%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG081+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 : Fri Sep 25 02:38:46 PM UTC 2026
% Result : Theorem 1.64s 1.49s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 47
% Syntax : Number of formulae : 867 ( 134 unt; 11 def)
% Number of atoms : 4518 (1417 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 4154 (1644 ~;2152 |; 305 &)
% ( 3 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 11 prp; 0-8 aty)
% Number of functors : 28 ( 28 usr; 7 con; 0-8 aty)
% Number of variables : 1373 ( 0 sgn1292 !; 81 ?; 873 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
fof(f3,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( szszuzczcdt0(X0) != sz00
& aNaturalNumber0(szszuzczcdt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
fof(f4,axiom,
! [X0] :
( ( X0 != sz00
& aNaturalNumber0(X0) )
=> ? [X1] :
( X0 = szszuzczcdt0(X1)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
fof(f7,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f10,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f12,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(f13,axiom,
! [X0] :
( aScalar0(X0)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(X0)) = X0
& sdtpldt0(smndt0(X0),X0) = sz0z00
& sdtpldt0(X0,smndt0(X0)) = sz0z00
& sdtasdt0(sz0z00,X0) = sz0z00
& sdtasdt0(X0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).
fof(f16,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> 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/sandbox/benchmark/theBenchmark.p',mDistr2) ).
fof(f17,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1))
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).
fof(f18,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> sdtasdt0(smndt0(X0),smndt0(X1)) = sdtasdt0(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).
fof(f20,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
fof(f21,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMon) ).
fof(f24,axiom,
! [X0,X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
fof(f25,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
fof(f26,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X0) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).
fof(f27,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
fof(f28,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtasdt0(X0,X0) = sdtasdt0(X1,X1)
& sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aVector0(X0) )
=> aScalar0(sdtlbdtrb0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
fof(f32,axiom,
! [X0] :
( aVector0(X0)
=> ( aDimensionOf0(X0) != sz00
=> ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInit) ).
fof(f33,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) != sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEqInit) ).
fof(f34,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
fof(f35,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) = sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sdtasasdt0(X0,X1) = sz0z00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).
fof(f36,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) != sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPN) ).
fof(f37,axiom,
! [X0] :
( aVector0(X0)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
fof(f38,axiom,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
fof(f39,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> ( iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1652) ).
fof(f40,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
fof(f41,conjecture,
( ( aDimensionOf0(xs) != sz00
=> ? [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))
& X13 = sdtasdt0(X10,X12)
& aScalar0(X13) )
& X12 = sdtasdt0(X7,X5)
& aScalar0(X12) )
& X11 = sdtasdt0(X6,X9)
& aScalar0(X11) )
& X10 = sdtasdt0(X4,X8)
& aScalar0(X10) )
& X9 = sdtasdt0(X2,X3)
& aScalar0(X9) )
& X8 = sdtasdt0(X3,X3)
& aScalar0(X8) )
& X7 = sdtasdt0(X2,X2)
& aScalar0(X7) )
& X6 = sdtasasdt0(X0,X1)
& aScalar0(X6) )
& X5 = sdtasasdt0(X1,X1)
& aScalar0(X5) )
& X4 = sdtasasdt0(X0,X0)
& aScalar0(X4) )
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(X3) )
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(X2) )
& X1 = sziznziztdt0(xt)
& aVector0(X1) )
& X0 = sziznziztdt0(xs)
& aVector0(X0) ) )
=> 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] :
( ? [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))
& X13 = sdtasdt0(X10,X12)
& aScalar0(X13) )
& X12 = sdtasdt0(X7,X5)
& aScalar0(X12) )
& X11 = sdtasdt0(X6,X9)
& aScalar0(X11) )
& X10 = sdtasdt0(X4,X8)
& aScalar0(X10) )
& X9 = sdtasdt0(X2,X3)
& aScalar0(X9) )
& X8 = sdtasdt0(X3,X3)
& aScalar0(X8) )
& X7 = sdtasdt0(X2,X2)
& aScalar0(X7) )
& X6 = sdtasasdt0(X0,X1)
& aScalar0(X6) )
& X5 = sdtasasdt0(X1,X1)
& aScalar0(X5) )
& X4 = sdtasasdt0(X0,X0)
& aScalar0(X4) )
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(X3) )
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(X2) )
& X1 = sziznziztdt0(xt)
& aVector0(X1) )
& X0 = sziznziztdt0(xs)
& aVector0(X0) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f48,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != sz00
& aNaturalNumber0(szszuzczcdt0(X0)) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f49,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aNaturalNumber0(X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aNaturalNumber0(X1) ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ aScalar0(X0)
| aScalar0(smndt0(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f59,plain,
! [X0] :
( ~ aScalar0(X0)
| ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(X0)) = X0
& sdtpldt0(smndt0(X0),X0) = sz0z00
& sdtpldt0(X0,smndt0(X0)) = sz0z00
& sdtasdt0(sz0z00,X0) = sz0z00
& sdtasdt0(X0,sz0z00) = sz0z00
& sdtpldt0(sz0z00,X0) = X0
& sdtpldt0(X0,sz0z00) = X0 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
inference(ennf_transformation,[],[f16]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1))
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1))
& sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(smndt0(X0),smndt0(X1)) = sdtasdt0(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(smndt0(X0),smndt0(X1)) = sdtasdt0(X0,X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(X0,X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f72,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f28]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f88,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f90,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) ) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f92,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sz0z00 ),
inference(ennf_transformation,[],[f35]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sz0z00 ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ),
inference(ennf_transformation,[],[f36]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ~ aVector0(X0)
| sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1))) ),
inference(ennf_transformation,[],[f39]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1))) ),
inference(flattening,[],[f100]) ).
fof(f102,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))
& X13 = sdtasdt0(X10,X12)
& aScalar0(X13) )
& X12 = sdtasdt0(X7,X5)
& aScalar0(X12) )
& X11 = sdtasdt0(X6,X9)
& aScalar0(X11) )
& X10 = sdtasdt0(X4,X8)
& aScalar0(X10) )
& X9 = sdtasdt0(X2,X3)
& aScalar0(X9) )
& X8 = sdtasdt0(X3,X3)
& aScalar0(X8) )
& X7 = sdtasdt0(X2,X2)
& aScalar0(X7) )
& X6 = sdtasasdt0(X0,X1)
& aScalar0(X6) )
& X5 = sdtasasdt0(X1,X1)
& aScalar0(X5) )
& X4 = sdtasasdt0(X0,X0)
& aScalar0(X4) )
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(X3) )
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(X2) )
& X1 = sziznziztdt0(xt)
& aVector0(X1) )
& X0 = sziznziztdt0(xs)
& aVector0(X0) ) )
& ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(ennf_transformation,[],[f42]) ).
fof(f108,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(sK4(X0)) = X0
& aNaturalNumber0(sK4(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f50]) ).
fof(f109,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(nnf_transformation,[],[f90]) ).
fof(f110,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ! [X1] :
( ( sziznziztdt0(X0) != X1
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) )
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& aVector0(X1) ) )
& ( ( aNaturalNumber0(sK5(X0,X1))
& sdtlbdtrb0(X1,sK5(X0,X1)) != sdtlbdtrb0(X0,sK5(X0,X1)) )
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| X1 = sziznziztdt0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f111]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ sP3(X0,X1,X2)
| ? [X3] :
( ? [X4] :
( ? [X5] :
( sP2(X1,X0,X2,X3,X5,X4)
& X5 = sdtasasdt0(X1,X1)
& aScalar0(X5) )
& X4 = sdtasasdt0(X0,X0)
& aScalar0(X4) )
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(X3) ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ sP3(X0,X1,X2)
| ( sP2(X1,X0,X2,sK6(X0,X1,X2),sK8(X0,X1,X2),sK7(X0,X1,X2))
& sdtasasdt0(X1,X1) = sK8(X0,X1,X2)
& aScalar0(sK8(X0,X1,X2))
& sdtasasdt0(X0,X0) = sK7(X0,X1,X2)
& aScalar0(sK7(X0,X1,X2))
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK6(X0,X1,X2)
& aScalar0(sK6(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6(X0,X1,X2)),skolemize(X4,sK7(X0,X1,X2)),skolemize(X5,sK8(X0,X1,X2))],[f113]) ).
fof(f115,plain,
! [X1,X0,X2,X3,X5,X4] :
( ~ sP2(X1,X0,X2,X3,X5,X4)
| ? [X6] :
( ? [X7] :
( ? [X8] :
( sP1(X3,X2,X8,X4,X6,X7,X5)
& X8 = sdtasdt0(X3,X3)
& aScalar0(X8) )
& X7 = sdtasdt0(X2,X2)
& aScalar0(X7) )
& X6 = sdtasasdt0(X0,X1)
& aScalar0(X6) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f116,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP2(X0,X1,X2,X3,X4,X5)
| ? [X6] :
( ? [X7] :
( ? [X8] :
( sP1(X3,X2,X8,X5,X6,X7,X4)
& X8 = sdtasdt0(X3,X3)
& aScalar0(X8) )
& X7 = sdtasdt0(X2,X2)
& aScalar0(X7) )
& sdtasasdt0(X1,X0) = X6
& aScalar0(X6) ) ),
inference(rectify,[],[f115]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP2(X0,X1,X2,X3,X4,X5)
| ( sP1(X3,X2,sK11(X0,X1,X2,X3,X4,X5),X5,sK9(X0,X1,X2,X3,X4,X5),sK10(X0,X1,X2,X3,X4,X5),X4)
& sdtasdt0(X3,X3) = sK11(X0,X1,X2,X3,X4,X5)
& aScalar0(sK11(X0,X1,X2,X3,X4,X5))
& sdtasdt0(X2,X2) = sK10(X0,X1,X2,X3,X4,X5)
& aScalar0(sK10(X0,X1,X2,X3,X4,X5))
& sdtasasdt0(X1,X0) = sK9(X0,X1,X2,X3,X4,X5)
& aScalar0(sK9(X0,X1,X2,X3,X4,X5)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X6,sK9(X0,X1,X2,X3,X4,X5)),skolemize(X7,sK10(X0,X1,X2,X3,X4,X5)),skolemize(X8,sK11(X0,X1,X2,X3,X4,X5))],[f116]) ).
fof(f118,plain,
! [X3,X2,X8,X4,X6,X7,X5] :
( ~ sP1(X3,X2,X8,X4,X6,X7,X5)
| ? [X9] :
( ? [X10] :
( ? [X11] :
( sP0(X5,X7,X10,X4,X6,X11,X8,X9)
& X11 = sdtasdt0(X6,X9)
& aScalar0(X11) )
& X10 = sdtasdt0(X4,X8)
& aScalar0(X10) )
& X9 = sdtasdt0(X2,X3)
& aScalar0(X9) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sP1(X0,X1,X2,X3,X4,X5,X6)
| ? [X7] :
( ? [X8] :
( ? [X9] :
( sP0(X6,X5,X8,X3,X4,X9,X2,X7)
& sdtasdt0(X4,X7) = X9
& aScalar0(X9) )
& sdtasdt0(X3,X2) = X8
& aScalar0(X8) )
& sdtasdt0(X1,X0) = X7
& aScalar0(X7) ) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sP1(X0,X1,X2,X3,X4,X5,X6)
| ( sP0(X6,X5,sK13(X0,X1,X2,X3,X4,X5,X6),X3,X4,sK14(X0,X1,X2,X3,X4,X5,X6),X2,sK12(X0,X1,X2,X3,X4,X5,X6))
& sK14(X0,X1,X2,X3,X4,X5,X6) = sdtasdt0(X4,sK12(X0,X1,X2,X3,X4,X5,X6))
& aScalar0(sK14(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X3,X2) = sK13(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK13(X0,X1,X2,X3,X4,X5,X6))
& sdtasdt0(X1,X0) = sK12(X0,X1,X2,X3,X4,X5,X6)
& aScalar0(sK12(X0,X1,X2,X3,X4,X5,X6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X7,sK12(X0,X1,X2,X3,X4,X5,X6)),skolemize(X8,sK13(X0,X1,X2,X3,X4,X5,X6)),skolemize(X9,sK14(X0,X1,X2,X3,X4,X5,X6))],[f119]) ).
fof(f124,plain,
( ( sz00 = aDimensionOf0(xs)
| ( sP3(sK17,sK18,sK19)
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK19
& aScalar0(sK19)
& sziznziztdt0(xt) = sK18
& aVector0(sK18)
& sziznziztdt0(xs) = sK17
& aVector0(sK17) ) )
& ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f107]) ).
fof(f125,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f126,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 != szszuzczcdt0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f127,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f128,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(sK4(X0)) = X0 ),
inference(cnf_transformation,[],[f108]) ).
fof(f129,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK4(X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f130,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f52]) ).
fof(f131,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f132,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f134,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f135,plain,
! [X0] :
( ~ aScalar0(X0)
| aScalar0(smndt0(X0)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f136,plain,
! [X0] :
( ~ aScalar0(X0)
| sz0z00 = smndt0(sz0z00) ),
inference(cnf_transformation,[],[f59]) ).
fof(f137,plain,
! [X0] :
( ~ aScalar0(X0)
| smndt0(smndt0(X0)) = X0 ),
inference(cnf_transformation,[],[f59]) ).
fof(f138,plain,
! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f139,plain,
! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f140,plain,
! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtasdt0(sz0z00,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f141,plain,
! [X0] :
( ~ aScalar0(X0)
| sz0z00 = sdtasdt0(X0,sz0z00) ),
inference(cnf_transformation,[],[f59]) ).
fof(f142,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(sz0z00,X0) = X0 ),
inference(cnf_transformation,[],[f59]) ).
fof(f143,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtpldt0(X0,sz0z00) = X0 ),
inference(cnf_transformation,[],[f59]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f151,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| smndt0(sdtasdt0(X0,X1)) = sdtasdt0(smndt0(X0),X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f152,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f153,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(smndt0(X0),smndt0(X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f154,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f155,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f74]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f159,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f160,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f161,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| sdtlseqdt0(sz0z00,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f162,plain,
! [X0] :
( ~ aScalar0(X0)
| sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f85]) ).
fof(f164,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f165,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aVector0(X0)
| aScalar0(sdtlbdtrb0(X0,X1)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f166,plain,
! [X3,X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3) ),
inference(cnf_transformation,[],[f112]) ).
fof(f167,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f168,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sziznziztdt0(X0) != X1
| aVector0(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f169,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aNaturalNumber0(sK5(X0,X1))
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| sziznziztdt0(X0) = X1 ),
inference(cnf_transformation,[],[f112]) ).
fof(f170,plain,
! [X0,X1] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sdtlbdtrb0(X1,sK5(X0,X1)) != sdtlbdtrb0(X0,sK5(X0,X1))
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ~ aVector0(X1)
| sziznziztdt0(X0) = X1 ),
inference(cnf_transformation,[],[f112]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f172,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f173,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f174,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| sz00 = aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ),
inference(cnf_transformation,[],[f98]) ).
fof(f175,plain,
! [X0] :
( ~ aVector0(X0)
| sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f176,plain,
aVector0(xt),
inference(cnf_transformation,[],[f38]) ).
fof(f177,plain,
aVector0(xs),
inference(cnf_transformation,[],[f38]) ).
fof(f178,plain,
! [X0,X1] :
( ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f179,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f40]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| sP2(X1,X0,X2,sK6(X0,X1,X2),sK8(X0,X1,X2),sK7(X0,X1,X2)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f187,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP2(X0,X1,X2,X3,X4,X5)
| sP1(X3,X2,sK11(X0,X1,X2,X3,X4,X5),X5,sK9(X0,X1,X2,X3,X4,X5),sK10(X0,X1,X2,X3,X4,X5),X4) ),
inference(cnf_transformation,[],[f117]) ).
fof(f194,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(X0,X1,X2,X3,X4,X5,X6)
| sP0(X6,X5,sK13(X0,X1,X2,X3,X4,X5,X6),X3,X4,sK14(X0,X1,X2,X3,X4,X5,X6),X2,sK12(X0,X1,X2,X3,X4,X5,X6)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f209,plain,
( sz00 = aDimensionOf0(xs)
| sP3(sK17,sK18,sK19) ),
inference(cnf_transformation,[],[f124]) ).
