TSTP Solution File: SWW174+1 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : SWW174+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:26:31 EDT 2024
% Result : Theorem 229.42s 29.21s
% Output : Proof 229.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW174+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.36 % Computer : n025.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Wed Jun 19 09:40:24 EDT 2024
% 0.12/0.36 % CPUTime :
% 229.42/29.21 Command-line arguments: --flatten
% 229.42/29.21
% 229.42/29.21 % SZS status Theorem
% 229.42/29.21
% 229.81/29.25 % SZS output start Proof
% 229.81/29.25 Take the following subset of the input axioms:
% 229.81/29.25 fof(arity_Complex__Ocomplex__Fields_Ofield, axiom, class_Fields_Ofield(tc_Complex_Ocomplex)).
% 229.81/29.25 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Complex_Ocomplex)).
% 229.81/29.25 fof(arity_Complex__Ocomplex__RealVector_Oreal__field, axiom, class_RealVector_Oreal__field(tc_Complex_Ocomplex)).
% 229.81/29.25 fof(arity_Int__Oint__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_Int_Oint)).
% 229.81/29.25 fof(arity_RealDef__Oreal__Fields_Ofield, axiom, class_Fields_Ofield(tc_RealDef_Oreal)).
% 229.81/29.25 fof(arity_RealDef__Oreal__Groups_Omonoid__mult, axiom, class_Groups_Omonoid__mult(tc_RealDef_Oreal)).
% 229.81/29.25 fof(arity_RealDef__Oreal__Int_Onumber__ring, axiom, class_Int_Onumber__ring(tc_RealDef_Oreal)).
% 229.81/29.25 fof(arity_RealDef__Oreal__RealVector_Oreal__field, axiom, class_RealVector_Oreal__field(tc_RealDef_Oreal)).
% 229.81/29.25 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)).
% 229.81/29.25 fof(conj_0, conjecture, c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))=c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))).
% 229.81/29.25 fof(fact_Numeral1__eq1__nat, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls))).
% 229.81/29.25 fof(fact_One__nat__def, axiom, c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 229.81/29.25 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, axiom, ![V_x, T_a, V_q]: (class_Rings_Ocomm__semiring__1(T_a) => c_Groups_Otimes__class_Otimes(T_a, c_Power_Opower__class_Opower(T_a, V_x, V_q), V_x)=c_Power_Opower__class_Opower(T_a, V_x, c_Nat_OSuc(V_q)))).
% 229.81/29.25 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, axiom, ![V_m, T_a2]: (class_Rings_Ocomm__semiring__1(T_a2) => c_Groups_Oplus__class_Oplus(T_a2, V_m, V_m)=c_Groups_Otimes__class_Otimes(T_a2, c_Groups_Oplus__class_Oplus(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Oone__class_Oone(T_a2)), V_m))).
% 229.81/29.25 fof(fact_double__number__of__Bit0, axiom, ![V_w, T_a2]: (class_Int_Onumber__ring(T_a2) => c_Groups_Otimes__class_Otimes(T_a2, c_Groups_Oplus__class_Oplus(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Oone__class_Oone(T_a2)), c_Int_Onumber__class_Onumber__of(T_a2, V_w))=c_Int_Onumber__class_Onumber__of(T_a2, c_Int_OBit0(V_w)))).
% 229.81/29.25 fof(fact_mult__2__right, axiom, ![V_z, T_a2]: (class_Int_Onumber__ring(T_a2) => c_Groups_Otimes__class_Otimes(T_a2, V_z, c_Int_Onumber__class_Onumber__of(T_a2, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))=c_Groups_Oplus__class_Oplus(T_a2, V_z, V_z))).
% 229.81/29.25 fof(fact_number__of__is__id, axiom, ![V_k]: c_Int_Onumber__class_Onumber__of(tc_Int_Oint, V_k)=V_k).
% 229.81/29.25 fof(fact_numeral__2__eq__2, axiom, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 229.81/29.25 fof(fact_power__one__right, axiom, ![V_a, T_a2]: (class_Groups_Omonoid__mult(T_a2) => c_Power_Opower__class_Opower(T_a2, V_a, c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a)).
% 229.81/29.25
% 229.81/29.25 Now clausify the problem and encode Horn clauses using encoding 3 of
% 229.81/29.25 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 229.81/29.25 We repeatedly replace C & s=t => u=v by the two clauses:
% 229.81/29.25 fresh(y, y, x1...xn) = u
% 229.81/29.25 C => fresh(s, t, x1...xn) = v
% 229.81/29.25 where fresh is a fresh function symbol and x1..xn are the free
% 229.81/29.25 variables of u and v.
% 229.81/29.25 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 229.81/29.25 input problem has no model of domain size 1).
% 229.81/29.25
% 229.81/29.25 The encoding turns the above axioms into the following unit equations and goals:
% 229.81/29.25
% 229.81/29.25 Axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field): class_RealVector_Oreal__field(tc_Complex_Ocomplex) = true2.
% 229.81/29.25 Axiom 2 (arity_RealDef__Oreal__RealVector_Oreal__field): class_RealVector_Oreal__field(tc_RealDef_Oreal) = true2.
