%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO270+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:52:18 AM UTC 2026
% Result : Theorem 4.40s 1.59s
% Output : Refutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 28 unt; 5 def)
% Number of atoms : 313 ( 180 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 390 ( 171 ~; 184 |; 23 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-6 aty)
% Number of variables : 151 ( 0 sgn 147 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] :
( vf(vd1049,X0) = vf(X0,vd1047)
& vf(vd1047,vd1049) = vf(vd1049,X0)
& rpoint(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(208)') ).
fof(f2,negated_conjecture,
~ ? [X0] :
( vf(vd1049,X0) = vf(X0,vd1047)
& vf(vd1047,vd1049) = vf(vd1049,X0)
& rpoint(X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
( vd1049 = vd1050
& vd1047 != vd1049
& rpoint(vd1050)
& vd1047 = vd1048
& rpoint(vd1048) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(pred(conjunct2(207), 4), and(holds(conjunct2(207), 1051, 0), and(pred(conjunct2(207), 1), and(pred(conjunct1(207), 2), pred(conjunct1(207), 1)))))') ).
fof(f5,axiom,
! [X0,X1,X2,X3] :
( ( X2 = X3
& X0 != X2
& rpoint(X3)
& X0 = X1
& rpoint(X1) )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> vf(X0,X2) = vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 1)') ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( X2 = X3
& X0 != X2
& rpoint(X3)
& X0 = X1
& rpoint(X1) )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> vf(X0,X2) = vf(X0,vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 3)') ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( ( X2 = X3
& X0 != X2
& rpoint(X3)
& X0 = X1
& rpoint(X1) )
=> ! [X4] :
( X4 = vskolem1061(X0,X1,X2,X3)
=> ! [X5] :
( X5 = vskolem1063(X4,X0,X1,X2,X3)
=> rpoint(vskolem1064(X5,X4,X0,X1,X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(proof(209), 0), 6)') ).
fof(f17,axiom,
! [X0,X1] :
( ( ? [X2] :
( X1 = X2
& rpoint(X2) )
& ? [X3] :
( X0 = X3
& rpoint(X3) ) )
=> vf(X0,X1) = vf(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))') ).
fof(f122,plain,
! [X0] :
( vf(vd1049,X0) != vf(X0,vd1047)
| vf(vd1049,X0) != vf(vd1047,vd1049)
| ~ rpoint(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ! [X5] :
( vf(X0,X2) = vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5 )
| vskolem1061(X0,X1,X2,X3) != X4 )
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ! [X5] :
( vf(X0,X2) = vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5 )
| vskolem1061(X0,X1,X2,X3) != X4 )
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(flattening,[],[f125]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ! [X5] :
( vf(X0,X2) = vf(X0,vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5 )
| vskolem1061(X0,X1,X2,X3) != X4 )
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ! [X5] :
( vf(X0,X2) = vf(X0,vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5 )
| vskolem1061(X0,X1,X2,X3) != X4 )
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(flattening,[],[f129]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ! [X5] :
( rpoint(vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5 )
| vskolem1061(X0,X1,X2,X3) != X4 )
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ! [X5] :
( rpoint(vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5 )
| vskolem1061(X0,X1,X2,X3) != X4 )
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(flattening,[],[f135]) ).
fof(f149,plain,
! [X0,X1] :
( vf(X0,X1) = vf(X1,X0)
| ! [X2] :
( X1 != X2
| ~ rpoint(X2) )
| ! [X3] :
( X0 != X3
| ~ rpoint(X3) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f150,plain,
! [X0,X1] :
( vf(X0,X1) = vf(X1,X0)
| ! [X2] :
( X1 != X2
| ~ rpoint(X2) )
| ! [X3] :
( X0 != X3
| ~ rpoint(X3) ) ),
inference(flattening,[],[f149]) ).
