%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG079+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:25 PM UTC 2026
% Result : Theorem 2.63s 6.51s
% Output : Refutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 97 ( 34 unt; 4 def)
% Number of atoms : 232 ( 59 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 240 ( 105 ~; 102 |; 25 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 14 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2) )
=> ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
fof(f36,axiom,
! [X0,X1] :
( ( aVector0(X0)
& aVector0(X1) )
=> ( ( aDimensionOf0(X0) = aDimensionOf0(X1)
& aDimensionOf0(X1) != sz00 )
=> sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
fof(f38,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(f41,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
fof(f42,axiom,
( aVector0(xp)
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(f44,axiom,
( aScalar0(xA)
& xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
fof(f46,axiom,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(f47,axiom,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(f48,axiom,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(f49,axiom,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f50,axiom,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(f51,axiom,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(f60,axiom,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2905) ).
fof(f61,conjecture,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f62,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(negated_conjecture,[status(cth)],[f61]) ).
fof(f63,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(flattening,[],[f62]) ).
fof(f72,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f73,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(flattening,[],[f72]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(ennf_transformation,[],[f16]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(flattening,[],[f87]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(flattening,[],[f91]) ).
fof(f129,plain,
aVector0(xs),
inference(cnf_transformation,[],[f38]) ).
fof(f132,plain,
sz00 != aDimensionOf0(xs),
inference(cnf_transformation,[],[f41]) ).
fof(f133,plain,
xp = sziznziztdt0(xs),
inference(cnf_transformation,[],[f42]) ).
fof(f137,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(cnf_transformation,[],[f44]) ).
fof(f141,plain,
xC = sdtasasdt0(xp,xp),
inference(cnf_transformation,[],[f46]) ).
fof(f142,plain,
aScalar0(xC),
inference(cnf_transformation,[],[f46]) ).
fof(f144,plain,
aScalar0(xD),
inference(cnf_transformation,[],[f47]) ).
fof(f146,plain,
aScalar0(xE),
inference(cnf_transformation,[],[f48]) ).
fof(f147,plain,
xF = sdtasdt0(xA,xA),
inference(cnf_transformation,[],[f49]) ).
fof(f148,plain,
aScalar0(xF),
inference(cnf_transformation,[],[f49]) ).
fof(f150,plain,
aScalar0(xG),
inference(cnf_transformation,[],[f50]) ).
fof(f152,plain,
aScalar0(xH),
inference(cnf_transformation,[],[f51]) ).
fof(f165,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtpldt0(sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sdtasdt0(xF,xG)))),
inference(cnf_transformation,[],[f60]) ).
fof(f166,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(cnf_transformation,[],[f63]) ).
fof(f168,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(cnf_transformation,[],[f88]) ).
fof(f185,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f212,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f238,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| ~ aScalar0(xH)
| ~ aScalar0(xE)
| ~ aScalar0(X0) ),
inference(superposition,[],[f166,f185]) ).
fof(f242,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| ~ aScalar0(xE)
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f238,f152]) ).
fof(f286,plain,
! [X0] :
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f242,f146]) ).
fof(f288,definition,
( spl2_11
<=> ! [X0] : ~ aScalar0(X0) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f289,plain,
( ! [X0] : ~ aScalar0(X0)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f291,definition,
( spl2_12
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f293,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| spl2_12 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f295,plain,
( spl2_11
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f286,f291,f288]) ).
fof(f410,plain,
( $false
| ~ spl2_11 ),
inference(resolution,[],[f289,f212]) ).
fof(f441,plain,
~ spl2_11,
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f476,plain,
xC = sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),
inference(superposition,[],[f141,f133]) ).
fof(f1002,plain,
xF = sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))),
inference(superposition,[],[f147,f137]) ).
fof(f1285,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| ~ aScalar0(xC)
| ~ aScalar0(xF)
| ~ aScalar0(xD)
| ~ aScalar0(xG) ),
inference(superposition,[],[f165,f180]) ).
fof(f1290,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| ~ aScalar0(xF)
| ~ aScalar0(xD)
| ~ aScalar0(xG) ),
inference(forward_subsumption_resolution,[],[f1285,f142]) ).
fof(f1303,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| ~ aScalar0(xD)
| ~ aScalar0(xG) ),
inference(forward_subsumption_resolution,[],[f1290,f148]) ).
