problem([]==>x:pnat=>m:pnat=>n:pnat=>exp(x,times(n,m))=exp(exp(x,n),m)in pnat,
ind_strat(induction(lemma(plusind)-[(m:pnat)-plus(v1,v0)])then[base_case(sym_eval(normalize_term([reduction([2,1],[exp1,equ(pnat,left)])]))),base_case(sym_eval(normalize_term([reduction([2,1],[exp2,equ(pnat,left)]),reduction([2,2,1],[exp1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[2,1],[expplus,equ(pnat,left)],[])then[wave(direction_out,[2,1,1],[dist,equ(pnat,left)],[])then[wave(direction_out,[1,1],[expplus,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],v2),weak_fertilize(right,in,[2],v3)]))then elementary(intro(new[x])then[intro(new[n])then[identity,wfftacs],wfftacs])))])]),lambda(v0,lambda(v1,lambda(v2,lambda(v3,su(su(su(v6,[v5 of v2],[v6]),[v4 of v0],[v5]),[v3 of v1],[v4]))of lambda(m,su(lambda(v5,su(su(su(su(su(v0,[v9 of m],[v0]),[v8 of lambda(v1,lambda(v0,lambda(v2,lambda(v3,lambda(v4,lambda(v5,su(su(su(su(lambda(v6,su(su(v8,[v7 of v5],[v8]),[v6 of v4],[v7]))of lambda(v4,lambda(v5,su(su(su(su(lambda(v6,su(su(v8,[v7 of v5],[v8]),[v6 of v4],[v7]))of lambda(v4,lambda(v5,su(su(su(su(lambda(v6,su(su(v8,[v7 of v5],[v8]),[v6 of v4],[v7]))of lambda(v4,lambda(v5,su(su(lambda(v6,su(su(v8,[v7 of v5],[v8]),[v6 of v4],[v7]))of lambda(v4,lambda(v5,su(su(lambda(v6,su(su(v8,[v7 of v5],[v8]),[v6 of v4],[v7]))of lambda(x,lambda(n,axiom)),[v6 of v5],[v7]),[v3 of v4],[v6]))),[v6 of v5],[v7]),[v2 of v4],[v6]))),[v7 of times(v5,v0)],[v8]),[v6 of times(v5,v1)],[v7]),[expplus of v4],[v6]),[term_of(expplus)],[expplus]))),[v7 of v0],[v8]),[v6 of v1],[v7]),[dist of v5],[v6]),[term_of(dist)],[dist]))),[v7 of v0],[v8]),[v6 of v1],[v7]),[expplus of exp(v4,v5)],[v6]),[term_of(expplus)],[expplus])))))))],[v9]),[v7 of lambda(v0,lambda(v1,su(su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of _161582,[exp1 of exp(v0,v1)],[v2]),[term_of(exp1)],[exp1]))),[v2 of 0],[v3]),[exp2 of exp(v0,v1)],[v2]),[term_of(exp2)],[exp2])))],[v8]),[v6 of lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of _161494,[exp1 of exp(v0,v1)],[v2]),[term_of(exp1)],[exp1])))],[v7]),[v5 of lambda(m,x:pnat=>n:pnat=>exp(x,times(n,m))=exp(exp(x,n),m)in pnat)],[v6]))of v4,[term_of(plusind)],[v4]))))),
[problem([m:pnat]==>x:pnat=>n:pnat=>exp(x,times(n,0))=s(0)in pnat,
 ind_strat(induction(lemma(pnat_primitive)-[(n:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1,1],[times1,equ(pnat,left)]),reduction([1,1],[exp1,equ(pnat,left)])]))then[elementary(intro(new[x])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[2,1,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1,1],[expplus,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)]))))])]),lambda(v0,lambda(v1,lambda(v2,su(su(v4,[v3 of v0],[v4]),[v2 of v1],[v3]))of lambda(n,p_ind(n,lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(x,axiom),[exp1 of v0],[v1]),[term_of(exp1)],[exp1])),[times1 of 0],[v1]),[term_of(times1)],[times1])),[v0,v1,lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(lambda(v3,su(v4,[v3 of v2],[v4]))of _160991,[v1 of v2],[v3])),[v4 of 0],[v5]),[v3 of times(v0,0)],[v4]),[expplus of v2],[v3]),[term_of(expplus)],[expplus])),[v3 of 0],[v4]),[times2 of v0],[v3]),[term_of(times2)],[times2]))])))),
