TSTP Solution File: RNG077+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG077+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:49:18 EDT 2023
% Result : Theorem 78.02s 42.56s
% Output : Refutation 78.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 91
% Syntax : Number of formulae : 200 ( 47 unt; 32 typ; 0 def)
% Number of atoms : 529 ( 181 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1685 ( 123 ~; 101 |; 153 &;1205 @)
% ( 1 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 20 con; 0-2 aty)
% Number of variables : 176 ( 0 ^; 174 !; 2 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(aVector0_type,type,
aVector0: $i > $o ).
thf(aDimensionOf0_type,type,
aDimensionOf0: $i > $i ).
thf(sz00_type,type,
sz00: $i ).
thf(sziznziztdt0_type,type,
sziznziztdt0: $i > $i ).
thf(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
thf(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
thf(sdtlbdtrb0_type,type,
sdtlbdtrb0: $i > $i > $i ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(xP_type,type,
xP: $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(xH_type,type,
xH: $i ).
thf(xE_type,type,
xE: $i ).
thf(xs_type,type,
xs: $i ).
thf(aScalar0_type,type,
aScalar0: $i > $o ).
thf(xB_type,type,
xB: $i ).
thf(xt_type,type,
xt: $i ).
thf(xA_type,type,
xA: $i ).
thf(sz0z00_type,type,
sz0z00: $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(xq_type,type,
xq: $i ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(xC_type,type,
xC: $i ).
thf(xp_type,type,
xp: $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(xD_type,type,
xD: $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(xR_type,type,
xR: $i ).
thf(xS_type,type,
xS: $i ).
thf(xF_type,type,
xF: $i ).
thf(xN_type,type,
xN: $i ).
thf(xG_type,type,
xG: $i ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ A ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( aDimensionOf0 @ ( sziznziztdt0 @ A ) )
= ( aDimensionOf0 @ ( sziznziztdt0 @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(33,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
thf(156,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B ) )
=> ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ A @ B ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
thf(173,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B ) )
=> ( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ A @ B ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
thf(194,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(60,axiom,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
thf(254,plain,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(25,axiom,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
thf(138,plain,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(13,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( ( ( aDimensionOf0 @ A )
!= sz00 )
=> ! [B: $i] :
( ( B
= ( sziznziztdt0 @ A ) )
<=> ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
thf(88,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( ( ( aDimensionOf0 @ A )
!= sz00 )
=> ! [B: $i] :
( ( ( B
= ( sziznziztdt0 @ A ) )
=> ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) ) )
& ( ( ( aVector0 @ B )
& ( ( szszuzczcdt0 @ ( aDimensionOf0 @ B ) )
= ( aDimensionOf0 @ A ) )
& ! [C: $i] :
( ( aNaturalNumber0 @ C )
=> ( ( sdtlbdtrb0 @ B @ C )
= ( sdtlbdtrb0 @ A @ C ) ) ) )
=> ( B
= ( sziznziztdt0 @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ A ) @ ( sziznziztdt0 @ B ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ A @ ( aDimensionOf0 @ A ) ) @ ( sdtlbdtrb0 @ B @ ( aDimensionOf0 @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
!= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= ( sdtpldt0 @ ( sdtasasdt0 @ ( sziznziztdt0 @ A ) @ ( sziznziztdt0 @ B ) ) @ ( sdtasdt0 @ ( sdtlbdtrb0 @ A @ ( aDimensionOf0 @ A ) ) @ ( sdtlbdtrb0 @ B @ ( aDimensionOf0 @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(17,axiom,
( ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
thf(113,plain,
( ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(115,plain,
aVector0 @ xq,
inference(cnf,[status(esa)],[113]) ).
thf(52,axiom,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
thf(217,plain,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(47,axiom,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
thf(202,plain,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(18,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNat) ).
thf(117,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(119,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( ( szszuzczcdt0 @ A )
!= sz00 ) ),
inference(cnf,[status(esa)],[117]) ).
thf(120,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
thf(247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(26,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
thf(142,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(31,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSort) ).
thf(153,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(41,axiom,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
thf(183,plain,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(185,plain,
aScalar0 @ xH,
inference(cnf,[status(esa)],[183]) ).
thf(5,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtr) ).