fof(f216,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cnf_transformation,[],[f124]) ).
fof(f217,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aVector0(sziznziztdt0(X0)) ),
inference(equality_resolution,[],[f168]) ).
fof(f218,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) ),
inference(equality_resolution,[],[f167]) ).
fof(f219,plain,
! [X3,X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| ~ aNaturalNumber0(X3)
| sdtlbdtrb0(X0,X3) = sdtlbdtrb0(sziznziztdt0(X0),X3) ),
inference(equality_resolution,[],[f166]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f125]) ).
tcf(c_50,plain,
! [X0: $i] :
( aNaturalNumber0(szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_51,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != sz00 ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_52,plain,
! [X0: $i] :
( aNaturalNumber0(sK4(X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_53,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( szszuzczcdt0(sK4(X0)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != szszuzczcdt0(X1) ) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_55,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_56,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f132]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_59,plain,
! [X0: $i] :
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz0z00) = X0 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_61,plain,
! [X0: $i] :
( ( sdtpldt0(sz0z00,X0) = X0 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz0z00) = sz0z00 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,X0) = sz0z00 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_64,plain,
! [X0: $i] :
( ( sdtpldt0(X0,smndt0(X0)) = sz0z00 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_65,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),X0) = sz0z00 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_66,plain,
! [X0: $i] :
( ( smndt0(smndt0(X0)) = X0 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_67,plain,
! [X0: $i] :
( ( smndt0(sz0z00) = sz0z00 )
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) = sdtasdt0(X0,sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2)) = sdtasdt0(sdtpldt0(X0,X1),X2) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X0,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) = sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,smndt0(X1)) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(X0),X1) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(X0),smndt0(X1)) = sdtasdt0(X0,X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_78,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_86,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ( sdtasdt0(X0,X0) != sdtasdt0(X1,X1) ) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_88,plain,
! [X0: $i] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtlbdtrb0(X1,X0))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( ( sziznziztdt0(X0) = X1 )
| ( aDimensionOf0(X0) = sz00 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X1)) != aDimensionOf0(X0) )
| ( sdtlbdtrb0(X0,sK5(X0,X1)) != sdtlbdtrb0(X1,sK5(X0,X1)) ) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK5(X1,X0))
| ( sziznziztdt0(X1) = X0 )
| ( aDimensionOf0(X1) = sz00 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_92,plain,
! [X0: $i] :
( aVector0(sziznziztdt0(X0))
| ( aDimensionOf0(X0) = sz00 )
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_93,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = sz00 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0) )
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = sz00 )
| ( sdtlbdtrb0(sziznziztdt0(X1),X0) = sdtlbdtrb0(X1,X0) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = sz00 )
| ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasasdt0(X0,X1))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( ( sdtasasdt0(X0,X1) = sz0z00 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X1) != sz00 )
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = sz00 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) = sdtasasdt0(X0,X1) )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_99,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_100,plain,
aVector0(xs),
inference(cnf_transformation,[],[f177]) ).
tcf(c_101,plain,
aVector0(xt),
inference(cnf_transformation,[],[f176]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_103,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f179]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X1,X0,X2,sK6(X0,X1,X2),sK8(X0,X1,X2),sK7(X0,X1,X2))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sP1(X3,X2,sK11(X0,X1,X2,X3,X4,X5),X5,sK9(X0,X1,X2,X3,X4,X5),sK10(X0,X1,X2,X3,X4,X5),X4)
| ~ sP2(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sP0(X6,X5,sK13(X0,X1,X2,X3,X4,X5,X6),X3,X4,sK14(X0,X1,X2,X3,X4,X5,X6),X2,sK12(X0,X1,X2,X3,X4,X5,X6))
| ~ sP1(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_133,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cnf_transformation,[],[f216]) ).
tcf(c_140,negated_conjecture,
( sP3(sK17,sK18,sK19)
| ( aDimensionOf0(xs) = sz00 ) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_148,plain,
( ( smndt0(sz0z00) = sz0z00 )
| ~ aScalar0(sz0z00) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_216,plain,
smndt0(sz0z00) = sz0z00,
inference(global_subsumption_just,[status(thm)],[c_67,c_56,c_148]) ).
tcf(c_1765,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ aScalar0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_71]) ).
tcf(c_1766,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_71]) ).
tcf(c_1767,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_71]) ).
tcf(c_1768,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_69]) ).
tcf(c_1769,plain,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_69]) ).
tcf(c_1770,definition,
iPr_def_13 = aDimensionOf0(xt),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1771,definition,
iPr_def_14 = aDimensionOf0(xs),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1772,definition,
iPr_def_15 = sdtasasdt0(xs,xt),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1773,definition,
iPr_def_16 = sdtasdt0(iPr_def_15,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_1774,definition,
iPr_def_17 = sdtasasdt0(xs,xs),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_1775,definition,
iPr_def_18 = sdtasasdt0(xt,xt),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_1776,definition,
iPr_def_19 = sdtasdt0(iPr_def_17,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_1780,negated_conjecture,
~ sdtlseqdt0(iPr_def_16,iPr_def_19),
inference(demodulation,[status(thm)],[c_133,c_1775,c_1774,c_1776,c_1772,c_1773]) ).
tcf(c_1804,plain,
( ~ iPr_def_10
| ~ aScalar0(sz0z00) ),
inference(instantiation,[status(thm)],[c_1765]) ).
tcf(c_2789,plain,
iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_1767,c_56,c_1804,c_1767]) ).
tcf(c_2791,plain,
iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_1769,c_56,c_1804,c_1769]) ).
tcf(c_2793,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_1765,c_56,c_1804]) ).
tcf(c_2864,plain,
( sdtlseqdt0(sz0z00,iPr_def_16)
| ~ aScalar0(iPr_def_15) ),
inference(superposition,[status(thm)],[c_1773,c_86]) ).
tcf(c_2875,plain,
( sdtlseqdt0(sz0z00,iPr_def_17)
| ~ aVector0(xs) ),
inference(superposition,[status(thm)],[c_1774,c_99]) ).
tcf(c_2876,plain,
( sdtlseqdt0(sz0z00,iPr_def_18)
| ~ aVector0(xt) ),
inference(superposition,[status(thm)],[c_1775,c_99]) ).
tcf(c_2877,plain,
sdtlseqdt0(sz0z00,iPr_def_18),
inference(forward_subsumption_resolution,[status(thm)],[c_2876,c_101]) ).
tcf(c_2878,plain,
sdtlseqdt0(sz0z00,iPr_def_17),
inference(forward_subsumption_resolution,[status(thm)],[c_2875,c_100]) ).
tcf(c_2890,plain,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_60]) ).
tcf(c_2891,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),sz0z00) = smndt0(X0) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_60]) ).
tcf(c_2900,plain,
! [X0: $i] :
( ( sdtpldt0(sz0z00,smndt0(X0)) = smndt0(X0) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_61]) ).
tcf(c_2908,plain,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_62]) ).
tcf(c_2909,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(X0),sz0z00) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_62]) ).
tcf(c_2913,plain,
( sdtlseqdt0(sz0z00,sz0z00)
| ~ aScalar0(sz0z00) ),
inference(superposition,[status(thm)],[c_2908,c_86]) ).
tcf(c_2914,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(forward_subsumption_resolution,[status(thm)],[c_2913,c_56]) ).
tcf(c_2919,plain,
sdtpldt0(smndt0(sz0z00),sz0z00) = smndt0(sz0z00),
inference(superposition,[status(thm)],[c_56,c_2891]) ).
tcf(c_2920,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(smndt0(X0)),sz0z00) = smndt0(smndt0(X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_2891]) ).
tcf(c_2930,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,smndt0(X0)) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_63]) ).
tcf(c_2938,plain,
smndt0(smndt0(sz0z00)) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_66]) ).
tcf(c_2939,plain,
! [X0: $i] :
( ( smndt0(smndt0(smndt0(X0))) = smndt0(X0) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_66]) ).
tcf(c_2961,plain,
! [X0: $i,X1: $i] :
( ( smndt0(smndt0(sdtpldt0(X0,X1))) = sdtpldt0(X0,X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_66]) ).
tcf(c_2962,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,sdtpldt0(X0,X1)) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_63]) ).
tcf(c_2963,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtpldt0(X0,X1)),sz0z00) = smndt0(sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_2891]) ).
tcf(c_2964,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtpldt0(X0,X1),sz0z00) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_62]) ).
tcf(c_2965,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz0z00,sdtpldt0(X0,X1)) = sdtpldt0(X0,X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_61]) ).
tcf(c_2966,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),sz0z00) = sdtpldt0(X0,X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_60]) ).
tcf(c_2998,plain,
( aScalar0(iPr_def_16)
| ~ aScalar0(iPr_def_15) ),
inference(superposition,[status(thm)],[c_1773,c_58]) ).
tcf(c_2999,plain,
( aScalar0(iPr_def_19)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(iPr_def_17) ),
inference(superposition,[status(thm)],[c_1776,c_58]) ).
tcf(c_3000,plain,
! [X0: $i,X1: $i] :
( ( smndt0(smndt0(sdtasdt0(X0,X1))) = sdtasdt0(X0,X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_66]) ).
tcf(c_3001,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,sdtasdt0(X0,X1)) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_63]) ).
tcf(c_3002,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtasdt0(X0,X1)),sz0z00) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_2891]) ).
tcf(c_3003,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),sz0z00) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_62]) ).
tcf(c_3004,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz0z00,sdtasdt0(X0,X1)) = sdtasdt0(X0,X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_61]) ).
tcf(c_3005,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sz0z00) = sdtasdt0(X0,X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_60]) ).
tcf(c_3049,plain,
sdtpldt0(sz0z00,smndt0(sz0z00)) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_64]) ).
tcf(c_3050,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),smndt0(sdtpldt0(X0,X1))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_64]) ).
tcf(c_3051,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),smndt0(sdtasdt0(X0,X1))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_64]) ).
tcf(c_3052,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),smndt0(smndt0(X0))) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_64]) ).
tcf(c_3069,plain,
sdtpldt0(smndt0(sz0z00),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_65]) ).
tcf(c_3070,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtpldt0(X0,X1)),sdtpldt0(X0,X1)) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_65]) ).
tcf(c_3071,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtasdt0(X0,X1)),sdtasdt0(X0,X1)) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_65]) ).
tcf(c_3072,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(smndt0(X0)),smndt0(X0)) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_65]) ).
tcf(c_3091,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtlbdtrb0(X1,X0)),sdtlbdtrb0(X1,X0)) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_65]) ).
tcf(c_3092,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtlbdtrb0(X1,X0),smndt0(sdtlbdtrb0(X1,X0))) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_64]) ).
tcf(c_3093,plain,
! [X0: $i,X1: $i] :
( ( smndt0(smndt0(sdtlbdtrb0(X1,X0))) = sdtlbdtrb0(X1,X0) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_66]) ).
tcf(c_3094,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,sdtlbdtrb0(X1,X0)) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_63]) ).
tcf(c_3095,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtlbdtrb0(X1,X0)),sz0z00) = smndt0(sdtlbdtrb0(X1,X0)) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_2891]) ).
tcf(c_3096,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtlbdtrb0(X1,X0),sz0z00) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_62]) ).
tcf(c_3097,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz0z00,sdtlbdtrb0(X1,X0)) = sdtlbdtrb0(X1,X0) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_61]) ).
tcf(c_3098,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtlbdtrb0(X1,X0),sz0z00) = sdtlbdtrb0(X1,X0) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_60]) ).
tcf(c_3135,plain,
sdtasdt0(smndt0(sz0z00),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_2909]) ).
tcf(c_3136,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(sdtpldt0(X0,X1)),sz0z00) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_2909]) ).
tcf(c_3137,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(sdtasdt0(X0,X1)),sz0z00) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_2909]) ).
tcf(c_3138,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(smndt0(X0)),sz0z00) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_2909]) ).
tcf(c_3139,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(sdtlbdtrb0(X1,X0)),sz0z00) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_2909]) ).
tcf(c_3160,plain,
sdtasdt0(sz0z00,smndt0(sz0z00)) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_2930]) ).
tcf(c_3161,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,smndt0(sdtpldt0(X0,X1))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_2930]) ).
tcf(c_3162,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,smndt0(sdtasdt0(X0,X1))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_2930]) ).
tcf(c_3163,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,smndt0(smndt0(X0))) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_2930]) ).
tcf(c_3164,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,smndt0(sdtlbdtrb0(X1,X0))) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_2930]) ).
tcf(c_3195,plain,
sdtpldt0(sz0z00,smndt0(sz0z00)) = smndt0(sz0z00),
inference(superposition,[status(thm)],[c_56,c_2900]) ).
tcf(c_3196,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz0z00,smndt0(sdtpldt0(X0,X1))) = smndt0(sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_2900]) ).
tcf(c_3197,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz0z00,smndt0(sdtasdt0(X0,X1))) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_2900]) ).
tcf(c_3198,plain,
! [X0: $i] :
( ( sdtpldt0(sz0z00,smndt0(smndt0(X0))) = smndt0(smndt0(X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_2900]) ).
tcf(c_3199,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sz0z00,smndt0(sdtlbdtrb0(X1,X0))) = smndt0(sdtlbdtrb0(X1,X0)) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_2900]) ).
tcf(c_3220,plain,
smndt0(smndt0(smndt0(sz0z00))) = smndt0(sz0z00),
inference(superposition,[status(thm)],[c_56,c_2939]) ).
tcf(c_3221,plain,
! [X0: $i,X1: $i] :
( ( smndt0(smndt0(smndt0(sdtpldt0(X0,X1)))) = smndt0(sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_2939]) ).
tcf(c_3222,plain,
! [X0: $i,X1: $i] :
( ( smndt0(smndt0(smndt0(sdtasdt0(X0,X1)))) = smndt0(sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_2939]) ).
tcf(c_3223,plain,
! [X0: $i] :
( ( smndt0(smndt0(smndt0(smndt0(X0)))) = smndt0(smndt0(X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_2939]) ).
tcf(c_3224,plain,
! [X0: $i,X1: $i] :
( ( smndt0(smndt0(smndt0(sdtlbdtrb0(X1,X0)))) = smndt0(sdtlbdtrb0(X1,X0)) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_2939]) ).
tcf(c_3247,plain,
sdtpldt0(smndt0(smndt0(sz0z00)),sz0z00) = smndt0(smndt0(sz0z00)),
inference(superposition,[status(thm)],[c_56,c_2920]) ).
tcf(c_3248,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(smndt0(sdtpldt0(X0,X1))),sz0z00) = smndt0(smndt0(sdtpldt0(X0,X1))) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_2920]) ).
tcf(c_3249,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(smndt0(sdtasdt0(X0,X1))),sz0z00) = smndt0(smndt0(sdtasdt0(X0,X1))) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_2920]) ).
tcf(c_3250,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(smndt0(smndt0(X0))),sz0z00) = smndt0(smndt0(smndt0(X0))) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_2920]) ).
tcf(c_3251,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(smndt0(sdtlbdtrb0(X1,X0))),sz0z00) = smndt0(smndt0(sdtlbdtrb0(X1,X0))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_2920]) ).
tcf(c_3279,plain,
( sdtlseqdt0(iPr_def_19,iPr_def_16)
| ~ aScalar0(iPr_def_19)
| ~ aScalar0(iPr_def_16) ),
inference(superposition,[status(thm)],[c_83,c_1780]) ).
tcf(c_3322,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,smndt0(X0)) = smndt0(sdtasdt0(sz0z00,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_56,c_75]) ).
tcf(c_3323,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtpldt0(X0,X1),smndt0(X2)) = smndt0(sdtasdt0(sdtpldt0(X0,X1),X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_75]) ).
tcf(c_3324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),smndt0(X2)) = smndt0(sdtasdt0(sdtasdt0(X0,X1),X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_75]) ).
tcf(c_3325,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(X0),smndt0(X1)) = smndt0(sdtasdt0(smndt0(X0),X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_75]) ).
