TSTP Solution File: RNG081+2 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:57:33 EDT 2024
% Result : Theorem 3.97s 1.11s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f13,axiom,
! [X0] :
( aScalar0(X0)
=> ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(f27,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(f34,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(f35,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( sz00 = aDimensionOf0(X1)
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sz0z00 = sdtasasdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
fof(f38,axiom,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(f40,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(f41,conjecture,
( ( sz00 != aDimensionOf0(xs)
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtasdt0(X10,X12) = X13
& aScalar0(X13) )
& sdtasdt0(X7,X5) = X12
& aScalar0(X12) )
& sdtasdt0(X6,X9) = X11
& aScalar0(X11) )
& sdtasdt0(X4,X8) = X10
& aScalar0(X10) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasdt0(X2,X2) = X7
& aScalar0(X7) )
& sdtasasdt0(X0,X1) = X6
& aScalar0(X6) )
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
& aScalar0(X3) )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xt,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
& sziznziztdt0(xs) = X0
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& aVector0(X0) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ( ( sz00 != aDimensionOf0(xs)
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtasdt0(X10,X12) = X13
& aScalar0(X13) )
& sdtasdt0(X7,X5) = X12
& aScalar0(X12) )
& sdtasdt0(X6,X9) = X11
& aScalar0(X11) )
& sdtasdt0(X4,X8) = X10
& aScalar0(X10) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasdt0(X2,X2) = X7
& aScalar0(X7) )
& sdtasasdt0(X0,X1) = X6
& aScalar0(X6) )
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
& aScalar0(X3) )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xt,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
& sziznziztdt0(xs) = X0
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& aVector0(X0) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(negated_conjecture,[],[f41]) ).
fof(f48,plain,
~ ( ( sz00 != aDimensionOf0(xs)
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtasdt0(X10,X12) = X13
& aScalar0(X13) )
& sdtasdt0(X7,X5) = X12
& aScalar0(X12) )
& sdtasdt0(X6,X9) = X11
& aScalar0(X11) )
& sdtasdt0(X4,X8) = X10
& aScalar0(X10) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasdt0(X2,X2) = X7
& aScalar0(X7) )
& sdtasasdt0(X0,X1) = X6
& aScalar0(X6) )
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
& aScalar0(X3) )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X14] :
( aNaturalNumber0(X14)
=> sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
& sziznziztdt0(xs) = X0
& ! [X15] :
( aNaturalNumber0(X15)
=> sdtlbdtrb0(X0,X15) = sdtlbdtrb0(xs,X15) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& aVector0(X0) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(rectify,[],[f42]) ).
fof(f60,plain,
! [X0] :
( ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtasdt0(X0,sz0z00)
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 )
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f84,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f94,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f95,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f97,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(flattening,[],[f96]) ).
fof(f103,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtasdt0(X10,X12) = X13
& aScalar0(X13) )
& sdtasdt0(X7,X5) = X12
& aScalar0(X12) )
& sdtasdt0(X6,X9) = X11
& aScalar0(X11) )
& sdtasdt0(X4,X8) = X10
& aScalar0(X10) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasdt0(X2,X2) = X7
& aScalar0(X7) )
& sdtasasdt0(X0,X1) = X6
& aScalar0(X6) )
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
& aScalar0(X3) )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X14] :
( sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14)
| ~ aNaturalNumber0(X14) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
& sziznziztdt0(xs) = X0
& ! [X15] :
( sdtlbdtrb0(X0,X15) = sdtlbdtrb0(xs,X15)
| ~ aNaturalNumber0(X15) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& aVector0(X0) )
| sz00 = aDimensionOf0(xs) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f104,plain,
! [X8,X5,X7,X4,X9,X6,X10,X11] :
( ? [X12] :
( ? [X13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtasdt0(X10,X12) = X13
& aScalar0(X13) )
& sdtasdt0(X7,X5) = X12
& aScalar0(X12) )
| ~ sP0(X8,X5,X7,X4,X9,X6,X10,X11) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f105,plain,
! [X6,X4,X7,X5,X8,X3,X2] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( sP0(X8,X5,X7,X4,X9,X6,X10,X11)
& sdtasdt0(X6,X9) = X11
& aScalar0(X11) )
& sdtasdt0(X4,X8) = X10
& aScalar0(X10) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) )
| ~ sP1(X6,X4,X7,X5,X8,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f106,plain,
! [X2,X3,X5,X4,X1,X0] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( sP1(X6,X4,X7,X5,X8,X3,X2)
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasdt0(X2,X2) = X7
& aScalar0(X7) )
& sdtasasdt0(X0,X1) = X6
& aScalar0(X6) )
| ~ sP2(X2,X3,X5,X4,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sP2(X2,X3,X5,X4,X1,X0)
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
& aScalar0(X3) )
| ~ sP3(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f108,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( sP3(X0,X1,X2)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X14] :
( sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14)
| ~ aNaturalNumber0(X14) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
| ~ sP4(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f109,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ? [X0] :
( sP4(X0)
& sziznziztdt0(xs) = X0
& ! [X15] :
( sdtlbdtrb0(X0,X15) = sdtlbdtrb0(xs,X15)
| ~ aNaturalNumber0(X15) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& aVector0(X0) )
| sz00 = aDimensionOf0(xs) ) ),
inference(definition_folding,[],[f103,f108,f107,f106,f105,f104]) ).
