TSTP Solution File: RNG074+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG074+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 11:49:17 EDT 2023
% Result : Theorem 5.08s 2.23s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 96
% Syntax : Number of formulae : 163 ( 33 unt; 31 typ; 0 def)
% Number of atoms : 392 ( 119 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 1179 ( 16 ~; 2 |; 155 &; 903 @)
% ( 1 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 20 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 134 !; 2 ?; 136 :)
% 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(iLess0_type,type,
iLess0: $i > $i > $o ).
thf(aScalar0_type,type,
aScalar0: $i > $o ).
thf(sz0z00_type,type,
sz0z00: $i ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(sdtlseqdt0_type,type,
sdtlseqdt0: $i > $i > $o ).
thf(sdtasasdt0_type,type,
sdtasasdt0: $i > $i > $i ).
thf(xs_type,type,
xs: $i ).
thf(xt_type,type,
xt: $i ).
thf(xp_type,type,
xp: $i ).
thf(xq_type,type,
xq: $i ).
thf(xA_type,type,
xA: $i ).
thf(xB_type,type,
xB: $i ).
thf(xC_type,type,
xC: $i ).
thf(xD_type,type,
xD: $i ).
thf(xE_type,type,
xE: $i ).
thf(xF_type,type,
xF: $i ).
thf(xG_type,type,
xG: $i ).
thf(xH_type,type,
xH: $i ).
thf(xR_type,type,
xR: $i ).
thf(xP_type,type,
xP: $i ).
thf(xS_type,type,
xS: $i ).
thf(xN_type,type,
xN: $i ).
thf(23,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
thf(153,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(64,axiom,
( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ xR @ xS ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ xP @ xP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2628) ).
thf(267,plain,
( ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ xR @ xS ) )
& ( sdtlseqdt0 @ sz0z00 @ ( sdtpldt0 @ xP @ xP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(27,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(162,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)],[27]) ).
thf(61,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtpldt0 @ xR @ xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2405) ).
thf(263,plain,
sdtlseqdt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xP ) ) @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtpldt0 @ xR @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(33,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDimNat) ).
thf(175,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( aNaturalNumber0 @ ( aDimensionOf0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(60,axiom,
sdtlseqdt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xP @ xP ) @ ( sdtasdt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2104) ).
thf(262,plain,
sdtlseqdt0 @ ( sdtpldt0 @ ( sdtasdt0 @ xP @ xP ) @ ( sdtasdt0 @ xP @ xP ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ xR @ xR ) @ ( sdtasdt0 @ xS @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(18,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(136,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)],[18]) ).
thf(3,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(68,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)],[3]) ).
thf(32,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mVcSort) ).
thf(174,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,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(185,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)],[37]) ).
thf(16,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(110,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)],[16]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',m__1652) ).
thf(196,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)],[41]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLess) ).
thf(152,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
thf(228,plain,
( ( aScalar0 @ xE )
& ( xE
= ( sdtasasdt0 @ xp @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(59,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2004) ).
thf(261,plain,
sdtlseqdt0 @ ( sdtasdt0 @ xP @ xP ) @ xN,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(47,axiom,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
thf(216,plain,
( ( aScalar0 @ xB )
& ( xB
= ( sdtlbdtrb0 @ xt @ ( aDimensionOf0 @ xt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( sdtlseqdt0 @ A @ B )
| ( sdtlseqdt0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(35,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(179,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)],[35]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(55,axiom,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
thf(248,plain,
( ( aScalar0 @ xP )
& ( xP
= ( sdtasdt0 @ xE @ xH ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(65,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtpldt0 @ xR @ xS ) ) @ ( sdtasdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2654) ).
thf(270,plain,
sdtlseqdt0 @ ( sdtasdt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtpldt0 @ xR @ xS ) ) @ ( sdtasdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xP @ xP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(48,axiom,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
thf(220,plain,
( ( aScalar0 @ xC )
& ( xC
= ( sdtasasdt0 @ xp @ xp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(11,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).
thf(102,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatSort) ).
thf(85,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(43,axiom,
( ( aDimensionOf0 @ xs )
!= sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1692) ).
thf(201,plain,
( ( aDimensionOf0 @ xs )
!= sz00 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(58,axiom,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1967) ).
thf(260,plain,
sdtlseqdt0 @ ( sdtasdt0 @ xE @ xE ) @ ( sdtasdt0 @ xC @ xD ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(26,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(160,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)],[26]) ).
thf(56,axiom,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
thf(252,plain,
( ( aScalar0 @ xS )
& ( xS
= ( sdtasdt0 @ xF @ xD ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(49,axiom,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
thf(224,plain,
( ( aScalar0 @ xD )
& ( xD
= ( sdtasasdt0 @ xq @ xq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(38,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(188,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)],[38]) ).
thf(30,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
thf(169,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,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(141,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)],[19]) ).
thf(57,axiom,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
thf(256,plain,
( ( aScalar0 @ xN )
& ( xN
= ( sdtasdt0 @ xR @ xS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(40,axiom,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
thf(193,plain,
( ( aVector0 @ xs )
& ( aVector0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
thf(212,plain,
( ( aScalar0 @ xA )
& ( xA
= ( sdtlbdtrb0 @ xs @ ( aDimensionOf0 @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
thf(96,plain,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( ( szszuzczcdt0 @ A )
= ( szszuzczcdt0 @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
thf(244,plain,
( ( aScalar0 @ xR )
& ( xR
= ( sdtasdt0 @ xC @ xG ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(63,axiom,
sdtlseqdt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtpldt0 @ xP @ xP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2610) ).
