0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.34	% Computer   : n003.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1200
0.12/0.34	% WCLimit    : 120
0.12/0.34	% DateTime   : Tue Jul 13 16:47:39 EDT 2021
0.12/0.34	% CPUTime    : 
287.29/36.89	% SZS status Theorem
287.29/36.89	
288.24/37.02	% SZS output start Proof
288.24/37.02	Take the following subset of the input axioms:
288.24/37.02	  fof(arity_RealDef_Oreal___Int_Onumber, axiom, number(real)).
288.24/37.02	  fof(arity_RealDef_Oreal___Rings_Ocomm__semiring, axiom, comm_semiring(real)).
288.24/37.02	  fof(arity_RealDef_Oreal___Rings_Odvd, axiom, dvd(real)).
288.24/37.02	  fof(arity_RealDef_Oreal___Rings_Olinordered__semiring__1, axiom, linord1278240602ring_1(real)).
288.24/37.02	  fof(arity_RealDef_Oreal___Rings_Oordered__cancel__semiring, axiom, ordere453448008miring(real)).
288.24/37.02	  fof(conj_0, conjecture, zero_zero(int)!=hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))).
288.24/37.02	  fof(fact_0_n1pos, axiom, hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))))).
288.24/37.02	  fof(fact_113_transfer__int__nat__numerals_I1_J, axiom, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat))=zero_zero(int)).
288.24/37.02	  fof(fact_114_tn0, axiom, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn))).
288.24/37.02	  fof(fact_14_n0, axiom, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n))).
288.24/37.02	  fof(fact_173_transfer__int__nat__numerals_I2_J, axiom, hAPP(nat, int, semiring_1_of_nat(int), one_one(nat))=one_one(int)).
288.24/37.02	  fof(fact_189_pos2, axiom, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls)))))).
288.24/37.02	  fof(fact_251_zle__refl, axiom, ![W]: hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), W), W))).
288.24/37.02	  fof(fact_256_zle__antisym, axiom, ![W, Z]: ((ti(int, Z)=ti(int, W) <= hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), W), Z))) <= hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), W)))).
288.24/37.02	  fof(fact_32_rel__simps_I2_J, axiom, ~hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls))).
288.24/37.02	  fof(fact_380_zless__le, axiom, ![Z_1, Wa]: (hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Z_1), Wa)) <=> (hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z_1), Wa)) & ti(int, Z_1)!=ti(int, Wa)))).
288.24/37.02	  fof(fact_47_zadd__commute, axiom, ![W, Z]: plus_plus(int, W, Z)=plus_plus(int, Z, W)).
288.24/37.02	  fof(fact_519_succ__def, axiom, ![K_1]: plus_plus(int, K_1, one_one(int))=succ(K_1)).
288.24/37.02	  fof(fact_544_power2__ge__self, axiom, ![X]: hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), hAPP(nat, int, power_power(int, X), number_number_of(nat, bit0(bit1(pls))))))).
288.24/37.02	  fof(fact_57_bin__less__0__simps_I1_J, axiom, ~hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))).
288.24/37.02	  fof(fact_718_zprime__2, axiom, hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))).
288.24/37.02	  fof(fact_73_Pls__def, axiom, pls=zero_zero(int)).
288.24/37.02	  fof(fact_752_rel__simps_I6_J, axiom, hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls))).
288.24/37.02	  fof(fact_776_succ__Min, axiom, pls=succ(min)).
288.24/37.02	  fof(tsy_c_Int_OPls_res, hypothesis, ti(int, pls)=pls).
288.24/37.02	  fof(tsy_c_Int_Osucc_res, axiom, ![B_1_1]: succ(B_1_1)=ti(int, succ(B_1_1))).
288.24/37.02	
288.24/37.02	Now clausify the problem and encode Horn clauses using encoding 3 of
288.24/37.02	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
288.24/37.02	We repeatedly replace C & s=t => u=v by the two clauses:
288.24/37.02	  fresh(y, y, x1...xn) = u
288.24/37.02	  C => fresh(s, t, x1...xn) = v
288.24/37.02	where fresh is a fresh function symbol and x1..xn are the free
288.24/37.02	variables of u and v.
