C# (Visual C# Interactive Compiler), 303(削除) 303 (削除ここまで) 227 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,nn=>{int i=n.Max(x=>x.Max())+1),n[0]j=n.Count).Aggregate,t=0,k,m=0,z;for(;t<Math.Pow(IEnumerable<IEnumerable<int>>i,j)new[];){newk=t++;var int[0]},s=n.Select(_=>(a:k%i+1,bk/=i)=>a.SelectMany(x=>b.Select(y=>xa).AppendToList(y)))).Single;if(x=>nn.All(l=>{int z=0;var i=x.ToListx=>();var p=lz=0,b:x.All(o=>o==i[z++]|o<1o=>o==s[z++]|o<1);x=x,s=s.Skip(1).Select((a,b)=>a+i[b]=>a+s[b]);return p;}.ToList()).b))m++;}m/=m-1;}
Throws an exception if falsetrue, runs normally if truefalse.
C# (Visual C# Interactive Compiler), 303 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())+1),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))
Throws an exception if false, runs normally if true.
C# (Visual C# Interactive Compiler), (削除) 303 (削除ここまで) 227 bytes
n=>{int i=n.Max(x=>x.Max()),j=n.Count,t=0,k,m=0,z;for(;t<Math.Pow(i,j);){k=t++;var s=n.Select(_=>(a:k%i+1,k/=i).a).ToList();if(n.All(x=>(z=0,b:x.All(o=>o==s[z++]|o<1),s=s.Skip(1).Select((a,b)=>a+s[b]).ToList()).b))m++;}m/=m-1;}
Throws exception if true, runs normally if false.
C# (Visual C# Interactive Compiler), 303 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())+1),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))
Throws an exception if false, runs normally if true.
C# (Visual C# Interactive Compiler), 303 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())+1),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))
C# (Visual C# Interactive Compiler), 303 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())+1),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))
Throws an exception if false, runs normally if true.
C# (Visual C# Interactive Compiler), 301303 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())+1),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))
C# (Visual C# Interactive Compiler), 301 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))
C# (Visual C# Interactive Compiler), 303 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())+1),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))