fof(f407,plain,
! [X0] :
( vf(vd1049,X0) != vf(X0,vd1047)
| vf(vd1049,X0) != vf(vd1047,vd1049)
| ~ rpoint(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f408,plain,
rpoint(vd1048),
inference(cnf_transformation,[],[f3]) ).
fof(f409,plain,
vd1047 = vd1048,
inference(cnf_transformation,[],[f3]) ).
fof(f410,plain,
rpoint(vd1050),
inference(cnf_transformation,[],[f3]) ).
fof(f411,plain,
vd1049 != vd1047,
inference(cnf_transformation,[],[f3]) ).
fof(f412,plain,
vd1049 = vd1050,
inference(cnf_transformation,[],[f3]) ).
fof(f414,plain,
! [X2,X3,X0,X1,X4,X5] :
( vf(X2,vskolem1064(X5,X4,X0,X1,X2,X3)) = vf(X0,X2)
| vskolem1063(X4,X0,X1,X2,X3) != X5
| vskolem1061(X0,X1,X2,X3) != X4
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f416,plain,
! [X2,X3,X0,X1,X4,X5] :
( vf(X0,X2) = vf(X0,vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5
| vskolem1061(X0,X1,X2,X3) != X4
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f419,plain,
! [X2,X3,X0,X1,X4,X5] :
( rpoint(vskolem1064(X5,X4,X0,X1,X2,X3))
| vskolem1063(X4,X0,X1,X2,X3) != X5
| vskolem1061(X0,X1,X2,X3) != X4
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f431,plain,
! [X2,X3,X0,X1] :
( vf(X0,X1) = vf(X1,X0)
| X1 != X2
| ~ rpoint(X2)
| X0 != X3
| ~ rpoint(X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f654,plain,
! [X0] :
( vf(vd1050,X0) != vf(X0,vd1048)
| vf(vd1050,X0) != vf(vd1048,vd1050)
| ~ rpoint(X0) ),
inference(definition_unfolding,[],[f407,f412,f409,f412,f409,f412]) ).
fof(f655,plain,
vd1050 != vd1048,
inference(definition_unfolding,[],[f411,f412,f409]) ).
fof(f669,plain,
! [X2,X3,X0,X1,X4] :
( vf(X0,X2) = vf(X2,vskolem1064(vskolem1063(X4,X0,X1,X2,X3),X4,X0,X1,X2,X3))
| vskolem1061(X0,X1,X2,X3) != X4
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f414]) ).
fof(f670,plain,
! [X2,X3,X0,X1] :
( vf(X0,X2) = vf(X2,vskolem1064(vskolem1063(vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3))
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f669]) ).
fof(f671,plain,
! [X3,X0,X1] :
( vf(X3,vskolem1064(vskolem1063(vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3)) = vf(X0,X3)
| X0 = X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f670]) ).
fof(f672,plain,
! [X3,X1] :
( ~ rpoint(X3)
| X1 = X3
| vf(X3,vskolem1064(vskolem1063(vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3)) = vf(X1,X3)
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f671]) ).
fof(f677,plain,
! [X2,X3,X0,X1,X4] :
( vf(X0,X2) = vf(X0,vskolem1064(vskolem1063(X4,X0,X1,X2,X3),X4,X0,X1,X2,X3))
| vskolem1061(X0,X1,X2,X3) != X4
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f416]) ).
fof(f678,plain,
! [X2,X3,X0,X1] :
( vf(X0,X2) = vf(X0,vskolem1064(vskolem1063(vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3))
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f677]) ).
fof(f679,plain,
! [X3,X0,X1] :
( vf(X0,X3) = vf(X0,vskolem1064(vskolem1063(vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3))
| X0 = X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f678]) ).
fof(f680,plain,
! [X3,X1] :
( ~ rpoint(X3)
| X1 = X3
| vf(X1,X3) = vf(X1,vskolem1064(vskolem1063(vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3))
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f679]) ).