fof(f117,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( sP3(X0,X1,X2)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X14] :
( sdtlbdtrb0(X1,X14) = sdtlbdtrb0(xt,X14)
| ~ aNaturalNumber0(X14) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f108]) ).
fof(f118,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( sP3(X0,X1,X2)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X3] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(xt,X3)
| ~ aNaturalNumber0(X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
| ~ sP4(X0) ),
inference(rectify,[],[f117]) ).
fof(f119,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( sP3(X0,X1,X2)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = X1
& ! [X3] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(xt,X3)
| ~ aNaturalNumber0(X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& aVector0(X1) )
=> ( ? [X2] :
( sP3(X0,sK7(X0),X2)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& sziznziztdt0(xt) = sK7(X0)
& ! [X3] :
( sdtlbdtrb0(xt,X3) = sdtlbdtrb0(sK7(X0),X3)
| ~ aNaturalNumber0(X3) )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sK7(X0)))
& aVector0(sK7(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X0] :
( ? [X2] :
( sP3(X0,sK7(X0),X2)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
=> ( sP3(X0,sK7(X0),sK8(X0))
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK8(X0)
& aScalar0(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0] :
( ( sP3(X0,sK7(X0),sK8(X0))
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK8(X0)
& aScalar0(sK8(X0))
& sziznziztdt0(xt) = sK7(X0)
& ! [X3] :
( sdtlbdtrb0(xt,X3) = sdtlbdtrb0(sK7(X0),X3)
| ~ aNaturalNumber0(X3) )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sK7(X0)))
& aVector0(sK7(X0)) )
| ~ sP4(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f118,f120,f119]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sP2(X2,X3,X5,X4,X1,X0)
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
& aScalar0(X3) )
| ~ sP3(X0,X1,X2) ),
inference(nnf_transformation,[],[f107]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sP2(X2,X3,X5,X4,X1,X0)
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3
& aScalar0(X3) )
=> ( ? [X4] :
( ? [X5] :
( sP2(X2,sK9(X0,X1,X2),X5,X4,X1,X0)
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK9(X0,X1,X2)
& aScalar0(sK9(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ? [X4] :
( ? [X5] :
( sP2(X2,sK9(X0,X1,X2),X5,X4,X1,X0)
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = X4
& aScalar0(X4) )
=> ( ? [X5] :
( sP2(X2,sK9(X0,X1,X2),X5,sK10(X0,X1,X2),X1,X0)
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
& sdtasasdt0(X0,X0) = sK10(X0,X1,X2)
& aScalar0(sK10(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ? [X5] :
( sP2(X2,sK9(X0,X1,X2),X5,sK10(X0,X1,X2),X1,X0)
& sdtasasdt0(X1,X1) = X5
& aScalar0(X5) )
=> ( sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0)
& sdtasasdt0(X1,X1) = sK11(X0,X1,X2)
& aScalar0(sK11(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ( sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0)
& sdtasasdt0(X1,X1) = sK11(X0,X1,X2)
& aScalar0(sK11(X0,X1,X2))
& sdtasasdt0(X0,X0) = sK10(X0,X1,X2)
& aScalar0(sK10(X0,X1,X2))
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK9(X0,X1,X2)
& aScalar0(sK9(X0,X1,X2)) )
| ~ sP3(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f122,f125,f124,f123]) ).