 [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,0))=s(0)in pnat]==>x:pnat=>times(exp(x,times(v0,0)),exp(x,0))=exp(x,times(v0,0))in pnat,
  sym_eval(normalize_term([reduction([2,1,1],[exp1,equ(pnat,left)])])),lambda(v2,su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of _160801,[exp1 of v2],[v3]),[term_of(exp1)],[exp1])),
  [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,0))=s(0)in pnat]==>x:pnat=>times(exp(x,times(v0,0)),s(0))=exp(x,times(v0,0))in pnat,
   generalise(exp(x,times(v0,0)),v2:pnat),lambda(v2,lambda(v3,su(su(v5,[v4 of v3],[v5]),[v2 of exp(v3,times(v0,0))],[v4])))of _160677,
   [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,0))=s(0)in pnat]==>v2:pnat=>x:pnat=>times(v2,s(0))=v2 in pnat,
    ind_strat(induction(lemma(pnat_primitive)-[(v2:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,1],[times1,equ(pnat,left)])]))then[elementary(intro(new[x])then[identity,wfftacs])]),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,[1],v4)]))))])]),lambda(v2,p_ind(v2,lambda(v3,su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(x,axiom),[times1 of s(0)],[v4]),[term_of(times1)],[times1])),[v3,v4,lambda(v5,su(su(su(lambda(v6,su(v7,[v6 of v5],[v7]))of lambda(v5,su(lambda(v6,su(v7,[v6 of v5],[v7]))of _160345,[v4 of v5],[v6])),[v6 of s(0)],[v7]),[times2 of v3],[v6]),[term_of(times2)],[times2]))])),
    [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,0))=s(0)in pnat,v2:pnat,v3:pnat,v4:x:pnat=>times(v3,s(0))=v3 in pnat]==>x:pnat=>plus(times(v3,s(0)),s(0))=s(times(v3,s(0)))in pnat,
     generalise(times(v3,s(0)),v5:pnat),lambda(v5,lambda(v6,su(su(v8,[v7 of v6],[v8]),[v5 of times(v3,s(0))],[v7])))of _160174,
     [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,0))=s(0)in pnat,v2:pnat,v3:pnat,v4:x:pnat=>times(v3,s(0))=v3 in pnat]==>v5:pnat=>x:pnat=>plus(v5,s(0))=s(v5)in pnat,
      ind_strat(induction(lemma(plusind)-[(v5:pnat)-plus(v7,v6)])then[base_case(sym_eval(normalize_term([reduction([1,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[x])then[identity,wfftacs])]),base_case(sym_eval(normalize_term([reduction([1,1],[plus2,equ(pnat,left)]),reduction([1,1,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[x])then[identity,wfftacs])]),step_case(ripple(direction_out,unblock_then_wave(direction_out,unblock_lazy([unblock(meta_ripple,unused,unused),idtac])then wave(direction_out,[2,1],[plus2,equ(pnat,right)],[])))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)]))))])]),lambda(v5,su(lambda(v11,su(su(su(su(su(v6,[v15 