%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG081+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:35:26 PM UTC 2026
% Result : Theorem 2.92s 1.35s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 83 ( 20 unt; 4 def)
% Number of atoms : 422 ( 138 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 477 ( 138 ~; 119 |; 210 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-8 aty)
% Number of variables : 252 ( 177 !; 75 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f20,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
fof(f24,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
fof(f35,axiom,
! [X0,X1] :
( ( aVector0(X0)
& aVector0(X1) )
=> ( ( aDimensionOf0(X0) = aDimensionOf0(X1)
& aDimensionOf0(X1) = sz00 )
=> sdtasasdt0(X0,X1) = sz0z00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).
fof(f37,axiom,
! [X0] :
( aVector0(X0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
fof(f38,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
fof(f40,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
fof(f41,conjecture,
( ( aDimensionOf0(xs) != sz00
=> ? [X0] :
( aVector0(X0)
& X0 = sziznziztdt0(xs)
& ? [X1] :
( aVector0(X1)
& X1 = sziznziztdt0(xt)
& ? [X2] :
( aScalar0(X2)
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [X3] :
( aScalar0(X3)
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [X4] :
( aScalar0(X4)
& X4 = sdtasasdt0(X0,X0)
& ? [X5] :
( aScalar0(X5)
& X5 = sdtasasdt0(X1,X1)
& ? [X6] :
( aScalar0(X6)
& X6 = sdtasasdt0(X0,X1)
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasdt0(X2,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& ? [X9] :
( aScalar0(X9)
& X9 = sdtasdt0(X2,X3)
& ? [X10] :
( aScalar0(X10)
& X10 = sdtasdt0(X4,X8)
& ? [X11] :
( aScalar0(X11)
& X11 = sdtasdt0(X6,X9)
& ? [X12] :
( aScalar0(X12)
& X12 = sdtasdt0(X7,X5)
& ? [X13] :
( aScalar0(X13)
& X13 = sdtasdt0(X10,X12)
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ( ( aDimensionOf0(xs) != sz00
=> ? [X0] :
( aVector0(X0)
& X0 = sziznziztdt0(xs)
& ? [X1] :
( aVector0(X1)
& X1 = sziznziztdt0(xt)
& ? [X2] :
( aScalar0(X2)
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [X3] :
( aScalar0(X3)
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [X4] :
( aScalar0(X4)
& X4 = sdtasasdt0(X0,X0)
& ? [X5] :
( aScalar0(X5)
& X5 = sdtasasdt0(X1,X1)
& ? [X6] :
( aScalar0(X6)
& X6 = sdtasasdt0(X0,X1)
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasdt0(X2,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& ? [X9] :
( aScalar0(X9)
& X9 = sdtasdt0(X2,X3)
& ? [X10] :
( aScalar0(X10)
& X10 = sdtasdt0(X4,X8)
& ? [X11] :
( aScalar0(X11)
& X11 = sdtasdt0(X6,X9)
& ? [X12] :
( aScalar0(X12)
& X12 = sdtasdt0(X7,X5)
& ? [X13] :
( aScalar0(X13)
& X13 = sdtasdt0(X10,X12)
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f50,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ? [X0] :
( aVector0(X0)
& X0 = sziznziztdt0(xs)
& ? [X1] :
( aVector0(X1)
& X1 = sziznziztdt0(xt)
& ? [X2] :
( aScalar0(X2)
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& ? [X3] :
( aScalar0(X3)
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [X4] :
( aScalar0(X4)
& X4 = sdtasasdt0(X0,X0)
& ? [X5] :
( aScalar0(X5)
& X5 = sdtasasdt0(X1,X1)
& ? [X6] :
( aScalar0(X6)
& X6 = sdtasasdt0(X0,X1)
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasdt0(X2,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& ? [X9] :
( aScalar0(X9)
& X9 = sdtasdt0(X2,X3)
& ? [X10] :
( aScalar0(X10)
& X10 = sdtasdt0(X4,X8)
& ? [X11] :
( aScalar0(X11)
& X11 = sdtasdt0(X6,X9)
& ? [X12] :
( aScalar0(X12)
& X12 = sdtasdt0(X7,X5)
& ? [X13] :
( aScalar0(X13)
& X13 = sdtasdt0(X10,X12)
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| sz00 = aDimensionOf0(xs) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f58,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f62,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f63,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sz0z00
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f64,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sz0z00
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(flattening,[],[f63]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(ennf_transformation,[],[f24]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(flattening,[],[f95]) ).
