Is it relevant that the RESTORE HEADER you did was:

restore headeronly

from disk = 'D:\ManualBackups\TWS_RE7_Live_20151011[highlight="#ffff11"]120000[/highlight].trn'

restore headeronly

from disk = 'D:\ManualBackups\TWS_RE7_Live_20151011[highlight="#ffff11"]114500[/highlight].trn'

restore headeronly

from disk = 'D:\ManualBackups\TWS_RE7_Live_20151011[highlight="#ffff11"]113000[/highlight].trn'

but the query shows:

backup_set_id backup_start_date physical_device_name

5986 2015-10-11 [highlight="#ffff11"]12:30[/highlight]:00.000 TWS_RE7_Inhouse_Tables_Live_20151011[highlight="#ffff11"]013000[/highlight].trn

5984 2015-10-11 [highlight="#ffff11"]12:15[/highlight]:00.000 TWS_RE7_Inhouse_Tables_Live_20151011[highlight="#ffff11"]011500[/highlight].trn

5982 2015-10-11 [highlight="#ffff11"]12:00[/highlight]:00.000 TWS_RE7_Inhouse_Tables_Live_20151011[highlight="#ffff11"]010000[/highlight].trn

5980 2015-10-11 [highlight="#ffff11"]11:45[/highlight]:00.000 TWS_RE7_Inhouse_Tables_Live_20151011[highlight="#ffff11"]004500[/highlight].trn

Is filename being constructed from a 24-hour clock and some files overwritten (or an additional backup appended to perhaps?)

To see any filenames that are reused you could add the following to my earlier query (probably need to extend the date/time range of the query to be sure to include any other usage of the same filename)

JOIN

(

SELECTmedia_set_id

FROMmsdb.dbo.backupset AS BS

GROUP BY media_set_id

HAVING COUNT(*) > 1

) AS DUP

ON DUP.media_set_id = BS.media_set_id