288.24/37.02	A predicate p(X) is encoded as p(X)=true (this is sound, because the
288.24/37.02	input problem has no model of domain size 1).
288.24/37.02	
288.24/37.02	The encoding turns the above axioms into the following unit equations and goals:
288.24/37.02	
288.24/37.02	Axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1): linord1278240602ring_1(real) = true2.
288.24/37.02	Axiom 2 (arity_RealDef_Oreal___Rings_Ocomm__semiring): comm_semiring(real) = true2.
288.24/37.02	Axiom 3 (arity_RealDef_Oreal___Rings_Oordered__cancel__semiring): ordere453448008miring(real) = true2.
288.24/37.02	Axiom 4 (arity_RealDef_Oreal___Int_Onumber): number(real) = true2.
288.24/37.02	Axiom 5 (fact_776_succ__Min): pls = succ(min).
288.24/37.02	Axiom 6 (arity_RealDef_Oreal___Rings_Odvd): dvd(real) = true2.
288.24/37.02	Axiom 7 (fact_73_Pls__def): pls = zero_zero(int).
288.24/37.02	Axiom 8 (tsy_c_Int_OPls_res): ti(int, pls) = pls.
288.24/37.02	Axiom 9 (tsy_c_Int_Osucc_res): succ(X) = ti(int, succ(X)).
288.24/37.02	Axiom 10 (fact_47_zadd__commute): plus_plus(int, X, Y) = plus_plus(int, Y, X).
288.24/37.02	Axiom 11 (fact_256_zle__antisym): fresh1017(X, X, Y, Z) = ti(int, Y).
288.24/37.02	Axiom 12 (fact_256_zle__antisym): fresh1016(X, X, Y, Z) = ti(int, Z).
288.24/37.02	Axiom 13 (fact_380_zless__le_1): fresh838(X, X, Y, Z) = true2.
288.24/37.02	Axiom 14 (fact_519_succ__def): plus_plus(int, X, one_one(int)) = succ(X).
288.24/37.02	Axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1): fresh705(X, X, Y, Z) = hBOOL(hAPP(int, bool, Y, Z)).
288.24/37.02	Axiom 16 (tsy_c_hAPP_0_arg1): fresh91(X, X, Y, Z, W) = hAPP(W, fun(W, bool), Y, Z).
288.24/37.02	Axiom 17 (fact_173_transfer__int__nat__numerals_I2_J): hAPP(nat, int, semiring_1_of_nat(int), one_one(nat)) = one_one(int).
288.24/37.02	Axiom 18 (fact_113_transfer__int__nat__numerals_I1_J): hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)) = zero_zero(int).
288.24/37.02	Axiom 19 (fact_718_zprime__2): hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))) = true2.
288.24/37.02	Axiom 20 (fact_251_zle__refl): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X)) = true2.
288.24/37.02	Axiom 21 (fact_683_transfer__nat__int__relations_I3_J): fresh1729(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), Y)).
288.24/37.02	Axiom 22 (fact_387_transfer__nat__int__relations_I2_J): fresh1578(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Z), Y)).
288.24/37.02	Axiom 23 (fact_49_less__special_I3_J): fresh1666(X, X, Y, Z) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Z), pls)).
288.24/37.02	Axiom 24 (fact_752_rel__simps_I6_J): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)) = true2.
288.24/37.02	Axiom 25 (fact_114_tn0): hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)) = true2.
288.24/37.02	Axiom 26 (fact_14_n0): hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)) = true2.
288.24/37.02	Axiom 27 (fact_256_zle__antisym): fresh1017(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), Y)), true2, Y, X) = fresh1016(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Y), X)), true2, Y, X).
288.24/37.02	Axiom 28 (fact_380_zless__le_1): fresh838(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), X), Y)), true2, X, Y) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), Y)).
288.24/37.02	Axiom 29 (fact_189_pos2): hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))) = true2.
288.24/37.02	Axiom 30 (conj_0): zero_zero(int) = hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))).
