Here is the contents of the log file (by the way I mess up before and only put the logfilewriter command before the send() function, I didn't realize it needed to go before the connect() function) :
2016-05-27 08:03:25.587 Opening log file.
2016-05-27 08:03:25.590 INFO Smtp(1) Info: Connecting to <our IP Address>:587 using Smtp 1.0.4086.0.
2016-05-27 08:03:25.605 DEBUG Smtp(1) Info: Connection succeeded.
2016-05-27 08:03:25.608 INFO Smtp(1) Response: 220 our.Mailserver.com Microsoft ESMTP MAIL Service ready at Fri, 27 May 2016 08:03:26 -0400
2016-05-27 08:03:25.611 INFO Smtp(1) Command: EHLO rfp219
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-our.mailserver.com Hello [10.2.2.18]
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-SIZE 36700160
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-PIPELINING
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-DSN
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-ENHANCEDSTATUSCODES
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-STARTTLS
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-AUTH GSSAPI NTLM
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-8BITMIME
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250-BINARYMIME
2016-05-27 08:03:25.613 INFO Smtp(1) Response: 250 CHUNKING
2016-05-27 08:03:25.614 INFO Smtp(1) Command: STARTTLS
2016-05-27 08:03:25.616 INFO Smtp(1) Response: 220 2.0.0 SMTP server ready
2016-05-27 08:03:25.616 DEBUG Smtp(1) Info: Upgrading connection to TLS/SSL.
2016-05-27 08:03:25.630 INFO Smtp(1) TLS: State StateChange:Negotiating
2016-05-27 08:03:25.630 DEBUG Smtp(1) TLS: HandshakeMessage:ClientHello was sent.
2016-05-27 08:03:25.638 DEBUG Smtp(1) TLS: HandshakeMessage:ServerHello was received.
2016-05-27 08:03:25.645 DEBUG Smtp(1) TLS: HandshakeMessage:Certificate was received.
2016-05-27 08:03:25.645 DEBUG Smtp(1) TLS: HandshakeMessage:ServerHelloDone was received.
2016-05-27 08:03:25.648 DEBUG Smtp(1) TLS: Verifying server certificate ('CN=our.mailserver.com, OU=IT, O=CompanyNAme, L=city, S=state, C=US').
2016-05-27 08:03:25.672 DEBUG Smtp(1) TLS: Certificate verification result: Accept
2016-05-27 08:03:25.756 DEBUG Smtp(1) TLS: HandshakeMessage:ClientKeyExchange was sent.
2016-05-27 08:03:25.764 DEBUG Smtp(1) TLS: CipherSpec:ChangeCipherSpec was sent.
2016-05-27 08:03:25.765 DEBUG Smtp(1) TLS: HandshakeMessage:Finished was sent.
2016-05-27 08:03:25.811 DEBUG Smtp(1) TLS: CipherSpec:ChangeCipherSpec was received.
2016-05-27 08:03:25.812 DEBUG Smtp(1) TLS: HandshakeMessage:Finished was received.
2016-05-27 08:03:25.813 INFO Smtp(1) TLS: State StateChange:Secured
2016-05-27 08:03:25.815 INFO Smtp(1) TLS: Connection secured using cipher: TLS 1.0, RSA, 256bit AES in CBC mode, SHA1
2016-05-27 08:03:25.816 DEBUG Smtp(1) TLS: Session ID:
20-3F-00-00-A1-BA-A8-8C-43-98-4B-49-B3-68-00-AD-8A-7A-68-FC-66-71-C5-93
FD-5C-0E-1E-05-23-83-DF
2016-05-27 08:03:25.816 DEBUG Smtp(1) Info: Connection upgraded to TLS/SSL.
2016-05-27 08:03:25.817 INFO Smtp(1) Command: EHLO rlp569
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-our.mailserver.com Hello [10.2.2.18]
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-SIZE 36700160
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-PIPELINING
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-DSN
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-ENHANCEDSTATUSCODES
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-AUTH GSSAPI NTLM LOGIN
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-8BITMIME
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250-BINARYMIME
2016-05-27 08:03:25.820 INFO Smtp(1) Response: 250 CHUNKING
2016-05-27 08:03:25.831 INFO Smtp(1) Command: AUTH LOGIN
2016-05-27 08:03:25.832 INFO Smtp(1) Response: 334 VXNlcm5hbWU6
2016-05-27 08:03:25.832 INFO Smtp(1) Command: a2lkc3lzdGVt
2016-05-27 08:03:25.833 INFO Smtp(1) Response: 334 UGFzc3dvcmQ6
2016-05-27 08:03:25.833 INFO Smtp(1) Command:
2016-05-27 08:03:25.851 INFO Smtp(1) Response: 235 2.7.0 Authentication successful
2016-05-27 08:03:25.916 INFO Smtp(1) Command: MAIL FROM:<doNotReply@our.mailserver.com> SIZE=626
2016-05-27 08:03:25.918 INFO Smtp(1) Response: 250 2.1.0 Sender OK
2016-05-27 08:03:25.919 INFO Smtp(1) Command: RCPT TO:<xcvsdf@our.mailserver.com> NOTIFY=FAILURE
2016-05-27 08:03:25.920 INFO Smtp(1) Response: 250 2.1.5 Recipient OK
2016-05-27 08:03:25.920 INFO Smtp(1) Command: RCPT TO:<bsdfbb@our.mailserver.com> NOTIFY=FAILURE
2016-05-27 08:03:25.922 INFO Smtp(1) Command: RCPT TO:<techSupport@our.mailserver.com> NOTIFY=FAILURE
2016-05-27 08:03:25.922 INFO Smtp(1) Response: 250 2.1.5 Recipient OK
2016-05-27 08:03:25.922 INFO Smtp(1) Command: RCPT TO:<sdfsdfsdfwet@our.mailserver.com> NOTIFY=FAILURE
2016-05-27 08:03:25.923 INFO Smtp(1) Response: 250 2.1.5 Recipient OK
2016-05-27 08:03:25.925 INFO Smtp(1) Response: 250 2.1.5 Recipient OK
2016-05-27 08:03:25.926 INFO Smtp(1) Command: BDAT 626 LAST
2016-05-27 08:04:00.700 INFO Smtp(1) Response: 250 2.6.0 <d5ff9af60ade6748829b72178004d353@nhy654> [InternalId=301483] Queued mail for delivery
2016-05-27 08:04:00.700 INFO Smtp(1) Command: QUIT
2016-05-27 08:04:00.701 DEBUG Smtp(1) TLS: Closing TLS socket.
2016-05-27 08:04:00.702 INFO Smtp(1) TLS: Alert Alert:Alert was sent.
2016-05-27 08:04:00.702 INFO Smtp(1) TLS: State StateChange:Closed
Looks pretty close to the log you linked. What do you think?