problem([]==>a:pnat=>b:pnat=>c:pnat=>times(a,times(b,c))=times(times(a,b),c)in pnat,
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)]))))])]),lambda(a,p_ind(a,lambda(v0,lambda(v1,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 lambda(v0,lambda(v1,su(su(lambda(v2,su(su(v4,[v3 of v1],[v4]),[v2 of v0],[v3]))of lambda(b,lambda(c,axiom)),[times1 of v1],[v2]),[term_of(times1)],[times1]))),[times1 of v0],[v2]),[term_of(times1)],[times1]))),[times1 of times(v0,v1)],[v2]),[term_of(times1)],[times1]))),[v0,v1,lambda(v2,lambda(v3,su(su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of lambda(v2,lambda(v3,su(su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of lambda(v2,lambda(v3,su(su(lambda(v4,su(su(v6,[v5 of v3],[v6]),[v4 of v2],[v5]))of _196121,[v4 of v3],[v5]),[v1 of v2],[v4]))),[v4 of v2],[v5]),[times2 of v0],[v4]),[term_of(times2)],[times2]))),[v4 of times(v2,v3)],[v5]),[times2 of v0],[v4]),[term_of(times2)],[times2])))])),
[problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat]==>b:pnat=>c:pnat=>plus(times(times(v0,b),c),times(b,c))=times(plus(times(v0,b),b),c)in pnat,
 generalise(times(v0,b),v2:pnat),lambda(v2,lambda(v3,lambda(v4,su(su(su(v7,[v6 of v4],[v7]),[v5 of v3],[v6]),[v2 of times(v0,v3)],[v5]))))of _195930,
 [problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat]==>v2:pnat=>b:pnat=>c:pnat=>plus(times(v2,c),times(b,c))=times(plus(v2,b),c)in pnat,
  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)]))))])]),lambda(v2,p_ind(v2,lambda(v3,lambda(v4,su(su(lambda(v5,su(su(v7,[v6 of v4],[v7]),[v5 of v3],[v6]))of lambda(v3,lambda(v4,su(su(lambda(v5,su(su(v7,[v6 of v4],[v7]),[v5 of v3],[v6]))of lambda(v3,lambda(v4,su(su(lambda(v5,su(su(v7,[v6 of v4],[v7]),[v5 of v3],[v6]))of lambda(b,lambda(c,axiom)),[plus1 of v3],[v5]),[term_of(plus1)],[plus1]))),[plus1 of times(v3,v4)],[v5]),[term_of(plus1)],[plus1]))),[times1 of v4],[v5]),[term_of(times1)],[times1]))),[v3,v4,lambda(v5,lambda(v6,su(su(su(lambda(v7,su(su(v9,[v8 of v6],[v9]),[v7 of v5],[v8]))of lambda(v5,lambda(v6,su(su(su(lambda(v7,su(su(v9,[v8 of v6],[v9]),[v7 of v5],[v8]))of lambda(v5,lambda(v6,su(su(su(lambda(v7,su(su(v9,[v8 of v6],[v9]),[v7 of v5],[v8]))of lambda(v5,lambda(v6,su(su(lambda(v7,su(su(v9,[v8 of v6],[v9]),[v7 of v5],[v8]))of _195230,[v7 of v6],[v8]),[v4 of v5],[v7]))),[v7 of v6],[v8]),[times2 of v3],[v7]),[term_of(times2)],[times2]))),[v7 of v6],[v8]),[times2 of plus(v3,v5)],[v7]),[term_of(times2)],[times2]))),[v7 of v5],[v8]),[plus2 of v3],[v7]),[term_of(plus2)],[plus2])))])),