fof(f1328,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG)))
| ~ aScalar0(xG) ),
inference(forward_subsumption_resolution,[],[f1303,f144]) ).
fof(f1339,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(forward_subsumption_resolution,[],[f1328,f150]) ).
fof(f1371,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xE,xH)),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),sdtasdt0(sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(xD,xG))),
inference(forward_demodulation,[],[f1339,f1002]) ).
fof(f1549,definition,
( spl2_81
<=> sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(xD,xG))) ),
introduced(definition,[new_symbols(definition,[spl2_81])],[avatar_definition]) ).
fof(f1550,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(xD,xG)))
| ~ spl2_81 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f1551,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(xD,xG)))
| spl2_81 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f1959,definition,
( spl2_106
<=> sdtpldt0(xE,xH) = sdtpldt0(xH,xE) ),
introduced(definition,[new_symbols(definition,[spl2_106])],[avatar_definition]) ).
fof(f1960,plain,
( sdtpldt0(xE,xH) != sdtpldt0(xH,xE)
| spl2_106 ),
inference(avatar_component_clause,[],[f1959]) ).
fof(f1961,plain,
( sdtpldt0(xE,xH) = sdtpldt0(xH,xE)
| ~ spl2_106 ),
inference(avatar_component_clause,[],[f1959]) ).
fof(f1978,plain,
( sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs)
| aDimensionOf0(xs) != aDimensionOf0(xs)
| sz00 = aDimensionOf0(xs)
| ~ aVector0(xs)
| ~ aVector0(xs) ),
inference(superposition,[],[f168,f476]) ).
fof(f1988,plain,
( sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs)
| aDimensionOf0(xs) != aDimensionOf0(xs)
| sz00 = aDimensionOf0(xs)
| ~ aVector0(xs) ),
inference(duplicate_literal_removal,[],[f1978]) ).
fof(f1989,plain,
( sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs)
| sz00 = aDimensionOf0(xs)
| ~ aVector0(xs) ),
inference(trivial_inequality_removal,[],[f1988]) ).
fof(f1992,plain,
( sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs)
| ~ aVector0(xs) ),
inference(forward_subsumption_resolution,[],[f1989,f132]) ).
fof(f1993,plain,
sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) = sdtasasdt0(xs,xs),
inference(forward_subsumption_resolution,[],[f1992,f129]) ).
fof(f2362,plain,
( ! [X0] :
( sdtpldt0(xH,xE) != sdtpldt0(xH,xE)
| ~ aScalar0(xE)
| ~ aScalar0(xH)
| ~ aScalar0(X0) )
| spl2_106 ),
inference(superposition,[],[f1960,f185]) ).
fof(f2363,plain,
( ! [X0] :
( ~ aScalar0(xE)
| ~ aScalar0(xH)
| ~ aScalar0(X0) )
| spl2_106 ),
inference(trivial_inequality_removal,[],[f2362]) ).
fof(f2365,plain,
( ! [X0] :
( ~ aScalar0(xH)
| ~ aScalar0(X0) )
| spl2_106 ),
inference(forward_subsumption_resolution,[],[f2363,f146]) ).
fof(f2367,plain,
( ! [X0] : ~ aScalar0(X0)
| spl2_106 ),
inference(forward_subsumption_resolution,[],[f2365,f152]) ).
fof(f2369,plain,
( spl2_11
| spl2_106 ),
inference(avatar_split_clause,[],[f2367,f1959,f288]) ).
fof(f2410,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(xD,xG)))
| spl2_12 ),
inference(superposition,[],[f293,f1002]) ).
fof(f2492,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtasasdt0(xs,xs),sdtpldt0(xD,xG)))
| spl2_12 ),
inference(forward_demodulation,[],[f2410,f1993]) ).
fof(f5439,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(xD,xG)))
| ~ aScalar0(xE)
| ~ aScalar0(xH)
| ~ aScalar0(xE)
| ~ aScalar0(xH) ),
inference(superposition,[],[f1371,f180]) ).
fof(f5444,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),sdtpldt0(xD,xG)))
| ~ aScalar0(xE)
| ~ aScalar0(xH) ),
inference(duplicate_literal_removal,[],[f5439]) ).
fof(f5450,plain,
( ~ aScalar0(xE)
| ~ aScalar0(xH)
| spl2_81 ),
inference(forward_subsumption_resolution,[],[f5444,f1551]) ).