fof(f127,plain,
! [X2,X3,X5,X4,X1,X0] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( sP1(X6,X4,X7,X5,X8,X3,X2)
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasdt0(X2,X2) = X7
& aScalar0(X7) )
& sdtasasdt0(X0,X1) = X6
& aScalar0(X6) )
| ~ sP2(X2,X3,X5,X4,X1,X0) ),
inference(nnf_transformation,[],[f106]) ).
fof(f128,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( sP1(X6,X3,X7,X2,X8,X1,X0)
& sdtasdt0(X1,X1) = X8
& aScalar0(X8) )
& sdtasdt0(X0,X0) = X7
& aScalar0(X7) )
& sdtasasdt0(X5,X4) = X6
& aScalar0(X6) )
| ~ sP2(X0,X1,X2,X3,X4,X5) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( sP1(X6,X3,X7,X2,X8,X1,X0)
& sdtasdt0(X1,X1) = X8
& aScalar0(X8) )
& sdtasdt0(X0,X0) = X7
& aScalar0(X7) )
& sdtasasdt0(X5,X4) = X6
& aScalar0(X6) )
=> ( ? [X7] :
( ? [X8] :
( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,X7,X2,X8,X1,X0)
& sdtasdt0(X1,X1) = X8
& aScalar0(X8) )
& sdtasdt0(X0,X0) = X7
& aScalar0(X7) )
& sdtasasdt0(X5,X4) = sK12(X0,X1,X2,X3,X4,X5)
& aScalar0(sK12(X0,X1,X2,X3,X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X7] :
( ? [X8] :
( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,X7,X2,X8,X1,X0)
& sdtasdt0(X1,X1) = X8
& aScalar0(X8) )
& sdtasdt0(X0,X0) = X7
& aScalar0(X7) )
=> ( ? [X8] :
( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,X8,X1,X0)
& sdtasdt0(X1,X1) = X8
& aScalar0(X8) )
& sdtasdt0(X0,X0) = sK13(X0,X1,X2,X3,X4,X5)
& aScalar0(sK13(X0,X1,X2,X3,X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X8] :
( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,X8,X1,X0)
& sdtasdt0(X1,X1) = X8
& aScalar0(X8) )
=> ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0)
& sdtasdt0(X1,X1) = sK14(X0,X1,X2,X3,X4,X5)
& aScalar0(sK14(X0,X1,X2,X3,X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0)
& sdtasdt0(X1,X1) = sK14(X0,X1,X2,X3,X4,X5)
& aScalar0(sK14(X0,X1,X2,X3,X4,X5))
& sdtasdt0(X0,X0) = sK13(X0,X1,X2,X3,X4,X5)
& aScalar0(sK13(X0,X1,X2,X3,X4,X5))
& sdtasasdt0(X5,X4) = sK12(X0,X1,X2,X3,X4,X5)
& aScalar0(sK12(X0,X1,X2,X3,X4,X5)) )
| ~ sP2(X0,X1,X2,X3,X4,X5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f128,f131,f130,f129]) ).
fof(f133,plain,
! [X6,X4,X7,X5,X8,X3,X2] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( sP0(X8,X5,X7,X4,X9,X6,X10,X11)
& sdtasdt0(X6,X9) = X11
& aScalar0(X11) )
& sdtasdt0(X4,X8) = X10
& aScalar0(X10) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) )
| ~ sP1(X6,X4,X7,X5,X8,X3,X2) ),
inference(nnf_transformation,[],[f105]) ).