fof(f97,definition,
! [X5,X7,X10,X4,X6,X11,X8,X9] :
( ? [X12] :
( aScalar0(X12)
& X12 = sdtasdt0(X7,X5)
& ? [X13] :
( aScalar0(X13)
& X13 = sdtasdt0(X10,X12)
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) )
| ~ sP0(X5,X7,X10,X4,X6,X11,X8,X9) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f98,definition,
! [X3,X2,X8,X4,X6,X7,X5] :
( ? [X9] :
( aScalar0(X9)
& X9 = sdtasdt0(X2,X3)
& ? [X10] :
( aScalar0(X10)
& X10 = sdtasdt0(X4,X8)
& ? [X11] :
( aScalar0(X11)
& X11 = sdtasdt0(X6,X9)
& sP0(X5,X7,X10,X4,X6,X11,X8,X9) ) ) )
| ~ sP1(X3,X2,X8,X4,X6,X7,X5) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f99,definition,
! [X1,X0,X2,X3,X5,X4] :
( ? [X6] :
( aScalar0(X6)
& X6 = sdtasasdt0(X0,X1)
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasdt0(X2,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& sP1(X3,X2,X8,X4,X6,X7,X5) ) ) )
| ~ sP2(X1,X0,X2,X3,X5,X4) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f100,definition,
! [X0,X1,X2] :
( ? [X3] :
( aScalar0(X3)
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [X4] :
( aScalar0(X4)
& X4 = sdtasasdt0(X0,X0)
& ? [X5] :
( aScalar0(X5)
& X5 = sdtasasdt0(X1,X1)
& sP2(X1,X0,X2,X3,X5,X4) ) ) )
| ~ sP3(X0,X1,X2) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f101,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ? [X0] :
( aVector0(X0)
& X0 = sziznziztdt0(xs)
& ? [X1] :
( aVector0(X1)
& X1 = sziznziztdt0(xt)
& ? [X2] :
( aScalar0(X2)
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& sP3(X0,X1,X2) ) ) )
| sz00 = aDimensionOf0(xs) ) ),
inference(definition_folding,[],[f50,f100,f99,f98,f97]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ? [X3] :
( aScalar0(X3)
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& ? [X4] :
( aScalar0(X4)
& X4 = sdtasasdt0(X0,X0)
& ? [X5] :
( aScalar0(X5)
& X5 = sdtasasdt0(X1,X1)
& sP2(X1,X0,X2,X3,X5,X4) ) ) )
| ~ sP3(X0,X1,X2) ),
inference(nnf_transformation,[],[f100]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( aScalar0(sK4(X0,X1,X2))
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK4(X0,X1,X2)
& aScalar0(sK5(X0,X1,X2))
& sdtasasdt0(X0,X0) = sK5(X0,X1,X2)
& aScalar0(sK6(X0,X1,X2))
& sdtasasdt0(X1,X1) = sK6(X0,X1,X2)
& sP2(X1,X0,X2,sK4(X0,X1,X2),sK6(X0,X1,X2),sK5(X0,X1,X2)) )
| ~ sP3(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X4,sK5(X0,X1,X2)),skolemize(X5,sK6(X0,X1,X2))],[f102]) ).