fof(f5464,plain,
( ~ aScalar0(xH)
| spl2_81 ),
inference(forward_subsumption_resolution,[],[f5450,f146]) ).
fof(f5478,plain,
( $false
| spl2_81 ),
inference(forward_subsumption_resolution,[],[f5464,f152]) ).
fof(f5479,plain,
spl2_81,
inference(avatar_contradiction_clause,[],[f5478]) ).
fof(f5528,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtasasdt0(xs,xs),sdtpldt0(xD,xG)))
| ~ spl2_81 ),
inference(forward_demodulation,[],[f1550,f1993]) ).
fof(f5533,plain,
( sdtlseqdt0(sdtasdt0(sdtpldt0(xH,xE),sdtpldt0(xH,xE)),sdtasdt0(sdtasasdt0(xs,xs),sdtpldt0(xD,xG)))
| ~ spl2_81
| ~ spl2_106 ),
inference(forward_demodulation,[],[f5528,f1961]) ).
fof(f5537,plain,
( $false
| spl2_12
| ~ spl2_81
| ~ spl2_106 ),
inference(forward_subsumption_resolution,[],[f5533,f2492]) ).
fof(f5538,plain,
( spl2_12
| ~ spl2_81
| ~ spl2_106 ),
inference(avatar_contradiction_clause,[],[f5537]) ).
cnf(s5,plain,
( spl2_11
| ~ spl2_12 ),
inference(sat_conversion,[],[f295]) ).
cnf(s33,plain,
~ spl2_11,
inference(sat_conversion,[],[f441]) ).
cnf(s155,plain,
( spl2_11
| spl2_106 ),
inference(sat_conversion,[],[f2369]) ).
cnf(s373,plain,
spl2_81,
inference(sat_conversion,[],[f5479]) ).
cnf(s383,plain,
( spl2_12
| ~ spl2_81
| ~ spl2_106 ),
inference(sat_conversion,[],[f5538]) ).
cnf(s452,plain,
spl2_106,
inference(rat,[],[s155,s33]) ).
cnf(s467,plain,
spl2_12,
inference(rat,[],[s383,s373,s452]) ).
cnf(s488,plain,
$false,
inference(rat,[],[s5,s467,s33]) ).
fof(f5546,plain,
$false,
inference(avatar_sat_refutation,[],[s488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG079+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.39 % Computer : n003.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sun Sep 27 23:11:04 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.11/5.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 2.63/6.51 % (1033462)Detected formulas, will run a generic FOF schedule.
% 2.63/6.51 % (1033473)dis-21_1_sil=8000:lcm=predicate:random_seed=359018987: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)
% 2.63/6.51 % (1033473)Instruction limit reached!
% 2.63/6.51 % (1033473)------------------------------
% 2.63/6.51 % (1033473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033473)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033473)Termination reason: Instruction limit
% 2.63/6.51 % (1033473)Termination phase: Saturation
% 2.63/6.51 % (1033473)Time elapsed: 0.032 s
% 2.63/6.51 % (1033473)Peak memory usage: 89 MB
% 2.63/6.51 % (1033473)Instructions burned: 131 (million)
% 2.63/6.51 % (1033467)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=1394222545:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/6.51 % (1033470)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=48935160:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/6.51 % (1033469)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=2753927401:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/6.51 % (1033468)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=533568522:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/6.51 % (1033472)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=735530722:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/6.51 % (1033471)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3762549839:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/6.51 % (1033470)Instruction limit reached!
% 2.63/6.51 % (1033470)------------------------------
% 2.63/6.51 % (1033470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033470)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033470)Termination reason: Instruction limit
% 2.63/6.51 % (1033470)Termination phase: Saturation
% 2.63/6.51 % (1033470)Time elapsed: 0.052 s
% 2.63/6.51 % (1033470)Peak memory usage: 89 MB
% 2.63/6.51 % (1033470)Instructions burned: 111 (million)
% 2.63/6.51 % (1033471)Instruction limit reached!
% 2.63/6.51 % (1033471)------------------------------
% 2.63/6.51 % (1033471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033471)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033471)Termination reason: Instruction limit
% 2.63/6.51 % (1033471)Termination phase: Saturation
% 2.63/6.51 % (1033471)Time elapsed: 0.070 s
% 2.63/6.51 % (1033471)Peak memory usage: 89 MB
% 2.63/6.51 % (1033471)Instructions burned: 120 (million)
% 2.63/6.51 % (1033479)lrs+10_1_sil=8000:sp=occurrence:random_seed=2132862380:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.63/6.51 % (1033472)Instruction limit reached!