  [problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat,v2:pnat,v3:pnat,v4:b:pnat=>c:pnat=>plus(times(v3,c),times(b,c))=times(plus(v3,b),c)in pnat]==>b:pnat=>c:pnat=>plus(plus(times(v3,c),c),times(b,c))=plus(plus(times(v3,c),times(b,c)),c)in pnat,
   generalise(times(b,c),v5:pnat),lambda(v5,lambda(v6,lambda(v7,su(su(su(v10,[v9 of v7],[v10]),[v8 of v6],[v9]),[v5 of times(v6,v7)],[v8]))))of _194968,
   [problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat,v2:pnat,v3:pnat,v4:b:pnat=>c:pnat=>plus(times(v3,c),times(b,c))=times(plus(v3,b),c)in pnat]==>v5:pnat=>b:pnat=>c:pnat=>plus(plus(times(v3,c),c),v5)=plus(plus(times(v3,c),v5),c)in pnat,
    generalise(times(v3,c),v6:pnat),lambda(v5,lambda(v7,lambda(v8,lambda(v9,su(su(su(su(v12,[v11 of v9],[v12]),[v10 of v8],[v11]),[v6 of v7],[v10]),[v5 of times(v3,v9)],[v6])))))of _194763,
    [problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat,v2:pnat,v3:pnat,v4:b:pnat=>c:pnat=>plus(times(v3,c),times(b,c))=times(plus(v3,b),c)in pnat]==>v6:pnat=>v5:pnat=>b:pnat=>c:pnat=>plus(plus(v6,c),v5)=plus(plus(v6,v5),c)in pnat,
     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])))])]),lambda(v6,p_ind(v6,lambda(v7,lambda(v5,lambda(v8,su(su(lambda(v9,su(su(su(v12,[v11 of v8],[v12]),[v10 of v5],[v11]),[v9 of v7],[v10]))of lambda(v7,lambda(v5,lambda(v8,su(su(lambda(v9,su(su(su(v12,[v11 of v8],[v12]),[v10 of v5],[v11]),[v9 of v7],[v10]))of _194241,[plus1 of v7],[v9]),[term_of(plus1)],[plus1])))),[plus1 of v8],[v9]),[term_of(plus1)],[plus1])))),[v7,v8,lambda(v9,lambda(v10,lambda(v11,su(su(su(lambda(v5,su(su(su(v14,[v13 of v11],[v14]),[v12 of v10],[v13]),[v5 of v9],[v12]))of lambda(v9,lambda(v10,lambda(v11,su(su(su(lambda(v5,su(su(su(v14,[v13 of v11],[v14]),[v12 of v10],[v13]),[v5 of v9],[v12]))of lambda(v9,lambda(v10,lambda(v11,su(su(su(lambda(v5,su(su(su(v14,[v13 of v11],[v14]),[v12 of v10],[v13]),[v5 of v9],[v12]))of lambda(v9,lambda(v10,lambda(v11,su(su(su(lambda(v5,su(su(su(v14,[v13 of v11],[v14]),[v12 of v10],[v13]),[v5 of v9],[v12]))of lambda(v9,lambda(v10,lambda(v11,su(su(su(lambda(v5,su(su(su(v14,[v13 of v11],[v14]),[v12 of v10],[v13]),[v5 of v9],[v12]))of lambda(v5,lambda(b,lambda(c,axiom))),[v12 of v11],[v13]),[v5 of v10],[v12]),[v8 of v9],[v5])))),[v5 of v9],[v12]),[plus2 of plus(v7,v11)],[v5]),[term_of(plus2)],[plus2])))),[v5 of v11],[v12]),[plus2 of v7],[v5]),[term_of(plus2)],[plus2])))),[v5 of v11],[v12]),[plus2 of plus(v7,v9)],[v5]),[term_of(plus2)],[plus2])))),[v5 of v9],[v12]),[plus2 of v7],[v5]),[term_of(plus2)],[plus2]))))])),