of v5],[v6]),[v14 of lambda(v7,lambda(v6,lambda(v8,lambda(v9,lambda(v10,su(su(su(lambda(v11,su(v12,[v11 of v10],[v12]))of lambda(v10,su(lambda(v11,su(v12,[v11 of v10],[v12]))of _159732,[v8 of v10],[v11])),[v11 of v6],[v12]),[plus2 of v7],[v11]),[term_of(plus2)],[plus2]))))))],[v15]),[v13 of lambda(v6,su(su(su(lambda(v7,su(v8,[v7 of v6],[v8]))of lambda(v6,su(su(lambda(v7,su(v8,[v7 of v6],[v8]))of lambda(x,axiom),[plus1 of s(0)],[v7]),[term_of(plus1)],[plus1])),[v7 of s(0)],[v8]),[plus2 of 0],[v7]),[term_of(plus2)],[plus2]))],[v14]),[v12 of lambda(v6,su(su(lambda(v7,su(v8,[v7 of v6],[v8]))of lambda(x,axiom),[plus1 of s(0)],[v7]),[term_of(plus1)],[plus1]))],[v13]),[v11 of lambda(v5,x:pnat=>plus(v5,s(0))=s(v5)in pnat)],[v12]))of v10,[term_of(plusind)],[v10])),
      [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,0))=s(0)in pnat,v2:pnat,v3:pnat,v4:x:pnat=>times(v3,s(0))=v3 in pnat,v5:pnat,v7:pnat,v6:pnat,v8:x:pnat=>plus(v7,s(0))=s(v7)in pnat,v9:x:pnat=>plus(v6,s(0))=s(v6)in pnat]==>x:pnat=>plus(plus(v7,v6),s(0))=plus(plus(v7,s(0)),v6)in pnat,
       ind_strat(induction(lemma(pnat_primitive)-[(v7:pnat)-s(v10)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([1,2,1],[plus1,equ(pnat,left)]),reduction([2,1],[plus2,equ(pnat,left)]),reduction([1,2,1],[plus1,equ(pnat,left)])]))then[elementary(hyp(v9))]),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],v11)]))then elementary(intro(new[x])then[identity,wfftacs])))])]),p_ind(v7,lambda(v10,su(su(lambda(v11,su(v12,[v11 of v10],[v12]))of lambda(v10,su(su(lambda(v11,su(v12,[v11 of v10],[v12]))of lambda(v10,su(su(su(lambda(v11,su(v12,[v11 of v10],[v12]))of lambda(v10,su(su(lambda(v11,su(v12,[v11 of v10],[v12]))of v9,[plus1 of v6],[v11]),[term_of(plus1)],[plus1])),[v11 of v6],[v12]),[plus2 of 0],[v11]),[term_of(plus2)],[plus2])),[plus1 of s(0)],[v11]),[term_of(plus1)],[plus1])),[plus1 of v6],[v11]),[term_of(plus1)],[plus1])),[v10,v11,lambda(v12,su(su(su(lambda(v13,su(v14,[v13 of v12],[v14]))of lambda(v12,su(su(su(lambda(v13,su(v14,[v13 of v12],[v14]))of lambda(v12,su(su(su(lambda(v13,su(v14,[v13 of v12],[v14]))of lambda(v12,su(su(su(lambda(v13,su(v14,[v13 of v12],[v14]))of lambda(v12,su(lambda(v13,su(v14,[v13 of v12],[v14]))of lambda(x,axiom),[v11 of v12],[v13])),[v13 of s(0)],[v14]),[plus2 of plus(v10,v6)],[v13]),[term_of(plus2)],[plus2])),[v13 of v6],[v14]),[plus2 of v10],[v13]),[term_of(plus2)],[plus2])),[v13 of v6],[v14]),[plus2 of plus(v10,s(0))],[v13]),[term_of(plus2)],[plus2])),[v13 of s(0)],[v14]),[plus2 of v10],[v13]),[term_of(plus2)],[plus2]))]),
       [
       ]) ext _159732
      ]) ext _160174
     ]) ext _160345
    ]) ext _160677
   ]) ext _160801
  ]) ext _160991
 ]) ext _161494,
 problem([m:pnat]==>x:pnat=>n:pnat=>exp(x,times(n,s(0)))=times(exp(x,n),s(0))in pnat,
