/*  This is a proof plan for theorem:
    evenp: []==>x:pnat=>y:pnat=>(even(x)#even(y))=>even(plus(x,y))
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 440ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(x:pnat)-s(s(v0))])

*/

proof_plan([]==>x:pnat=>y:pnat=>(even(x)#even(y))=>even(plus(x,y)),evenp,440,ind_strat(induction(lemma(twos)-[(x:pnat)-s(s(v0))])then[base_case(sym_eval(normalize_term([reduction([1,1],[even1,equ(u(1),left)]),reduction([1,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[intro(new[v0])then[elim(v0)then hyp(v2),wfftacs],wfftacs])]),base_case(sym_eval(normalize_term([reduction([1,1],[even2,equ(u(1),left)]),reduction([1,2],[plus2,equ(pnat,left)]),reduction([1,1,2],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[intro(new[v0])then[elim(v0)then elim(v1),wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,2],[plus2,equ(pnat,left)],[])then[wave(direction_out,[2],[even3,equ(u(1),left)],[])then[wave(direction_out,[1,1],[even3,equ(u(1),left)],[])]]])then[unblock_then_fertilize(strong,unblock_fertilize_lazy([idtac])then fertilize(strong,v1))])]),dplan).