fof(f134,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( sP0(X4,X3,X2,X1,X7,X0,X8,X9)
& sdtasdt0(X0,X7) = X9
& aScalar0(X9) )
& sdtasdt0(X1,X4) = X8
& aScalar0(X8) )
& sdtasdt0(X6,X5) = X7
& aScalar0(X7) )
| ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( sP0(X4,X3,X2,X1,X7,X0,X8,X9)
& sdtasdt0(X0,X7) = X9
& aScalar0(X9) )
& sdtasdt0(X1,X4) = X8
& aScalar0(X8) )
& sdtasdt0(X6,X5) = X7
& aScalar0(X7) )
=> ( ? [X8] :
( ? [X9] :
( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,X8,X9)
& sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
& aScalar0(X9) )
& sdtasdt0(X1,X4) = X8
& aScalar0(X8) )
& sdtasdt0(X6,X5) = sK15(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK15(X0,X1,X2,X3,X4,X5,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X8] :
( ? [X9] :
( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,X8,X9)
& sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
& aScalar0(X9) )
& sdtasdt0(X1,X4) = X8
& aScalar0(X8) )
=> ( ? [X9] :
( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),X9)
& sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
& aScalar0(X9) )
& sdtasdt0(X1,X4) = sK16(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK16(X0,X1,X2,X3,X4,X5,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ? [X9] :
( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),X9)
& sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = X9
& aScalar0(X9) )
=> ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = sK17(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK17(X0,X1,X2,X3,X4,X5,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X0,sK15(X0,X1,X2,X3,X4,X5,X6)) = sK17(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK17(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X1,X4) = sK16(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK16(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X6,X5) = sK15(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK15(X0,X1,X2,X3,X4,X5,X6)) )
| ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f134,f137,f136,f135]) ).
fof(f139,plain,
! [X8,X5,X7,X4,X9,X6,X10,X11] :
( ? [X12] :
( ? [X13] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtasdt0(X10,X12) = X13
& aScalar0(X13) )
& sdtasdt0(X7,X5) = X12
& aScalar0(X12) )
| ~ sP0(X8,X5,X7,X4,X9,X6,X10,X11) ),
inference(nnf_transformation,[],[f104]) ).
fof(f140,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ? [X8] :
( ? [X9] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
& sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,X8))
& sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
& sdtasdt0(X6,X8) = X9
& aScalar0(X9) )
& sdtasdt0(X2,X1) = X8
& aScalar0(X8) )
| ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(rectify,[],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ? [X8] :
( ? [X9] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
& sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,X8))
& sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
& sdtasdt0(X6,X8) = X9
& aScalar0(X9) )
& sdtasdt0(X2,X1) = X8
& aScalar0(X8) )
=> ( ? [X9] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
& sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
& sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
& sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = X9
& aScalar0(X9) )
& sdtasdt0(X2,X1) = sK18(X0,X1,X2,X3,X4,X5,X6,X7)
& aScalar0(sK18(X0,X1,X2,X3,X4,X5,X6,X7)) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ? [X9] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
& sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
& sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
& sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = X9
& aScalar0(X9) )
=> ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
& sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
& sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
& sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7)
& aScalar0(sK19(X0,X1,X2,X3,X4,X5,X6,X7)) ) ),
introduced(choice_axiom,[]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X5,X4),sdtpldt0(X5,X4)),sdtasdt0(sdtpldt0(X3,X2),sdtpldt0(X1,X0)))
& sdtlseqdt0(sdtpldt0(X7,X7),sdtpldt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)))
& sdtlseqdt0(sdtasdt0(X5,X5),sdtasdt0(X3,X1))
& sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7)
& aScalar0(sK19(X0,X1,X2,X3,X4,X5,X6,X7))
& sdtasdt0(X2,X1) = sK18(X0,X1,X2,X3,X4,X5,X6,X7)
& aScalar0(sK18(X0,X1,X2,X3,X4,X5,X6,X7)) )
| ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f140,f142,f141]) ).
fof(f144,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ? [X0] :
( sP4(X0)
& sziznziztdt0(xs) = X0
& ! [X1] :
( sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1)
| ~ aNaturalNumber0(X1) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& aVector0(X0) )
| sz00 = aDimensionOf0(xs) ) ),
inference(rectify,[],[f109]) ).
fof(f145,plain,
( ? [X0] :
( sP4(X0)
& sziznziztdt0(xs) = X0
& ! [X1] :
( sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1)
| ~ aNaturalNumber0(X1) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& aVector0(X0) )
=> ( sP4(sK20)
& sziznziztdt0(xs) = sK20
& ! [X1] :
( sdtlbdtrb0(xs,X1) = sdtlbdtrb0(sK20,X1)
| ~ aNaturalNumber0(X1) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sK20))
& aVector0(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f146,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ( sP4(sK20)
& sziznziztdt0(xs) = sK20
& ! [X1] :
( sdtlbdtrb0(xs,X1) = sdtlbdtrb0(sK20,X1)
| ~ aNaturalNumber0(X1) )
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sK20))
& aVector0(sK20) )
| sz00 = aDimensionOf0(xs) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f144,f145]) ).