tcf(c_3326,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtlbdtrb0(X2,X0),smndt0(X1)) = smndt0(sdtasdt0(sdtlbdtrb0(X2,X0),X1)) )
| ~ aVector0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_75]) ).
tcf(c_3357,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(sz0z00),X0) = smndt0(sdtasdt0(sz0z00,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_56,c_76]) ).
tcf(c_3358,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(smndt0(sdtpldt0(X0,X1)),X2) = smndt0(sdtasdt0(sdtpldt0(X0,X1),X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_76]) ).
tcf(c_3359,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(smndt0(sdtasdt0(X0,X1)),X2) = smndt0(sdtasdt0(sdtasdt0(X0,X1),X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_76]) ).
tcf(c_3360,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(smndt0(X0)),X1) = smndt0(sdtasdt0(smndt0(X0),X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_76]) ).
tcf(c_3361,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(smndt0(sdtlbdtrb0(X2,X0)),X1) = smndt0(sdtasdt0(sdtlbdtrb0(X2,X0),X1)) )
| ~ aVector0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_76]) ).
tcf(c_3362,plain,
! [X0: $i] :
( ( smndt0(sdtasdt0(sz0z00,X0)) = sdtasdt0(sz0z00,X0) )
| ~ aScalar0(X0) ),
inference(light_normalisation,[status(thm)],[c_3357,c_216]) ).
tcf(c_3400,plain,
sdtasdt0(smndt0(smndt0(sz0z00)),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_3138]) ).
tcf(c_3401,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(smndt0(sdtpldt0(X0,X1))),sz0z00) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_3138]) ).
tcf(c_3402,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(smndt0(sdtasdt0(X0,X1))),sz0z00) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_3138]) ).
tcf(c_3403,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(smndt0(smndt0(X0))),sz0z00) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_3138]) ).
tcf(c_3404,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(smndt0(sdtlbdtrb0(X1,X0))),sz0z00) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_3138]) ).
tcf(c_3427,plain,
sdtasdt0(sz0z00,smndt0(smndt0(sz0z00))) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_3163]) ).
tcf(c_3428,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,smndt0(smndt0(sdtpldt0(X0,X1)))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_3163]) ).
tcf(c_3429,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,smndt0(smndt0(sdtasdt0(X0,X1)))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_3163]) ).
tcf(c_3430,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,smndt0(smndt0(smndt0(X0)))) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_3163]) ).
tcf(c_3431,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz0z00,smndt0(smndt0(sdtlbdtrb0(X1,X0)))) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_3163]) ).
tcf(c_3458,plain,
sdtpldt0(smndt0(sz0z00),smndt0(smndt0(sz0z00))) = sz0z00,
inference(superposition,[status(thm)],[c_56,c_3052]) ).
tcf(c_3459,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtpldt0(X0,X1)),smndt0(smndt0(sdtpldt0(X0,X1)))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_3052]) ).
tcf(c_3460,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtasdt0(X0,X1)),smndt0(smndt0(sdtasdt0(X0,X1)))) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_3052]) ).
tcf(c_3461,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(smndt0(X0)),smndt0(smndt0(smndt0(X0)))) = sz0z00 )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_3052]) ).
tcf(c_3462,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(smndt0(sdtlbdtrb0(X1,X0)),smndt0(smndt0(sdtlbdtrb0(X1,X0)))) = sz0z00 )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_3052]) ).
tcf(c_3693,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(sz0z00),smndt0(X0)) = sdtasdt0(sz0z00,X0) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_56,c_77]) ).
tcf(c_3694,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(smndt0(sdtpldt0(X0,X1)),smndt0(X2)) = sdtasdt0(sdtpldt0(X0,X1),X2) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_77]) ).
tcf(c_3695,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(smndt0(sdtasdt0(X0,X1)),smndt0(X2)) = sdtasdt0(sdtasdt0(X0,X1),X2) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_77]) ).
tcf(c_3696,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(smndt0(X0)),smndt0(X1)) = sdtasdt0(smndt0(X0),X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_77]) ).
tcf(c_3697,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(smndt0(sdtlbdtrb0(X2,X0)),smndt0(X1)) = sdtasdt0(sdtlbdtrb0(X2,X0),X1) )
| ~ aVector0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_77]) ).
tcf(c_3698,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,smndt0(X0)) = sdtasdt0(sz0z00,X0) )
| ~ aScalar0(X0) ),
inference(light_normalisation,[status(thm)],[c_3693,c_216]) ).
tcf(c_3779,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(xt,X0))
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_96]) ).
tcf(c_3781,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(X0,xt))
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_96]) ).
tcf(c_3782,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(equality_resolution,[status(thm)],[c_96]) ).
tcf(c_3785,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(X0,xt))
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3781,c_101]) ).
tcf(c_3793,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(xt,X0))
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3779,c_101]) ).
tcf(c_3820,plain,
( aScalar0(iPr_def_17)
| ~ aVector0(xs) ),
inference(superposition,[status(thm)],[c_1774,c_3782]) ).
tcf(c_3821,plain,
( aScalar0(iPr_def_18)
| ~ aVector0(xt) ),
inference(superposition,[status(thm)],[c_1775,c_3782]) ).
tcf(c_3822,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(sdtasasdt0(X1,X1)),smndt0(X0)) = sdtasdt0(sdtasasdt0(X1,X1),X0) )
| ~ aVector0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_77]) ).
tcf(c_3823,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(sdtasasdt0(X0,X0)),smndt0(smndt0(sdtasasdt0(X0,X0)))) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_3052]) ).
tcf(c_3824,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,smndt0(smndt0(sdtasasdt0(X0,X0)))) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_3163]) ).
tcf(c_3825,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(smndt0(sdtasasdt0(X0,X0))),sz0z00) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_3138]) ).
tcf(c_3826,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(smndt0(sdtasasdt0(X1,X1)),X0) = smndt0(sdtasdt0(sdtasasdt0(X1,X1),X0)) )
| ~ aVector0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_76]) ).
tcf(c_3827,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasasdt0(X1,X1),smndt0(X0)) = smndt0(sdtasdt0(sdtasasdt0(X1,X1),X0)) )
| ~ aVector0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_75]) ).
tcf(c_3828,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(smndt0(sdtasasdt0(X0,X0))),sz0z00) = smndt0(smndt0(sdtasasdt0(X0,X0))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_2920]) ).
tcf(c_3829,plain,
! [X0: $i] :
( ( smndt0(smndt0(smndt0(sdtasasdt0(X0,X0)))) = smndt0(sdtasasdt0(X0,X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_2939]) ).
tcf(c_3830,plain,
! [X0: $i] :
( ( sdtpldt0(sz0z00,smndt0(sdtasasdt0(X0,X0))) = smndt0(sdtasasdt0(X0,X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_2900]) ).
tcf(c_3831,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,smndt0(sdtasasdt0(X0,X0))) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_2930]) ).
tcf(c_3832,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(sdtasasdt0(X0,X0)),sz0z00) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_2909]) ).
tcf(c_3833,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(sdtasasdt0(X0,X0)),sdtasasdt0(X0,X0)) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_65]) ).
tcf(c_3834,plain,
! [X0: $i] :
( ( sdtpldt0(sdtasasdt0(X0,X0),smndt0(sdtasasdt0(X0,X0))) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_64]) ).
tcf(c_3835,plain,
! [X0: $i] :
( ( smndt0(smndt0(sdtasasdt0(X0,X0))) = sdtasasdt0(X0,X0) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_66]) ).
tcf(c_3836,plain,
! [X0: $i] :
( ( sdtasdt0(sz0z00,sdtasasdt0(X0,X0)) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_63]) ).
tcf(c_3837,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(sdtasasdt0(X0,X0)),sz0z00) = smndt0(sdtasasdt0(X0,X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_2891]) ).
tcf(c_3838,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasasdt0(X0,X0),sz0z00) = sz0z00 )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_62]) ).
tcf(c_3839,plain,
! [X0: $i] :
( ( sdtpldt0(sz0z00,sdtasasdt0(X0,X0)) = sdtasasdt0(X0,X0) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_61]) ).
tcf(c_3840,plain,
! [X0: $i] :
( ( sdtpldt0(sdtasasdt0(X0,X0),sz0z00) = sdtasasdt0(X0,X0) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_60]) ).
tcf(c_3841,plain,
aScalar0(iPr_def_18),
inference(forward_subsumption_resolution,[status(thm)],[c_3821,c_101]) ).
tcf(c_3842,plain,
aScalar0(iPr_def_17),
inference(forward_subsumption_resolution,[status(thm)],[c_3820,c_100]) ).
tcf(c_3884,plain,
( aScalar0(iPr_def_19)
| ~ aScalar0(iPr_def_17) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2999,c_3841]) ).
tcf(c_3885,plain,
aScalar0(iPr_def_19),
inference(forward_subsumption_resolution,[status(thm)],[c_3884,c_3842]) ).
tcf(c_3886,plain,
( sdtlseqdt0(iPr_def_19,iPr_def_16)
| ~ aScalar0(iPr_def_16) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3279,c_3885]) ).
tcf(c_3918,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(iPr_def_18),smndt0(X0)) = sdtasdt0(iPr_def_18,X0) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_77]) ).
tcf(c_3919,plain,
sdtpldt0(smndt0(iPr_def_18),smndt0(smndt0(iPr_def_18))) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_3052]) ).
tcf(c_3920,plain,
sdtasdt0(sz0z00,smndt0(smndt0(iPr_def_18))) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_3163]) ).
tcf(c_3921,plain,
sdtasdt0(smndt0(smndt0(iPr_def_18)),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_3138]) ).
tcf(c_3922,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(iPr_def_18),X0) = smndt0(sdtasdt0(iPr_def_18,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_76]) ).
tcf(c_3923,plain,
! [X0: $i] :
( ( sdtasdt0(iPr_def_18,smndt0(X0)) = smndt0(sdtasdt0(iPr_def_18,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_75]) ).
tcf(c_3924,plain,
sdtpldt0(smndt0(smndt0(iPr_def_18)),sz0z00) = smndt0(smndt0(iPr_def_18)),
inference(superposition,[status(thm)],[c_3841,c_2920]) ).
tcf(c_3925,plain,
smndt0(smndt0(smndt0(iPr_def_18))) = smndt0(iPr_def_18),
inference(superposition,[status(thm)],[c_3841,c_2939]) ).
tcf(c_3926,plain,
sdtpldt0(sz0z00,smndt0(iPr_def_18)) = smndt0(iPr_def_18),
inference(superposition,[status(thm)],[c_3841,c_2900]) ).
tcf(c_3927,plain,
sdtasdt0(sz0z00,smndt0(iPr_def_18)) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_2930]) ).
tcf(c_3928,plain,
sdtasdt0(smndt0(iPr_def_18),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_2909]) ).
tcf(c_3929,plain,
sdtpldt0(smndt0(iPr_def_18),iPr_def_18) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_65]) ).
tcf(c_3930,plain,
sdtpldt0(iPr_def_18,smndt0(iPr_def_18)) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_64]) ).
tcf(c_3931,plain,
smndt0(smndt0(iPr_def_18)) = iPr_def_18,
inference(superposition,[status(thm)],[c_3841,c_66]) ).
tcf(c_3932,plain,
sdtasdt0(sz0z00,iPr_def_18) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_63]) ).
tcf(c_3933,plain,
sdtpldt0(smndt0(iPr_def_18),sz0z00) = smndt0(iPr_def_18),
inference(superposition,[status(thm)],[c_3841,c_2891]) ).
tcf(c_3934,plain,
sdtasdt0(iPr_def_18,sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3841,c_62]) ).
tcf(c_3935,plain,
sdtpldt0(sz0z00,iPr_def_18) = iPr_def_18,
inference(superposition,[status(thm)],[c_3841,c_61]) ).
tcf(c_3936,plain,
sdtpldt0(iPr_def_18,sz0z00) = iPr_def_18,
inference(superposition,[status(thm)],[c_3841,c_60]) ).
tcf(c_3971,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(iPr_def_17),smndt0(X0)) = sdtasdt0(iPr_def_17,X0) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_77]) ).
tcf(c_3972,plain,
sdtpldt0(smndt0(iPr_def_17),smndt0(smndt0(iPr_def_17))) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_3052]) ).
tcf(c_3973,plain,
sdtasdt0(sz0z00,smndt0(smndt0(iPr_def_17))) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_3163]) ).
tcf(c_3974,plain,
sdtasdt0(smndt0(smndt0(iPr_def_17)),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_3138]) ).
tcf(c_3975,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(iPr_def_17),X0) = smndt0(sdtasdt0(iPr_def_17,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_76]) ).
tcf(c_3976,plain,
! [X0: $i] :
( ( sdtasdt0(iPr_def_17,smndt0(X0)) = smndt0(sdtasdt0(iPr_def_17,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_75]) ).
tcf(c_3977,plain,
sdtpldt0(smndt0(smndt0(iPr_def_17)),sz0z00) = smndt0(smndt0(iPr_def_17)),
inference(superposition,[status(thm)],[c_3842,c_2920]) ).
tcf(c_3978,plain,
smndt0(smndt0(smndt0(iPr_def_17))) = smndt0(iPr_def_17),
inference(superposition,[status(thm)],[c_3842,c_2939]) ).
tcf(c_3979,plain,
sdtpldt0(sz0z00,smndt0(iPr_def_17)) = smndt0(iPr_def_17),
inference(superposition,[status(thm)],[c_3842,c_2900]) ).
tcf(c_3980,plain,
sdtasdt0(sz0z00,smndt0(iPr_def_17)) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_2930]) ).
tcf(c_3981,plain,
sdtasdt0(smndt0(iPr_def_17),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_2909]) ).
tcf(c_3982,plain,
sdtpldt0(smndt0(iPr_def_17),iPr_def_17) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_65]) ).
tcf(c_3983,plain,
sdtpldt0(iPr_def_17,smndt0(iPr_def_17)) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_64]) ).
tcf(c_3984,plain,
smndt0(smndt0(iPr_def_17)) = iPr_def_17,
inference(superposition,[status(thm)],[c_3842,c_66]) ).
tcf(c_3985,plain,
sdtasdt0(sz0z00,iPr_def_17) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_63]) ).
tcf(c_3986,plain,
sdtpldt0(smndt0(iPr_def_17),sz0z00) = smndt0(iPr_def_17),
inference(superposition,[status(thm)],[c_3842,c_2891]) ).
tcf(c_3987,plain,
sdtasdt0(iPr_def_17,sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3842,c_62]) ).
tcf(c_3988,plain,
sdtpldt0(sz0z00,iPr_def_17) = iPr_def_17,
inference(superposition,[status(thm)],[c_3842,c_61]) ).
tcf(c_3989,plain,
sdtpldt0(iPr_def_17,sz0z00) = iPr_def_17,
inference(superposition,[status(thm)],[c_3842,c_60]) ).
tcf(c_4021,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(iPr_def_19),smndt0(X0)) = sdtasdt0(iPr_def_19,X0) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3885,c_77]) ).
tcf(c_4022,plain,
sdtpldt0(smndt0(iPr_def_19),smndt0(smndt0(iPr_def_19))) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_3052]) ).
tcf(c_4023,plain,
sdtasdt0(sz0z00,smndt0(smndt0(iPr_def_19))) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_3163]) ).
tcf(c_4024,plain,
sdtasdt0(smndt0(smndt0(iPr_def_19)),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_3138]) ).
tcf(c_4025,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(iPr_def_19),X0) = smndt0(sdtasdt0(iPr_def_19,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3885,c_76]) ).
tcf(c_4026,plain,
! [X0: $i] :
( ( sdtasdt0(iPr_def_19,smndt0(X0)) = smndt0(sdtasdt0(iPr_def_19,X0)) )
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3885,c_75]) ).
tcf(c_4027,plain,
sdtpldt0(smndt0(smndt0(iPr_def_19)),sz0z00) = smndt0(smndt0(iPr_def_19)),
inference(superposition,[status(thm)],[c_3885,c_2920]) ).
tcf(c_4028,plain,
smndt0(smndt0(smndt0(iPr_def_19))) = smndt0(iPr_def_19),
inference(superposition,[status(thm)],[c_3885,c_2939]) ).