288.24/37.02	Axiom 31 (fact_544_power2__ge__self): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), hAPP(nat, int, power_power(int, X), number_number_of(nat, bit0(bit1(pls)))))) = true2.
288.24/37.02	Axiom 32 (fact_0_n1pos): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))) = true2.
288.24/37.02	
288.24/37.02	Lemma 33: zero_zero(int) = succ(min).
288.24/37.02	Proof:
288.24/37.02	  zero_zero(int)
288.24/37.02	= { by axiom 7 (fact_73_Pls__def) R->L }
288.24/37.02	  pls
288.24/37.02	= { by axiom 5 (fact_776_succ__Min) }
288.24/37.02	  succ(min)
288.24/37.02	
288.24/37.02	Lemma 34: comm_semiring(real) = linord1278240602ring_1(real).
288.24/37.02	Proof:
288.24/37.02	  comm_semiring(real)
288.24/37.02	= { by axiom 2 (arity_RealDef_Oreal___Rings_Ocomm__semiring) }
288.24/37.02	  true2
288.24/37.02	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.02	  linord1278240602ring_1(real)
288.24/37.02	
288.24/37.02	Lemma 35: ordere453448008miring(real) = comm_semiring(real).
288.24/37.02	Proof:
288.24/37.02	  ordere453448008miring(real)
288.24/37.02	= { by axiom 3 (arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) }
288.24/37.02	  true2
288.24/37.02	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.02	  linord1278240602ring_1(real)
288.24/37.02	= { by lemma 34 R->L }
288.24/37.02	  comm_semiring(real)
288.24/37.02	
288.24/37.02	Lemma 36: number(real) = ordere453448008miring(real).
288.24/37.02	Proof:
288.24/37.02	  number(real)
288.24/37.02	= { by axiom 4 (arity_RealDef_Oreal___Int_Onumber) }
288.24/37.02	  true2
288.24/37.02	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.02	  linord1278240602ring_1(real)
288.24/37.02	= { by lemma 34 R->L }
288.24/37.02	  comm_semiring(real)
288.24/37.02	= { by lemma 35 R->L }
288.24/37.02	  ordere453448008miring(real)
288.24/37.02	
288.24/37.02	Lemma 37: dvd(real) = number(real).
288.24/37.02	Proof:
288.24/37.02	  dvd(real)
288.24/37.02	= { by axiom 6 (arity_RealDef_Oreal___Rings_Odvd) }
288.24/37.02	  true2
288.24/37.02	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.02	  linord1278240602ring_1(real)
288.24/37.02	= { by lemma 34 R->L }
288.24/37.02	  comm_semiring(real)
288.24/37.02	= { by lemma 35 R->L }
288.24/37.02	  ordere453448008miring(real)
288.24/37.02	= { by lemma 36 R->L }
288.24/37.02	  number(real)
288.24/37.02	
288.24/37.02	Lemma 38: plus_plus(int, one_one(int), X) = succ(X).
288.24/37.02	Proof:
288.24/37.02	  plus_plus(int, one_one(int), X)
288.24/37.02	= { by axiom 17 (fact_173_transfer__int__nat__numerals_I2_J) R->L }
288.24/37.02	  plus_plus(int, hAPP(nat, int, semiring_1_of_nat(int), one_one(nat)), X)
288.24/37.02	= { by axiom 10 (fact_47_zadd__commute) }
288.24/37.02	  plus_plus(int, X, hAPP(nat, int, semiring_1_of_nat(int), one_one(nat)))
288.24/37.02	= { by axiom 17 (fact_173_transfer__int__nat__numerals_I2_J) }
288.24/37.02	  plus_plus(int, X, one_one(int))
288.24/37.02	= { by axiom 14 (fact_519_succ__def) }
288.24/37.02	  succ(X)
288.24/37.02	
288.24/37.02	Lemma 39: hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))) = dvd(real).