fof(f689,plain,
! [X2,X3,X0,X1,X4] :
( rpoint(vskolem1064(vskolem1063(X4,X0,X1,X2,X3),X4,X0,X1,X2,X3))
| vskolem1061(X0,X1,X2,X3) != X4
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f419]) ).
fof(f690,plain,
! [X2,X3,X0,X1] :
( rpoint(vskolem1064(vskolem1063(vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3),vskolem1061(X0,X1,X2,X3),X0,X1,X2,X3))
| X2 != X3
| X0 = X2
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f689]) ).
fof(f691,plain,
! [X3,X0,X1] :
( rpoint(vskolem1064(vskolem1063(vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3),vskolem1061(X0,X1,X3,X3),X0,X1,X3,X3))
| X0 = X3
| ~ rpoint(X3)
| X0 != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f690]) ).
fof(f692,plain,
! [X3,X1] :
( rpoint(vskolem1064(vskolem1063(vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3),vskolem1061(X1,X1,X3,X3),X1,X1,X3,X3))
| X1 = X3
| ~ rpoint(X3)
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f691]) ).
fof(f721,plain,
! [X2,X3,X0] :
( vf(X0,X2) = vf(X2,X0)
| ~ rpoint(X2)
| X0 != X3
| ~ rpoint(X3) ),
inference(equality_resolution,[],[f431]) ).
fof(f722,plain,
! [X2,X3] :
( ~ rpoint(X3)
| ~ rpoint(X2)
| vf(X3,X2) = vf(X2,X3) ),
inference(equality_resolution,[],[f721]) ).
fof(f1391,definition,
! [X0] : sF46(X0) = vf(vd1050,X0),
introduced(definition,[new_symbols(definition,[sF46])],[function_definition]) ).
fof(f1392,plain,
! [X0] : vf(vd1050,X0) = sF46(X0),
inference(reorient_equations,[],[f1391]) ).
fof(f1393,definition,
! [X0] : sF47(X0) = vf(X0,vd1048),
introduced(definition,[new_symbols(definition,[sF47])],[function_definition]) ).
fof(f1394,plain,
! [X0] : vf(X0,vd1048) = sF47(X0),
inference(reorient_equations,[],[f1393]) ).
fof(f1395,definition,
sF48 = vf(vd1048,vd1050),
introduced(definition,[new_symbols(definition,[sF48])],[function_definition]) ).
fof(f1396,plain,
vf(vd1048,vd1050) = sF48,
inference(reorient_equations,[],[f1395]) ).
fof(f1397,plain,
! [X0] :
( sF46(X0) != sF47(X0)
| sF46(X0) != sF48
| ~ rpoint(X0) ),
inference(definition_folding,[],[f654,f1396,f1392,f1394,f1392]) ).
fof(f1450,plain,
sF46(vd1048) = sF47(vd1050),
inference(superposition,[],[f1392,f1394]) ).
fof(f1453,plain,
! [X0] :
( ~ rpoint(X0)
| vf(X0,vd1048) = vf(vd1048,X0) ),
inference(resolution,[],[f408,f722]) ).
fof(f1455,plain,
! [X0] :
( vd1048 = X0
| vf(X0,vd1048) = vf(vd1048,vskolem1064(vskolem1063(vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048),vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048))
| ~ rpoint(X0) ),
inference(resolution,[],[f672,f408]) ).
fof(f1464,plain,
! [X0] :
( vd1048 = X0
| vf(X0,vd1048) = vf(X0,vskolem1064(vskolem1063(vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048),vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048))
| ~ rpoint(X0) ),
inference(resolution,[],[f680,f408]) ).
fof(f1483,plain,
! [X0] :
( ~ rpoint(X0)
| sF47(X0) = vf(vd1048,X0) ),
inference(forward_demodulation,[],[f1453,f1394]) ).
fof(f1484,plain,
! [X0] :
( ~ rpoint(X0)
| vd1048 = X0
| sF47(X0) = vf(vd1048,vskolem1064(vskolem1063(vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048),vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048)) ),
inference(forward_demodulation,[],[f1455,f1394]) ).
