolem1120(X0,X1,X3,X3,X5,X5,X7,X7),X0,X3)
| ~ rless(vf(X5,X7),vf(X0,X3))
| X5 = X7
| X0 = X3
| ~ rpoint(X7)
| ~ rpoint(X5)
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f702]) ).
fof(f704,plain,
! [X3,X1,X7,X5] :
( rR(vskolem1120(X1,X1,X3,X3,X5,X5,X7,X7),X1,X3)
| ~ rless(vf(X5,X7),vf(X1,X3))
| X5 = X7
| X1 = X3
| ~ rpoint(X7)
| ~ rpoint(X5)
| ~ rpoint(X3)
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f703]) ).
fof(f705,plain,
! [X2,X3,X0,X1,X7,X4,X5] :
( rpoint(vskolem1120(X0,X1,X2,X3,X4,X5,X7,X7))
| ~ rless(vf(X4,X7),vf(X0,X2))
| X4 = X7
| X0 = X2
| ~ rpoint(X7)
| X4 != X5
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f451]) ).
fof(f706,plain,
! [X2,X3,X0,X1,X7,X5] :
( rpoint(vskolem1120(X0,X1,X2,X3,X5,X5,X7,X7))
| ~ rless(vf(X5,X7),vf(X0,X2))
| X5 = X7
| X0 = X2
| ~ rpoint(X7)
| ~ rpoint(X5)
| X2 != X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f705]) ).
fof(f707,plain,
! [X3,X0,X1,X7,X5] :
( rpoint(vskolem1120(X0,X1,X3,X3,X5,X5,X7,X7))
| ~ rless(vf(X5,X7),vf(X0,X3))
| X5 = X7
| X0 = X3
| ~ rpoint(X7)
| ~ rpoint(X5)
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f706]) ).
fof(f708,plain,
! [X3,X1,X7,X5] :
( rpoint(vskolem1120(X1,X1,X3,X3,X5,X5,X7,X7))
| ~ rless(vf(X5,X7),vf(X1,X3))
| X5 = X7
| X1 = X3
| ~ rpoint(X7)
| ~ rpoint(X5)
| ~ rpoint(X3)
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f707]) ).
fof(f897,plain,
! [X2,X3,X1,X4,X5] :
( ~ rR(X1,X2,X2)
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4)
| X2 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f505]) ).
fof(f898,plain,
! [X3,X1,X4,X5] :
( ~ rR(X1,X3,X3)
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4)
| X3 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f897]) ).
fof(f899,plain,
! [X3,X4,X5] :
( ~ rR(X4,X3,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 != X5
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f898]) ).
fof(f900,plain,
! [X4,X5] :
( ~ rR(X4,X5,X5)
| ~ rpoint(X5)
| ~ rpoint(X4)
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f899]) ).
fof(f1464,plain,
! [X4,X5] :
( ~ rR(X4,X5,X5)
| ~ rpoint(X5)
| ~ rpoint(X4) ),
inference(duplicate_literal_removal,[],[f900]) ).
fof(f1566,plain,
rpoint(vd1302),
inference(superposition,[],[f427,f429]) ).
fof(f1568,plain,
rpoint(vd1287),
inference(superposition,[],[f433,f434]) ).
fof(f1570,plain,
rpoint(vd1288),
inference(superposition,[],[f435,f436]) ).
fof(f1572,plain,
rpoint(vd1289),
inference(superposition,[],[f437,f438]) ).
fof(f1574,plain,
rpoint(vd1299),
inference(superposition,[],[f445,f444]) ).
fof(f1867,plain,
! [X2,X3,X0,X1] :
( ~ rR(vskolem1120(X2,X2,X3,X3,X0,X0,X1,X1),vd1287,vd1302)
| X0 = X1
| X2 = X3
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rpoint(X3)
| ~ rpoint(X2)
| ~ rless(vf(X0,X1),vf(X2,X3))
| vf(vd1287,vd1299) != vf(vd1287,vskolem1120(X2,X2,X3,X3,X0,X0,X1,X1)) ),
inference(resolution,[],[f708,f422]) ).
fof(f1902,plain,
! [X0,X1] :
( ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| X0 = X1
| vd1287 = vd1302
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rpoint(vd1302)
| ~ rpoint(vd1287)
| X0 = X1
| vd1287 = vd1302
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rpoint(vd1302)
| ~ rpoint(vd1287)
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| vf(vd1287,vd1299) != vf(vd1287,vskolem1120(vd1287,vd1287,vd1302,vd1302,X0,X0,X1,X1)) ),
inference(resolution,[],[f704,f1867]) ).
fof(f1903,plain,
! [X0,X1] :
( ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| X0 = X1
| vd1287 = vd1302
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rpoint(vd1302)
| ~ rpoint(vd1287)
| vf(vd1287,vd1299) != vf(vd1287,vskolem1120(vd1287,vd1287,vd1302,vd1302,X0,X0,X1,X1)) ),
inference(duplicate_literal_removal,[],[f1902]) ).