thf(67,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(68,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(70,plain,
! [A: $i] :
( ( A = sz00 )
| ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(1,conjecture,
( ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) )
= ( sdtpldt0 @ ( sdtasdt0 @ xE @ xH ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
( ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ xE @ xH ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(61,plain,
( ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtpldt0 @ ( sdtasdt0 @ xE @ xH ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(62,plain,
( ( sdtpldt0 @ ( sdtasdt0 @ xE @ xH ) @ ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) ) )
!= ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(258,plain,
( ( ( sdtasdt0 @ xE @ xH )
!= ( sdtpldt0 @ xP @ xP ) )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(435,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ( ( sdtasdt0 @ sz00 @ xH )
!= ( sdtpldt0 @ xP @ xP ) )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( A != xE ) ),
inference(paramod_ordered,[status(thm)],[70,258]) ).
thf(436,plain,
( ~ ( aNaturalNumber0 @ xE )
| ( aNaturalNumber0 @ ( sk1 @ xE ) )
| ( ( sdtasdt0 @ sz00 @ xH )
!= ( sdtpldt0 @ xP @ xP ) )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) ) ),
inference(pattern_uni,[status(thm)],[435:[bind(A,$thf( xE ))]]) ).
thf(43,axiom,
sdtlseqdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xR @ xS ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1983) ).
thf(189,plain,
sdtlseqdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xR @ xS ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(8,axiom,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
thf(76,plain,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(78,plain,
aScalar0 @ xB,
inference(cnf,[status(esa)],[76]) ).
thf(259,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( ( sdtasdt0 @ xE @ xH )
!= ( sdtasdt0 @ xH @ xH ) )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtpldt0 @ xP @ xP ) ) ),
inference(eqfactor_ordered,[status(thm)],[258]) ).
thf(261,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( ( sdtasdt0 @ xE @ xH )
!= ( sdtasdt0 @ xH @ xH ) )
| ( ( sdtasdt0 @ xH @ xE )
!= xP )
| ( ( sdtasdt0 @ xH @ xH )
!= xP ) ),
inference(simp,[status(thm)],[259]) ).
thf(51,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).
thf(216,plain,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtpldt0 @ A @ C ) @ ( sdtpldt0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
thf(84,plain,
aScalar0 @ sz0z00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
thf(147,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(53,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz0z00 )
= A )
& ( ( sdtpldt0 @ sz0z00 @ A )
= A )
& ( ( sdtasdt0 @ A @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ A )
= sz0z00 )
& ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ A ) )
= A )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
thf(221,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz0z00 )
= A )
& ( ( sdtpldt0 @ sz0z00 @ A )
= A )
& ( ( sdtasdt0 @ A @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ A )
= sz0z00 )
& ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ A ) )
= A )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(22,axiom,
( ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
thf(130,plain,
( ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(132,plain,
aVector0 @ xp,
inference(cnf,[status(esa)],[130]) ).
thf(131,plain,
( xp
= ( sziznziztdt0 @ xs ) ),
inference(cnf,[status(esa)],[130]) ).
thf(133,plain,
( ( sziznziztdt0 @ xs )
= xp ),
inference(lifteq,[status(thm)],[131]) ).
thf(6,axiom,
( ( aDimensionOf0 @ xs )
!= sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
thf(72,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(73,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(polarity_switch,[status(thm)],[72]) ).
thf(74,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(lifteq,[status(thm)],[73]) ).
thf(48,axiom,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
thf(206,plain,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(114,plain,
( xq
= ( sziznziztdt0 @ xt ) ),
inference(cnf,[status(esa)],[113]) ).
thf(116,plain,
( ( sziznziztdt0 @ xt )
= xq ),
inference(lifteq,[status(thm)],[114]) ).
thf(56,axiom,
sdtlseqdt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtasdt0 @ xH @ xH ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2796) ).
thf(243,plain,
sdtlseqdt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtpldt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtasdt0 @ xH @ xH ) ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xC @ xD ) @ ( sdtpldt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtasdt0 @ xH @ xH ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(44,axiom,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
thf(190,plain,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(192,plain,
aScalar0 @ xS,
inference(cnf,[status(esa)],[190]) ).
thf(59,axiom,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
thf(250,plain,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(252,plain,
aScalar0 @ xP,
inference(cnf,[status(esa)],[250]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B )
| ( ( szszuzczcdt0 @ A )
!= ( szszuzczcdt0 @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[63]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( szszuzczcdt0 @ A )
!= ( szszuzczcdt0 @ B ) )
| ( A = B )
| ~ ( aNaturalNumber0 @ A )
| ~ ( aNaturalNumber0 @ B ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(20,axiom,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
thf(124,plain,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(50,axiom,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
thf(212,plain,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(15,axiom,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
thf(107,plain,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(109,plain,
aVector0 @ xs,
inference(cnf,[status(esa)],[107]) ).
thf(256,plain,
aScalar0 @ xG,
inference(cnf,[status(esa)],[254]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIHOrd) ).