tcf(c_4029,plain,
sdtpldt0(sz0z00,smndt0(iPr_def_19)) = smndt0(iPr_def_19),
inference(superposition,[status(thm)],[c_3885,c_2900]) ).
tcf(c_4030,plain,
sdtasdt0(sz0z00,smndt0(iPr_def_19)) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_2930]) ).
tcf(c_4031,plain,
sdtasdt0(smndt0(iPr_def_19),sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_2909]) ).
tcf(c_4032,plain,
sdtpldt0(smndt0(iPr_def_19),iPr_def_19) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_65]) ).
tcf(c_4033,plain,
sdtpldt0(iPr_def_19,smndt0(iPr_def_19)) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_64]) ).
tcf(c_4034,plain,
smndt0(smndt0(iPr_def_19)) = iPr_def_19,
inference(superposition,[status(thm)],[c_3885,c_66]) ).
tcf(c_4035,plain,
sdtasdt0(sz0z00,iPr_def_19) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_63]) ).
tcf(c_4036,plain,
sdtpldt0(smndt0(iPr_def_19),sz0z00) = smndt0(iPr_def_19),
inference(superposition,[status(thm)],[c_3885,c_2891]) ).
tcf(c_4037,plain,
sdtasdt0(iPr_def_19,sz0z00) = sz0z00,
inference(superposition,[status(thm)],[c_3885,c_62]) ).
tcf(c_4038,plain,
sdtpldt0(sz0z00,iPr_def_19) = iPr_def_19,
inference(superposition,[status(thm)],[c_3885,c_61]) ).
tcf(c_4039,plain,
sdtpldt0(iPr_def_19,sz0z00) = iPr_def_19,
inference(superposition,[status(thm)],[c_3885,c_60]) ).
tcf(c_4358,plain,
! [X0: $i] :
( ( sdtasdt0(X0,X0) = sz0z00 )
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasdt0(X0,X0),sz0z00) ),
inference(superposition,[status(thm)],[c_86,c_79]) ).
tcf(c_4359,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,X0) = sz0z00 )
| ~ aScalar0(sz0z00)
| ~ aVector0(X0)
| ~ aScalar0(sdtasasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasasdt0(X0,X0),sz0z00) ),
inference(superposition,[status(thm)],[c_99,c_79]) ).
tcf(c_4361,plain,
( ( sz0z00 = iPr_def_16 )
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(iPr_def_15)
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(iPr_def_16,sz0z00) ),
inference(superposition,[status(thm)],[c_2864,c_79]) ).
tcf(c_4362,plain,
( ( sz0z00 = iPr_def_17 )
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(iPr_def_17,sz0z00) ),
inference(superposition,[status(thm)],[c_2878,c_79]) ).
tcf(c_4363,plain,
( ( sz0z00 = iPr_def_18 )
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(iPr_def_18,sz0z00) ),
inference(superposition,[status(thm)],[c_2877,c_79]) ).
tcf(c_4365,plain,
( ( sz0z00 = iPr_def_18 )
| ~ sdtlseqdt0(iPr_def_18,sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4363,c_3841,c_56]) ).
tcf(c_4368,plain,
( ( sz0z00 = iPr_def_17 )
| ~ sdtlseqdt0(iPr_def_17,sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4362,c_3842,c_56]) ).
tcf(c_4371,plain,
( ( sz0z00 = iPr_def_16 )
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(iPr_def_15)
| ~ sdtlseqdt0(iPr_def_16,sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4361,c_56]) ).
tcf(c_4376,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,X0) = sz0z00 )
| ~ aVector0(X0)
| ~ aScalar0(sdtasasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasasdt0(X0,X0),sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4359,c_56]) ).
tcf(c_4381,plain,
! [X0: $i] :
( ( sdtasdt0(X0,X0) = sz0z00 )
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasdt0(X0,X0),sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4358,c_56]) ).
tcf(c_4398,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sz0z00 )
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sz0z00) ),
inference(superposition,[status(thm)],[c_84,c_79]) ).
tcf(c_4399,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4398,c_56]) ).
tcf(c_4419,plain,
( sdtlseqdt0(sz0z00,iPr_def_19)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(iPr_def_17)
| ~ sdtlseqdt0(sz0z00,iPr_def_18)
| ~ sdtlseqdt0(sz0z00,iPr_def_17) ),
inference(superposition,[status(thm)],[c_1776,c_85]) ).
tcf(c_4420,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sz0z00 )
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sz0z00) ),
inference(superposition,[status(thm)],[c_85,c_79]) ).
tcf(c_4421,plain,
sdtlseqdt0(sz0z00,iPr_def_19),
inference(forward_subsumption_resolution,[status(thm)],[c_4419,c_3841,c_3842,c_2877,c_2878]) ).
tcf(c_4422,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sz0z00 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4420,c_56]) ).
tcf(c_4449,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X0,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_83,c_80]) ).
tcf(c_4451,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_84,c_80]) ).
tcf(c_4452,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_85,c_80]) ).
tcf(c_4453,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasdt0(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_86,c_80]) ).
tcf(c_4454,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(sz0z00)
| ~ aVector0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(sdtasasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasasdt0(X0,X0),X1) ),
inference(superposition,[status(thm)],[c_99,c_80]) ).
tcf(c_4456,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(iPr_def_15)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_2864,c_80]) ).
tcf(c_4457,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X0) ),
inference(superposition,[status(thm)],[c_2878,c_80]) ).
tcf(c_4458,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X0) ),
inference(superposition,[status(thm)],[c_2877,c_80]) ).
tcf(c_4459,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_19,X0)
| ~ aScalar0(iPr_def_19)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_3886,c_80]) ).
tcf(c_4460,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_19,X0)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4459,c_3885]) ).
tcf(c_4465,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4458,c_3841,c_56]) ).
tcf(c_4469,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4457,c_3842,c_56]) ).
tcf(c_4473,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(iPr_def_15)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4456,c_56]) ).
tcf(c_4485,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,X1)
| ~ aVector0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(sdtasasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasasdt0(X0,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4454,c_56]) ).
tcf(c_4491,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(X0,X0))
| ~ sdtlseqdt0(sdtasdt0(X0,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4453,c_56]) ).
tcf(c_4497,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4452,c_56]) ).
tcf(c_4506,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4451,c_56]) ).
tcf(c_4529,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(iPr_def_19)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_19,X0) ),
inference(superposition,[status(thm)],[c_4421,c_80]) ).
tcf(c_4530,plain,
( ( sz0z00 = iPr_def_19 )
| ~ aScalar0(iPr_def_19)
| ~ aScalar0(sz0z00)
| ~ sdtlseqdt0(iPr_def_19,sz0z00) ),
inference(superposition,[status(thm)],[c_4421,c_79]) ).
tcf(c_4531,plain,
( ( sz0z00 = iPr_def_19 )
| ~ sdtlseqdt0(iPr_def_19,sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4530,c_3885,c_56]) ).
tcf(c_4534,plain,
! [X0: $i] :
( sdtlseqdt0(sz0z00,X0)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_19,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4529,c_3885,c_56]) ).
tcf(c_4590,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_19,X0)
| sdtlseqdt0(X0,iPr_def_16)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_83,c_4460]) ).
tcf(c_4616,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_19,X1)
| sdtlseqdt0(X0,iPr_def_16)
| ~ aScalar0(iPr_def_19)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_4590,c_80]) ).
tcf(c_4617,plain,
! [X0: $i] :
( sdtlseqdt0(X0,iPr_def_16)
| ( X0 = iPr_def_19 )
| ~ aScalar0(iPr_def_19)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X0,iPr_def_19) ),
inference(superposition,[status(thm)],[c_4590,c_79]) ).
tcf(c_4618,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_19,X1)
| sdtlseqdt0(X1,X0)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_4590,c_80]) ).
tcf(c_4619,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_19,X0)
| ( X0 = iPr_def_16 )
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_4590,c_79]) ).
tcf(c_4632,plain,
! [X0: $i] :
( sdtlseqdt0(X0,iPr_def_16)
| ( X0 = iPr_def_19 )
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X0,iPr_def_19) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4617,c_3885]) ).
tcf(c_4638,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_19,X1)
| sdtlseqdt0(X0,iPr_def_16)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4616,c_3885]) ).
tcf(c_4974,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(sz0z00,X0),X1) = sdtpldt0(sz0z00,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_56,c_68]) ).
tcf(c_4975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(sdtpldt0(X0,X1),X2),X3) = sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_68]) ).
tcf(c_4976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(X0,X1),X2),X3) = sdtpldt0(sdtasdt0(X0,X1),sdtpldt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_68]) ).
tcf(c_4977,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(smndt0(X0),X1),X2) = sdtpldt0(smndt0(X0),sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_68]) ).
tcf(c_4978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(sdtlbdtrb0(X3,X0),X1),X2) = sdtpldt0(sdtlbdtrb0(X3,X0),sdtpldt0(X1,X2)) )
| ~ aVector0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_68]) ).
tcf(c_4979,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(iPr_def_19,X0),X1) = sdtpldt0(iPr_def_19,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3885,c_68]) ).
tcf(c_4980,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(iPr_def_17,X0),X1) = sdtpldt0(iPr_def_17,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_68]) ).
tcf(c_4981,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(iPr_def_18,X0),X1) = sdtpldt0(iPr_def_18,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_68]) ).
tcf(c_4982,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(sdtasasdt0(X2,X2),X0),X1) = sdtpldt0(sdtasasdt0(X2,X2),sdtpldt0(X0,X1)) )
| ~ aVector0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_68]) ).
tcf(c_5053,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(sz0z00,X0),X1) = sdtasdt0(sz0z00,sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_56,c_70]) ).
tcf(c_5054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(sdtpldt0(X0,X1),X2),X3) = sdtasdt0(sdtpldt0(X0,X1),sdtasdt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_70]) ).
tcf(c_5055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(sdtasdt0(X0,X1),X2),X3) = sdtasdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_70]) ).
tcf(c_5056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(smndt0(X0),X1),X2) = sdtasdt0(smndt0(X0),sdtasdt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_70]) ).
tcf(c_5057,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(sdtasdt0(sdtlbdtrb0(X3,X0),X1),X2) = sdtasdt0(sdtlbdtrb0(X3,X0),sdtasdt0(X1,X2)) )
| ~ aVector0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_70]) ).
tcf(c_5058,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(iPr_def_19,X0),X1) = sdtasdt0(iPr_def_19,sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3885,c_70]) ).
tcf(c_5059,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(iPr_def_17,X0),X1) = sdtasdt0(iPr_def_17,sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_70]) ).
tcf(c_5060,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(iPr_def_18,X0),X1) = sdtasdt0(iPr_def_18,sdtasdt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_70]) ).
tcf(c_5061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(sdtasasdt0(X2,X2),X0),X1) = sdtasdt0(sdtasasdt0(X2,X2),sdtasdt0(X0,X1)) )
| ~ aVector0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_70]) ).
tcf(c_5140,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(sz0z00,X0),sdtasdt0(sz0z00,X1)) = sdtasdt0(sz0z00,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_56,c_72]) ).
tcf(c_5141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(sdtpldt0(X0,X1),X2),sdtasdt0(sdtpldt0(X0,X1),X3)) = sdtasdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_72]) ).
tcf(c_5142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(sdtasdt0(X0,X1),X2),sdtasdt0(sdtasdt0(X0,X1),X3)) = sdtasdt0(sdtasdt0(X0,X1),sdtpldt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_72]) ).
tcf(c_5143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(smndt0(X0),X1),sdtasdt0(smndt0(X0),X2)) = sdtasdt0(smndt0(X0),sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_72]) ).
tcf(c_5144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(sdtlbdtrb0(X3,X0),X1),sdtasdt0(sdtlbdtrb0(X3,X0),X2)) = sdtasdt0(sdtlbdtrb0(X3,X0),sdtpldt0(X1,X2)) )
| ~ aVector0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_72]) ).
tcf(c_5145,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(iPr_def_19,X0),sdtasdt0(iPr_def_19,X1)) = sdtasdt0(iPr_def_19,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3885,c_72]) ).
tcf(c_5146,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(iPr_def_17,X0),sdtasdt0(iPr_def_17,X1)) = sdtasdt0(iPr_def_17,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_72]) ).
tcf(c_5147,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(iPr_def_18,X0),sdtasdt0(iPr_def_18,X1)) = sdtasdt0(iPr_def_18,sdtpldt0(X0,X1)) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_72]) ).
tcf(c_5148,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(sdtasasdt0(X2,X2),X0),sdtasdt0(sdtasasdt0(X2,X2),X1)) = sdtasdt0(sdtasasdt0(X2,X2),sdtpldt0(X0,X1)) )
| ~ aVector0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_72]) ).
tcf(c_5519,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(sz0z00,X1),sdtasdt0(X0,X1)) = sdtasdt0(sdtpldt0(sz0z00,X0),X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_56,c_73]) ).
tcf(c_5520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(sdtpldt0(X0,X1),X3),sdtasdt0(X2,X3)) = sdtasdt0(sdtpldt0(sdtpldt0(X0,X1),X2),X3) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_73]) ).
tcf(c_5521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(sdtasdt0(X0,X1),X3),sdtasdt0(X2,X3)) = sdtasdt0(sdtpldt0(sdtasdt0(X0,X1),X2),X3) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_73]) ).
tcf(c_5522,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(smndt0(X0),X2),sdtasdt0(X1,X2)) = sdtasdt0(sdtpldt0(smndt0(X0),X1),X2) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_73]) ).
tcf(c_5523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtasdt0(sdtlbdtrb0(X3,X0),X2),sdtasdt0(X1,X2)) = sdtasdt0(sdtpldt0(sdtlbdtrb0(X3,X0),X1),X2) )
| ~ aVector0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_73]) ).
tcf(c_5524,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(iPr_def_19,X1),sdtasdt0(X0,X1)) = sdtasdt0(sdtpldt0(iPr_def_19,X0),X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3885,c_73]) ).
tcf(c_5525,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(iPr_def_17,X1),sdtasdt0(X0,X1)) = sdtasdt0(sdtpldt0(iPr_def_17,X0),X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_73]) ).
tcf(c_5526,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtasdt0(iPr_def_18,X1),sdtasdt0(X0,X1)) = sdtasdt0(sdtpldt0(iPr_def_18,X0),X1) )
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_73]) ).
tcf(c_5527,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(sdtasasdt0(X2,X2),X1),sdtasdt0(X0,X1)) = sdtasdt0(sdtpldt0(sdtasasdt0(X2,X2),X0),X1) )
| ~ aVector0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_73]) ).
tcf(c_5674,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(superposition,[status(thm)],[c_2890,c_81]) ).
tcf(c_5675,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_18,sdtpldt0(X0,X1))
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(superposition,[status(thm)],[c_3935,c_81]) ).
tcf(c_5676,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_18,sdtpldt0(X1,X0))
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(superposition,[status(thm)],[c_3936,c_81]) ).
tcf(c_5677,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),sz0z00)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X0,sz0z00) ),
inference(superposition,[status(thm)],[c_2890,c_81]) ).
tcf(c_5678,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_18)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,iPr_def_18)
| ~ sdtlseqdt0(X0,sz0z00) ),
inference(superposition,[status(thm)],[c_3935,c_81]) ).
tcf(c_5679,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_18)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X0,iPr_def_18) ),
inference(superposition,[status(thm)],[c_3936,c_81]) ).
tcf(c_5680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sdtlseqdt0(sdtpldt0(X3,X4),X2)
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X4,X1)
| ~ sdtlseqdt0(X3,X0)
| ~ aScalar0(sdtpldt0(X3,X4))
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_81,c_80]) ).
tcf(c_5681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X2,X3) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X3,X1)
| ~ sdtlseqdt0(X2,X0)
| ~ aScalar0(sdtpldt0(X2,X3))
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) ),
inference(superposition,[status(thm)],[c_81,c_79]) ).
tcf(c_5682,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X0,sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5677,c_56]) ).
tcf(c_5689,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_18)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X0,iPr_def_18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5679,c_3841,c_56]) ).
tcf(c_5695,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_18)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,iPr_def_18)
| ~ sdtlseqdt0(X0,sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5678,c_3841,c_56]) ).