     [problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat,v2:pnat,v3:pnat,v4:b:pnat=>c:pnat=>plus(times(v3,c),times(b,c))=times(plus(v3,b),c)in pnat,v6:pnat]==>v5:pnat=>b:pnat=>c:pnat=>plus(c,v5)=plus(v5,c)in pnat,
      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)]))))])]),lambda(v7,lambda(v5,lambda(v8,lambda(v9,su(su(su(v12,[v11 of v5],[v12]),[v10 of v7],[v11]),[v9 of v8],[v10]))of lambda(c,p_ind(c,lambda(v7,lambda(v5,su(su(lambda(v8,su(su(v10,[v9 of v5],[v10]),[v8 of v7],[v9]))of _193443,[plus1 of v7],[v8]),[term_of(plus1)],[plus1]))),[v7,v8,lambda(v9,lambda(v10,su(su(su(lambda(v5,su(su(v12,[v11 of v10],[v12]),[v5 of v9],[v11]))of lambda(v9,lambda(v10,su(su(lambda(v5,su(su(v12,[v11 of v10],[v12]),[v5 of v9],[v11]))of _193336,[v5 of v10],[v11]),[v8 of v9],[v5]))),[v5 of v9],[v11]),[plus2 of v7],[v5]),[term_of(plus2)],[plus2])))]))))),
      [problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat,v2:pnat,v3:pnat,v4:b:pnat=>c:pnat=>plus(times(v3,c),times(b,c))=times(plus(v3,b),c)in pnat,v6:pnat,c:pnat]==>v5:pnat=>b:pnat=>v5=plus(v5,0)in pnat,
       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])))])]),lambda(v5,p_ind(v5,lambda(v7,su(su(lambda(v8,su(v9,[v8 of v7],[v9]))of lambda(b,axiom),[plus1 of 0],[v8]),[term_of(plus1)],[plus1])),[v7,v8,lambda(v9,su(su(su(lambda(v10,su(v11,[v10 of v9],[v11]))of lambda(v9,su(lambda(v10,su(v11,[v10 of v9],[v11]))of lambda(b,axiom),[v8 of v9],[v10])),[v10 of 0],[v11]),[plus2 of v7],[v10]),[term_of(plus2)],[plus2]))])),
       [
       ]) ext _193443,
       problem([a:pnat,v0:pnat,v1:b:pnat=>c:pnat=>times(v0,times(b,c))=times(times(v0,b),c)in pnat,v2:pnat,v3:pnat,v4:b:pnat=>c:pnat=>plus(times(v3,c),times(b,c))=times(plus(v3,b),c)in pnat,v6:pnat,c:pnat,v7:pnat,v8:v5:pnat=>b:pnat=>plus(v7,v5)=plus(v5,v7)in pnat]==>v5:pnat=>b:pnat=>s(plus(v5,v7))=plus(v5,s(v7))in pnat,
       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])))])]),lambda(v5,p_ind(v5,lambda(v9,su(su(lambda(v10,su(v11,[v10 of v9],[v11]))of lambda(v9,su(su(lambda(v10,su(v11,[v10 of v9],[v11]))of lambda(b,axiom),[plus1 of s(v7)],[v10]),[term_of(plus1)],[plus1])),[plus1 of v7],[v10]),[term_of(plus1)],[plus1])),[v9,v10,lambda(v11,su(su(su(lambda(v12,su(v13,[v12 of v11],[v13]))of lambda(v11,su(su(su(lambda(v12,su(v13,[v12 of v11],[v13]))of lambda(v11,su(lambda(v12,su(v13,[v12 of v11],[v13]))of lambda(b,axiom),[v10 of v11],[v12])),[v12 of v7],[v13]),[plus2 of v9],[v12]),[term_of(plus2)],[plus2])),[v12 of s(v7)],[v13]),[plus2 of v9],[v12]),[term_of(plus2)],[plus2]))])),
       [
       ]) ext _193336
      ]) ext _194241
     ]) ext _194763
    ]) ext _194968
   ]) ext _195230
  ]) ext _195930
 ]) ext _196121
]).