thf(134,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
thf(128,plain,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ C ) )
=> ( sdtlseqdt0 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B )
& ( ( sdtasdt0 @ A @ A )
= ( sdtasdt0 @ B @ B ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
thf(244,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ sz0z00 @ A )
& ( sdtlseqdt0 @ sz0z00 @ B )
& ( ( sdtasdt0 @ A @ A )
= ( sdtasdt0 @ B @ B ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(262,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( xE != xH )
| ( xH != xH )
| ( ( sdtasdt0 @ xH @ xE )
!= xP )
| ( ( sdtasdt0 @ xH @ xH )
!= xP ) ),
inference(simp,[status(thm)],[259]) ).
thf(264,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( xE != xH )
| ( ( sdtasdt0 @ xH @ xE )
!= xP )
| ( ( sdtasdt0 @ xH @ xH )
!= xP ) ),
inference(simp,[status(thm)],[262]) ).
thf(29,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
thf(149,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ sz0z00 @ C )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
thf(176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ sz0z00 @ C )
& ( sdtlseqdt0 @ C @ D ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(204,plain,
aScalar0 @ xN,
inference(cnf,[status(esa)],[202]) ).
thf(69,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( A = sz00 )
| ( A
= ( szszuzczcdt0 @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(71,plain,
! [A: $i] :
( ( A = sz00 )
| ( ( szszuzczcdt0 @ ( sk1 @ A ) )
= A )
| ~ ( aNaturalNumber0 @ A ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
thf(144,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
& ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
thf(159,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
& ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
thf(187,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(219,plain,
aScalar0 @ xE,
inference(cnf,[status(esa)],[217]) ).
thf(208,plain,
aScalar0 @ xF,
inference(cnf,[status(esa)],[206]) ).
thf(140,plain,
aScalar0 @ xD,
inference(cnf,[status(esa)],[138]) ).
thf(4,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatSort) ).
thf(66,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ B ) @ ( sdtasasdt0 @ A @ B ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ A ) @ ( sdtasasdt0 @ B @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1652) ).
thf(240,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ B ) @ ( sdtasasdt0 @ A @ B ) ) @ ( sdtasdt0 @ ( sdtasasdt0 @ A @ A ) @ ( sdtasasdt0 @ B @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(108,plain,
aVector0 @ xt,
inference(cnf,[status(esa)],[107]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= sz0z00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= sz0z00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(437,plain,
! [A: $i] :
( ~ ( aNaturalNumber0 @ A )
| ( aNaturalNumber0 @ ( sk1 @ A ) )
| ( ( sdtasdt0 @ xE @ sz00 )
!= ( sdtpldt0 @ xP @ xP ) )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( A != xH ) ),
inference(paramod_ordered,[status(thm)],[70,258]) ).
thf(438,plain,
( ~ ( aNaturalNumber0 @ xH )
| ( aNaturalNumber0 @ ( sk1 @ xH ) )
| ( ( sdtasdt0 @ xE @ sz00 )
!= ( sdtpldt0 @ xP @ xP ) )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) ) ),
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( xH ))]]) ).
thf(9,axiom,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
thf(80,plain,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(260,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( xE != xH )
| ( xH != xH )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtpldt0 @ xP @ xP ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(263,plain,
( ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtasdt0 @ xH @ xH ) )
| ( xE != xH )
| ( ( sdtpldt0 @ ( sdtasdt0 @ xH @ xE ) @ ( sdtasdt0 @ xH @ xH ) )
!= ( sdtpldt0 @ xP @ xP ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
= ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).
thf(199,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
= ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) ) ),
inference(cnf,[status(esa)],[176]) ).
thf(32,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
thf(154,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLess) ).
thf(87,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNat) ).
thf(158,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mVcSort) ).
thf(75,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(82,plain,
aScalar0 @ xA,
inference(cnf,[status(esa)],[80]) ).
thf(214,plain,
aScalar0 @ xR,
inference(cnf,[status(esa)],[212]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
thf(168,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(126,plain,
aScalar0 @ xC,
inference(cnf,[status(esa)],[124]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
thf(178,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(276,plain,
! [A: $i] :
( ( ( szszuzczcdt0 @ A )
!= sz00 )
| ( ( aNaturalNumber0 @ sz00 )
!= ( aNaturalNumber0 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[158,120]) ).
thf(277,plain,
( ( szszuzczcdt0 @ sz00 )
!= sz00 ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( sz00 ))]]) ).