fof(f154,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f161,plain,
! [X0] :
( sz0z00 = sdtasdt0(sz0z00,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f184,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f194,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f195,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f198,plain,
aVector0(xs),
inference(cnf_transformation,[],[f38]) ).
fof(f199,plain,
aVector0(xt),
inference(cnf_transformation,[],[f38]) ).
fof(f201,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f40]) ).
fof(f208,plain,
! [X0] :
( sP3(X0,sK7(X0),sK8(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f215,plain,
! [X2,X0,X1] :
( sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f126]) ).
fof(f222,plain,
! [X2,X3,X0,X1,X4,X5] :
( sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0)
| ~ sP2(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f132]) ).
fof(f229,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6))
| ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[],[f138]) ).
fof(f233,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7)
| ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f143]) ).
fof(f237,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,[],[f143]) ).
fof(f242,plain,
( sP4(sK20)
| sz00 = aDimensionOf0(xs) ),
inference(cnf_transformation,[],[f146]) ).
fof(f243,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cnf_transformation,[],[f146]) ).
cnf(c_56,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f154]) ).
cnf(c_64,plain,
( ~ aScalar0(X0)
| sdtasdt0(sz0z00,X0) = sz0z00 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_86,plain,
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_96,plain,
( aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_97,plain,
( aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(X1) != sz00
| ~ aVector0(X0)
| ~ aVector0(X1)
| sdtasasdt0(X0,X1) = sz0z00 ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_100,plain,
aVector0(xt),
inference(cnf_transformation,[],[f199]) ).
cnf(c_101,plain,
aVector0(xs),
inference(cnf_transformation,[],[f198]) ).
cnf(c_103,plain,
aDimensionOf0(xt) = aDimensionOf0(xs),
inference(cnf_transformation,[],[f201]) ).
cnf(c_104,plain,
( ~ sP4(X0)
| sP3(X0,sK7(X0),sK8(X0)) ),
inference(cnf_transformation,[],[f208]) ).
cnf(c_111,plain,
( ~ sP3(X0,X1,X2)
| sP2(X2,sK9(X0,X1,X2),sK11(X0,X1,X2),sK10(X0,X1,X2),X1,X0) ),
inference(cnf_transformation,[],[f215]) ).
cnf(c_118,plain,
( ~ sP2(X0,X1,X2,X3,X4,X5)
| sP1(sK12(X0,X1,X2,X3,X4,X5),X3,sK13(X0,X1,X2,X3,X4,X5),X2,sK14(X0,X1,X2,X3,X4,X5),X1,X0) ),
inference(cnf_transformation,[],[f222]) ).
cnf(c_125,plain,
( ~ sP1(X0,X1,X2,X3,X4,X5,X6)
| sP0(X4,X3,X2,X1,sK15(X0,X1,X2,X3,X4,X5,X6),X0,sK16(X0,X1,X2,X3,X4,X5,X6),sK17(X0,X1,X2,X3,X4,X5,X6)) ),
inference(cnf_transformation,[],[f229]) ).
cnf(c_132,plain,
( ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7)
| sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(cnf_transformation,[],[f237]) ).
cnf(c_136,plain,
( ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7)
| sdtasdt0(X6,sK18(X0,X1,X2,X3,X4,X5,X6,X7)) = sK19(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f233]) ).
cnf(c_140,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cnf_transformation,[],[f243]) ).
cnf(c_141,negated_conjecture,
( aDimensionOf0(xs) = sz00
| sP4(sK20) ),
inference(cnf_transformation,[],[f242]) ).
cnf(c_246,plain,
~ sP0(X0,X1,X2,X3,X4,X5,X6,X7),
inference(global_subsumption_just,[status(thm)],[c_136,c_140,c_132]) ).
cnf(c_262,plain,
~ sP1(X0,X1,X2,X3,X4,X5,X6),
inference(backward_subsumption_resolution,[status(thm)],[c_125,c_246]) ).
cnf(c_266,plain,
~ sP2(X0,X1,X2,X3,X4,X5),
inference(backward_subsumption_resolution,[status(thm)],[c_118,c_262]) ).
cnf(c_270,plain,
~ sP3(X0,X1,X2),
inference(backward_subsumption_resolution,[status(thm)],[c_111,c_266]) ).
cnf(c_274,plain,
~ sP4(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_104,c_270]) ).