fof(f104,plain,
! [X1,X0,X2,X3,X5,X4] :
( ? [X6] :
( aScalar0(X6)
& X6 = sdtasasdt0(X0,X1)
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasdt0(X2,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& sP1(X3,X2,X8,X4,X6,X7,X5) ) ) )
| ~ sP2(X1,X0,X2,X3,X5,X4) ),
inference(nnf_transformation,[],[f99]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(X1,X0) = X6
& ? [X7] :
( aScalar0(X7)
& X7 = sdtasdt0(X2,X2)
& ? [X8] :
( aScalar0(X8)
& X8 = sdtasdt0(X3,X3)
& sP1(X3,X2,X8,X5,X6,X7,X4) ) ) )
| ~ sP2(X0,X1,X2,X3,X4,X5) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( aScalar0(sK7(X0,X1,X2,X3,X4,X5))
& sdtasasdt0(X1,X0) = sK7(X0,X1,X2,X3,X4,X5)
& aScalar0(sK8(X0,X1,X2,X3,X4,X5))
& sdtasdt0(X2,X2) = sK8(X0,X1,X2,X3,X4,X5)
& aScalar0(sK9(X0,X1,X2,X3,X4,X5))
& sdtasdt0(X3,X3) = sK9(X0,X1,X2,X3,X4,X5)
& sP1(X3,X2,sK9(X0,X1,X2,X3,X4,X5),X5,sK7(X0,X1,X2,X3,X4,X5),sK8(X0,X1,X2,X3,X4,X5),X4) )
| ~ sP2(X0,X1,X2,X3,X4,X5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X6,sK7(X0,X1,X2,X3,X4,X5)),skolemize(X7,sK8(X0,X1,X2,X3,X4,X5)),skolemize(X8,sK9(X0,X1,X2,X3,X4,X5))],[f105]) ).
fof(f107,plain,
! [X3,X2,X8,X4,X6,X7,X5] :
( ? [X9] :
( aScalar0(X9)
& X9 = sdtasdt0(X2,X3)
& ? [X10] :
( aScalar0(X10)
& X10 = sdtasdt0(X4,X8)
& ? [X11] :
( aScalar0(X11)
& X11 = sdtasdt0(X6,X9)
& sP0(X5,X7,X10,X4,X6,X11,X8,X9) ) ) )
| ~ sP1(X3,X2,X8,X4,X6,X7,X5) ),
inference(nnf_transformation,[],[f98]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X7] :
( aScalar0(X7)
& sdtasdt0(X1,X0) = X7
& ? [X8] :
( aScalar0(X8)
& sdtasdt0(X3,X2) = X8
& ? [X9] :
( aScalar0(X9)
& sdtasdt0(X4,X7) = X9
& sP0(X6,X5,X8,X3,X4,X9,X2,X7) ) ) )
| ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( aScalar0(sK10(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X1,X0) = sK10(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK11(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X3,X2) = sK11(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK12(X0,X1,X2,X3,X4,X5,X6))
& sK12(X0,X1,X2,X3,X4,X5,X6) = sdtasdt0(X4,sK10(X0,X1,X2,X3,X4,X5,X6))
& sP0(X6,X5,sK11(X0,X1,X2,X3,X4,X5,X6),X3,X4,sK12(X0,X1,X2,X3,X4,X5,X6),X2,sK10(X0,X1,X2,X3,X4,X5,X6)) )
| ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X7,sK10(X0,X1,X2,X3,X4,X5,X6)),skolemize(X8,sK11(X0,X1,X2,X3,X4,X5,X6)),skolemize(X9,sK12(X0,X1,X2,X3,X4,X5,X6))],[f108]) ).
fof(f110,plain,
! [X5,X7,X10,X4,X6,X11,X8,X9] :
( ? [X12] :
( aScalar0(X12)
& X12 = sdtasdt0(X7,X5)
& ? [X13] :
( aScalar0(X13)
& X13 = sdtasdt0(X10,X12)
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) )
| ~ sP0(X5,X7,X10,X4,X6,X11,X8,X9) ),
inference(nnf_transformation,[],[f97]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ? [X8] :
( aScalar0(X8)
& sdtasdt0(X1,X0) = X8
& ? [X9] :
( aScalar0(X9)
& sdtasdt0(X2,X8) = X9
& sdtlseqdt0(sdtasdt0(X4,X4),sdtasdt0(X3,X0))
& sdtlseqdt0(sdtpldt0(X5,X5),sdtpldt0(X2,X8))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X4,X7)),sdtasdt0(sdtpldt0(X3,X1),sdtpldt0(X0,X6)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ) )
| ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( aScalar0(sK13(X0,X1,X2,X3,X4,X5,X6,X7))
& sdtasdt0(X1,X0) = sK13(X0,X1,X2,X3,X4,X5,X6,X7)
& aScalar0(sK14(X0,X1,X2,X3,X4,X5,X6,X7))
& sK14(X0,X1,X2,X3,X4,X5,X6,X7) = sdtasdt0(X2,sK13(X0,X1,X2,X3,X4,X5,X6,X7))
& sdtlseqdt0(sdtasdt0(X4,X4),sdtasdt0(X3,X0))
& sdtlseqdt0(sdtpldt0(X5,X5),sdtpldt0(X2,sK13(X0,X1,X2,X3,X4,X5,X6,X7)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X4,X7)),sdtasdt0(sdtpldt0(X3,X1),sdtpldt0(X0,X6)))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
| ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X8,sK13(X0,X1,X2,X3,X4,X5,X6,X7)),skolemize(X9,sK14(X0,X1,X2,X3,X4,X5,X6,X7))],[f111]) ).