 ind_strat(induction(lemma(pnat_primitive)-[(n:pnat)-s(v0)])then[base_case(sym_eval(normalize_term([reduction([2,1,1],[times1,equ(pnat,left)]),reduction([1,1],[exp1,equ(pnat,left)]),reduction([1,2,1],[exp1,equ(pnat,left)]),reduction([2,1],[times2,equ(pnat,left)]),reduction([1,2,1],[times1,equ(pnat,left)]),reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[x])then[identity,wfftacs])]),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[exp2,equ(pnat,left)],[])then[wave(direction_out,[2,1,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[1,1],[expplus,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 ripple_and_cancel([unblock(wave_front,[2,1,1],[exp2,equ(pnat,left)]),unblock(wave_front,[2,2,1,1],[exp1,equ(pnat,left)])]))))])]),lambda(v0,lambda(v1,lambda(v2,su(su(v4,[v3 of v0],[v4]),[v2 of v1],[v3]))of lambda(n,p_ind(n,lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(v0,su(su(lambda(v1,su(v2,[v1 of v0],[v2]))of lambda(x,axiom),[plus1 of s(0)],[v1]),[term_of(plus1)],[plus1])),[times1 of s(0)],[v1]),[term_of(times1)],[times1])),[v1 of s(0)],[v2]),[times2 of 0],[v1]),[term_of(times2)],[times2])),[exp1 of v0],[v1]),[term_of(exp1)],[exp1])),[exp1 of v0],[v1]),[term_of(exp1)],[exp1])),[times1 of s(0)],[v1]),[term_of(times1)],[times1])),[v0,v1,lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of lambda(v2,su(su(lambda(v3,su(v4,[v3 of v2],[v4]))of _157793,[exp1 of v2],[v3]),[term_of(exp1)],[exp1])),[v3 of 0],[v4]),[exp2 of v2],[v3]),[term_of(exp2)],[exp2])),[v1 of v2],[v3])),[v4 of s(0)],[v5]),[v3 of times(v0,s(0))],[v4]),[expplus of v2],[v3]),[term_of(expplus)],[expplus])),[v3 of s(0)],[v4]),[times2 of v0],[v3]),[term_of(times2)],[times2])),[v3 of v0],[v4]),[exp2 of v2],[v3]),[term_of(exp2)],[exp2]))])))),
 [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,s(0)))=times(exp(x,v0),s(0))in pnat]==>x:pnat=>times(times(exp(x,v0),s(0)),times(x,s(0)))=times(times(x,exp(x,v0)),s(0))in pnat,
  generalise(exp(x,v0),v2:pnat),lambda(v2,lambda(v3,su(su(v5,[v4 of v3],[v5]),[v2 of exp(v3,v0)],[v4])))of _157551,
  [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,s(0)))=times(exp(x,v0),s(0))in pnat]==>v2:pnat=>x:pnat=>times(times(v2,s(0)),times(x,s(0)))=times(times(x,v2),s(0))in pnat,
   ind_strat(induction(lemma(plusind)-[(v2:pnat)-plus(v4,v3)])then[base_case(sym_eval(normalize_term([reduction([1,1,1],[times1,equ(pnat,left)]),reduction([1,1],[times1,equ(pnat,left)])]))),base_case(sym_eval(normalize_term([reduction([1,1,1],[times2,equ(pnat,left)]),reduction([1,1,1,1],[times1,equ(pnat,left)]),reduction([1,1,1],[plus1,equ(pnat,left)]),reduction([1,1],[times2,equ(pnat,left)]),reduction([1,1,1],[times1,equ(pnat,left)]),reduction([1,1],[plus1,equ(pnat,left)])]))),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[dist,equ(pnat,left)],[])then[wave(direction_out,[2,1],[disttwo,equ(pnat,left)],[])then[wave(direction_out,[1,1,1],[disttwo,equ(pnat,left)],[])then[wave(direction_out,[1,1],[disttwo,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],v5),weak_fertilize(right,in,[2],v6)]))then