fof(f1488,plain,
! [X0] :
( ~ rpoint(X0)
| vd1048 = X0
| sF47(X0) = vf(X0,vskolem1064(vskolem1063(vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048),vskolem1061(X0,X0,vd1048,vd1048),X0,X0,vd1048,vd1048)) ),
inference(forward_demodulation,[],[f1464,f1394]) ).
fof(f1496,definition,
( spl49_13
<=> sF48 = sF46(vd1048) ),
introduced(definition,[new_symbols(definition,[spl49_13])],[avatar_definition]) ).
fof(f1497,plain,
( sF48 = sF46(vd1048)
| ~ spl49_13 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1498,plain,
( sF48 != sF46(vd1048)
| spl49_13 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f1513,plain,
vf(vd1048,vd1050) = sF47(vd1050),
inference(resolution,[],[f1483,f410]) ).
fof(f1516,plain,
vf(vd1048,vd1050) = sF46(vd1048),
inference(forward_demodulation,[],[f1513,f1450]) ).
fof(f1517,plain,
sF48 = sF46(vd1048),
inference(forward_demodulation,[],[f1516,f1396]) ).
fof(f1518,plain,
( $false
| spl49_13 ),
inference(forward_subsumption_resolution,[],[f1517,f1498]) ).
fof(f1519,plain,
spl49_13,
inference(avatar_contradiction_clause,[],[f1518]) ).
fof(f1530,plain,
( vd1050 = vd1048
| sF47(vd1050) = vf(vd1048,vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)) ),
inference(resolution,[],[f1484,f410]) ).
fof(f1533,plain,
sF47(vd1050) = vf(vd1048,vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)),
inference(forward_subsumption_resolution,[],[f1530,f655]) ).
fof(f1534,plain,
sF46(vd1048) = vf(vd1048,vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)),
inference(forward_demodulation,[],[f1533,f1450]) ).
fof(f1535,plain,
( sF48 = vf(vd1048,vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_13 ),
inference(forward_demodulation,[],[f1534,f1497]) ).
fof(f1541,plain,
( vd1050 = vd1048
| sF47(vd1050) = vf(vd1050,vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)) ),
inference(resolution,[],[f1488,f410]) ).
fof(f1544,plain,
sF47(vd1050) = vf(vd1050,vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)),
inference(forward_subsumption_resolution,[],[f1541,f655]) ).
fof(f1545,plain,
sF47(vd1050) = sF46(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)),
inference(forward_demodulation,[],[f1544,f1392]) ).
fof(f1546,plain,
sF46(vd1048) = sF46(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)),
inference(forward_demodulation,[],[f1545,f1450]) ).
fof(f1547,plain,
( sF48 = sF46(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_13 ),
inference(forward_demodulation,[],[f1546,f1497]) ).
fof(f1599,definition,
( spl49_18
<=> rpoint(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)) ),
introduced(definition,[new_symbols(definition,[spl49_18])],[avatar_definition]) ).
fof(f1600,plain,
( rpoint(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_18 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f1601,plain,
( ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| spl49_18 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f1634,plain,
( vd1050 = vd1048
| ~ rpoint(vd1048)
| ~ rpoint(vd1050)
| spl49_18 ),
inference(resolution,[],[f1601,f692]) ).
fof(f1635,plain,
( ~ rpoint(vd1048)
| ~ rpoint(vd1050)
| spl49_18 ),
inference(forward_subsumption_resolution,[],[f1634,f655]) ).
fof(f1636,plain,
( ~ rpoint(vd1050)
| spl49_18 ),
inference(forward_subsumption_resolution,[],[f1635,f408]) ).
fof(f1637,plain,
( $false
| spl49_18 ),
inference(forward_subsumption_resolution,[],[f1636,f410]) ).
fof(f1638,plain,
spl49_18,
inference(avatar_contradiction_clause,[],[f1637]) ).