fof(f113,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ( aVector0(sK15)
& sziznziztdt0(xs) = sK15
& aVector0(sK16)
& sziznziztdt0(xt) = sK16
& aScalar0(sK17)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK17
& sP3(sK15,sK16,sK17) )
| sz00 = aDimensionOf0(xs) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X0,sK15),skolemize(X1,sK16),skolemize(X2,sK17)],[f101]) ).
fof(f119,plain,
aVector0(xt),
inference(cnf_transformation,[],[f38]) ).
fof(f120,plain,
aVector0(xs),
inference(cnf_transformation,[],[f38]) ).
fof(f122,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f40]) ).
fof(f123,plain,
! [X2,X0,X1] :
( sP2(X1,X0,X2,sK4(X0,X1,X2),sK6(X0,X1,X2),sK5(X0,X1,X2))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4,X5] :
( sP1(X3,X2,sK9(X0,X1,X2,X3,X4,X5),X5,sK7(X0,X1,X2,X3,X4,X5),sK8(X0,X1,X2,X3,X4,X5),X4)
| ~ sP2(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f106]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP0(X6,X5,sK11(X0,X1,X2,X3,X4,X5,X6),X3,X4,sK12(X0,X1,X2,X3,X4,X5,X6),X2,sK10(X0,X1,X2,X3,X4,X5,X6))
| ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[],[f109]) ).
fof(f144,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f112]) ).
fof(f152,plain,
( sP3(sK15,sK16,sK17)
| sz00 = aDimensionOf0(xs) ),
inference(cnf_transformation,[],[f113]) ).
fof(f159,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cnf_transformation,[],[f113]) ).
fof(f164,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f167,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f168,plain,
! [X0,X1] :
( aDimensionOf0(X0) != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(cnf_transformation,[],[f96]) ).
fof(f198,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f594,plain,
! [X0] :
( aDimensionOf0(X0) != aDimensionOf0(xt)
| sz0z00 = sdtasasdt0(xs,X0)
| sz00 != aDimensionOf0(X0)
| ~ aVector0(xs)
| ~ aVector0(X0) ),
inference(superposition,[],[f168,f122]) ).
fof(f612,plain,
! [X0] :
( sz0z00 = sdtasasdt0(X0,X0)
| sz00 != aDimensionOf0(X0)
| ~ aVector0(X0)
| ~ aVector0(X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f613,plain,
! [X0] :
( sz00 != aDimensionOf0(X0)
| sz0z00 = sdtasasdt0(X0,X0)
| ~ aVector0(X0) ),
inference(duplicate_literal_removal,[],[f612]) ).
fof(f646,plain,
! [X0] :
( aDimensionOf0(X0) != aDimensionOf0(xt)
| sz0z00 = sdtasasdt0(xs,X0)
| sz00 != aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(forward_subsumption_resolution,[],[f594,f120]) ).
fof(f925,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7),
inference(forward_subsumption_resolution,[],[f144,f159]) ).
fof(f948,plain,
( ~ sdtlseqdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xs))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xt))
| ~ sdtlseqdt0(sdtasasdt0(xs,xt),sdtasasdt0(xt,xt))
| ~ aScalar0(sdtasasdt0(xs,xt))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xs,xt))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(resolution,[],[f197,f159]) ).
fof(f970,plain,
( ~ sdtlseqdt0(sdtasasdt0(xs,xt),sdtasasdt0(xt,xt))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xt))
| ~ sdtlseqdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xs,xt))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(duplicate_literal_removal,[],[f948]) ).
