Mysql – Is there a cleaner way to write this SQL where clause?

I have a large query with the below WHERE clause that I’m hoping may be written in a cleaner / possible more efficient way. Each combination is specific and needs to be accounted for. EDIT Per the first comment i have modified the question. Again this is a very small part of a much larger query, so I’m not quite sure if this is the right route to take.

DB

SET SQL_MODE = "NO_AUTO_VALUE_ON_ZERO";
START TRANSACTION;
SET time_zone = "+00:00";

--
-- Database: `querytest`
--
CREATE DATABASE IF NOT EXISTS `querytest` DEFAULT CHARACTER SET utf8 COLLATE utf8_general_ci;
USE `querytest`;

-- --------------------------------------------------------

--
-- Table structure for table `table1`
--

CREATE TABLE `table1` (
  `col0` int(11) NOT NULL,
  `col1` varchar(255) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

--
-- Dumping data for table `table1`
--

INSERT INTO `table1` (`col0`, `col1`) VALUES
(1, 'val1'),
(2, 'val2'),
(3, 'val3');

-- --------------------------------------------------------

--
-- Table structure for table `table2`
--

CREATE TABLE `table2` (
  `col0` int(11) NOT NULL,
  `col1` varchar(255) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

--
-- Dumping data for table `table2`
--

INSERT INTO `table2` (`col0`, `col1`) VALUES
(1, 'val1'),
(2, 'val2'),
(3, 'val3');

-- --------------------------------------------------------

--
-- Table structure for table `table3`
--

CREATE TABLE `table3` (
  `col0` int(11) NOT NULL,
  `col1` varchar(255) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

--
-- Dumping data for table `table3`
--

INSERT INTO `table3` (`col0`, `col1`) VALUES
(1, 'val1'),
(2, 'val2'),
(3, 'val3');

-- --------------------------------------------------------

--
-- Table structure for table `table4`
--

CREATE TABLE `table4` (
  `col0` int(11) NOT NULL,
  `col1` varchar(255) DEFAULT NULL,
  `col2` varchar(255) DEFAULT NULL,
  `col3` varchar(255) DEFAULT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8;

--
-- Dumping data for table `table4`
--

INSERT INTO `table4` (`col0`, `col1`, `col2`, `col3`) VALUES
(1, 'val2', NULL, 'val3'),
(2, NULL, NULL, NULL),
(3, NULL, 'val3', NULL),
(4, NULL, NULL, 'val3'),
(5, 'val1', NULL, NULL),
(6, NULL, 'val2', 'val3');

--
-- Indexes for dumped tables
--

--
-- Indexes for table `table1`
--
ALTER TABLE `table1`
  ADD PRIMARY KEY (`col0`),
  ADD KEY `col1` (`col1`);

--
-- Indexes for table `table2`
--
ALTER TABLE `table2`
  ADD PRIMARY KEY (`col0`),
  ADD KEY `col1` (`col1`);

--
-- Indexes for table `table3`
--
ALTER TABLE `table3`
  ADD PRIMARY KEY (`col0`),
  ADD KEY `col1` (`col1`);

--
-- Indexes for table `table4`
--
ALTER TABLE `table4`
  ADD PRIMARY KEY (`col0`),
  ADD KEY `col1` (`col1`),
  ADD KEY `col2` (`col2`),
  ADD KEY `col3` (`col3`);

--
-- AUTO_INCREMENT for dumped tables
--

--
-- AUTO_INCREMENT for table `table1`
--
ALTER TABLE `table1`
  MODIFY `col0` int(11) NOT NULL AUTO_INCREMENT, AUTO_INCREMENT=4;

--
-- AUTO_INCREMENT for table `table2`
--
ALTER TABLE `table2`
  MODIFY `col0` int(11) NOT NULL AUTO_INCREMENT, AUTO_INCREMENT=4;

--
-- AUTO_INCREMENT for table `table3`
--
ALTER TABLE `table3`
  MODIFY `col0` int(11) NOT NULL AUTO_INCREMENT, AUTO_INCREMENT=4;

--
-- AUTO_INCREMENT for table `table4`
--
ALTER TABLE `table4`
  MODIFY `col0` int(11) NOT NULL AUTO_INCREMENT, AUTO_INCREMENT=7;

--
-- Constraints for dumped tables
--

--
-- Constraints for table `table4`
--
ALTER TABLE `table4`
  ADD CONSTRAINT `table4_ibfk_1` FOREIGN KEY (`col1`) REFERENCES `table1` (`col1`) ON DELETE CASCADE ON UPDATE CASCADE,
  ADD CONSTRAINT `table4_ibfk_2` FOREIGN KEY (`col2`) REFERENCES `table2` (`col1`) ON DELETE CASCADE ON UPDATE CASCADE,
  ADD CONSTRAINT `table4_ibfk_3` FOREIGN KEY (`col3`) REFERENCES `table3` (`col1`) ON DELETE CASCADE ON UPDATE CASCADE;
COMMIT;

QUERY

SELECT table4.col0, table4.col1, table4.col2, table4.col3

FROM table4

LEFT JOIN table1
ON table1.col1 = table4.col1

LEFT JOIN table2
ON table2.col1 = table4.col2

LEFT JOIN table3
ON table3.col1 = table4.col3

WHERE 
(
    (
     table1.col1 = 'val1' 
     AND 
     table2.col1 = 'val2' 
     AND 
     table3.col1 = 'val3'
    )

    OR 

    (
     table1.col1 = 'val1' 
     AND 
     table4.col2 IS NULL
     AND 
     table4.col3 IS NULL
    )

    OR 

    (
     table1.col1 = 'val1' 
     AND 
     table2.col1 = 'val2'
     AND 
     table4.col3 IS NULL
    )

    OR 

    (
     table1.col1 = 'val1' 
     AND 
     table4.col2 IS NULL
     AND 
     table3.col1 = 'val3'
    )

    OR 

    (
     table4.col1 IS NULL
     AND 
     table2.col1 = 'val2' 
     AND 
     table4.col3 IS NULL
    )

    OR

    (
     table4.col1 IS NULL
     AND 
     table4.col2 IS NULL
     AND 
     table3.col1 = 'val3'
    )

    OR

    (
     table4.col1 IS NULL
     AND 
     table2.col1 = 'val2' 
     AND 
     table3.col1 = 'val3'
    )

    OR

    (
     table4.col1 IS NULL
     AND 
     table4.col2 IS NULL
     AND 
     table4.col3 IS NULL
    )
)

EXPECTED DATA

col0 col1 col2 col3
2 NULL NULL NULL
4 NULL NULL val3
5 val1 NULL NULL
6 NULL val2 val3

Thank You!