tcf(c_5701,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_18,sdtpldt0(X1,X0))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5676,c_3841,c_56]) ).
tcf(c_5707,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_18,sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5675,c_3841,c_56]) ).
tcf(c_5751,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_17,sdtpldt0(X0,X1))
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(superposition,[status(thm)],[c_3988,c_81]) ).
tcf(c_5752,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_17)
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,iPr_def_17)
| ~ sdtlseqdt0(X0,sz0z00) ),
inference(superposition,[status(thm)],[c_3988,c_81]) ).
tcf(c_5753,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_17)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,iPr_def_17)
| ~ sdtlseqdt0(X0,sz0z00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5752,c_3842,c_56]) ).
tcf(c_5759,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_17,sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5751,c_3842,c_56]) ).
tcf(c_5769,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_17,sdtpldt0(X1,X0))
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(superposition,[status(thm)],[c_3989,c_81]) ).
tcf(c_5770,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_17)
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(sz0z00)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X0,iPr_def_17) ),
inference(superposition,[status(thm)],[c_3989,c_81]) ).
tcf(c_5771,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_17)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X0,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5770,c_3842,c_56]) ).
tcf(c_5777,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_17,sdtpldt0(X1,X0))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X1)
| ~ sdtlseqdt0(sz0z00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5769,c_3842,c_56]) ).
tcf(c_6248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(X0,X1),X3),sdtasdt0(sdtpldt0(X0,X1),X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) = sdtasdt0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(X3,X4)) )
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_57,c_74]) ).
tcf(c_6249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(X0,X1),X3),sdtasdt0(sdtasdt0(X0,X1),X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) = sdtasdt0(sdtpldt0(sdtasdt0(X0,X1),X2),sdtpldt0(X3,X4)) )
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_58,c_74]) ).
tcf(c_6250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(smndt0(X0),X2),sdtasdt0(smndt0(X0),X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) = sdtasdt0(sdtpldt0(smndt0(X0),X1),sdtpldt0(X2,X3)) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_59,c_74]) ).
tcf(c_6251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtlbdtrb0(X4,X0),X2),sdtasdt0(sdtlbdtrb0(X4,X0),X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))) = sdtasdt0(sdtpldt0(sdtlbdtrb0(X4,X0),X1),sdtpldt0(X2,X3)) )
| ~ aVector0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_89,c_74]) ).
tcf(c_6252,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(iPr_def_17,X1),sdtasdt0(iPr_def_17,X2)),sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))) = sdtasdt0(sdtpldt0(iPr_def_17,X0),sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3842,c_74]) ).
tcf(c_6253,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(iPr_def_18,X1),sdtasdt0(iPr_def_18,X2)),sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))) = sdtasdt0(sdtpldt0(iPr_def_18,X0),sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3841,c_74]) ).
tcf(c_6254,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(sdtasasdt0(X3,X3),X1),sdtasdt0(sdtasasdt0(X3,X3),X2)),sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))) = sdtasdt0(sdtpldt0(sdtasasdt0(X3,X3),X0),sdtpldt0(X1,X2)) )
| ~ aVector0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(superposition,[status(thm)],[c_3782,c_74]) ).
fof(f103,definition,
! [X5,X7,X10,X4,X6,X11,X8,X9] :
( ~ sP0(X5,X7,X10,X4,X6,X11,X8,X9)
| ? [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))
& X13 = sdtasdt0(X10,X12)
& aScalar0(X13) )
& X12 = sdtasdt0(X7,X5)
& aScalar0(X12) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f104,definition,
! [X3,X2,X8,X4,X6,X7,X5] :
( ~ sP1(X3,X2,X8,X4,X6,X7,X5)
| ? [X9] :
( ? [X10] :
( ? [X11] :
( sP0(X5,X7,X10,X4,X6,X11,X8,X9)
& X11 = sdtasdt0(X6,X9)
& aScalar0(X11) )
& X10 = sdtasdt0(X4,X8)
& aScalar0(X10) )
& X9 = sdtasdt0(X2,X3)
& aScalar0(X9) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f105,definition,
! [X1,X0,X2,X3,X5,X4] :
( ~ sP2(X1,X0,X2,X3,X5,X4)
| ? [X6] :
( ? [X7] :
( ? [X8] :
( sP1(X3,X2,X8,X4,X6,X7,X5)
& X8 = sdtasdt0(X3,X3)
& aScalar0(X8) )
& X7 = sdtasdt0(X2,X2)
& aScalar0(X7) )
& X6 = sdtasasdt0(X0,X1)
& aScalar0(X6) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f106,definition,
! [X0,X1,X2] :
( ~ sP3(X0,X1,X2)
| ? [X3] :
( ? [X4] :
( ? [X5] :
( sP2(X1,X0,X2,X3,X5,X4)
& X5 = sdtasasdt0(X1,X1)
& aScalar0(X5) )
& X4 = sdtasasdt0(X0,X0)
& aScalar0(X4) )
& X3 = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(X3) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f107,plain,
( ( sz00 = aDimensionOf0(xs)
| ? [X0] :
( ? [X1] :
( ? [X2] :
( sP3(X0,X1,X2)
& X2 = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(X2) )
& X1 = sziznziztdt0(xt)
& aVector0(X1) )
& X0 = sziznziztdt0(xs)
& aVector0(X0) ) )
& ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(definition_folding,[],[f102,f106,f105,f104,f103]) ).
fof(f121,plain,
! [X5,X7,X10,X4,X6,X11,X8,X9] :
( ~ sP0(X5,X7,X10,X4,X6,X11,X8,X9)
| ? [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))
& X13 = sdtasdt0(X10,X12)
& aScalar0(X13) )
& X12 = sdtasdt0(X7,X5)
& aScalar0(X12) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f122,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sP0(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(X4,X7),sdtpldt0(X4,X7)),sdtasdt0(sdtpldt0(X3,X1),sdtpldt0(X0,X6)))
& sdtlseqdt0(sdtpldt0(X5,X5),sdtpldt0(X2,X8))
& sdtlseqdt0(sdtasdt0(X4,X4),sdtasdt0(X3,X0))
& sdtasdt0(X2,X8) = X9
& aScalar0(X9) )
& sdtasdt0(X1,X0) = X8
& aScalar0(X8) ) ),
inference(rectify,[],[f121]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sP0(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(X4,X7),sdtpldt0(X4,X7)),sdtasdt0(sdtpldt0(X3,X1),sdtpldt0(X0,X6)))
& sdtlseqdt0(sdtpldt0(X5,X5),sdtpldt0(X2,sK15(X0,X1,X2,X3,X4,X5,X6,X7)))
& sdtlseqdt0(sdtasdt0(X4,X4),sdtasdt0(X3,X0))
& sK16(X0,X1,X2,X3,X4,X5,X6,X7) = sdtasdt0(X2,sK15(X0,X1,X2,X3,X4,X5,X6,X7))
& aScalar0(sK16(X0,X1,X2,X3,X4,X5,X6,X7))
& sdtasdt0(X1,X0) = sK15(X0,X1,X2,X3,X4,X5,X6,X7)
& aScalar0(sK15(X0,X1,X2,X3,X4,X5,X6,X7)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X8,sK15(X0,X1,X2,X3,X4,X5,X6,X7)),skolemize(X9,sK16(X0,X1,X2,X3,X4,X5,X6,X7))],[f122]) ).
fof(f201,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ 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,[],[f123]) ).
fof(f205,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7)
| sK16(X0,X1,X2,X3,X4,X5,X6,X7) = sdtasdt0(X2,sK15(X0,X1,X2,X3,X4,X5,X6,X7)) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( sdtasdt0(X2,sK15(X0,X1,X2,X3,X4,X5,X6,X7)) = sK16(X0,X1,X2,X3,X4,X5,X6,X7) )
| ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( 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,[],[f201]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : ~ sP0(X0,X1,X2,X3,X4,X5,X6,X7),
inference(global_subsumption_just,[status(thm)],[c_128,c_133,c_132]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : ~ sP1(X0,X1,X2,X3,X4,X5,X6),
inference(backward_subsumption_resolution,[status(thm)],[c_124,c_233]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : ~ sP2(X0,X1,X2,X3,X4,X5),
inference(backward_subsumption_resolution,[status(thm)],[c_117,c_249]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i,X2: $i] : ~ sP3(X0,X1,X2),
inference(backward_subsumption_resolution,[status(thm)],[c_110,c_253]) ).
tcf(c_261,plain,
aDimensionOf0(xs) = sz00,
inference(backward_subsumption_resolution,[status(thm)],[c_140,c_257]) ).
tcf(c_624,plain,
aDimensionOf0(xt) = sz00,
inference(light_normalisation,[status(thm)],[c_103,c_261]) ).
tcf(c_939,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ~ iLess0(aDimensionOf0(X0),sz00)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(light_normalisation,[status(thm)],[c_102,c_261]) ).
tcf(c_1003,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X1,X2),sdtasasdt0(X1,X2)),sdtasdt0(sdtasasdt0(X1,X1),sdtasasdt0(X2,X2)))
| ~ aVector0(X2)
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0)
| ( aDimensionOf0(X1) != X0 )
| ( aDimensionOf0(X1) != aDimensionOf0(X2) )
| ( szszuzczcdt0(X0) != sz00 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_939]) ).
tcf(c_1004,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ~ aNaturalNumber0(aDimensionOf0(X0))
| ( aDimensionOf0(X0) != aDimensionOf0(X1) )
| ( szszuzczcdt0(aDimensionOf0(X0)) != sz00 ) ),
inference(unflattening,[status(thm)],[c_1003]) ).
tcf(c_1006,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != sz00 )
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(global_subsumption_just,[status(thm)],[c_1004,c_88,c_1004]) ).
tcf(c_1007,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) )
| ( szszuzczcdt0(aDimensionOf0(X0)) != sz00 ) ),
inference(renaming,[status(thm)],[c_1006]) ).
tcf(c_1777,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) )
| ( szszuzczcdt0(aDimensionOf0(X0)) != sz00 ) ),
inference(demodulation,[status(thm)],[c_1007]) ).
tcf(c_1778,plain,
iPr_def_13 = sz00,
inference(demodulation,[status(thm)],[c_624,c_1770]) ).
tcf(c_1779,plain,
iPr_def_14 = sz00,
inference(demodulation,[status(thm)],[c_261,c_1771]) ).
tcf(c_2723,plain,
iPr_def_13 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_1779,c_1778]) ).
tcf(c_2724,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_1777,c_1778]) ).
tcf(c_2730,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X0,X0)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X0,X0)))
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(equality_resolution,[status(thm)],[c_2724]) ).
tcf(c_2741,plain,
aNaturalNumber0(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_49,c_1778]) ).
tcf(c_2742,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xt,xt),sdtasasdt0(xt,xt)),sdtasdt0(sdtasasdt0(xt,xt),sdtasasdt0(xt,xt)))
| ~ aVector0(xt)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_2730]) ).
tcf(c_2743,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xt,X0),sdtasasdt0(xt,X0)),sdtasdt0(sdtasasdt0(xt,xt),sdtasasdt0(X0,X0)))
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(xt)) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_2724]) ).
tcf(c_2744,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xt),sdtasasdt0(X0,xt)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(xt,xt)))
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_2724]) ).
tcf(c_2745,plain,
( sdtlseqdt0(sdtasdt0(iPr_def_18,iPr_def_18),sdtasdt0(iPr_def_18,iPr_def_18))
| ~ aVector0(xt)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2742,c_1775]) ).
tcf(c_2749,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xt),sdtasasdt0(X0,xt)),sdtasdt0(sdtasasdt0(X0,X0),iPr_def_18))
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2744,c_1775]) ).
tcf(c_2755,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xt,X0),sdtasasdt0(xt,X0)),sdtasdt0(iPr_def_18,sdtasasdt0(X0,X0)))
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2743,c_1770,c_1775]) ).
tcf(c_2763,plain,
aDimensionOf0(xs) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_1771,c_2723]) ).
tcf(c_2764,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xs,xs)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xs,xs)))
| ~ aVector0(xs)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_2730]) ).
tcf(c_2765,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,X0),sdtasasdt0(xs,X0)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(X0,X0)))
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(xs)) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_2724]) ).
tcf(c_2766,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xs),sdtasasdt0(X0,xs)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(xs,xs)))
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_2724]) ).
tcf(c_2767,plain,
( sdtlseqdt0(sdtasdt0(iPr_def_17,iPr_def_17),sdtasdt0(iPr_def_17,iPr_def_17))
| ~ aVector0(xs)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2764,c_1774]) ).
tcf(c_2768,plain,
( sdtlseqdt0(sdtasdt0(iPr_def_17,iPr_def_17),sdtasdt0(iPr_def_17,iPr_def_17))
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2767,c_100]) ).
tcf(c_2771,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xs),sdtasasdt0(X0,xs)),sdtasdt0(sdtasasdt0(X0,X0),iPr_def_17))
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2766,c_1774]) ).
tcf(c_2772,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xs),sdtasasdt0(X0,xs)),sdtasdt0(sdtasasdt0(X0,X0),iPr_def_17))
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2771,c_100]) ).
tcf(c_2777,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,X0),sdtasasdt0(xs,X0)),sdtasdt0(iPr_def_17,sdtasasdt0(X0,X0)))
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2765,c_1774,c_2763]) ).
tcf(c_2778,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,X0),sdtasasdt0(xs,X0)),sdtasdt0(iPr_def_17,sdtasasdt0(X0,X0)))
| ~ aVector0(X0)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2777,c_100]) ).
tcf(c_2808,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xt,X0),sdtasasdt0(xt,X0)),sdtasdt0(iPr_def_18,sdtasasdt0(X0,X0)))
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 )
| ~ aVector0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2755,c_101,c_2755]) ).
tcf(c_2809,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xt,X0),sdtasasdt0(xt,X0)),sdtasdt0(iPr_def_18,sdtasasdt0(X0,X0)))
| ~ aVector0(X0)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(renaming,[status(thm)],[c_2808]) ).
tcf(c_2819,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xt),sdtasasdt0(X0,xt)),sdtasdt0(sdtasasdt0(X0,X0),iPr_def_18))
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 )
| ~ aVector0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2749,c_101,c_2749]) ).
tcf(c_2820,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xt),sdtasasdt0(X0,xt)),sdtasdt0(sdtasasdt0(X0,X0),iPr_def_18))
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(renaming,[status(thm)],[c_2819]) ).
tcf(c_2830,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),iPr_def_18))
| ~ aVector0(xs)
| ( aDimensionOf0(xs) != iPr_def_13 )
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_2820]) ).
tcf(c_2831,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xt,xt),sdtasasdt0(xt,xt)),sdtasdt0(sdtasasdt0(xt,xt),iPr_def_18))
| ~ aVector0(xt)
| ( aDimensionOf0(xt) != iPr_def_13 )
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_2820]) ).
tcf(c_2837,plain,
( sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),iPr_def_18))
| ~ aVector0(xs)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_2830,c_2763]) ).
tcf(c_2838,plain,
( sdtlseqdt0(iPr_def_16,iPr_def_19)
| ~ aVector0(xs)
| ( szszuzczcdt0(iPr_def_13) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2837,c_1772,c_1773,c_1774,c_1776]) ).
tcf(c_2839,plain,
szszuzczcdt0(iPr_def_13) != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_2838,c_1780,c_100]) ).
tcf(c_2879,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_51,c_1778]) ).
tcf(c_2944,plain,
! [X0: $i] :
( aNaturalNumber0(sK4(X0))
| ( X0 = iPr_def_13 )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_52,c_1778]) ).
tcf(c_3181,plain,
! [X0: $i] :
( aVector0(sziznziztdt0(X0))
| ( aDimensionOf0(X0) = iPr_def_13 )
| ~ aVector0(X0) ),
inference(light_normalisation,[status(thm)],[c_92,c_1778]) ).
tcf(c_3288,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( szszuzczcdt0(sK4(X0)) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_53,c_1778]) ).
tcf(c_3298,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(X0))) = szszuzczcdt0(X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3288]) ).