elementary(intro(new[x])then[identity,wfftacs])))])]),lambda(v2,su(lambda(v8,su(su(su(su(su(v3,[v12 of v2],[v3]),[v11 of lambda(v4,lambda(v3,lambda(v5,lambda(v6,lambda(v7,su(su(su(su(lambda(v8,su(v9,[v8 of v7],[v9]))of lambda(v7,su(su(su(su(lambda(v8,su(v9,[v8 of v7],[v9]))of lambda(v7,su(su(su(su(lambda(v8,su(v9,[v8 of v7],[v9]))of lambda(v7,su(su(su(su(lambda(v8,su(v9,[v8 of v7],[v9]))of lambda(v7,su(lambda(v8,su(v9,[v8 of v7],[v9]))of lambda(v7,su(lambda(v8,su(v9,[v8 of v7],[v9]))of lambda(x,axiom),[v6 of v7],[v8])),[v5 of v7],[v8])),[v9 of times(v3,s(0))],[v10]),[v8 of times(v4,s(0))],[v9]),[disttwo of times(v7,s(0))],[v8]),[term_of(disttwo)],[disttwo])),[v9 of v3],[v10]),[v8 of v4],[v9]),[disttwo of s(0)],[v8]),[term_of(disttwo)],[disttwo])),[v9 of times(v7,v3)],[v10]),[v8 of times(v7,v4)],[v9]),[disttwo of s(0)],[v8]),[term_of(disttwo)],[disttwo])),[v9 of v3],[v10]),[v8 of v4],[v9]),[dist of v7],[v8]),[term_of(dist)],[dist]))))))],[v12]),[v10 of lambda(v3,su(su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(v3,su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(v3,su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(v3,su(su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(v3,su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(v3,su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of _156524,[plus1 of times(v3,s(0))],[v4]),[term_of(plus1)],[plus1])),[times1 of times(v3,s(0))],[v4]),[term_of(times1)],[times1])),[v4 of times(v3,s(0))],[v5]),[times2 of 0],[v4]),[term_of(times2)],[times2])),[plus1 of s(0)],[v4]),[term_of(plus1)],[plus1])),[times1 of s(0)],[v4]),[term_of(times1)],[times1])),[v4 of s(0)],[v5]),[times2 of 0],[v4]),[term_of(times2)],[times2]))],[v11]),[v9 of lambda(v3,su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of lambda(v3,su(su(lambda(v4,su(v5,[v4 of v3],[v5]))of _156348,[times1 of times(v3,s(0))],[v4]),[term_of(times1)],[times1])),[times1 of s(0)],[v4]),[term_of(times1)],[times1]))],[v10]),[v8 of lambda(v2,x:pnat=>times(times(v2,s(0)),times(x,s(0)))=times(times(x,v2),s(0))in pnat)],[v9]))of v7,[term_of(plusind)],[v7])),
   [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,s(0)))=times(exp(x,v0),s(0))in pnat,v2:pnat]==>x:pnat=>0=times(times(x,0),s(0))in pnat,