288.24/37.02	Proof:
288.24/37.02	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.02	= { by axiom 19 (fact_718_zprime__2) }
288.24/37.02	  true2
288.24/37.02	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.02	  linord1278240602ring_1(real)
288.24/37.02	= { by lemma 34 R->L }
288.24/37.02	  comm_semiring(real)
288.24/37.02	= { by lemma 35 R->L }
288.24/37.02	  ordere453448008miring(real)
288.24/37.02	= { by lemma 36 R->L }
288.24/37.02	  number(real)
288.24/37.02	= { by lemma 37 R->L }
288.24/37.02	  dvd(real)
288.24/37.02	
288.24/37.02	Lemma 40: fresh705(X, X, fresh91(Y, Y, ord_less(int), Z, int), W) = fresh1578(V, V, W, Z).
288.24/37.02	Proof:
288.24/37.02	  fresh705(X, X, fresh91(Y, Y, ord_less(int), Z, int), W)
288.24/37.02	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.24/37.02	  fresh705(X, X, hAPP(int, fun(int, bool), ord_less(int), Z), W)
288.24/37.02	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.24/37.02	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Z), W))
288.24/37.02	= { by axiom 22 (fact_387_transfer__nat__int__relations_I2_J) R->L }
288.24/37.03	  fresh1578(V, V, W, Z)
288.24/37.03	
288.24/37.03	Lemma 41: fresh1578(X, X, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)), Y) = fresh1666(Z, Z, W, Y).
288.24/37.03	Proof:
288.24/37.03	  fresh1578(X, X, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)), Y)
288.24/37.03	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) }
288.24/37.03	  fresh1578(X, X, zero_zero(int), Y)
288.24/37.03	= { by lemma 33 }
288.24/37.03	  fresh1578(X, X, succ(min), Y)
288.24/37.03	= { by axiom 5 (fact_776_succ__Min) R->L }
288.24/37.03	  fresh1578(X, X, pls, Y)
288.24/37.03	= { by lemma 40 R->L }
288.24/37.03	  fresh705(V, V, fresh91(U, U, ord_less(int), Y, int), pls)
288.24/37.03	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.24/37.03	  fresh705(V, V, hAPP(int, fun(int, bool), ord_less(int), Y), pls)
288.24/37.03	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Y), pls))
288.24/37.03	= { by axiom 23 (fact_49_less__special_I3_J) R->L }
288.24/37.03	  fresh1666(Z, Z, W, Y)
288.24/37.03	
288.24/37.03	Lemma 42: fresh705(X, X, fresh91(Y, Y, ord_less_eq(int), Z, int), W) = fresh1729(V, V, W, Z).
288.24/37.03	Proof:
288.24/37.03	  fresh705(X, X, fresh91(Y, Y, ord_less_eq(int), Z, int), W)
288.24/37.03	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.24/37.03	  fresh705(X, X, hAPP(int, fun(int, bool), ord_less_eq(int), Z), W)
288.24/37.03	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), Z), W))
288.24/37.03	= { by axiom 21 (fact_683_transfer__nat__int__relations_I3_J) R->L }
288.24/37.03	  fresh1729(V, V, W, Z)
288.24/37.03	
288.24/37.03	Lemma 43: hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X)) = hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))).
288.24/37.03	Proof:
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X))
288.24/37.03	= { by axiom 20 (fact_251_zle__refl) }
288.24/37.03	  true2
288.24/37.03	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.03	  linord1278240602ring_1(real)
288.24/37.03	= { by lemma 34 R->L }
288.24/37.03	  comm_semiring(real)
288.24/37.03	= { by lemma 35 R->L }
288.24/37.03	  ordere453448008miring(real)
288.24/37.03	= { by lemma 36 R->L }
288.24/37.03	  number(real)
288.24/37.03	= { by lemma 37 R->L }
288.24/37.03	  dvd(real)
288.24/37.03	= { by lemma 39 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.03	
288.24/37.03	Lemma 44: hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X)).
288.24/37.03	Proof:
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls))
288.24/37.03	= { by axiom 24 (fact_752_rel__simps_I6_J) }
288.24/37.03	  true2
288.24/37.03	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.03	  linord1278240602ring_1(real)
288.24/37.03	= { by lemma 34 R->L }
288.24/37.03	  comm_semiring(real)
288.24/37.03	= { by lemma 35 R->L }
288.24/37.03	  ordere453448008miring(real)
288.24/37.03	= { by lemma 36 R->L }
288.24/37.03	  number(real)
288.24/37.03	= { by lemma 37 R->L }
288.24/37.03	  dvd(real)
288.24/37.03	= { by lemma 39 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 43 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X))
288.24/37.03	
288.24/37.03	Lemma 45: hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)).