tcf(c_3299,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(X0))) = sK4(X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3288]) ).
tcf(c_3300,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(X0))) = aDimensionOf0(X0) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3288]) ).
tcf(c_3487,plain,
! [X0: $i] :
( ( szszuzczcdt0(sK4(szszuzczcdt0(X0))) = szszuzczcdt0(X0) )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3298,c_2879]) ).
tcf(c_3494,plain,
! [X0: $i] :
( ( szszuzczcdt0(sK4(szszuzczcdt0(szszuzczcdt0(X0)))) = szszuzczcdt0(szszuzczcdt0(X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3487]) ).
tcf(c_3495,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(X0)))) = szszuzczcdt0(sK4(X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3487]) ).
tcf(c_3496,plain,
! [X0: $i] :
( ( szszuzczcdt0(sK4(szszuzczcdt0(aDimensionOf0(X0)))) = szszuzczcdt0(aDimensionOf0(X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3487]) ).
tcf(c_3497,plain,
szszuzczcdt0(sK4(szszuzczcdt0(iPr_def_13))) = szszuzczcdt0(iPr_def_13),
inference(superposition,[status(thm)],[c_2741,c_3487]) ).
tcf(c_3513,plain,
( aNaturalNumber0(szszuzczcdt0(iPr_def_13))
| ~ aNaturalNumber0(sK4(szszuzczcdt0(iPr_def_13))) ),
inference(superposition,[status(thm)],[c_3497,c_50]) ).
tcf(c_3526,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(X0)))) = aDimensionOf0(sziznziztdt0(X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_3300]) ).
tcf(c_3528,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(xt))) = aDimensionOf0(xt) ) ),
inference(superposition,[status(thm)],[c_101,c_3300]) ).
tcf(c_3529,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( szszuzczcdt0(sK4(iPr_def_13)) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3528,c_1770]) ).
tcf(c_3543,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(szszuzczcdt0(X0))))) = szszuzczcdt0(sK4(szszuzczcdt0(X0))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3495]) ).
tcf(c_3544,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(X0))))) = szszuzczcdt0(sK4(sK4(X0))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3495]) ).
tcf(c_3545,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(aDimensionOf0(X0))))) = szszuzczcdt0(sK4(aDimensionOf0(X0))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3495]) ).
tcf(c_3572,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(szszuzczcdt0(X0)))) = sK4(szszuzczcdt0(X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3299]) ).
tcf(c_3573,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(X0)))) = sK4(sK4(X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3299]) ).
tcf(c_3574,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(aDimensionOf0(X0)))) = sK4(aDimensionOf0(X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3299]) ).
tcf(c_3606,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_3526]) ).
tcf(c_3608,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(xt)))) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(superposition,[status(thm)],[c_101,c_3526]) ).
tcf(c_3628,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(szszuzczcdt0(X0)))))) = szszuzczcdt0(sK4(sK4(szszuzczcdt0(X0)))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3544]) ).
tcf(c_3629,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(X0)))))) = szszuzczcdt0(sK4(sK4(sK4(X0)))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3544]) ).
tcf(c_3630,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(aDimensionOf0(X0)))))) = szszuzczcdt0(sK4(sK4(aDimensionOf0(X0)))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3544]) ).
tcf(c_3658,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(szszuzczcdt0(X0))))) = sK4(sK4(szszuzczcdt0(X0))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3573]) ).
tcf(c_3659,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(X0))))) = sK4(sK4(sK4(X0))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3573]) ).
tcf(c_3660,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(aDimensionOf0(X0))))) = sK4(sK4(aDimensionOf0(X0))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3573]) ).
tcf(c_3733,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) = aDimensionOf0(X0) )
| ~ aVector0(X0) ),
inference(light_normalisation,[status(thm)],[c_93,c_1778]) ).
tcf(c_3743,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(X0)))) = aDimensionOf0(sziznziztdt0(X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_3733]) ).
tcf(c_3745,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt) ) ),
inference(superposition,[status(thm)],[c_101,c_3733]) ).
tcf(c_3746,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3745,c_1770]) ).
tcf(c_3762,plain,
! [X0: $i] :
( ( sK4(szszuzczcdt0(iPr_def_13)) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK4(szszuzczcdt0(iPr_def_13)))
| ( szszuzczcdt0(X0) != szszuzczcdt0(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_3497,c_54]) ).
tcf(c_3778,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(xs,X0))
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_96]) ).
tcf(c_3780,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(X0,xs))
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_96]) ).
tcf(c_3789,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(X0,xs))
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3780,c_100]) ).
tcf(c_3797,plain,
! [X0: $i] :
( aScalar0(sdtasasdt0(xs,X0))
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3778,c_100]) ).
tcf(c_4077,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_3743]) ).
tcf(c_4079,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(superposition,[status(thm)],[c_101,c_3743]) ).
tcf(c_4115,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(szszuzczcdt0(X0))))))) = szszuzczcdt0(sK4(sK4(sK4(szszuzczcdt0(X0))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3629]) ).
tcf(c_4116,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(X0))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(X0))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3629]) ).
tcf(c_4117,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(aDimensionOf0(X0))))))) = szszuzczcdt0(sK4(sK4(sK4(aDimensionOf0(X0))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3629]) ).
tcf(c_4168,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_3606]) ).
tcf(c_4170,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) ) ),
inference(superposition,[status(thm)],[c_101,c_3606]) ).
tcf(c_4192,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_4077]) ).
tcf(c_4194,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) ) ),
inference(superposition,[status(thm)],[c_101,c_4077]) ).
tcf(c_4218,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))) = sK4(sK4(sK4(szszuzczcdt0(X0)))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_3659]) ).
tcf(c_4219,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(X0)))))) = sK4(sK4(sK4(sK4(X0)))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_3659]) ).
tcf(c_4220,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))) = sK4(sK4(sK4(aDimensionOf0(X0)))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_3659]) ).
tcf(c_4271,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4116]) ).
tcf(c_4272,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(X0)))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(X0)))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4116]) ).
tcf(c_4273,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4116]) ).
tcf(c_4309,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_4168]) ).
tcf(c_4311,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) ) ),
inference(superposition,[status(thm)],[c_101,c_4168]) ).
tcf(c_4670,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_4192]) ).
tcf(c_4672,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) ) ),
inference(superposition,[status(thm)],[c_101,c_4192]) ).
tcf(c_4702,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))))) = sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4219]) ).
tcf(c_4703,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(X0))))))) = sK4(sK4(sK4(sK4(sK4(X0))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4219]) ).
tcf(c_4704,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(aDimensionOf0(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0))))))) = sK4(sK4(sK4(sK4(aDimensionOf0(X0))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4219]) ).
tcf(c_4747,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4272]) ).
tcf(c_4748,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(X0))))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(X0))))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4272]) ).
tcf(c_4749,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(aDimensionOf0(X0))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0))))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0))))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4272]) ).
tcf(c_4807,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_4309]) ).
tcf(c_4809,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) ) ),
inference(superposition,[status(thm)],[c_101,c_4309]) ).
tcf(c_4839,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_4670]) ).
tcf(c_4841,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) = iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))))) = aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) ) ),
inference(superposition,[status(thm)],[c_101,c_4670]) ).
tcf(c_4875,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))))) = sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4703]) ).
tcf(c_4876,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(X0))))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(sK4(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(sK4(X0)))))))) = sK4(sK4(sK4(sK4(sK4(sK4(X0)))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4703]) ).
tcf(c_4877,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(aDimensionOf0(X0))))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))))) = sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4703]) ).
tcf(c_4917,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),X0) = sdtlbdtrb0(X1,X0) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_94,c_1778]) ).
tcf(c_4930,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(X0)) = sdtlbdtrb0(X1,szszuzczcdt0(X0)) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4917]) ).
tcf(c_4931,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(X0)) = sdtlbdtrb0(X1,sK4(X0)) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4917]) ).
tcf(c_4932,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),aDimensionOf0(X0)) = sdtlbdtrb0(X1,aDimensionOf0(X0)) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4917]) ).
tcf(c_4933,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),iPr_def_13) = sdtlbdtrb0(X0,iPr_def_13) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_2741,c_4917]) ).
tcf(c_5266,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(X0)),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(X0),iPr_def_13) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_4933]) ).
tcf(c_5268,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(xt),iPr_def_13) = sdtlbdtrb0(xt,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_101,c_4933]) ).
tcf(c_5284,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(szszuzczcdt0(X0))) = sdtlbdtrb0(X1,szszuzczcdt0(szszuzczcdt0(X0))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4930]) ).
tcf(c_5285,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(X0))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(X0))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4930]) ).
tcf(c_5286,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(aDimensionOf0(X0))) = sdtlbdtrb0(X1,szszuzczcdt0(aDimensionOf0(X0))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4930]) ).
tcf(c_5287,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(X0,szszuzczcdt0(iPr_def_13)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_2741,c_4930]) ).
tcf(c_5325,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(X0)),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(X0),szszuzczcdt0(iPr_def_13)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_5287]) ).
tcf(c_5327,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(xt),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(xt,szszuzczcdt0(iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_101,c_5287]) ).
tcf(c_5343,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),aDimensionOf0(sziznziztdt0(X0))) = sdtlbdtrb0(X1,aDimensionOf0(sziznziztdt0(X0))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_4932]) ).
tcf(c_5344,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(xs)) = sdtlbdtrb0(X0,aDimensionOf0(xs)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_100,c_4932]) ).
tcf(c_5345,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(xt)) = sdtlbdtrb0(X0,aDimensionOf0(xt)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_101,c_4932]) ).
tcf(c_5362,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(X0)),iPr_def_13) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_5266]) ).
tcf(c_5364,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(xt)),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(xt),iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_101,c_5266]) ).
tcf(c_5394,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(szszuzczcdt0(X0))) = sdtlbdtrb0(X1,sK4(szszuzczcdt0(X0))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4931]) ).
tcf(c_5395,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(X0))) = sdtlbdtrb0(X1,sK4(sK4(X0))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4931]) ).
tcf(c_5396,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(aDimensionOf0(X0))) = sdtlbdtrb0(X1,sK4(aDimensionOf0(X0))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4931]) ).
tcf(c_5425,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(X0)),szszuzczcdt0(iPr_def_13)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_5325]) ).
tcf(c_5427,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(xt)),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(xt),szszuzczcdt0(iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_101,c_5325]) ).
tcf(c_5447,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(szszuzczcdt0(X0)))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(szszuzczcdt0(X0)))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_5285]) ).
tcf(c_5448,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(X0)))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(X0)))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_5285]) ).
tcf(c_5449,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(aDimensionOf0(X0)))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(aDimensionOf0(X0)))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_5285]) ).
tcf(c_5578,plain,
! [X0: $i,X1: $i] :
( ( sdtasasdt0(X0,X1) = sz0z00 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X1) != iPr_def_13 )
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(light_normalisation,[status(thm)],[c_97,c_1778]) ).
tcf(c_5594,plain,
! [X0: $i] :
( ( sdtasasdt0(xs,X0) = sz0z00 )
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_5578]) ).
tcf(c_5595,plain,
! [X0: $i] :
( ( sdtasasdt0(xt,X0) = sz0z00 )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_5578]) ).
tcf(c_5596,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xs) = sz0z00 )
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(xs) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_5578]) ).
tcf(c_5597,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xt) = sz0z00 )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(xt) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_5578]) ).
tcf(c_5598,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,X0) = sz0z00 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(equality_resolution,[status(thm)],[c_5578]) ).
tcf(c_5602,plain,
! [X0: $i] :
( ( sdtasasdt0(xt,X0) = sz0z00 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5595,c_101]) ).
tcf(c_5606,plain,
! [X0: $i] :
( ( sdtasasdt0(xs,X0) = sz0z00 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5594,c_100]) ).
tcf(c_5610,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xt) = sz0z00 )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_5597,c_1770]) ).
tcf(c_5611,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xt) = sz0z00 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5610,c_101]) ).
tcf(c_5615,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xs) = sz0z00 )
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_5596,c_2763]) ).
tcf(c_5616,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xs) = sz0z00 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5615,c_100]) ).
tcf(c_5633,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(light_normalisation,[status(thm)],[c_95,c_1778]) ).
tcf(c_5652,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_5633]) ).
tcf(c_5654,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(xt)) )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5652,c_101]) ).
tcf(c_5807,plain,
( ( sdtasasdt0(xs,xs) = sz0z00 )
| ~ aVector0(xs) ),
inference(superposition,[status(thm)],[c_2763,c_5598]) ).
tcf(c_5808,plain,
( ( sdtasasdt0(xt,xt) = sz0z00 )
| ~ aVector0(xt) ),
inference(superposition,[status(thm)],[c_1770,c_5598]) ).
tcf(c_5809,plain,
( ( sz0z00 = iPr_def_18 )
| ~ aVector0(xt) ),
inference(light_normalisation,[status(thm)],[c_5808,c_1775]) ).
tcf(c_5810,plain,
sz0z00 = iPr_def_18,
inference(forward_subsumption_resolution,[status(thm)],[c_5809,c_101]) ).
tcf(c_5811,plain,
( ( sz0z00 = iPr_def_17 )
| ~ aVector0(xs) ),
inference(light_normalisation,[status(thm)],[c_5807,c_1774]) ).
tcf(c_5812,plain,
sz0z00 = iPr_def_17,
inference(forward_subsumption_resolution,[status(thm)],[c_5811,c_100]) ).
tcf(c_5813,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,X0) = iPr_def_18 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_5598,c_5810]) ).
tcf(c_5814,plain,
sdtpldt0(iPr_def_17,iPr_def_18) = iPr_def_17,
inference(demodulation,[status(thm)],[c_3989,c_5810]) ).
tcf(c_5815,plain,
sdtpldt0(iPr_def_18,iPr_def_17) = iPr_def_17,
inference(demodulation,[status(thm)],[c_3988,c_5810]) ).
tcf(c_5816,plain,
sdtasdt0(iPr_def_17,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_3987,c_5810]) ).
tcf(c_5817,plain,
! [X0: $i,X1: $i] :
( ( sdtasasdt0(X0,X1) = iPr_def_18 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X1) != iPr_def_13 )
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(demodulation,[status(thm)],[c_5578,c_5810]) ).
tcf(c_5818,plain,
sdtasdt0(iPr_def_18,iPr_def_17) = iPr_def_18,
inference(demodulation,[status(thm)],[c_3985,c_5810]) ).
tcf(c_5823,plain,
sdtlseqdt0(iPr_def_18,iPr_def_19),
inference(demodulation,[status(thm)],[c_4421,c_5810]) ).
tcf(c_5824,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_18,sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(iPr_def_18,X0) ),
inference(demodulation,[status(thm)],[c_85,c_5810]) ).
tcf(c_5825,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_18,sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(iPr_def_18,X0) ),
inference(demodulation,[status(thm)],[c_84,c_5810]) ).
tcf(c_5826,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),smndt0(smndt0(X0))) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_3052,c_5810]) ).
tcf(c_5827,plain,
! [X0: $i] :
( ( sdtasdt0(iPr_def_18,smndt0(smndt0(X0))) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_3163,c_5810]) ).
tcf(c_5828,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(smndt0(X0)),iPr_def_18) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_3138,c_5810]) ).
tcf(c_5829,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(smndt0(X0)),iPr_def_18) = smndt0(smndt0(X0)) )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_2920,c_5810]) ).
tcf(c_5830,plain,
! [X0: $i] :
( ( sdtpldt0(iPr_def_18,smndt0(X0)) = smndt0(X0) )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_2900,c_5810]) ).
tcf(c_5831,plain,
! [X0: $i] :
( ( sdtasdt0(iPr_def_18,smndt0(X0)) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_2930,c_5810]) ).
tcf(c_5832,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(X0),iPr_def_18) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_2909,c_5810]) ).
tcf(c_5833,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),X0) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_65,c_5810]) ).
tcf(c_5834,plain,
! [X0: $i] :
( ( sdtpldt0(X0,smndt0(X0)) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_64,c_5810]) ).
tcf(c_5836,plain,
! [X0: $i] :
( ( sdtasdt0(iPr_def_18,X0) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_63,c_5810]) ).