cnf(c_278,plain,
aDimensionOf0(xs) = sz00,
inference(backward_subsumption_resolution,[status(thm)],[c_141,c_274]) ).
cnf(c_641,plain,
aDimensionOf0(xt) = sz00,
inference(light_normalisation,[status(thm)],[c_103,c_278]) ).
cnf(c_1782,plain,
sdtasasdt0(xs,xt) = sP3_iProver_def,
definition ).
cnf(c_1783,plain,
sdtasdt0(sP3_iProver_def,sP3_iProver_def) = sP4_iProver_def,
definition ).
cnf(c_1784,plain,
sdtasasdt0(xs,xs) = sP5_iProver_def,
definition ).
cnf(c_1785,plain,
sdtasasdt0(xt,xt) = sP6_iProver_def,
definition ).
cnf(c_1786,plain,
sdtasdt0(sP5_iProver_def,sP6_iProver_def) = sP7_iProver_def,
definition ).
cnf(c_1787,negated_conjecture,
~ sdtlseqdt0(sP4_iProver_def,sP7_iProver_def),
inference(demodulation,[status(thm)],[c_140,c_1785,c_1784,c_1786,c_1782,c_1783]) ).
cnf(c_2885,plain,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_64]) ).
cnf(c_2890,plain,
( ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(superposition,[status(thm)],[c_2885,c_86]) ).
cnf(c_2891,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(forward_subsumption_resolution,[status(thm)],[c_2890,c_56]) ).
cnf(c_3789,plain,
( aDimensionOf0(X0) != sz00
| ~ aVector0(X0)
| ~ aVector0(xs)
| aScalar0(sdtasasdt0(xs,X0)) ),
inference(superposition,[status(thm)],[c_278,c_96]) ).
cnf(c_3793,plain,
( ~ aVector0(X0)
| aScalar0(sdtasasdt0(X0,X0)) ),
inference(equality_resolution,[status(thm)],[c_96]) ).
cnf(c_3808,plain,
( aDimensionOf0(X0) != sz00
| ~ aVector0(X0)
| aScalar0(sdtasasdt0(xs,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3789,c_101]) ).
cnf(c_3881,plain,
( ~ aVector0(xt)
| aScalar0(sP6_iProver_def) ),
inference(superposition,[status(thm)],[c_1785,c_3793]) ).
cnf(c_3906,plain,
aScalar0(sP6_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_3881,c_100]) ).
cnf(c_4040,plain,
sdtasdt0(sz0z00,sP6_iProver_def) = sz0z00,
inference(superposition,[status(thm)],[c_3906,c_64]) ).
cnf(c_4362,plain,
( ~ aVector0(xt)
| aScalar0(sdtasasdt0(xs,xt)) ),
inference(superposition,[status(thm)],[c_641,c_3808]) ).
cnf(c_4363,plain,
( ~ aVector0(xt)
| aScalar0(sP3_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_4362,c_1782]) ).
cnf(c_4364,plain,
aScalar0(sP3_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_4363,c_100]) ).
cnf(c_4773,plain,
sdtasdt0(sz0z00,sP3_iProver_def) = sz0z00,
inference(superposition,[status(thm)],[c_4364,c_64]) ).
cnf(c_5511,plain,
( aDimensionOf0(X0) != sz00
| ~ aVector0(X0)
| ~ aVector0(xs)
| sdtasasdt0(xs,X0) = sz0z00 ),
inference(superposition,[status(thm)],[c_278,c_97]) ).
cnf(c_5513,plain,
( aDimensionOf0(X0) != sz00
| aDimensionOf0(xs) != sz00
| ~ aVector0(X0)
| ~ aVector0(xs)
| sdtasasdt0(X0,xs) = sz0z00 ),
inference(superposition,[status(thm)],[c_278,c_97]) ).
cnf(c_5523,plain,
( aDimensionOf0(X0) != sz00
| ~ aVector0(X0)
| sdtasasdt0(xs,X0) = sz0z00 ),
inference(forward_subsumption_resolution,[status(thm)],[c_5511,c_101]) ).
cnf(c_5531,plain,
( aDimensionOf0(X0) != sz00
| ~ aVector0(X0)
| sdtasasdt0(X0,xs) = sz0z00 ),
inference(forward_subsumption_resolution,[status(thm)],[c_5513,c_101,c_278]) ).
