TASK DEFINITION: Given a sentence in Tagalog language, translate the sentence to English language keeping the meaning of the original sentence intact.
PROBLEM: Tagalog sentence: Sa katunayan siya-iisip niya ito proved false, pagkatapos ay ang mga susunod na araw natagpuan ang kanyang mga pagkakamali.

SOLUTION: In fact he thought he had proved it false, then the next day found his mistake.

PROBLEM: Tagalog sentence: Siya ay walang interes sa anumang modernong developments sa iba pang lugar ng matematika na hindi kaugnay sa solving problema tungkol sa orbits.

SOLUTION: He had no interest in any modern developments in other areas of mathematics which did not relate to solving problems about orbits.

PROBLEM: Tagalog sentence: Si Mojica at Lukban ay sumuko at si Kapitan Leon Rojas Sr. ay ang huling sumuko.

SOLUTION:
Mojica and Lukban eventually yielded to American sovereignty. Captain Leon Rojas, Sr. surrendered last.