288.24/37.03	Proof:
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn))
288.24/37.03	= { by axiom 25 (fact_114_tn0) }
288.24/37.03	  true2
288.24/37.03	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.03	  linord1278240602ring_1(real)
288.24/37.03	= { by lemma 34 R->L }
288.24/37.03	  comm_semiring(real)
288.24/37.03	= { by lemma 35 R->L }
288.24/37.03	  ordere453448008miring(real)
288.24/37.03	= { by lemma 36 R->L }
288.24/37.03	  number(real)
288.24/37.03	= { by lemma 37 R->L }
288.24/37.03	  dvd(real)
288.24/37.03	= { by lemma 39 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 43 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X))
288.24/37.03	= { by lemma 44 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls))
288.24/37.03	
288.24/37.03	Lemma 46: hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)) = hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)).
288.24/37.03	Proof:
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n))
288.24/37.03	= { by axiom 26 (fact_14_n0) }
288.24/37.03	  true2
288.24/37.03	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.03	  linord1278240602ring_1(real)
288.24/37.03	= { by lemma 34 R->L }
288.24/37.03	  comm_semiring(real)
288.24/37.03	= { by lemma 35 R->L }
288.24/37.03	  ordere453448008miring(real)
288.24/37.03	= { by lemma 36 R->L }
288.24/37.03	  number(real)
288.24/37.03	= { by lemma 37 R->L }
288.24/37.03	  dvd(real)
288.24/37.03	= { by lemma 39 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 43 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X))
288.24/37.03	= { by lemma 44 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls))
288.24/37.03	= { by lemma 45 R->L }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn))
288.24/37.03	
288.24/37.03	Lemma 47: hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))) = hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)).
288.24/37.03	Proof:
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.03	= { by axiom 29 (fact_189_pos2) }
288.24/37.03	  true2
288.24/37.03	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.03	  linord1278240602ring_1(real)
288.24/37.03	= { by lemma 34 R->L }
288.24/37.03	  comm_semiring(real)
288.24/37.03	= { by lemma 35 R->L }
288.24/37.03	  ordere453448008miring(real)
288.24/37.03	= { by lemma 36 R->L }
288.24/37.03	  number(real)
288.24/37.03	= { by lemma 37 R->L }
288.24/37.03	  dvd(real)
288.24/37.03	= { by lemma 39 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 43 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X))
288.24/37.03	= { by lemma 44 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls))
288.24/37.03	= { by lemma 45 R->L }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn))
288.24/37.03	= { by lemma 46 R->L }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n))
288.24/37.03	
288.24/37.03	Lemma 48: hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))) = true2.
288.24/37.03	Proof:
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 47 }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n))
288.24/37.03	= { by lemma 46 }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn))
288.24/37.03	= { by lemma 45 }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls))
288.24/37.03	= { by lemma 44 }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), X), X))
288.24/37.03	= { by lemma 43 }
288.24/37.03	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 39 }
288.24/37.03	  dvd(real)
288.24/37.03	= { by lemma 37 }
288.24/37.03	  number(real)
288.24/37.03	= { by lemma 36 }
288.24/37.03	  ordere453448008miring(real)
288.24/37.03	= { by lemma 35 }
288.24/37.03	  comm_semiring(real)
288.24/37.03	= { by lemma 34 }
288.24/37.03	  linord1278240602ring_1(real)
288.24/37.03	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) }
288.24/37.03	  true2
288.24/37.03	
288.24/37.03	Lemma 49: hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))) = hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)).
288.24/37.03	Proof:
288.24/37.03	  hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))
288.24/37.03	= { by axiom 30 (conj_0) R->L }
288.24/37.03	  zero_zero(int)
288.24/37.03	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) R->L }
288.24/37.03	  hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat))
288.24/37.03	
288.24/37.03	Lemma 50: fresh1578(X, X, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))) = hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))).