cnf(c_5746,plain,
( ~ aVector0(xs)
| sdtasasdt0(xs,xs) = sz0z00 ),
inference(superposition,[status(thm)],[c_278,c_5531]) ).
cnf(c_5749,plain,
( ~ aVector0(xs)
| sz0z00 = sP5_iProver_def ),
inference(light_normalisation,[status(thm)],[c_5746,c_1784]) ).
cnf(c_5750,plain,
sz0z00 = sP5_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_5749,c_101]) ).
cnf(c_5768,plain,
sdtasdt0(sP5_iProver_def,sP6_iProver_def) = sP5_iProver_def,
inference(demodulation,[status(thm)],[c_4040,c_5750]) ).
cnf(c_5853,plain,
sP5_iProver_def = sP7_iProver_def,
inference(light_normalisation,[status(thm)],[c_5768,c_1786]) ).
cnf(c_5857,plain,
~ sdtlseqdt0(sP4_iProver_def,sP5_iProver_def),
inference(demodulation,[status(thm)],[c_1787,c_5853]) ).
cnf(c_5898,plain,
( aDimensionOf0(X0) != sz00
| ~ aVector0(X0)
| sdtasasdt0(xs,X0) = sP5_iProver_def ),
inference(light_normalisation,[status(thm)],[c_5523,c_5750]) ).
cnf(c_5906,plain,
( ~ aVector0(xt)
| sdtasasdt0(xs,xt) = sP5_iProver_def ),
inference(superposition,[status(thm)],[c_641,c_5898]) ).
cnf(c_5907,plain,
( ~ aVector0(xt)
| sP3_iProver_def = sP5_iProver_def ),
inference(light_normalisation,[status(thm)],[c_5906,c_1782]) ).
cnf(c_5908,plain,
sP3_iProver_def = sP5_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_5907,c_100]) ).
cnf(c_5910,plain,
~ sdtlseqdt0(sP4_iProver_def,sP3_iProver_def),
inference(demodulation,[status(thm)],[c_5857,c_5908]) ).
cnf(c_5963,plain,
sz0z00 = sP3_iProver_def,
inference(light_normalisation,[status(thm)],[c_5750,c_5908]) ).
cnf(c_6175,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_5963,c_5910,c_4773,c_2891,c_1783]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : RNG081+2 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu May 2 21:42:51 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.97/1.11 % SZS status Started for theBenchmark.p
% 3.97/1.11 % SZS status Theorem for theBenchmark.p
% 3.97/1.11
% 3.97/1.11 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.97/1.11
% 3.97/1.11 ------ iProver source info
% 3.97/1.11
% 3.97/1.11 git: date: 2024-05-02 19:28:25 +0000
% 3.97/1.11 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.97/1.11 git: non_committed_changes: false
% 3.97/1.11
% 3.97/1.11 ------ Parsing...
% 3.97/1.11 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.97/1.11
% 3.97/1.11 ------ Preprocessing... sup_sim: 2 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.97/1.11
% 3.97/1.11 ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.97/1.11
% 3.97/1.11 ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 3.97/1.11 ------ Proving...
% 3.97/1.11 ------ Problem Properties
% 3.97/1.11
% 3.97/1.11
% 3.97/1.11 clauses 64
% 3.97/1.11 conjectures 1
% 3.97/1.11 EPR 12
% 3.97/1.11 Horn 52
% 3.97/1.11 unary 13
% 3.97/1.11 binary 17
% 3.97/1.11 lits 196
% 3.97/1.11 lits eq 58
% 3.97/1.11 fd_pure 0
% 3.97/1.11 fd_pseudo 0
% 3.97/1.11 fd_cond 1
% 3.97/1.11 fd_pseudo_cond 5
% 3.97/1.11 AC symbols 0
% 3.97/1.11
% 3.97/1.11 ------ Schedule dynamic 5 is on
% 3.97/1.11
% 3.97/1.11 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.97/1.11
% 3.97/1.11
% 3.97/1.11 ------
% 3.97/1.11 Current options:
% 3.97/1.11 ------
% 3.97/1.11
% 3.97/1.11
% 3.97/1.11
% 3.97/1.11
% 3.97/1.11 ------ Proving...
% 3.97/1.11
% 3.97/1.11
% 3.97/1.11 % SZS status Theorem for theBenchmark.p
% 3.97/1.11
% 3.97/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/1.11
% 3.97/1.12
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