/*  This is a proof plan for theorem:
    multzero: []==>x:pnat=>y:pnat=>z:pnat=>times(x,times(z,0))=times(y,times(z,0))in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 9270ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(x:pnat)-s(v0)]) then 
  [ind_strat([(y:pnat)-s(v0)]) then 
     base_case(...) then 
       ind_strat([(z:pnat)-s(v2)]) then 
         base_case(...),
   generalise(times(v0,times(z,0)),v2:pnat) then 
     ind_strat([(z:pnat)-s(v3)]) then 
       [ind_strat([(v2:pnat)-s(v3)]),
        generalise(times(v3,0),v5:pnat) then 
          ind_strat([(v2:pnat)-s(v6)]) then 
            ind_strat([(v5:pnat)-s(v6)])
       ]
  ]

*/

proof_plan([]==>x:pnat=>y:pnat=>z:pnat=>times(x,times(z,0))=times(y,times(z,0))in pnat,multzero,9270,ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[times1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[1,1],[times2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[],v1)]))))])])then[ind_strat(induction(lemma(pnat_primitive)-[(y:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(intro(new[z])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1],[times2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[1],v1)]))))])])then[base_case(sym_eval(normalize_term([reduction([2,1],[plus1,equ(pnat,left)])])))then[ind_strat(induction(lemma(pnat_primitive)-[(z:pnat)-s(v2)])then[base_case(sym_eval(normalize_term([reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[2,1],[times2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[1],v3)]))))])])then[base_case(sym_eval(normalize_term([reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(identity)])]]],generalise(times(v0,times(z,0)),v2:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(z:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([2,1,1],[times1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[2,1,1],[times2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[],v4)]))))])])then[ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[plus2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[1],v4)]))then elementary(intro(new[y])then[identity,wfftacs])))])]),generalise(times(v3,0),v5:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v6)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1],[plus2,equ(pnat,left)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[1],v7)]))then elementary(intro(new[v5])then[intro(new[y])then[identity,wfftacs],wfftacs])))])])then[ind_strat(induction(lemma(pnat_primitive)-[(v5:pnat)-s(v6)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[y])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[plus2,equ(pnat,left)],[]))then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(right,[weak_fertilize(right,in,[1],v7)]))then elementary(intro(new[y])then[identity,wfftacs])))])])]]]]],dplan).