fof(f1311,plain,
! [X2,X3,X0,X1,X6,X4,X5] : ~ sP1(X0,X1,X2,X3,X4,X5,X6),
inference(forward_subsumption_resolution,[],[f137,f925]) ).
fof(f1312,plain,
! [X2,X3,X0,X1,X4,X5] : ~ sP2(X0,X1,X2,X3,X4,X5),
inference(resolution,[],[f1311,f130]) ).
fof(f1313,plain,
! [X2,X0,X1] : ~ sP3(X0,X1,X2),
inference(resolution,[],[f1312,f123]) ).
fof(f1345,plain,
sz00 = aDimensionOf0(xs),
inference(resolution,[],[f1313,f152]) ).
fof(f1361,plain,
sz00 = aDimensionOf0(xt),
inference(superposition,[],[f1345,f122]) ).
fof(f2169,plain,
( sz00 != aDimensionOf0(xt)
| sz0z00 = sdtasasdt0(xs,xs)
| ~ aVector0(xs) ),
inference(superposition,[],[f613,f122]) ).
fof(f2179,plain,
( sz00 != sz00
| sz0z00 = sdtasasdt0(xt,xt)
| ~ aVector0(xt) ),
inference(superposition,[],[f613,f1361]) ).
fof(f2183,plain,
( sz0z00 = sdtasasdt0(xt,xt)
| ~ aVector0(xt) ),
inference(trivial_inequality_removal,[],[f2179]) ).
fof(f2193,plain,
sz0z00 = sdtasasdt0(xt,xt),
inference(forward_subsumption_resolution,[],[f2183,f119]) ).
fof(f2199,plain,
( sz0z00 = sdtasasdt0(xs,xs)
| ~ aVector0(xs) ),
inference(forward_subsumption_resolution,[],[f2169,f1361]) ).
fof(f2201,plain,
sz0z00 = sdtasasdt0(xs,xs),
inference(forward_subsumption_resolution,[],[f2199,f120]) ).
fof(f2217,plain,
( sdtlseqdt0(sz0z00,sz0z00)
| ~ aVector0(xs) ),
inference(superposition,[],[f167,f2201]) ).
fof(f2218,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(forward_subsumption_resolution,[],[f2217,f120]) ).
fof(f2754,plain,
! [X0] :
( sz00 != aDimensionOf0(X0)
| sz0z00 = sdtasasdt0(xs,X0)
| sz00 != aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(forward_demodulation,[],[f646,f1361]) ).
fof(f2755,plain,
! [X0] :
( sz00 != aDimensionOf0(X0)
| sz0z00 = sdtasasdt0(xs,X0)
| ~ aVector0(X0) ),
inference(duplicate_literal_removal,[],[f2754]) ).
fof(f2767,plain,
( sz00 != sz00
| sz0z00 = sdtasasdt0(xs,xt)
| ~ aVector0(xt) ),
inference(superposition,[],[f2755,f1361]) ).
fof(f2773,plain,
( sz0z00 = sdtasasdt0(xs,xt)
| ~ aVector0(xt) ),
inference(trivial_inequality_removal,[],[f2767]) ).
fof(f2784,plain,
sz0z00 = sdtasasdt0(xs,xt),
inference(forward_subsumption_resolution,[],[f2773,f119]) ).
fof(f2794,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt))
| ~ sdtlseqdt0(sz0z00,sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(superposition,[],[f970,f2784]) ).
fof(f2804,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(forward_subsumption_resolution,[],[f2794,f164]) ).
fof(f2809,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xt,xt))
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(forward_subsumption_resolution,[],[f2804,f198]) ).
fof(f2814,plain,
( ~ sdtlseqdt0(sz0z00,sz0z00)
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(forward_demodulation,[],[f2809,f2193]) ).
fof(f2817,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(forward_subsumption_resolution,[],[f2814,f2218]) ).
fof(f2821,plain,
( ~ sdtlseqdt0(sz0z00,sz0z00)
| ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(forward_demodulation,[],[f2817,f2201]) ).
fof(f2823,plain,
( ~ aScalar0(sdtasasdt0(xs,xs))
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(forward_subsumption_resolution,[],[f2821,f2218]) ).
fof(f2825,plain,
( ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasasdt0(xt,xt)) ),
inference(forward_demodulation,[],[f2823,f2201]) ).
fof(f2826,plain,
~ aScalar0(sdtasasdt0(xt,xt)),
inference(forward_subsumption_resolution,[],[f2825,f198]) ).
fof(f2827,plain,
~ aScalar0(sz0z00),
inference(forward_demodulation,[],[f2826,f2193]) ).
fof(f2828,plain,
$false,
inference(forward_subsumption_resolution,[],[f2827,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG081+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 % Computer : n006.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 23:08:26 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/1.35 % (3436306)Detected formulas, will run a generic FOF schedule.
