/*  This is a proof plan for theorem:
    assm: []==>a:pnat=>b:pnat=>c:pnat=>times(a,times(b,c))=times(times(a,b),c)in pnat
    planner = dplan, clam_version(2.7.0), oyster_version(1.20)

    Time taken to find plan: 7130ms
    Environment:
    []
 */

/* This is the pretty-printed form
ind_strat([(a:pnat)-s(v0)]) then 
  generalise(times(v0,b),v2:pnat) then 
    ind_strat([(v2:pnat)-s(v3)]) then 
      generalise(times(b,c),v5:pnat) then 
        generalise(times(v3,c),v6:pnat) then 
          ind_strat([(v6:pnat)-s(v7)]) then 
            ind_strat([(c:pnat)-s(v7)]) then 
              [ind_strat([(v5:pnat)-s(v7)]),
               ind_strat([(v5:pnat)-s(v9)])
              ]

*/

proof_plan([]==>a:pnat=>b:pnat=>c:pnat=>times(a,times(b,c))=times(times(a,b),c)in pnat,assm,7130,ind_strat(induction(lemma(pnat_primitive)-[(a:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([1,1],[times1,equ(pnat,left)]),reduction([1,2,1],[times1,equ(pnat,left)]),reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(intro(new[b])then[intro(new[c])then[identity,wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1,2,1],[times2,equ(pnat,left)],[])])then[unblock_then_fertilize(weak,unblock_fertilize_lazy([idtac])then fertilize(weak,fertilize_then_ripple(fertilize_left_or_right(left,[weak_fertilize(left,in,[1],v1)]))))])])then[generalise(times(v0,b),v2:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[times1,equ(pnat,left)]),reduction([1,1],[plus1,equ(pnat,left)]),reduction([1,2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[b])then[intro(new[c])then[identity,wfftacs],wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[2,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[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,[1],v4)]))))])])then[generalise(times(b,c),v5:pnat)then[generalise(times(v3,c),v6:pnat)then[ind_strat(induction(lemma(pnat_primitive)-[(v6:pnat)-s(v7)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([1,2,1],[plus1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[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],v8)]))then elementary(intro(new[v5])then[intro(new[b])then[intro(new[c])then[identity,wfftacs],wfftacs],wfftacs])))])])then[ind_strat(induction(lemma(pnat_primitive)-[(c:pnat)-s(v7)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))),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(left,[weak_fertilize(left,in,[1],v8)]))))])])then[ind_strat(induction(lemma(pnat_primitive)-[(v5:pnat)-s(v7)])then[base_case(sym_eval(normalize_term([reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[b])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1],[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],v8)]))then elementary(intro(new[b])then[identity,wfftacs])))])]),ind_strat(induction(lemma(pnat_primitive)-[(v5:pnat)-s(v9)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[b])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1],[plus2,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[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],v10)]))then elementary(intro(new[b])then[identity,wfftacs])))])])]]]]]]],dplan).