fof(f1671,plain,
( vf(vd1048,vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048)) = sF47(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_18 ),
inference(resolution,[],[f1600,f1483]) ).
fof(f1702,plain,
( sF48 = sF47(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_13
| ~ spl49_18 ),
inference(forward_demodulation,[],[f1671,f1535]) ).
fof(f1731,plain,
( sF48 != sF46(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| sF48 != sF46(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_13
| ~ spl49_18 ),
inference(superposition,[],[f1397,f1702]) ).
fof(f1732,plain,
( sF48 != sF46(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_13
| ~ spl49_18 ),
inference(duplicate_literal_removal,[],[f1731]) ).
fof(f1733,plain,
( ~ rpoint(vskolem1064(vskolem1063(vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048),vskolem1061(vd1050,vd1050,vd1048,vd1048),vd1050,vd1050,vd1048,vd1048))
| ~ spl49_13
| ~ spl49_18 ),
inference(forward_subsumption_resolution,[],[f1732,f1547]) ).
fof(f1734,plain,
( $false
| ~ spl49_13
| ~ spl49_18 ),
inference(forward_subsumption_resolution,[],[f1733,f1600]) ).
fof(f1735,plain,
( ~ spl49_13
| ~ spl49_18 ),
inference(avatar_contradiction_clause,[],[f1734]) ).
cnf(s19,plain,
spl49_13,
inference(sat_conversion,[],[f1519]) ).
cnf(s24,plain,
spl49_18,
inference(sat_conversion,[],[f1638]) ).
cnf(s32,plain,
( ~ spl49_13
| ~ spl49_18 ),
inference(sat_conversion,[],[f1735]) ).
cnf(s33,plain,
~ spl49_13,
inference(rat,[],[s32,s24]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s19,s33]) ).
fof(f1736,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO270+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 % Computer : n004.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sun Sep 27 07:57:51 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 Running first-order theorem proving
% 0.12/0.37 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
% 4.40/1.59 % (3187113)Detected formulas, will run a generic FOF schedule.
% 4.40/1.59 % (3187118)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=980060668:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.40/1.59 % (3187122)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3738244898:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.40/1.59 % (3187119)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=1814005835:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.40/1.59 % (3187120)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=504919612:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.40/1.59 % (3187121)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4033592827:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.40/1.59 % (3187122)Refutation not found, incomplete strategy
% 4.40/1.59 % (3187122)------------------------------
% 4.40/1.59 % (3187122)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3187122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3187122)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3187122)Termination reason: Refutation not found, incomplete strategy
% 4.40/1.59 % (3187122)Time elapsed: 0.003 s
% 4.40/1.59 % (3187122)Peak memory usage: 88 MB
% 4.40/1.59 % (3187122)Instructions burned: 2 (million)
% 4.40/1.59 % (3187121)Refutation not found, incomplete strategy
% 4.40/1.59 % (3187121)------------------------------
% 4.40/1.59 % (3187121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3187121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3187121)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3187121)Termination reason: Refutation not found, incomplete strategy
% 4.40/1.59 % (3187121)Time elapsed: 0.003 s
% 4.40/1.59 % (3187121)Peak memory usage: 88 MB
% 4.40/1.59 % (3187121)Instructions burned: 2 (million)
% 4.40/1.59 % (3187123)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3285897245:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.40/1.59 % (3187124)dis-21_1_sil=8000:lcm=predicate:random_seed=1066106360: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)
% 4.40/1.59 % (3187124)Instruction limit reached!
% 4.40/1.59 % (3187124)------------------------------
% 4.40/1.59 % (3187124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3187124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3187124)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3187124)Termination reason: Instruction limit
% 4.40/1.59 % (3187124)Termination phase: Saturation
% 4.40/1.59 % (3187124)Time elapsed: 0.059 s
% 4.40/1.59 % (3187124)Peak memory usage: 89 MB
% 4.40/1.59 % (3187124)Instructions burned: 131 (million)
% 4.40/1.59 % (3187123)Instruction limit reached!