fof(f1911,plain,
! [X0,X1] :
( ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| X0 = X1
| vd1287 = vd1302
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rpoint(vd1287)
| vf(vd1287,vd1299) != vf(vd1287,vskolem1120(vd1287,vd1287,vd1302,vd1302,X0,X0,X1,X1)) ),
inference(forward_subsumption_resolution,[],[f1903,f1566]) ).
fof(f1918,plain,
! [X0,X1] :
( ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| X0 = X1
| vd1287 = vd1302
| ~ rpoint(X1)
| ~ rpoint(X0)
| vf(vd1287,vd1299) != vf(vd1287,vskolem1120(vd1287,vd1287,vd1302,vd1302,X0,X0,X1,X1)) ),
inference(forward_subsumption_resolution,[],[f1911,f1568]) ).
fof(f1920,definition,
( spl52_25
<=> vd1287 = vd1302 ),
introduced(definition,[new_symbols(definition,[spl52_25])],[avatar_definition]) ).
fof(f1921,plain,
( vd1287 != vd1302
| spl52_25 ),
inference(avatar_component_clause,[],[f1920]) ).
fof(f1922,plain,
( vd1287 = vd1302
| ~ spl52_25 ),
inference(avatar_component_clause,[],[f1920]) ).
fof(f1924,definition,
( spl52_26
<=> ! [X0,X1] :
( ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| vf(vd1287,vd1299) != vf(vd1287,vskolem1120(vd1287,vd1287,vd1302,vd1302,X0,X0,X1,X1))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1 ) ),
introduced(definition,[new_symbols(definition,[spl52_26])],[avatar_definition]) ).
fof(f1925,plain,
( ! [X0,X1] :
( vf(vd1287,vd1299) != vf(vd1287,vskolem1120(vd1287,vd1287,vd1302,vd1302,X0,X0,X1,X1))
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1 )
| ~ spl52_26 ),
inference(avatar_component_clause,[],[f1924]) ).
fof(f1926,plain,
( spl52_25
| spl52_26 ),
inference(avatar_split_clause,[],[f1918,f1924,f1920]) ).
fof(f1929,plain,
( rR(vd1289,vd1287,vd1287)
| ~ spl52_25 ),
inference(superposition,[],[f428,f1922]) ).
fof(f1950,plain,
( ~ rpoint(vd1287)
| ~ rpoint(vd1289)
| ~ spl52_25 ),
inference(resolution,[],[f1929,f1464]) ).
fof(f1967,plain,
( ~ rpoint(vd1289)
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1950,f1568]) ).
fof(f1972,plain,
( $false
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1967,f1572]) ).
fof(f1973,plain,
~ spl52_25,
inference(avatar_contradiction_clause,[],[f1972]) ).
fof(f2010,plain,
( ! [X0,X1] :
( vf(vd1287,vd1299) != vf(X0,X1)
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| X0 = X1
| vd1287 = vd1302
| ~ rpoint(X1)
| ~ rpoint(X0)
| ~ rpoint(vd1302)
| ~ rpoint(vd1287) )
| ~ spl52_26 ),
inference(superposition,[],[f1925,f700]) ).
fof(f2011,plain,
( ! [X0,X1] :
( vf(vd1287,vd1299) != vf(X0,X1)
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1
| vd1287 = vd1302
| ~ rpoint(vd1302)
| ~ rpoint(vd1287) )
| ~ spl52_26 ),
inference(duplicate_literal_removal,[],[f2010]) ).
fof(f2014,plain,
( ! [X0,X1] :
( vf(vd1287,vd1299) != vf(X0,X1)
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1
| ~ rpoint(vd1302)
| ~ rpoint(vd1287) )
| spl52_25
| ~ spl52_26 ),
inference(forward_subsumption_resolution,[],[f2011,f1921]) ).
fof(f2015,plain,
( ! [X0,X1] :
( vf(vd1287,vd1299) != vf(X0,X1)
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| ~ rpoint(X0)
| ~ rpoint(X1)
| X0 = X1
| ~ rpoint(vd1287) )
| spl52_25
| ~ spl52_26 ),
inference(forward_subsumption_resolution,[],[f2014,f1566]) ).
fof(f2016,plain,
( ! [X0,X1] :
( ~ rpoint(X0)
| ~ rless(vf(X0,X1),vf(vd1287,vd1302))
| vf(vd1287,vd1299) != vf(X0,X1)
| ~ rpoint(X1)
| X0 = X1 )
| spl52_25
| ~ spl52_26 ),
inference(forward_subsumption_resolution,[],[f2015,f1568]) ).
fof(f2017,plain,
( ! [X0] :
( ~ rless(vf(vd1287,X0),vf(vd1287,vd1302))
| vf(vd1287,vd1299) != vf(vd1287,X0)
| ~ rpoint(X0)
| vd1287 = X0 )
| spl52_25
| ~ spl52_26 ),
inference(resolution,[],[f2016,f1568]) ).
fof(f2054,plain,
( vf(vd1287,vd1299) != vf(vd1287,vd1299)
| ~ rpoint(vd1299)
| vd1287 = vd1299
| spl52_25
| ~ spl52_26 ),
inference(resolution,[],[f2017,f423]) ).
