TSTP Solution File: RNG050+1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Tue May 21 02:37:34 EDT 2024
% Result : Theorem 5.20s 2.71s
% Output : Refutation 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 55
% Syntax : Number of formulae : 96 ( 12 unt; 16 typ; 0 def)
% Number of atoms : 308 ( 86 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 893 ( 15 ~; 2 |; 121 &; 650 @)
% ( 1 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 132 ( 0 ^ 130 !; 2 ?; 132 :)
% 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(xs_type,type,
xs: $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(sz0z00_type,type,
sz0z00: $i ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(aScalar0_type,type,
aScalar0: $i > $o ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(23,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
thf(101,plain,
aScalar0 @ sz0z00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHOrd) ).
thf(56,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(57,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',mScZero) ).
thf(132,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)],[30]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',mMNeg) ).
thf(70,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)],[12]) ).
thf(33,axiom,
aVector0 @ xs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).
thf(156,plain,
aVector0 @ xs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',mSqrt) ).
thf(98,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)],[22]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',mDefInit) ).
thf(103,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)],[25]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',mDistr2) ).
thf(80,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)],[14]) ).
thf(27,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
thf(123,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',mPosMon) ).
thf(95,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)],[21]) ).
thf(10,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mVcSort) ).
thf(67,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
& ( ( aDimensionOf0 @ B )
= sz00 ) )
=> ( ( sdtasasdt0 @ A @ B )
= sz0z00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).
thf(87,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)],[18]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',mDistr) ).
thf(75,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)],[13]) ).
thf(40,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
thf(170,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtlseqdt0 @ A @ B )
& ( sdtlseqdt0 @ B @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
thf(120,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)],[26]) ).
thf(28,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
thf(125,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
thf(157,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)],[34]) ).
thf(16,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).
thf(85,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).
thf(102,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',mDefSPN) ).
thf(92,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)],[20]) ).
thf(9,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
thf(65,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aVector0 @ B ) )
=> ( ( ( aDimensionOf0 @ A )
= ( aDimensionOf0 @ B ) )
=> ( aScalar0 @ ( sdtasasdt0 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
thf(129,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)],[29]) ).
thf(1,conjecture,
( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(41,plain,
~ ( ( ( ( aDimensionOf0 @ xs )
!= sz00 )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ xs @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',mArith) ).
thf(45,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)],[3]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',mLETrn) ).
thf(161,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)],[36]) ).
thf(31,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1516) ).
thf(149,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( ( iLess0 @ ( aDimensionOf0 @ A ) @ ( aDimensionOf0 @ xs ) )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(86,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
thf(159,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(32,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).
thf(151,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
thf(168,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',mEqInit) ).
thf(163,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)],[37]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtasdt0 @ ( smndt0 @ A ) @ ( smndt0 @ B ) )
= ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).
thf(62,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)],[8]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',mLEMon) ).
thf(90,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)],[19]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(173,plain,
$false,
inference(cvc4,[status(thm)],[101,56,57,132,70,156,59,98,103,80,123,95,67,87,75,170,120,125,157,85,102,92,65,129,41,166,45,161,149,54,86,159,151,168,163,68,62,90,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : RNG050+1 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n018.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.15/0.31 % WCLimit : 300
% 0.15/0.31 % DateTime : Sat May 18 12:30:24 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.92/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.11 % [INFO] Parsing done (194ms).
% 1.32/1.12 % [INFO] Running in sequential loop mode.
% 2.00/1.47 % [INFO] eprover registered as external prover.
% 2.00/1.47 % [INFO] cvc4 registered as external prover.
% 2.02/1.48 % [INFO] Scanning for conjecture ...
% 2.15/1.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.15/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 38 axioms. Running axiom selection ...
% 2.32/1.66 % [INFO] Axiom selection finished. Selected 38 axioms (removed 0 axioms).
% 2.59/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.59/1.74 % [INFO] Problem is first-order (TPTP FOF).
% 2.59/1.75 % [INFO] Type checking passed.
% 2.59/1.76 % [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 ...
% 5.20/2.70 % External prover 'cvc4' found a proof!
% 5.20/2.70 % [INFO] Killing All external provers ...
% 5.20/2.70 % Time passed: 2246ms (effective reasoning time: 1574ms)
% 5.20/2.70 % 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)>
% 5.20/2.71 % Axioms used in derivation (38): mLERef, mMulSc, mMNeg, mScSort, mLETrn, mDefSPZ, m__1516, mSqrt, mZeroNat, mIH, mElmSc, mNatSort, mSuccEqu, mNatExtr, mArith, mDefSPN, mDimNat, mLEMonM, mPosMon, mDefInit, mMDNeg, mLETot, mDistr, mEqInit, mSZeroSc, mVcSort, mLEASm, mSumSc, mScZero, mLEMon, mScPr, mLess, m__1542, mDistr2, mSqPos, mIHOrd, mNegSc, mSuccNat
% 5.20/2.71 % No. of inferences in proof: 80
% 5.20/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2246 ms resp. 1574 ms w/o parsing
% 5.20/2.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.20/2.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------