% 4.40/1.59 % (3187123)------------------------------
% 4.40/1.59 % (3187123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3187123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3187123)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3187123)Termination reason: Instruction limit
% 4.40/1.59 % (3187123)Termination phase: Saturation
% 4.40/1.59 % (3187123)Time elapsed: 0.094 s
% 4.40/1.59 % (3187123)Peak memory usage: 90 MB
% 4.40/1.59 % (3187123)Instructions burned: 140 (million)
% 4.40/1.59 % (3187132)lrs+10_1_sil=8000:sp=occurrence:random_seed=2620101115:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.40/1.59 % (3187122)------------------------------
% 4.40/1.59 % (3187122)------------------------------
% 4.40/1.59 % (3187121)------------------------------
% 4.40/1.59 % (3187121)------------------------------
% 4.40/1.59 % (3187133)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4056582898:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.40/1.59 % (3187133)Instruction limit reached!
% 4.40/1.59 % (3187133)------------------------------
% 4.40/1.59 % (3187133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3187133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3187133)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3187133)Termination reason: Instruction limit
% 4.40/1.59 % (3187133)Termination phase: Saturation
% 4.40/1.59 % (3187133)Time elapsed: 0.074 s
% 4.40/1.59 % (3187133)Peak memory usage: 93 MB
% 4.40/1.59 % (3187133)Instructions burned: 158 (million)
% 4.40/1.59 % (3187132)Instruction limit reached!
% 4.40/1.59 % (3187132)------------------------------
% 4.40/1.59 % (3187132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3187132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3187132)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3187132)Termination reason: Instruction limit
% 4.40/1.59 % (3187132)Termination phase: Saturation
% 4.40/1.59 % (3187132)Time elapsed: 0.153 s
% 4.40/1.59 % (3187132)Peak memory usage: 93 MB
% 4.40/1.59 % (3187132)Instructions burned: 286 (million)
% 4.40/1.59 % (3187135)lrs+1011_1_sil=32000:sp=occurrence:random_seed=41128659:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 4.40/1.59 % (3187136)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=133750297:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.40/1.59 % (3187118)First to succeed.
% 4.40/1.59 % (3187118)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3187113"
% 4.40/1.59 % (3187138)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2838947555:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.40/1.59 % (3187138)Also succeeded, but the first one will report.
% 4.40/1.59 % (3187136)Instruction limit reached!
% 4.40/1.59 % (3187136)------------------------------
% 4.40/1.59 % (3187136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.59 % (3187136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.59 % (3187136)CaDiCaL version: 2.1.3
% 4.40/1.59 % (3187136)Termination reason: Instruction limit
% 4.40/1.59 % (3187136)Termination phase: Saturation
% 4.40/1.59 % (3187136)Time elapsed: 0.119 s
% 4.40/1.59 % (3187136)Peak memory usage: 91 MB
% 4.40/1.59 % (3187136)Instructions burned: 249 (million)
% 4.40/1.59 % (3187139)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1817229090:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.40/1.59 % (3187118)Refutation found. Thanks to Tanya!
% 4.40/1.59 % SZS status Theorem for theBenchmark
% 4.40/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 5.94/1.79 % (3187118)------------------------------
% 5.94/1.79 % (3187118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.79 % (3187118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.79 % (3187118)CaDiCaL version: 2.1.3
% 5.94/1.79 % (3187118)Termination reason: Refutation
% 5.94/1.79 % (3187118)Time elapsed: 0.465 s
% 5.94/1.79 % (3187118)Peak memory usage: 132 MB
% 5.94/1.79 % (3187118)Instructions burned: 1088 (million)
% 5.94/1.79 % (3187118)------------------------------
% 5.94/1.79 % (3187118)------------------------------
% 5.94/1.79 % (3187113)Success in time 0.772 s
% 5.94/1.79 % Vampire exiting
%------------------------------------------------------------------------------