Does this code that contains system("/bin/ls") seems unbreakable?

I'm doing some ctf-like homework. It's to make a privileged program run /bin/sh. There's no source code, only works on binary assembly.

The program normally pass "/bin/ls %s" (stored at 0x804868f) to snprintf with argv[1]. So the output of snprintf (@main+222) would be sth like /bin/ls ~/. Then pass "/bin/ls ~/" to a system call (@main+236), like system(/bin/ls ~/).

The program filtered out some cmd line symbol by using strchr(e.g. @main+85), which are &, | and ;.

So I think you can't make the command become /bin/ls ;sh since it contains ;, for example.

My question is: Is this code seems to be unbreakable? Or how can we change the input to make the program run 'sh'.

Thanks in advance.

(also, I have no permission to modify /bin/ls)

Here's the code:

  0x08048454 <+0>: push   %ebp
  0x08048455 <+1>: mov    %esp,%ebp
  0x08048457 <+3>: sub    $0x428,%esp
  0x0804845d <+9>: and    $0xfffffff0,%esp
  0x08048460 <+12>:    mov    $0x0,%eax
  0x08048465 <+17>:    sub    %eax,%esp
  0x08048467 <+19>:    mov    0xc(%ebp),%eax
  0x0804846a <+22>:    add    $0x4,%eax
  0x0804846d <+25>:    cmpl   $0x0,(%eax)
  0x08048470 <+28>:    jne    0x8048496 <main+66>
  0x08048472 <+30>:    movl   $0x8048674,0x4(%esp)
  0x0804847a <+38>:    mov    0x80497ac,%eax
  0x0804847f <+43>:    mov    %eax,(%esp)
  0x08048482 <+46>:    call   0x8048348 <fprintf@plt>
  0x08048487 <+51>:    movl   $0xffffffff,-0x40c(%ebp)
  0x08048491 <+61>:    jmp    0x804854f <main+251>
  0x08048496 <+66>:    mov    0xc(%ebp),%eax
  0x08048499 <+69>:    add    $0x4,%eax
  0x0804849c <+72>:    movl   $0x3b,0x4(%esp)
  0x080484a4 <+80>:    mov    (%eax),%eax
  0x080484a6 <+82>:    mov    %eax,(%esp)
  0x080484a9 <+85>:    call   0x8048338 <strchr@plt>
  0x080484ae <+90>:    test   %eax,%eax
  0x080484b0 <+92>:    jne    0x80484ec <main+152>
  0x080484b2 <+94>:    mov    0xc(%ebp),%eax
  0x080484b5 <+97>:    add    $0x4,%eax
  0x080484b8 <+100>:   movl   $0x7c,0x4(%esp)
  0x080484c0 <+108>:   mov    (%eax),%eax
  0x080484c2 <+110>:   mov    %eax,(%esp)
  0x080484c5 <+113>:   call   0x8048338 <strchr@plt>
  0x080484ca <+118>:   test   %eax,%eax
  0x080484cc <+120>:   jne    0x80484ec <main+152>
  0x080484ce <+122>:   mov    0xc(%ebp),%eax
  0x080484d1 <+125>:   add    $0x4,%eax
  0x080484d4 <+128>:   movl   $0x26,0x4(%esp)
  0x080484dc <+136>:   mov    (%eax),%eax
  0x080484de <+138>:   mov    %eax,(%esp)
  0x080484e1 <+141>:   call   0x8048338 <strchr@plt>
  0x080484e6 <+146>:   test   %eax,%eax
  0x080484e8 <+148>:   jne    0x80484ec <main+152>
  0x080484ea <+150>:   jmp    0x804850d <main+185>
  0x080484ec <+152>:   movl   $0x804867c,0x4(%esp)
  0x080484f4 <+160>:   mov    0x80497ac,%eax
  0x080484f9 <+165>:   mov    %eax,(%esp)
  0x080484fc <+168>:   call   0x8048348 <fprintf@plt>
  0x08048501 <+173>:   movl   $0xffffffff,-0x40c(%ebp)
  0x0804850b <+183>:   jmp    0x804854f <main+251>
  0x0804850d <+185>:   mov    0xc(%ebp),%eax
  0x08048510 <+188>:   add    $0x4,%eax
  0x08048513 <+191>:   mov    (%eax),%eax
  0x08048515 <+193>:   mov    %eax,0xc(%esp)
  0x08048519 <+197>:   movl   $0x804868f,0x8(%esp)
  0x08048521 <+205>:   movl   $0x400,0x4(%esp)
  0x08048529 <+213>:   lea    -0x408(%ebp),%eax
  0x0804852f <+219>:   mov    %eax,(%esp)
  0x08048532 <+222>:   call   0x8048378 <snprintf@plt>
  0x08048537 <+227>:   lea    -0x408(%ebp),%eax
  0x0804853d <+233>:   mov    %eax,(%esp)
  0x08048540 <+236>:   call   0x8048358 <system@plt>
  0x08048545 <+241>:   movl   $0x0,-0x40c(%ebp)
  0x0804854f <+251>:   mov    -0x40c(%ebp),%eax
  0x08048555 <+257>:   leave  
  0x08048556 <+258>:   ret