thf(515,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ~ ( aScalar0 @ E )
| ~ ( aScalar0 @ F )
| ~ ( aScalar0 @ G )
| ~ ( aScalar0 @ H )
| ~ ( sdtlseqdt0 @ E @ F )
| ~ ( sdtlseqdt0 @ G @ H )
| ( sdtlseqdt0 @ ( sdtasdt0 @ E @ G ) @ ( sdtasdt0 @ F @ H ) )
| ( ( sdtlseqdt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ D ) )
!= ( sdtlseqdt0 @ sz0z00 @ G ) ) ),
inference(paramod_ordered,[status(thm)],[177,177]) ).
thf(572,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sdtlseqdt0 @ ( sdtasdt0 @ E @ G ) @ ( sdtasdt0 @ F @ H ) )
| ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ~ ( aScalar0 @ E )
| ~ ( aScalar0 @ F )
| ~ ( aScalar0 @ G )
| ~ ( aScalar0 @ H )
| ~ ( sdtlseqdt0 @ E @ F )
| ~ ( sdtlseqdt0 @ G @ H )
| ( ( sdtasdt0 @ A @ C )
!= sz0z00 )
| ( ( sdtasdt0 @ B @ D )
!= G ) ),
inference(simp,[status(thm)],[515]) ).
thf(607,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( sdtlseqdt0 @ ( sdtasdt0 @ E @ ( sdtasdt0 @ B @ D ) ) @ ( sdtasdt0 @ F @ G ) )
| ~ ( aScalar0 @ A )
| ~ ( aScalar0 @ B )
| ~ ( aScalar0 @ C )
| ~ ( aScalar0 @ D )
| ~ ( sdtlseqdt0 @ A @ B )
| ~ ( sdtlseqdt0 @ sz0z00 @ C )
| ~ ( sdtlseqdt0 @ C @ D )
| ~ ( aScalar0 @ E )
| ~ ( aScalar0 @ F )
| ~ ( aScalar0 @ ( sdtasdt0 @ B @ D ) )
| ~ ( aScalar0 @ G )
| ~ ( sdtlseqdt0 @ E @ F )
| ~ ( sdtlseqdt0 @ ( sdtasdt0 @ B @ D ) @ G )
| ( ( sdtasdt0 @ A @ C )
!= sz0z00 ) ),
inference(simp,[status(thm)],[572]) ).
thf(1966,plain,
$false,
inference(cvc4,[status(thm)],[110,156,173,194,254,138,88,170,115,217,202,120,247,142,153,185,436,189,78,261,216,238,121,84,147,61,221,132,133,74,206,116,243,117,85,70,192,252,65,124,212,109,256,134,128,105,244,264,149,176,204,71,144,159,187,113,219,76,208,140,66,240,108,130,135,438,80,63,263,67,199,177,154,72,250,87,258,158,75,82,214,151,168,190,183,210,107,126,62,178,277,607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG077+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 20:54:56 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (146ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.73/1.20 % [INFO] eprover registered as external prover.
% 1.73/1.20 % [INFO] cvc4 registered as external prover.
% 1.73/1.21 % [INFO] Scanning for conjecture ...
% 1.93/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.01/1.28 % [INFO] Found a conjecture and 58 axioms. Running axiom selection ...
% 2.25/1.34 % [INFO] Axiom selection finished. Selected 58 axioms (removed 0 axioms).
% 2.25/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.35/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 2.35/1.41 % [INFO] Type checking passed.
% 2.35/1.42 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 78.02/42.56 % External prover 'cvc4' found a proof!
% 78.02/42.56 % [INFO] Killing All external provers ...
% 78.02/42.56 % Time passed: 42037ms (effective reasoning time: 41581ms)
% 78.02/42.56 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 78.02/42.56 % Axioms used in derivation (58): mLERef, mMulSc, m__1930, mSqrt, mZeroNat, mIH, m__1766, mLess, m__1678, mSuccEqu, m__1820, mNatExtr, mArith, m__1783, mDefSPN, mMNeg, m__1854, mScSort, m__1983, mLETrn, m__1949, mDefSPZ, m__1746, mDimNat, m__1837, mLEMonM, mPosMon, mDefInit, m__1911, mMDNeg, mLETot, m__1800, mDistr, m__1967, mEqInit, mSZeroSc, mVcSort, mLEASm, mSumSc, mScZero, mLEMon, mScPr, m__1678_01, m__2796, m__1892, mElmSc, mDistr2, mSqPos, m__1709, m__1692, m__1652, mNatSort, m__1726, mIHOrd, mNegSc, mSuccNat, mScSqPos, m__1873
% 78.02/42.56 % No. of inferences in proof: 168
% 78.02/42.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 42037 ms resp. 41581 ms w/o parsing
% 78.53/42.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 78.53/42.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------