▁add ▁ ▁to ▁units Queue ; ▁▁▁▁▁▁▁▁ ▁remove ▁ ▁from ▁; ▁▁▁▁ ▁end ▁ ▁end ▁ ▁return ▁( un its Queue , ▁); ▁▁ ▁Then ▁we ▁re insert ▁the ▁units ▁▁▁▁ ▁Input : ▁A ▁proof ▁ ▁( with ▁a ▁single ▁root ) ▁and ▁a ▁queue ▁ ▁of ▁root ▁nodes ▁▁▁▁ ▁Output : ▁A ▁proof ▁▁▁▁▁ ← ▁; ▁▁ ▁while ▁ ▁do ▁▁▁▁▁▁▁▁ ← ▁first ▁element ▁of ▁; ▁▁▁▁▁▁▁▁ ← ▁tail ▁of ▁; ▁▁▁▁▁▁ ▁if ▁ ▁is ▁resol v able ▁with ▁root ▁of ▁ ▁then ▁▁▁▁▁▁▁▁▁▁▁ ← ▁resol vent ▁of ▁ ▁with ▁the ▁root ▁of ▁; ▁▁▁▁▁▁▁ ▁end ▁▁ ▁end ▁ ▁return ▁; ▁ ▁Notes ▁▁ ▁Category : Autom ated ▁theorem ▁prov ing ▁Category : Proof ▁theory <0x0A> </s> ▁I sh ar ▁Singh ▁Mar h ana ▁( 1 8 7 8 – 1 9 4 1 ), ▁Ak ali ▁activ ist ▁and ▁Gh adr ▁revolution ary , ▁was ▁born ▁on ▁ 1 ▁January ▁ 1 8 7 8 ▁younger ▁of ▁the ▁two ▁sons ▁of ▁Bh ai ▁J ind ▁Singh ▁a ▁Sand hu ▁J att ▁and ▁Mai ▁Ch and ▁K aur ▁of ▁Village ▁Mar h ana ▁near ▁T arn ▁Tar an ▁Sah ib ▁in ▁Am rit s ar ▁district ▁of ▁P un j ab , ▁a ▁Farm ing ▁family ▁ ▁He ▁lear nt ▁G ur mu k hi ▁in ▁the ▁village ▁g ur ud w ara ▁and ▁rec ited ▁av id ly ▁his ▁daily ▁h ym ns ▁every ▁morning ▁and ▁helped ▁his ▁father ▁and ▁elder ▁brother , ▁As a ▁Singh , ▁with ▁far ming .