You have 10 non standard nodes. I think they are HA standard nodes.
I do not use HA so can not get your flow working.
Here is an example of 3 different inputs, each pair of injects represents an input/entity. Of the 3 inputs only one has to be true to output true.
hope it helps, wish i could help more but as said do not use HA.
[{"id":"cbbcb4e0.bb2fb","type":"inject","z":"5a245aa1.510164","name":"true","props":[{"p":"payload"},{"p":"topic","vt":"str"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"topic_one","payload":"true","payloadType":"bool","x":70,"y":2020,"wires":[["3fbf2b17.bb7b94"]]},{"id":"3fbf2b17.bb7b94","type":"join","z":"5a245aa1.510164","name":"join","mode":"custom","build":"object","property":"payload","propertyType":"msg","key":"topic","joiner":"\\n","joinerType":"str","accumulate":true,"timeout":"","count":"1","reduceRight":false,"reduceExp":"","reduceInit":"","reduceInitType":"","reduceFixup":"","x":290,"y":2140,"wires":[["df2cce01.a7a3c8"]]},{"id":"df2cce01.a7a3c8","type":"change","z":"5a245aa1.510164","name":"","rules":[{"t":"set","p":"topic","pt":"msg","to":"$count($keys(payload))","tot":"jsonata"},{"t":"set","p":"payload","pt":"msg","to":"(payload.topic_one or payload.topic_two or payload.topic_three) ? true : false","tot":"jsonata"}],"action":"","property":"","from":"","to":"","reg":false,"x":500,"y":2160,"wires":[["2d5170bc.6c0ae"]]},{"id":"eb0354e.0410ea8","type":"inject","z":"5a245aa1.510164","name":"false","props":[{"p":"payload"},{"p":"topic","vt":"str"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"topic_one","payload":"false","payloadType":"bool","x":70,"y":2060,"wires":[["3fbf2b17.bb7b94"]]},{"id":"e718b71a.a5651","type":"inject","z":"5a245aa1.510164","name":"false","props":[{"p":"payload"},{"p":"topic","vt":"str"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"topic_two","payload":"false","payloadType":"bool","x":70,"y":2180,"wires":[["3fbf2b17.bb7b94"]]},{"id":"f11b3bf3.fbd988","type":"inject","z":"5a245aa1.510164","name":"true","props":[{"p":"payload"},{"p":"topic","vt":"str"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"topic_two","payload":"true","payloadType":"bool","x":70,"y":2140,"wires":[["3fbf2b17.bb7b94"]]},{"id":"9737c419.e72398","type":"inject","z":"5a245aa1.510164","name":"false","props":[{"p":"payload"},{"p":"topic","vt":"str"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"topic_three","payload":"false","payloadType":"bool","x":70,"y":2300,"wires":[["3fbf2b17.bb7b94"]]},{"id":"a85e7f30.5f83f","type":"inject","z":"5a245aa1.510164","name":"true","props":[{"p":"payload"},{"p":"topic","vt":"str"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"topic_three","payload":"true","payloadType":"bool","x":70,"y":2260,"wires":[["3fbf2b17.bb7b94"]]},{"id":"d8a6b6e1.2d4648","type":"inject","z":"5a245aa1.510164","name":"reset","props":[{"p":"reset","v":"true","vt":"bool"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"","x":330,"y":2320,"wires":[["3fbf2b17.bb7b94","2d5170bc.6c0ae"]]},{"id":"2d5170bc.6c0ae","type":"rbe","z":"5a245aa1.510164","name":"","func":"rbe","gap":"","start":"","inout":"out","property":"payload","x":530,"y":2200,"wires":[["61c50e09.5bad7"]]},{"id":"61c50e09.5bad7","type":"debug","z":"5a245aa1.510164","name":"","active":true,"tosidebar":true,"console":false,"tostatus":false,"complete":"false","statusVal":"","statusType":"auto","x":680,"y":2240,"wires":[]}]