thf(266,plain,
sdtlseqdt0 @ ( sdtpldt0 @ xR @ xS ) @ ( sdtpldt0 @ xP @ xP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29,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(166,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)],[29]) ).
thf(62,axiom,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xR @ xS ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2590) ).
thf(264,plain,
~ ( sdtlseqdt0 @ ( sdtpldt0 @ xP @ xP ) @ ( sdtpldt0 @ xR @ xS ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(21,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(149,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)],[21]) ).
thf(39,axiom,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
thf(191,plain,
! [A: $i] :
( ( aVector0 @ A )
=> ( sdtlseqdt0 @ sz0z00 @ ( sdtasasdt0 @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
( ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
thf(204,plain,
( ( aVector0 @ xp )
& ( xp
= ( sziznziztdt0 @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(20,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(144,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)],[20]) ).
thf(52,axiom,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
thf(236,plain,
( ( aScalar0 @ xG )
& ( xG
= ( sdtasdt0 @ xB @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5,axiom,
aNaturalNumber0 @ sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
thf(86,plain,
aNaturalNumber0 @ sz00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,axiom,
( ( sdtpldt0 @ xR @ xS )
= ( sdtpldt0 @ xP @ xP ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2679) ).
thf(271,plain,
( ( sdtpldt0 @ xR @ xS )
= ( sdtpldt0 @ xP @ xP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(45,axiom,
( ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
thf(208,plain,
( ( aVector0 @ xq )
& ( xq
= ( sziznziztdt0 @ xt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(12,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
thf(103,plain,
aScalar0 @ sz0z00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtr) ).
thf(91,plain,
! [A: $i] :
( ( ( aNaturalNumber0 @ A )
& ( A != sz00 ) )
=> ? [B: $i] :
( ( aNaturalNumber0 @ B )
& ( A
= ( szszuzczcdt0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,axiom,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
thf(240,plain,
( ( aScalar0 @ xH )
& ( xH
= ( sdtasdt0 @ xA @ xB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(24,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(155,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)],[24]) ).
thf(15,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
thf(108,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
$false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ $false,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(67,plain,
~ $false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,axiom,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
thf(199,plain,
( ( aDimensionOf0 @ xs )
= ( aDimensionOf0 @ xt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17,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(127,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)],[17]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mElmSc) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( ( aVector0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( aScalar0 @ ( sdtlbdtrb0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(36,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(182,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)],[36]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( aNaturalNumber0 @ A )
& ( aNaturalNumber0 @ B ) )
=> ( ( iLess0 @ A @ B )
=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIHOrd) ).
thf(99,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
thf(87,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( ( aNaturalNumber0 @ ( szszuzczcdt0 @ A ) )
& ( ( szszuzczcdt0 @ A )
!= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,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(158,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)],[25]) ).
thf(31,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(171,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)],[31]) ).
thf(51,axiom,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
thf(232,plain,
( ( aScalar0 @ xF )
& ( xF
= ( sdtasdt0 @ xA @ xA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(10,axiom,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
thf(100,plain,
! [A: $i] :
( ( aNaturalNumber0 @ A )
=> ( iLess0 @ A @ ( szszuzczcdt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(273,plain,
$false,
inference(cvc4,[status(thm)],[153,267,162,263,175,262,136,68,174,185,110,196,152,228,261,216,164,179,106,248,270,220,102,85,201,260,160,252,224,188,169,141,256,193,212,96,244,266,166,264,149,191,204,144,236,86,271,208,103,91,240,155,108,67,199,127,177,182,99,87,104,158,171,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG074+1 : TPTP v8.1.2. Released v4.0.0.
% 0.16/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n012.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 20:19:03 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.01/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.02 % [INFO] Parsing done (159ms).
% 1.28/1.03 % [INFO] Running in sequential loop mode.
% 1.97/1.24 % [INFO] eprover registered as external prover.
% 1.97/1.25 % [INFO] cvc4 registered as external prover.
% 1.97/1.25 % [INFO] Scanning for conjecture ...
% 1.97/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.17/1.33 % [INFO] Found a conjecture and 64 axioms. Running axiom selection ...
% 2.17/1.35 % [INFO] Axiom selection finished. Selected 64 axioms (removed 0 axioms).
% 2.17/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.37/1.42 % [INFO] Problem is first-order (TPTP FOF).
% 2.37/1.43 % [INFO] Type checking passed.
% 2.37/1.43 % [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 ...
% 5.08/2.23 % External prover 'cvc4' found a proof!
% 5.08/2.23 % [INFO] Killing All external provers ...
% 5.08/2.23 % Time passed: 1693ms (effective reasoning time: 1193ms)
% 5.08/2.23 % 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)>
% 5.08/2.23 % Axioms used in derivation (64): mLERef, mMulSc, mScSort, m__2104, mIH, m__1766, mLess, m__1678, m__1820, mNatExtr, mArith, m__2004, m__1783, mDefSPN, mMNeg, m__1854, m__1949, mLETrn, m__2405, mDefSPZ, m__2628, m__1746, m__1930, m__2654, m__2610, mSqrt, mZeroNat, m__2679, 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__1892, mElmSc, mDistr2, mSqPos, m__1709, m__1692, m__1652, mNatSort, m__1726, mIHOrd, mNegSc, mSuccNat, mSuccEqu, m__2590, mScSqPos, m__1873
% 5.08/2.23 % No. of inferences in proof: 132
% 5.08/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1693 ms resp. 1193 ms w/o parsing
% 5.38/2.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.38/2.33 % [INFO] Killing All external provers ...
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