fof(f2059,plain,
( ~ rpoint(vd1299)
| vd1287 = vd1299
| spl52_25
| ~ spl52_26 ),
inference(trivial_inequality_removal,[],[f2054]) ).
fof(f2061,plain,
( vd1287 = vd1299
| spl52_25
| ~ spl52_26 ),
inference(forward_subsumption_resolution,[],[f2059,f1574]) ).
fof(f2068,plain,
( rR(vd1288,vd1287,vd1287)
| spl52_25
| ~ spl52_26 ),
inference(superposition,[],[f426,f2061]) ).
fof(f2090,plain,
( ~ rpoint(vd1287)
| ~ rpoint(vd1288)
| spl52_25
| ~ spl52_26 ),
inference(resolution,[],[f2068,f1464]) ).
fof(f2107,plain,
( ~ rpoint(vd1288)
| spl52_25
| ~ spl52_26 ),
inference(forward_subsumption_resolution,[],[f2090,f1568]) ).
fof(f2112,plain,
( $false
| spl52_25
| ~ spl52_26 ),
inference(forward_subsumption_resolution,[],[f2107,f1570]) ).
fof(f2113,plain,
( spl52_25
| ~ spl52_26 ),
inference(avatar_contradiction_clause,[],[f2112]) ).
cnf(s22,plain,
( spl52_25
| spl52_26 ),
inference(sat_conversion,[],[f1926]) ).
cnf(s23,plain,
~ spl52_25,
inference(sat_conversion,[],[f1973]) ).
cnf(s25,plain,
( spl52_25
| ~ spl52_26 ),
inference(sat_conversion,[],[f2113]) ).
cnf(s26,plain,
~ spl52_26,
inference(rat,[],[s25,s23]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s22,s26,s23]) ).
fof(f2116,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO306+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 08:08:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.29/1.18 % (3233524)Detected formulas, will run a generic FOF schedule.
% 2.29/1.18 % (3233534)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1961351743:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.29/1.18 % (3233534)First to succeed.
% 2.29/1.18 % (3233534)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3233524"
% 2.29/1.18 % (3233530)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=1959910899:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.29/1.18 % (3233529)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=1407554608:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.29/1.18 % (3233531)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=3834410008:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.29/1.18 % (3233532)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2097181472:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.29/1.18 % (3233533)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=100148059:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.29/1.18 % (3233532)Refutation not found, incomplete strategy
% 2.29/1.18 % (3233532)------------------------------
% 2.29/1.18 % (3233532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.18 % (3233532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.18 % (3233532)CaDiCaL version: 2.1.3
% 2.29/1.18 % (3233532)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.18 % (3233532)Time elapsed: 0.003 s
% 2.29/1.18 % (3233532)Peak memory usage: 88 MB
% 2.29/1.18 % (3233532)Instructions burned: 3 (million)
% 2.29/1.18 % (3233535)dis-21_1_sil=8000:lcm=predicate:random_seed=683338493: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)
% 2.29/1.18 % (3233533)Instruction limit reached!
% 2.29/1.18 % (3233533)------------------------------
% 2.29/1.18 % (3233533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.18 % (3233533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.18 % (3233533)CaDiCaL version: 2.1.3
% 2.29/1.18 % (3233533)Termination reason: Instruction limit
% 2.29/1.18 % (3233533)Termination phase: Saturation
% 2.29/1.18 % (3233533)Time elapsed: 0.071 s
% 2.29/1.18 % (3233533)Peak memory usage: 88 MB
% 2.29/1.18 % (3233533)Instructions burned: 120 (million)
% 2.29/1.18 % (3233535)Instruction limit reached!
% 2.29/1.18 % (3233535)------------------------------
% 2.29/1.18 % (3233535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.18 % (3233535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.18 % (3233535)CaDiCaL version: 2.1.3
% 2.29/1.18 % (3233535)Termination reason: Instruction limit
% 2.29/1.18 % (3233535)Termination phase: Saturation
% 2.29/1.18 % (3233535)Time elapsed: 0.065 s
% 2.29/1.18 % (3233535)Peak memory usage: 90 MB
% 2.29/1.18 % (3233535)Instructions burned: 130 (million)
% 2.29/1.18 % (3233534)Refutation found. Thanks to Tanya!
% 2.29/1.18 % SZS status Theorem for theBenchmark
% 2.29/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/1.38 % (3233534)------------------------------
% 2.79/1.38 % (3233534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.38 % (3233534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.38 % (3233534)CaDiCaL version: 2.1.3
% 2.79/1.38 % (3233534)Termination reason: Refutation
% 2.79/1.38 % (3233534)Time elapsed: 0.022 s
% 2.79/1.38 % (3233534)Peak memory usage: 91 MB
% 2.79/1.38 % (3233534)Instructions burned: 64 (million)
% 2.79/1.38 % (3233534)------------------------------
% 2.79/1.38 % (3233534)------------------------------
% 2.79/1.38 % (3233524)Success in time 0.32 s
% 2.79/1.38 % Vampire exiting
%------------------------------------------------------------------------------