288.24/37.03	Proof:
288.24/37.03	  fresh1578(X, X, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 49 }
288.24/37.03	  fresh1578(X, X, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)))
288.24/37.03	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) }
288.24/37.03	  fresh1578(X, X, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), zero_zero(int))
288.24/37.03	= { by lemma 40 R->L }
288.24/37.03	  fresh705(Y, Y, fresh91(Z, Z, ord_less(int), zero_zero(int), int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))
288.24/37.03	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.24/37.03	  fresh705(Y, Y, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))
288.24/37.03	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), zero_zero(int)), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))))
288.24/37.03	= { by axiom 32 (fact_0_n1pos) }
288.24/37.03	  true2
288.24/37.03	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.24/37.03	  linord1278240602ring_1(real)
288.24/37.03	= { by lemma 34 R->L }
288.24/37.03	  comm_semiring(real)
288.24/37.03	= { by lemma 35 R->L }
288.24/37.03	  ordere453448008miring(real)
288.24/37.03	= { by lemma 36 R->L }
288.24/37.03	  number(real)
288.24/37.03	= { by lemma 37 R->L }
288.24/37.03	  dvd(real)
288.24/37.03	= { by lemma 39 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 43 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), W), W))
288.24/37.03	= { by lemma 44 R->L }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls))
288.24/37.03	= { by lemma 45 R->L }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn))
288.24/37.03	= { by lemma 46 R->L }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n))
288.24/37.03	= { by lemma 47 R->L }
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.03	
288.24/37.03	Lemma 51: fresh1578(X, X, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), Y) = fresh1666(Z, Z, W, Y).
288.24/37.03	Proof:
288.24/37.03	  fresh1578(X, X, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), Y)
288.24/37.03	= { by lemma 49 }
288.24/37.03	  fresh1578(X, X, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)), Y)
288.24/37.03	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) }
288.24/37.03	  fresh1578(X, X, zero_zero(int), Y)
288.24/37.03	= { by lemma 33 }
288.24/37.03	  fresh1578(X, X, succ(min), Y)
288.24/37.03	= { by axiom 5 (fact_776_succ__Min) R->L }
288.24/37.03	  fresh1578(X, X, pls, Y)
288.24/37.03	= { by lemma 40 R->L }
288.24/37.03	  fresh705(V, V, fresh91(U, U, ord_less(int), Y, int), pls)
288.24/37.03	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.24/37.03	  fresh705(V, V, hAPP(int, fun(int, bool), ord_less(int), Y), pls)
288.24/37.03	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), Y), pls))
288.24/37.03	= { by axiom 23 (fact_49_less__special_I3_J) R->L }
288.24/37.03	  fresh1666(Z, Z, W, Y)
288.24/37.03	
288.24/37.03	Lemma 52: fresh1666(X, X, Y, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))).
288.24/37.03	Proof:
288.24/37.03	  fresh1666(X, X, Y, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 49 }
288.24/37.03	  fresh1666(X, X, Y, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)))
288.24/37.03	= { by lemma 41 R->L }
288.24/37.03	  fresh1578(Z, Z, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)), hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)))
288.24/37.03	= { by lemma 41 }
288.24/37.03	  fresh1666(W, W, V, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)))
288.24/37.03	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) }
288.24/37.03	  fresh1666(W, W, V, zero_zero(int))
288.24/37.03	= { by lemma 33 }
288.24/37.03	  fresh1666(W, W, V, succ(min))
288.24/37.03	= { by axiom 5 (fact_776_succ__Min) R->L }
288.24/37.03	  fresh1666(W, W, V, pls)
288.24/37.03	= { by lemma 41 R->L }
288.24/37.03	  fresh1578(U, U, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)), pls)
288.24/37.03	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) }
288.24/37.03	  fresh1578(U, U, zero_zero(int), pls)
288.24/37.03	= { by lemma 40 R->L }
288.24/37.03	  fresh705(T, T, fresh91(S, S, ord_less(int), pls, int), zero_zero(int))
288.24/37.03	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.24/37.03	  fresh705(T, T, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))
288.24/37.03	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.24/37.03	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
288.24/37.03	
288.24/37.03	Lemma 53: hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))) = hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))).