tcf(c_5837,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),iPr_def_18) = smndt0(X0) )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_2891,c_5810]) ).
tcf(c_5838,plain,
sdtasdt0(iPr_def_18,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_2908,c_5810]) ).
tcf(c_5839,plain,
! [X0: $i] :
( ( sdtasdt0(X0,iPr_def_18) = iPr_def_18 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_62,c_5810]) ).
tcf(c_5840,plain,
! [X0: $i] :
( ( sdtpldt0(iPr_def_18,X0) = X0 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_61,c_5810]) ).
tcf(c_5841,plain,
sdtpldt0(iPr_def_18,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_2890,c_5810]) ).
tcf(c_5842,plain,
! [X0: $i] :
( ( sdtpldt0(X0,iPr_def_18) = X0 )
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_60,c_5810]) ).
tcf(c_5843,plain,
sdtlseqdt0(iPr_def_18,iPr_def_17),
inference(demodulation,[status(thm)],[c_2878,c_5810]) ).
tcf(c_5844,plain,
sdtlseqdt0(iPr_def_18,iPr_def_18),
inference(demodulation,[status(thm)],[c_2877,c_5810]) ).
tcf(c_5845,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_18,sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(demodulation,[status(thm)],[c_99,c_5810]) ).
tcf(c_5846,plain,
( sdtlseqdt0(iPr_def_18,iPr_def_16)
| ~ aScalar0(iPr_def_15) ),
inference(demodulation,[status(thm)],[c_2864,c_5810]) ).
tcf(c_5847,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_18,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_86,c_5810]) ).
tcf(c_5848,plain,
smndt0(iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_216,c_5810]) ).
tcf(c_5900,plain,
iPr_def_18 = iPr_def_19,
inference(demodulation,[status(thm)],[c_1776,c_5816]) ).
tcf(c_5902,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_18,X0)
| sdtlseqdt0(X0,iPr_def_16)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0) ),
inference(demodulation,[status(thm)],[c_4590,c_5900]) ).
tcf(c_5903,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_18,X0)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(demodulation,[status(thm)],[c_4460,c_5900]) ).
tcf(c_5904,plain,
( sdtlseqdt0(iPr_def_18,iPr_def_16)
| ~ aScalar0(iPr_def_16) ),
inference(demodulation,[status(thm)],[c_3886,c_5900]) ).
tcf(c_5906,plain,
~ sdtlseqdt0(iPr_def_16,iPr_def_18),
inference(demodulation,[status(thm)],[c_1780,c_5900]) ).
tcf(c_5942,plain,
( sdtlseqdt0(iPr_def_18,iPr_def_16)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(iPr_def_16) ),
inference(superposition,[status(thm)],[c_83,c_5906]) ).
tcf(c_5949,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_18,X0)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_5904,c_80]) ).
tcf(c_5973,plain,
! [X0: $i] :
( ( sdtasasdt0(xs,X0) = iPr_def_18 )
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_5817]) ).
tcf(c_5974,plain,
! [X0: $i] :
( ( sdtasasdt0(xt,X0) = iPr_def_18 )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_5817]) ).
tcf(c_5975,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xs) = iPr_def_18 )
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(xs) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_2763,c_5817]) ).
tcf(c_5976,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xt) = iPr_def_18 )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(xt) != iPr_def_13 )
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_5817]) ).
tcf(c_5978,plain,
! [X0: $i] :
( ( sdtasasdt0(xt,X0) = iPr_def_18 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5974,c_101]) ).
tcf(c_5982,plain,
! [X0: $i] :
( ( sdtasasdt0(xs,X0) = iPr_def_18 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5973,c_100]) ).
tcf(c_5986,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xt) = iPr_def_18 )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_5976,c_1770]) ).
tcf(c_5987,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xt) = iPr_def_18 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5986,c_101]) ).
tcf(c_5991,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xs) = iPr_def_18 )
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(ground_joinability,[status(thm)],[c_5975,c_2763]) ).
tcf(c_5992,plain,
! [X0: $i] :
( ( sdtasasdt0(X0,xs) = iPr_def_18 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5991,c_100]) ).
tcf(c_6010,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),aDimensionOf0(sziznziztdt0(sziznziztdt0(X0)))) = sdtlbdtrb0(X1,aDimensionOf0(sziznziztdt0(sziznziztdt0(X0)))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_5343]) ).
tcf(c_6012,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(sziznziztdt0(xt))) = sdtlbdtrb0(X0,aDimensionOf0(sziznziztdt0(xt))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_101,c_5343]) ).
tcf(c_6037,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(szszuzczcdt0(X0)))) = sdtlbdtrb0(X1,sK4(sK4(szszuzczcdt0(X0)))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_5395]) ).
tcf(c_6038,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(X0)))) = sdtlbdtrb0(X1,sK4(sK4(sK4(X0)))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_5395]) ).
tcf(c_6039,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(aDimensionOf0(X0)))) = sdtlbdtrb0(X1,sK4(sK4(aDimensionOf0(X0)))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_5395]) ).
tcf(c_6073,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),iPr_def_13) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_5362]) ).
tcf(c_6075,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(xt)),iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_101,c_5362]) ).
tcf(c_6088,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(iPr_def_18,X0)
| ( sdtasdt0(X0,X0) != sdtasdt0(X1,X1) ) ),
inference(light_normalisation,[status(thm)],[c_87,c_5810]) ).
tcf(c_6107,plain,
! [X0: $i] :
( ( X0 = iPr_def_15 )
| ~ aScalar0(iPr_def_15)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,iPr_def_15)
| ~ sdtlseqdt0(iPr_def_18,X0)
| ( sdtasdt0(X0,X0) != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1773,c_6088]) ).
tcf(c_6117,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK5(X1,X0))
| ( sziznziztdt0(X1) = X0 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(X1) ) ),
inference(light_normalisation,[status(thm)],[c_91,c_1778]) ).
tcf(c_6136,plain,
! [X0: $i] :
( aNaturalNumber0(sK5(X0,xs))
| ( sziznziztdt0(X0) = xs )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ~ aVector0(xs)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != szszuzczcdt0(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_2763,c_6117]) ).
tcf(c_6137,plain,
! [X0: $i] :
( aNaturalNumber0(sK5(X0,xt))
| ( sziznziztdt0(X0) = xt )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != szszuzczcdt0(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_1770,c_6117]) ).
tcf(c_6138,plain,
! [X0: $i] :
( aNaturalNumber0(sK5(X0,xt))
| ( sziznziztdt0(X0) = xt )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != szszuzczcdt0(iPr_def_13) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6137,c_101]) ).
tcf(c_6144,plain,
! [X0: $i] :
( aNaturalNumber0(sK5(X0,xs))
| ( sziznziztdt0(X0) = xs )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != szszuzczcdt0(iPr_def_13) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6136,c_100]) ).
tcf(c_6152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1) ),
inference(light_normalisation,[status(thm)],[c_82,c_5810]) ).
tcf(c_6177,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_16,sdtasdt0(X0,X1))
| ~ aScalar0(iPr_def_15)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,iPr_def_15)
| ~ sdtlseqdt0(iPr_def_15,X1)
| ~ sdtlseqdt0(iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_1773,c_6152]) ).
tcf(c_6178,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(X0,X1),iPr_def_16)
| ~ aScalar0(iPr_def_15)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X1)
| ~ sdtlseqdt0(X1,iPr_def_15)
| ~ sdtlseqdt0(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_1773,c_6152]) ).
tcf(c_6179,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sdtlseqdt0(sdtasdt0(X3,X4),X2)
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X4)
| ~ sdtlseqdt0(X4,X1)
| ~ sdtlseqdt0(X3,X0)
| ~ aScalar0(sdtasdt0(X3,X4))
| ~ aScalar0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_6152,c_80]) ).
tcf(c_6180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X2,X3) )
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_18,X3)
| ~ sdtlseqdt0(X3,X1)
| ~ sdtlseqdt0(X2,X0)
| ~ aScalar0(sdtasdt0(X2,X3))
| ~ aScalar0(sdtasdt0(X0,X1))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X3)) ),
inference(superposition,[status(thm)],[c_6152,c_79]) ).
tcf(c_6310,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_18,X0)
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X0) ),
inference(superposition,[status(thm)],[c_5843,c_80]) ).
tcf(c_6311,plain,
( ( iPr_def_17 = iPr_def_18 )
| ~ aScalar0(iPr_def_18)
| ~ aScalar0(iPr_def_17)
| ~ sdtlseqdt0(iPr_def_17,iPr_def_18) ),
inference(superposition,[status(thm)],[c_5843,c_79]) ).
tcf(c_6312,plain,
( ( iPr_def_17 = iPr_def_18 )
| ~ sdtlseqdt0(iPr_def_17,iPr_def_18) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6311,c_3841,c_3842]) ).
tcf(c_6315,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_18,X0)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6310,c_3841,c_3842]) ).
tcf(c_6322,plain,
iPr_def_17 = iPr_def_18,
inference(demodulation,[status(thm)],[c_5810,c_5812]) ).
tcf(c_6323,plain,
sdtlseqdt0(iPr_def_17,iPr_def_17),
inference(demodulation,[status(thm)],[c_5844,c_6322]) ).
tcf(c_6325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X2)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X0,X1) ),
inference(demodulation,[status(thm)],[c_6152,c_6322]) ).
tcf(c_6326,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X1)
| ~ sdtlseqdt0(iPr_def_17,X0)
| ( sdtasdt0(X0,X0) != sdtasdt0(X1,X1) ) ),
inference(demodulation,[status(thm)],[c_6088,c_6322]) ).
tcf(c_6327,plain,
! [X0: $i,X1: $i] :
( ( sdtasasdt0(X0,X1) = iPr_def_17 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X1) != iPr_def_13 )
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(demodulation,[status(thm)],[c_5817,c_6322]) ).
tcf(c_6328,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_17,X0)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(demodulation,[status(thm)],[c_5903,c_6322]) ).
tcf(c_6329,plain,
( sdtlseqdt0(iPr_def_17,iPr_def_16)
| ~ aScalar0(iPr_def_16) ),
inference(demodulation,[status(thm)],[c_5904,c_6322]) ).
tcf(c_6330,plain,
~ sdtlseqdt0(iPr_def_16,iPr_def_17),
inference(demodulation,[status(thm)],[c_5906,c_6322]) ).
tcf(c_6332,plain,
sdtasasdt0(xt,xt) = iPr_def_17,
inference(demodulation,[status(thm)],[c_1775,c_6322]) ).
tcf(c_6333,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,xt),sdtasasdt0(X0,xt)),sdtasdt0(sdtasasdt0(X0,X0),iPr_def_17))
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 )
| ( szszuzczcdt0(aDimensionOf0(X0)) != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_2820,c_6322]) ).
tcf(c_6366,plain,
( sdtlseqdt0(iPr_def_17,iPr_def_16)
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(iPr_def_16) ),
inference(superposition,[status(thm)],[c_83,c_6330]) ).
tcf(c_6373,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_17,X0)
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(iPr_def_16)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_6329,c_80]) ).
tcf(c_6388,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(szszuzczcdt0(X0))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(szszuzczcdt0(X0))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_5448]) ).
tcf(c_6389,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(sK4(X0))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(sK4(X0))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_5448]) ).
tcf(c_6390,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(aDimensionOf0(X0))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(aDimensionOf0(X0))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_5448]) ).
tcf(c_6424,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),szszuzczcdt0(iPr_def_13)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_5425]) ).
tcf(c_6426,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(xt)),szszuzczcdt0(iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_101,c_5425]) ).
tcf(c_6450,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = sdtlbdtrb0(X1,aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6010]) ).
tcf(c_6452,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))) = sdtlbdtrb0(X0,aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_101,c_6010]) ).
tcf(c_6491,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(szszuzczcdt0(X0))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(szszuzczcdt0(X0))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_6038]) ).
tcf(c_6492,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(sK4(X0))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(sK4(X0))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_6038]) ).
tcf(c_6493,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(aDimensionOf0(X0))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(aDimensionOf0(X0))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_6038]) ).
tcf(c_6534,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(sK4(szszuzczcdt0(X0)))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(sK4(szszuzczcdt0(X0)))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_6389]) ).
tcf(c_6535,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(sK4(sK4(X0)))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(sK4(sK4(X0)))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_6389]) ).
tcf(c_6536,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(sK4(aDimensionOf0(X0)))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(sK4(aDimensionOf0(X0)))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_6389]) ).
tcf(c_6575,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))),iPr_def_13) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6073]) ).
tcf(c_6577,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))),iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_101,c_6073]) ).
tcf(c_6591,plain,
sdtasdt0(sz0z00,iPr_def_17) = sz0z00,
inference(light_normalisation,[status(thm)],[c_3927,c_5848,c_6322]) ).
tcf(c_6592,plain,
sdtasdt0(iPr_def_17,iPr_def_17) = iPr_def_17,
inference(demodulation,[status(thm)],[c_6591,c_5812]) ).
tcf(c_6595,plain,
! [X0: $i,X1: $i] :
( ( sziznziztdt0(X0) = X1 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X1)) != aDimensionOf0(X0) )
| ( sdtlbdtrb0(X0,sK5(X0,X1)) != sdtlbdtrb0(X1,sK5(X0,X1)) ) ),
inference(light_normalisation,[status(thm)],[c_90,c_1778]) ).
tcf(c_6614,plain,
! [X0: $i] :
( ( sziznziztdt0(X0) = X0 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ~ aVector0(X0)
| ( szszuzczcdt0(aDimensionOf0(X0)) != aDimensionOf0(X0) ) ),
inference(equality_resolution,[status(thm)],[c_6595]) ).
tcf(c_6624,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) = sdtasasdt0(X0,X1) )
| ~ aVector0(X1)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != aDimensionOf0(X1) ) ),
inference(light_normalisation,[status(thm)],[c_98,c_1778]) ).
tcf(c_6643,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtasasdt0(X0,xt) )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_1770,c_6624]) ).
tcf(c_6644,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X0,aDimensionOf0(X0)))) = sdtasasdt0(X0,X0) )
| ~ aVector0(X0) ),
inference(equality_resolution,[status(thm)],[c_6624]) ).
tcf(c_6648,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(xt,iPr_def_13))) = sdtasasdt0(X0,xt) )
| ~ aVector0(xt)
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_6643,c_1770]) ).
tcf(c_6649,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(xt,iPr_def_13))) = sdtasasdt0(X0,xt) )
| ~ aVector0(X0)
| ( aDimensionOf0(X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6648,c_101]) ).
tcf(c_6666,plain,
iPr_def_17 = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_5900,c_6322]) ).
tcf(c_6667,plain,
smndt0(iPr_def_17) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_5848,c_6322]) ).
tcf(c_6688,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(sziznziztdt0(X0)),sziznziztdt0(sziznziztdt0(X0))),sdtasdt0(sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(sziznziztdt0(X0))),sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(sziznziztdt0(X0))))) = sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6644]) ).
tcf(c_6690,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt)))) = sdtasasdt0(xt,xt) ) ),
inference(superposition,[status(thm)],[c_101,c_6644]) ).
tcf(c_6691,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,iPr_def_13),sdtlbdtrb0(xt,iPr_def_13))) = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_6690,c_1770,c_6332]) ).
tcf(c_6707,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))),sdtasdt0(sdtlbdtrb0(sziznziztdt0(sziznziztdt0(X0)),aDimensionOf0(sziznziztdt0(sziznziztdt0(X0)))),sdtlbdtrb0(sziznziztdt0(sziznziztdt0(X0)),aDimensionOf0(sziznziztdt0(sziznziztdt0(X0)))))) = sdtasasdt0(sziznziztdt0(sziznziztdt0(X0)),sziznziztdt0(sziznziztdt0(X0))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6688]) ).
tcf(c_6709,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(sziznziztdt0(xt)),sziznziztdt0(sziznziztdt0(xt))),sdtasdt0(sdtlbdtrb0(sziznziztdt0(xt),aDimensionOf0(sziznziztdt0(xt))),sdtlbdtrb0(sziznziztdt0(xt),aDimensionOf0(sziznziztdt0(xt))))) = sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)) ) ),
inference(superposition,[status(thm)],[c_101,c_6688]) ).