% 2.92/1.35 % (3436311)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=3409348867:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.92/1.35 % (3436314)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2646017104:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.92/1.35 % (3436312)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=1075817684:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.92/1.35 % (3436316)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4170751771:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.92/1.35 % (3436313)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=3421468356:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.92/1.35 % (3436315)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2782532623:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.92/1.35 % (3436317)dis-21_1_sil=8000:lcm=predicate:random_seed=1589095383: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)
% 2.92/1.35 % (3436315)First to succeed.
% 2.92/1.35 % (3436315)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3436306"
% 2.92/1.35 % (3436317)Instruction limit reached!
% 2.92/1.35 % (3436317)------------------------------
% 2.92/1.35 % (3436317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.35 % (3436317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.35 % (3436317)CaDiCaL version: 2.1.3
% 2.92/1.35 % (3436317)Termination reason: Instruction limit
% 2.92/1.35 % (3436317)Termination phase: Saturation
% 2.92/1.35 % (3436317)Time elapsed: 0.058 s
% 2.92/1.35 % (3436317)Peak memory usage: 89 MB
% 2.92/1.35 % (3436317)Instructions burned: 130 (million)
% 2.92/1.35 % (3436314)Instruction limit reached!
% 2.92/1.35 % (3436314)------------------------------
% 2.92/1.35 % (3436314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.35 % (3436314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.35 % (3436314)CaDiCaL version: 2.1.3
% 2.92/1.35 % (3436314)Termination reason: Instruction limit
% 2.92/1.35 % (3436314)Termination phase: Saturation
% 2.92/1.35 % (3436314)Time elapsed: 0.066 s
% 2.92/1.35 % (3436314)Peak memory usage: 89 MB
% 2.92/1.35 % (3436314)Instructions burned: 109 (million)
% 2.92/1.35 % (3436316)Instruction limit reached!
% 2.92/1.35 % (3436316)------------------------------
% 2.92/1.35 % (3436316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.35 % (3436316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.35 % (3436316)CaDiCaL version: 2.1.3
% 2.92/1.35 % (3436316)Termination reason: Instruction limit
% 2.92/1.35 % (3436316)Termination phase: Saturation
% 2.92/1.35 % (3436316)Time elapsed: 0.085 s
% 2.92/1.35 % (3436316)Peak memory usage: 90 MB
% 2.92/1.35 % (3436316)Instructions burned: 141 (million)
% 2.92/1.35 % (3436325)lrs+10_1_sil=8000:sp=occurrence:random_seed=271515261:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.92/1.35 % (3436326)lrs+10_1_sil=32000:urr=on:br=off:random_seed=432407798:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.92/1.35 % (3436327)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2086439413:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.92/1.35 % (3436325)Also succeeded, but the first one will report.
% 2.92/1.35 % (3436315)Refutation found. Thanks to Tanya!
% 2.92/1.35 % SZS status Theorem for theBenchmark
% 2.92/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.96/1.54 % (3436315)------------------------------
% 3.96/1.54 % (3436315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.54 % (3436315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.54 % (3436315)CaDiCaL version: 2.1.3
% 3.96/1.54 % (3436315)Termination reason: Refutation
% 3.96/1.54 % (3436315)Time elapsed: 0.047 s
% 3.96/1.54 % (3436315)Peak memory usage: 89 MB
% 3.96/1.54 % (3436315)Instructions burned: 79 (million)
% 3.96/1.54 % (3436315)------------------------------
% 3.96/1.54 % (3436315)------------------------------
% 3.96/1.54 % (3436306)Success in time 0.476 s
% 3.96/1.55 % Vampire exiting
%------------------------------------------------------------------------------