288.24/37.03	Proof:
288.24/37.03	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.03	= { by lemma 50 R->L }
288.24/37.04	  fresh1578(Z, Z, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.04	= { by lemma 38 }
288.24/37.04	  fresh1578(Z, Z, succ(hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.04	= { by axiom 9 (tsy_c_Int_Osucc_res) }
288.24/37.04	  fresh1578(Z, Z, ti(int, succ(hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.24/37.04	= { by lemma 38 R->L }
288.24/37.04	  fresh1578(Z, Z, ti(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by axiom 12 (fact_256_zle__antisym) R->L }
288.47/37.04	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 47 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 46 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 45 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 44 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), V3), V3)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 43 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 39 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(dvd(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 37 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(number(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 36 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(ordere453448008miring(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 35 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(comm_semiring(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 34 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(linord1278240602ring_1(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) }
288.47/37.04	  fresh1578(Z, Z, fresh1016(true2, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by axiom 13 (fact_380_zless__le_1) R->L }
288.47/37.04	  fresh1578(Z, Z, fresh1016(fresh838(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 50 R->L }
288.47/37.04	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 47 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 46 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 45 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 44 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), W3), W3)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 43 }
288.47/37.04	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.04	= { by lemma 39 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), dvd(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 37 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), number(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 36 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), ordere453448008miring(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 35 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), comm_semiring(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 34 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), linord1278240602ring_1(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh1578(Z3, Z3, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 40 R->L }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh705(X3, X3, fresh91(Y3, Y3, ord_less(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(fresh705(X3, X3, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh838(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by axiom 28 (fact_380_zless__le_1) }
288.47/37.05	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) R->L }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh705(T2, T2, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by axiom 16 (tsy_c_hAPP_0_arg1) R->L }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh705(T2, T2, fresh91(S2, S2, ord_less_eq(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 42 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 47 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 46 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 45 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 44 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), U2), U2)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 43 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 39 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), dvd(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.05	= { by lemma 37 }
288.47/37.05	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), number(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 36 }
288.47/37.06	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), ordere453448008miring(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 35 }
288.47/37.06	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), comm_semiring(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 34 }
288.47/37.06	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), linord1278240602ring_1(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) }
288.47/37.06	  fresh1578(Z, Z, fresh1016(fresh1729(V2, V2, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 42 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1016(fresh705(Z2, Z2, fresh91(W2, W2, ord_less_eq(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.47/37.06	  fresh1578(Z, Z, fresh1016(fresh705(Z2, Z2, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.47/37.06	  fresh1578(Z, Z, fresh1016(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 27 (fact_256_zle__antisym) R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh705(X2, X2, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 16 (tsy_c_hAPP_0_arg1) R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh705(X2, X2, fresh91(Y2, Y2, ord_less_eq(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 42 }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), true2, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), linord1278240602ring_1(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 34 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), comm_semiring(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 35 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), ordere453448008miring(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 36 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 37 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), dvd(real), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 39 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 43 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), S), S)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 44 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 45 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 46 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 47 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh1729(T, T, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by lemma 42 R->L }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh705(V, V, fresh91(U, U, ord_less_eq(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n)), int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 16 (tsy_c_hAPP_0_arg1) }