    ind_strat(induction(lemma(pnat_primitive)-[(x:pnat)-s(v3)])then[base_case(sym_eval(normalize_term([reduction([1,2,1],[times1,equ(pnat,left)]),reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(identity)]),step_case(ripple(direction_out,wave(direction_out,[1,2,1],[times2,equ(pnat,left)],[])then[wave(direction_out,[2,1],[disttwo,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 ripple_and_cancel([unblock(wave_front,[2,2,1],[times1,equ(pnat,left)])]))))])]),lambda(x,p_ind(x,su(su(su(su(axiom,[times1 of s(0)],[v3]),[term_of(times1)],[times1]),[times1 of 0],[v3]),[term_of(times1)],[times1]),[v3,v4,su(su(su(su(su(su(su(su(su(_155897,[times1 of s(0)],[v5]),[term_of(times1)],[times1]),[v6 of 0],[v7]),[v5 of times(v3,0)],[v6]),[disttwo of s(0)],[v5]),[term_of(disttwo)],[disttwo]),[v5 of 0],[v6]),[times2 of v3],[v5]),[term_of(times2)],[times2])])),
    [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,s(0)))=times(exp(x,v0),s(0))in pnat,v2:pnat,x:pnat,v3:pnat,v4:0=times(times(v3,0),s(0))in pnat]==>0=plus(0,0)in pnat,
     sym_eval(normalize_term([reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(identity)],su(su(axiom,[plus1 of 0],[v5]),[term_of(plus1)],[plus1]),
     [
     ]) ext _155897
    ]) ext _156348,
    problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,s(0)))=times(exp(x,v0),s(0))in pnat,v2:pnat]==>x:pnat=>times(x,s(0))=times(times(x,s(0)),s(0))in pnat,
    generalise(times(x,s(0)),v3:pnat),lambda(v3,lambda(v4,su(su(v6,[v5 of v4],[v6]),[v3 of times(v4,s(0))],[v5])))of _155572,
    [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,s(0)))=times(exp(x,v0),s(0))in pnat,v2:pnat]==>v3:pnat=>x:pnat=>v3=times(v3,s(0))in pnat,
     ind_strat(induction(lemma(pnat_primitive)-[(v3:pnat)-s(v4)])then[base_case(sym_eval(normalize_term([reduction([2,1],[times1,equ(pnat,left)])]))then[elementary(intro(new[x])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],v5)]))))])]),lambda(v3,p_ind(v3,lambda(v4,su(su(lambda(v5,su(v6,[v5 of v4],[v6]))of lambda(x,axiom),[times1 of s(0)],[v5]),[term_of(times1)],[times1])),[v4,v5,lambda(v6,su(su(su(lambda(v7,su(v8,[v7 of v6],[v8]))of lambda(v6,su(lambda(v7,su(v8,[v7 of v6],[v8]))of _155228,[v5 of v6],[v7])),[v7 of s(0)],[v8]),[times2 of v4],[v7]),[term_of(times2)],[times2]))])),
     [problem([m:pnat,n:pnat,v0:pnat,v1:x:pnat=>exp(x,times(v0,s(0)))=times(exp(x,v0),s(0))in pnat,v2:pnat,v3:pnat,v4:pnat,v5:x:pnat=>v4=times(v4,s(0))in pnat]==>x:pnat=>s(v4)=plus(v4,s(0))in pnat,
      ind_strat(induction(lemma(pnat_primitive)-[(v4:pnat)-s(v6)])then[base_case(sym_eval(normalize_term([reduction([2,1],[plus1,equ(pnat,left)])]))then[elementary(intro(new[x])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],v7)]))then elementary(intro(new[x])then[identity,wfftacs])))])]),p_ind(v4,lambda(v6,su(su(lambda(v7,su(v8,[v7 of v6],[v8]))of lambda(x,axiom),[plus1 of s(0)],[v7]),[term_of(plus1)],[plus1])),[v6,v7,lambda(v8,su(su(su(lambda(v9,su(v10,[v9 of v8],[v10]))of lambda(v8,su(lambda(v9,su(v10,[v9 of v8],[v10]))of lambda(x,axiom),[v7 of v8],[v9])),[v9 of s(0)],[v10]),[plus2 of v6],[v9]),[term_of(plus2)],[plus2]))]),
      [
      ]) ext _155228
     ]) ext _155572
    ]) ext _156524
   ]) ext _157551
  ]) ext _157793
 ]) ext _161582
]).