tcf(c_6731,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))),szszuzczcdt0(iPr_def_13)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6424]) ).
tcf(c_6733,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))),szszuzczcdt0(iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_101,c_6424]) ).
tcf(c_6762,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) = sdtlbdtrb0(X1,aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6450]) ).
tcf(c_6764,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) = sdtlbdtrb0(X0,aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_101,c_6450]) ).
tcf(c_6820,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_6492]) ).
tcf(c_6821,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(sK4(sK4(X0)))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(sK4(sK4(X0)))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_6492]) ).
tcf(c_6822,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_6492]) ).
tcf(c_6878,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_6535]) ).
tcf(c_6879,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(X0))))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(X0))))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_6535]) ).
tcf(c_6880,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),szszuzczcdt0(sK4(sK4(sK4(sK4(aDimensionOf0(X0))))))) = sdtlbdtrb0(X1,szszuzczcdt0(sK4(sK4(sK4(sK4(aDimensionOf0(X0))))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_6535]) ).
tcf(c_6924,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))),iPr_def_13) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6575]) ).
tcf(c_6926,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))),iPr_def_13) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))),iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_101,c_6575]) ).
tcf(c_6943,plain,
sdtpldt0(sz0z00,iPr_def_17) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_4038,c_6666]) ).
tcf(c_6944,plain,
sdtpldt0(iPr_def_17,iPr_def_17) = iPr_def_17,
inference(demodulation,[status(thm)],[c_6943,c_5812]) ).
tcf(c_6946,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_17,sdtpldt0(X0,X1))
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X1)
| ~ sdtlseqdt0(iPr_def_17,X0) ),
inference(superposition,[status(thm)],[c_6944,c_81]) ).
tcf(c_6947,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_17)
| ~ aScalar0(iPr_def_17)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,iPr_def_17)
| ~ sdtlseqdt0(X0,iPr_def_17) ),
inference(superposition,[status(thm)],[c_6944,c_81]) ).
tcf(c_6948,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtpldt0(X0,X1),iPr_def_17)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,iPr_def_17)
| ~ sdtlseqdt0(X0,iPr_def_17) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6947,c_3842]) ).
tcf(c_6954,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(iPr_def_17,sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(iPr_def_17,X1)
| ~ sdtlseqdt0(iPr_def_17,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6946,c_3842]) ).
tcf(c_6985,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))))) = sdtlbdtrb0(X1,aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6762]) ).
tcf(c_6987,plain,
! [X0: $i] :
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X0),aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))))) = sdtlbdtrb0(X0,aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_101,c_6762]) ).
tcf(c_7016,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))),sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))),sdtasdt0(sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))),sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))))) = sdtasasdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))),sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6707]) ).
tcf(c_7018,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( sdtpldt0(sdtasasdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))),sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))),sdtasdt0(sdtlbdtrb0(sziznziztdt0(sziznziztdt0(xt)),aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))),sdtlbdtrb0(sziznziztdt0(sziznziztdt0(xt)),aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))))) = sdtasasdt0(sziznziztdt0(sziznziztdt0(xt)),sziznziztdt0(sziznziztdt0(xt))) ) ),
inference(superposition,[status(thm)],[c_101,c_6707]) ).
tcf(c_7044,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(X0)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(X0))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0)))))),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(X0))))),szszuzczcdt0(iPr_def_13)) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_3181,c_6731]) ).
tcf(c_7046,plain,
( ( aDimensionOf0(xt) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(xt)) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))) = iPr_def_13 )
| ( aDimensionOf0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt))))),szszuzczcdt0(iPr_def_13)) = sdtlbdtrb0(sziznziztdt0(sziznziztdt0(sziznziztdt0(sziznziztdt0(xt)))),szszuzczcdt0(iPr_def_13)) ) ),
inference(superposition,[status(thm)],[c_101,c_6731]) ).
tcf(c_7080,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_6821]) ).
tcf(c_7081,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( aDimensionOf0(X1) = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(X0))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(sK4(sK4(sK4(X0))))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(sK4(sK4(sK4(X0))))))) )
| ~ aVector0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_6821]) ).
tcf(c_7082,plain,
! [X0: $i,X1: $i] :
( ( aDimensionOf0(X1) = iPr_def_13 )
| ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(aDimensionOf0(X0))))) = iPr_def_13 )
| ( sdtlbdtrb0(sziznziztdt0(X1),sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0))))))) = sdtlbdtrb0(X1,sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0))))))) )
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_6821]) ).
tcf(c_7131,plain,
! [X0: $i] :
( ( szszuzczcdt0(X0) = iPr_def_13 )
| ( sK4(szszuzczcdt0(X0)) = iPr_def_13 )
| ( sK4(sK4(szszuzczcdt0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(szszuzczcdt0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(szszuzczcdt0(X0))))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(szszuzczcdt0(X0)))))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_50,c_4748]) ).
tcf(c_7132,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( sK4(X0) = iPr_def_13 )
| ( sK4(sK4(X0)) = iPr_def_13 )
| ( sK4(sK4(sK4(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(X0))))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(sK4(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(sK4(X0)))))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(sK4(X0)))))))) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_2944,c_4748]) ).
tcf(c_7133,plain,
! [X0: $i] :
( ( aDimensionOf0(X0) = iPr_def_13 )
| ( sK4(aDimensionOf0(X0)) = iPr_def_13 )
| ( sK4(sK4(aDimensionOf0(X0))) = iPr_def_13 )
| ( sK4(sK4(sK4(aDimensionOf0(X0)))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(aDimensionOf0(X0))))) = iPr_def_13 )
| ( sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))) = iPr_def_13 )
| ( szszuzczcdt0(sK4(szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))))))) = szszuzczcdt0(sK4(sK4(sK4(sK4(sK4(sK4(aDimensionOf0(X0)))))))) )
| ~ aVector0(X0) ),
inference(superposition,[status(thm)],[c_88,c_4748]) ).
tcf(c_7240,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_7133,c_7132,c_7131,c_7082,c_7081,c_7080,c_7046,c_7044,c_7018,c_7016,c_6987,c_6985,c_6954,c_6948,c_6947,c_6946,c_6944,c_6926,c_6924,c_6880,c_6879,c_6878,c_6822,c_6821,c_6820,c_6764,c_6762,c_6733,c_6731,c_6709,c_6707,c_6691,c_6690,c_6688,c_6667,c_6666,c_6649,c_6648,c_6644,c_6643,c_6624,c_6614,c_6595,c_6592,c_6577,c_6575,c_6536,c_6535,c_6534,c_6493,c_6492,c_6491,c_6452,c_6450,c_6426,c_6424,c_6390,c_6389,c_6388,c_6373,c_6366,c_6333,c_6332,c_6330,c_6329,c_6328,c_6327,c_6326,c_6325,c_6323,c_6322,c_6315,c_6312,c_6311,c_6310,c_6254,c_6253,c_6252,c_6251,c_6250,c_6249,c_6248,c_6180,c_6179,c_6178,c_6177,c_6152,c_6144,c_6138,c_6137,c_6136,c_6117,c_6107,c_6088,c_6075,c_6073,c_6039,c_6038,c_6037,c_6012,c_6010,c_5992,c_5991,c_5987,c_5986,c_5982,c_5978,c_5976,c_5975,c_5974,c_5973,c_5949,c_5942,c_5906,c_5904,c_5903,c_5902,c_5900,c_5848,c_5847,c_5846,c_5845,c_5843,c_5842,c_5840,c_5839,c_5837,c_5836,c_5844,c_5834,c_5833,c_5832,c_5831,c_5830,c_5829,c_5828,c_5827,c_5826,c_5825,c_5824,c_5823,c_5838,c_5841,c_5818,c_5817,c_5816,c_5815,c_5814,c_5813,c_5812,c_5811,c_5810,c_5809,c_5808,c_5807,c_5777,c_5771,c_5770,c_5769,c_5759,c_5753,c_5752,c_5751,c_5707,c_5701,c_5695,c_5689,c_5682,c_5681,c_5680,c_5679,c_5678,c_5677,c_5676,c_5675,c_5674,c_5654,c_5652,c_5633,c_5616,c_5615,c_5611,c_5610,c_5606,c_5602,c_5598,c_5597,c_5596,c_5595,c_5594,c_5578,c_5527,c_5526,c_5525,c_5524,c_5523,c_5522,c_5521,c_5520,c_5519,c_5449,c_5448,c_5447,c_5427,c_5425,c_5396,c_5395,c_5394,c_5364,c_5362,c_5345,c_5344,c_5343,c_5327,c_5325,c_5287,c_5286,c_5285,c_5284,c_5268,c_5266,c_5148,c_5147,c_5146,c_5145,c_5144,c_5143,c_5142,c_5141,c_5140,c_5061,c_5060,c_5059,c_5058,c_5057,c_5056,c_5055,c_5054,c_5053,c_4982,c_4981,c_4980,c_4979,c_4978,c_4977,c_4976,c_4975,c_4974,c_4933,c_4932,c_4931,c_4930,c_4917,c_4877,c_4876,c_4875,c_4841,c_4839,c_4809,c_4807,c_4749,c_4748,c_4747,c_4704,c_4703,c_4702,c_4672,c_4670,c_4638,c_4632,c_4619,c_4618,c_4617,c_4616,c_4590,c_4534,c_4531,c_4530,c_4529,c_4506,c_4497,c_4491,c_4485,c_4473,c_4469,c_4465,c_4460,c_4459,c_4458,c_4457,c_4456,c_4454,c_4453,c_4452,c_4451,c_4449,c_4422,c_4421,c_4420,c_4419,c_4399,c_4398,c_4381,c_4376,c_4371,c_4368,c_4365,c_4363,c_4362,c_4361,c_4359,c_4358,c_4311,c_4309,c_4273,c_4272,c_4271,c_4220,c_4219,c_4218,c_4194,c_4192,c_4170,c_4168,c_4117,c_4116,c_4115,c_4079,c_4077,c_4039,c_4038,c_4037,c_4036,c_4035,c_4034,c_4033,c_4032,c_4031,c_4030,c_4029,c_4028,c_4027,c_4026,c_4025,c_4024,c_4023,c_4022,c_4021,c_3989,c_3988,c_3987,c_3986,c_3985,c_3984,c_3983,c_3982,c_3981,c_3980,c_3979,c_3978,c_3977,c_3976,c_3975,c_3974,c_3973,c_3972,c_3971,c_3936,c_3935,c_3934,c_3933,c_3932,c_3931,c_3930,c_3929,c_3928,c_3927,c_3926,c_3925,c_3924,c_3923,c_3922,c_3921,c_3920,c_3919,c_3918,c_3886,c_3885,c_3842,c_3841,c_3840,c_3839,c_3838,c_3837,c_3836,c_3835,c_3834,c_3833,c_3832,c_3831,c_3830,c_3829,c_3828,c_3827,c_3826,c_3825,c_3824,c_3823,c_3822,c_3821,c_3820,c_3797,c_3793,c_3789,c_3785,c_3782,c_3781,c_3780,c_3779,c_3778,c_3762,c_3746,c_3745,c_3743,c_3733,c_3698,c_3697,c_3696,c_3695,c_3694,c_3693,c_3660,c_3659,c_3658,c_3630,c_3629,c_3628,c_3608,c_3606,c_3574,c_3573,c_3572,c_3545,c_3544,c_3543,c_3529,c_3528,c_3526,c_3513,c_3497,c_3496,c_3495,c_3494,c_3487,c_3462,c_3461,c_3460,c_3459,c_3458,c_3431,c_3430,c_3429,c_3428,c_3427,c_3404,c_3403,c_3402,c_3401,c_3400,c_3362,c_3361,c_3360,c_3359,c_3358,c_3357,c_3326,c_3325,c_3324,c_3323,c_3322,c_3300,c_3299,c_3298,c_3288,c_3279,c_3251,c_3250,c_3249,c_3248,c_3247,c_3224,c_3223,c_3222,c_3221,c_3220,c_3199,c_3198,c_3197,c_3196,c_3195,c_3181,c_3164,c_3163,c_3162,c_3161,c_3160,c_3139,c_3138,c_3137,c_3136,c_3135,c_3098,c_3097,c_3096,c_3095,c_3094,c_3093,c_3092,c_3091,c_3072,c_3071,c_3070,c_3069,c_3052,c_3051,c_3050,c_3049,c_3005,c_3004,c_3003,c_3002,c_3001,c_3000,c_2999,c_2998,c_2966,c_2965,c_2964,c_2963,c_2962,c_2961,c_2944,c_2939,c_2938,c_2930,c_2920,c_2919,c_2914,c_2909,c_2908,c_2900,c_2891,c_2890,c_2879,c_2878,c_2877,c_2876,c_2875,c_2864,c_2839,c_2838,c_2831,c_2830,c_2820,c_2809,c_2778,c_2777,c_2772,c_2771,c_2768,c_2767,c_2766,c_2765,c_2764,c_2763,c_2755,c_2749,c_2745,c_2744,c_2743,c_2742,c_2741,c_2730,c_2724,c_2723,c_2791,c_2789,c_2793,c_1780,c_1779,c_1778,c_1776,c_1775,c_1774,c_1773,c_1772,c_1771,c_1770,c_1769,c_1768,c_1767,c_1766,c_1765,c_1777,c_216,c_2913,c_101,c_100,c_99,c_98,c_97,c_96,c_95,c_94,c_93,c_92,c_91,c_90,c_89,c_88,c_87,c_86,c_85,c_84,c_83,c_82,c_81,c_80,c_79,c_78,c_77,c_76,c_75,c_74,c_73,c_72,c_70,c_68,c_66,c_65,c_64,c_63,c_62,c_61,c_60,c_59,c_58,c_57,c_56,c_54,c_53,c_52,c_51,c_50,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG081+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.57 % Computer : n026.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Thu Sep 24 08:10:41 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.61 Running first-order theorem proving
% 0.09/0.61 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.63
% 0.09/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.63
% 0.09/0.63 % Detected problem language: tptp
% 0.13/0.64 % Proving...
% 1.64/1.49 % SZS status Started for theBenchmark.p
% 1.64/1.49 % SZS status Theorem for theBenchmark.p
% 1.64/1.49
% 1.64/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.64/1.49
% 1.64/1.49 % ------ iProver source info
% 1.64/1.49
% 1.64/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 1.64/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.64/1.49 % git: non_committed_changes: false
% 1.64/1.49
% 1.64/1.49 % ------ Parsing...
% 1.64/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.64/1.49
% 1.64/1.49 % ------ Preprocessing... sup_sim: 2 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.64/1.49
% 1.64/1.49 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.64/1.49
% 1.64/1.49 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 1.64/1.49 % ------ Proving...
% 1.64/1.49 % ------ Problem Properties
% 1.64/1.49
% 1.64/1.49 %
% 1.64/1.49 % clauses 66
% 1.64/1.49 % conjectures 1
% 1.64/1.49 % EPR 14
% 1.64/1.49 % Horn 54
% 1.64/1.49 % unary 15
% 1.64/1.49 % binary 17
% 1.64/1.49 % lits 198
% 1.64/1.49 % lits eq 60
% 1.64/1.49 % fd_pure 0
% 1.64/1.49 % fd_pseudo 0
% 1.64/1.49 % fd_cond 1
% 1.64/1.49 % fd_pseudo_cond 5
% 1.64/1.49 % AC symbols 0
% 1.64/1.49
% 1.64/1.49 % ------ Schedule dynamic 5 is on
% 1.64/1.49
% 1.64/1.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.64/1.49
% 1.64/1.49
% 1.64/1.49 % ------
% 1.64/1.49 % Current options:
% 1.64/1.49 % ------
% 1.64/1.49
% 1.64/1.49
% 1.64/1.49 %
% 1.64/1.49
% 1.64/1.49 % ------ Proving...
% 1.64/1.49 %
% 1.64/1.49
% 1.64/1.49 % SZS status Theorem for theBenchmark.p
% 1.64/1.49
% 1.64/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.79/1.51
% 3.79/1.51
%------------------------------------------------------------------------------