288.47/37.06	  fresh1578(Z, Z, fresh1017(fresh705(V, V, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.06	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) }
288.47/37.07	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 31 (fact_544_power2__ge__self) }
288.47/37.07	  fresh1578(Z, Z, fresh1017(true2, hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 1 (arity_RealDef_Oreal___Rings_Olinordered__semiring__1) R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(linord1278240602ring_1(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 34 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(comm_semiring(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 35 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(ordere453448008miring(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 36 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(number(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 37 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(dvd(real), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 39 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(int, bool, zprime, number_number_of(int, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 43 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less_eq(int), W), W)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 44 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), min), pls)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 45 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), tn)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 46 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), n)), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 47 R->L }
288.47/37.07	  fresh1578(Z, Z, fresh1017(hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 11 (fact_256_zle__antisym) }
288.47/37.07	  fresh1578(Z, Z, ti(int, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 49 }
288.47/37.07	  fresh1578(Z, Z, ti(int, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) }
288.47/37.07	  fresh1578(Z, Z, ti(int, zero_zero(int)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 33 }
288.47/37.07	  fresh1578(Z, Z, ti(int, succ(min)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 5 (fact_776_succ__Min) R->L }
288.47/37.07	  fresh1578(Z, Z, ti(int, pls), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 8 (tsy_c_Int_OPls_res) }
288.47/37.07	  fresh1578(Z, Z, pls, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 5 (fact_776_succ__Min) }
288.47/37.07	  fresh1578(Z, Z, succ(min), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 33 R->L }
288.47/37.07	  fresh1578(Z, Z, zero_zero(int), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) R->L }
288.47/37.07	  fresh1578(Z, Z, hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat)), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 49 R->L }
288.47/37.07	  fresh1578(Z, Z, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 51 }
288.47/37.07	  fresh1666(X, X, Y, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 52 }
288.47/37.07	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
288.47/37.07	
288.47/37.07	Lemma 54: hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))) = pls.
288.47/37.07	Proof:
288.47/37.07	  hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls))))
288.47/37.07	= { by lemma 49 }
288.47/37.07	  hAPP(nat, int, semiring_1_of_nat(int), zero_zero(nat))
288.47/37.07	= { by axiom 18 (fact_113_transfer__int__nat__numerals_I1_J) }
288.47/37.07	  zero_zero(int)
288.47/37.07	= { by lemma 33 }
288.47/37.07	  succ(min)
288.47/37.07	= { by axiom 5 (fact_776_succ__Min) R->L }
288.47/37.07	  pls
288.47/37.07	
288.47/37.07	Goal 1 (fact_32_rel__simps_I2_J): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls)) = true2.
288.47/37.07	Proof:
288.47/37.07	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), pls))
288.47/37.07	= { by axiom 16 (tsy_c_hAPP_0_arg1) R->L }
288.47/37.07	  hBOOL(hAPP(int, bool, fresh91(X, X, ord_less(int), pls, int), pls))
288.47/37.07	= { by axiom 15 (fact_474_transfer__int__nat__quantifiers_I1_J_1) R->L }
288.47/37.07	  fresh705(Y, Y, fresh91(X, X, ord_less(int), pls, int), pls)
288.47/37.07	= { by lemma 40 }
288.47/37.07	  fresh1578(Z, Z, pls, pls)
288.47/37.07	= { by lemma 54 R->L }
288.47/37.07	  fresh1578(Z, Z, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), pls)
288.47/37.07	= { by lemma 54 R->L }
288.47/37.07	  fresh1578(Z, Z, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))), hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 51 }
288.47/37.07	  fresh1666(W, W, V, hAPP(nat, int, power_power(int, plus_plus(int, one_one(int), hAPP(nat, int, semiring_1_of_nat(int), n))), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 52 }
288.47/37.07	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
288.47/37.07	= { by lemma 53 R->L }
288.47/37.07	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 48 }
288.47/37.07	  true2
288.47/37.07	
288.47/37.07	Goal 2 (fact_57_bin__less__0__simps_I1_J): hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int))) = true2.
288.47/37.07	Proof:
288.47/37.07	  hBOOL(hAPP(int, bool, hAPP(int, fun(int, bool), ord_less(int), pls), zero_zero(int)))
288.47/37.07	= { by lemma 53 R->L }
288.47/37.07	  hBOOL(hAPP(nat, bool, hAPP(nat, fun(nat, bool), ord_less(nat), zero_zero(nat)), number_number_of(nat, bit0(bit1(pls)))))
288.47/37.07	= { by lemma 48 }
288.47/37.07	  true2
288.47/37.07	% SZS output end Proof
288.47/37.07	
288.47/37.07	RESULT: Theorem (the conjecture is true).
288.47/37.14	EOF