% 2.63/6.51 % (1033472)------------------------------
% 2.63/6.51 % (1033472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033472)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033472)Termination reason: Instruction limit
% 2.63/6.51 % (1033472)Termination phase: Saturation
% 2.63/6.51 % (1033472)Time elapsed: 0.090 s
% 2.63/6.51 % (1033472)Peak memory usage: 90 MB
% 2.63/6.51 % (1033472)Instructions burned: 140 (million)
% 2.63/6.51 % (1033482)lrs+10_1_sil=32000:urr=on:br=off:random_seed=39878149:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.63/6.51 % (1033479)Instruction limit reached!
% 2.63/6.51 % (1033479)------------------------------
% 2.63/6.51 % (1033479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033479)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033479)Termination reason: Instruction limit
% 2.63/6.51 % (1033479)Termination phase: Saturation
% 2.63/6.51 % (1033479)Time elapsed: 0.096 s
% 2.63/6.51 % (1033479)Peak memory usage: 93 MB
% 2.63/6.51 % (1033479)Instructions burned: 286 (million)
% 2.63/6.51 % (1033484)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2971671683:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.63/6.51 % (1033485)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=4276508609:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 2.63/6.51 % (1033482)Instruction limit reached!
% 2.63/6.51 % (1033482)------------------------------
% 2.63/6.51 % (1033482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033482)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033482)Termination reason: Instruction limit
% 2.63/6.51 % (1033482)Termination phase: Saturation
% 2.63/6.51 % (1033482)Time elapsed: 0.073 s
% 2.63/6.51 % (1033482)Peak memory usage: 92 MB
% 2.63/6.51 % (1033482)Instructions burned: 159 (million)
% 2.63/6.51 % (1033487)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3222289696:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 2.63/6.51 % (1033487)First to succeed.
% 2.63/6.51 % (1033487)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1033462"
% 2.63/6.51 % (1033485)Instruction limit reached!
% 2.63/6.51 % (1033485)------------------------------
% 2.63/6.51 % (1033485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033485)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033485)Termination reason: Instruction limit
% 2.63/6.51 % (1033485)Termination phase: Saturation
% 2.63/6.51 % (1033485)Time elapsed: 0.119 s
% 2.63/6.51 % (1033485)Peak memory usage: 96 MB
% 2.63/6.51 % (1033485)Instructions burned: 249 (million)
% 2.63/6.51 % (1033490)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=908434014:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 2.63/6.51 % (1033484)Instruction limit reached!
% 2.63/6.51 % (1033484)------------------------------
% 2.63/6.51 % (1033484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/6.51 % (1033484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/6.51 % (1033484)CaDiCaL version: 2.1.3
% 2.63/6.51 % (1033484)Termination reason: Instruction limit
% 2.63/6.51 % (1033484)Termination phase: Saturation
% 2.63/6.51 % (1033484)Time elapsed: 0.194 s
% 2.63/6.51 % (1033484)Peak memory usage: 93 MB
% 2.63/6.51 % (1033484)Instructions burned: 326 (million)
% 2.63/6.51 % (1033492)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1806259275:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 2.63/6.51 % (1033487)Refutation found. Thanks to Tanya!
% 2.63/6.51 % SZS status Theorem for theBenchmark
% 2.63/6.51 % SZS output start Proof for theBenchmark
% See solution above
% 5.04/6.69 % (1033487)------------------------------
% 5.04/6.69 % (1033487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/6.69 % (1033487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/6.69 % (1033487)CaDiCaL version: 2.1.3
% 5.04/6.69 % (1033487)Termination reason: Refutation
% 5.04/6.69 % (1033487)Time elapsed: 0.070 s
% 5.04/6.69 % (1033487)Peak memory usage: 91 MB
% 5.04/6.69 % (1033487)Instructions burned: 216 (million)
% 5.04/6.69 % (1033487)------------------------------
% 5.04/6.69 % (1033487)------------------------------
% 5.04/6.69 % (1033462)Success in time 0.637 s
% 5.04/6.69 % Vampire exiting
%------------------------------------------------------------------------------