% 229.81/29.25 Axiom 3 (arity_Complex__Ocomplex__Fields_Ofield): class_Fields_Ofield(tc_Complex_Ocomplex) = true2.
% 229.81/29.25 Axiom 4 (arity_RealDef__Oreal__Fields_Ofield): class_Fields_Ofield(tc_RealDef_Oreal) = true2.
% 229.81/29.25 Axiom 5 (arity_Complex__Ocomplex__Groups_Omonoid__mult): class_Groups_Omonoid__mult(tc_Complex_Ocomplex) = true2.
% 229.81/29.25 Axiom 6 (arity_Int__Oint__Groups_Omonoid__mult): class_Groups_Omonoid__mult(tc_Int_Oint) = true2.
% 229.81/29.25 Axiom 7 (arity_RealDef__Oreal__Groups_Omonoid__mult): class_Groups_Omonoid__mult(tc_RealDef_Oreal) = true2.
% 229.81/29.25 Axiom 8 (arity_RealDef__Oreal__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) = true2.
% 229.81/29.25 Axiom 9 (arity_RealDef__Oreal__Int_Onumber__ring): class_Int_Onumber__ring(tc_RealDef_Oreal) = true2.
% 229.81/29.25 Axiom 10 (fact_One__nat__def): c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 229.81/29.25 Axiom 11 (fact_number__of__is__id): c_Int_Onumber__class_Onumber__of(tc_Int_Oint, X) = X.
% 229.81/29.25 Axiom 12 (fact_Numeral1__eq1__nat): c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)).
% 229.81/29.25 Axiom 13 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J): fresh850(X, X, Y, Z) = c_Groups_Oplus__class_Oplus(Z, Y, Y).
% 229.81/29.25 Axiom 14 (fact_double__number__of__Bit0): fresh759(X, X, Y, Z) = c_Int_Onumber__class_Onumber__of(Z, c_Int_OBit0(Y)).
% 229.81/29.25 Axiom 15 (fact_mult__2__right): fresh579(X, X, Y, Z) = c_Groups_Oplus__class_Oplus(Z, Y, Y).
% 229.81/29.25 Axiom 16 (fact_power__one__right): fresh12(X, X, Y, Z) = Y.
% 229.81/29.25 Axiom 17 (fact_numeral__2__eq__2): c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 229.81/29.25 Axiom 18 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J): fresh861(X, X, Y, Z, W) = c_Power_Opower__class_Opower(W, Z, c_Nat_OSuc(Y)).
% 229.81/29.25 Axiom 19 (fact_power__one__right): fresh12(class_Groups_Omonoid__mult(X), true2, Y, X) = c_Power_Opower__class_Opower(X, Y, c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 229.81/29.25 Axiom 20 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J): fresh861(class_Rings_Ocomm__semiring__1(X), true2, Y, Z, X) = c_Groups_Otimes__class_Otimes(X, c_Power_Opower__class_Opower(X, Z, Y), Z).
% 229.81/29.25 Axiom 21 (fact_mult__2__right): fresh579(class_Int_Onumber__ring(X), true2, Y, X) = c_Groups_Otimes__class_Otimes(X, Y, c_Int_Onumber__class_Onumber__of(X, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 229.81/29.25 Axiom 22 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J): fresh850(class_Rings_Ocomm__semiring__1(X), true2, Y, X) = c_Groups_Otimes__class_Otimes(X, c_Groups_Oplus__class_Oplus(X, c_Groups_Oone__class_Oone(X), c_Groups_Oone__class_Oone(X)), Y).
% 229.81/29.25 Axiom 23 (fact_double__number__of__Bit0): fresh759(class_Int_Onumber__ring(X), true2, Y, X) = c_Groups_Otimes__class_Otimes(X, c_Groups_Oplus__class_Oplus(X, c_Groups_Oone__class_Oone(X), c_Groups_Oone__class_Oone(X)), c_Int_Onumber__class_Onumber__of(X, Y)).
% 229.81/29.25
% 229.81/29.25 Lemma 24: class_RealVector_Oreal__field(tc_RealDef_Oreal) = class_RealVector_Oreal__field(tc_Complex_Ocomplex).
% 229.81/29.25 Proof:
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25 = { by axiom 2 (arity_RealDef__Oreal__RealVector_Oreal__field) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25
% 229.81/29.25 Lemma 25: class_Fields_Ofield(tc_Complex_Ocomplex) = class_RealVector_Oreal__field(tc_RealDef_Oreal).
% 229.81/29.25 Proof:
% 229.81/29.25 class_Fields_Ofield(tc_Complex_Ocomplex)
% 229.81/29.25 = { by axiom 3 (arity_Complex__Ocomplex__Fields_Ofield) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 24 R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25
% 229.81/29.25 Lemma 26: class_Fields_Ofield(tc_RealDef_Oreal) = class_Fields_Ofield(tc_Complex_Ocomplex).
% 229.81/29.25 Proof:
% 229.81/29.25 class_Fields_Ofield(tc_RealDef_Oreal)
% 229.81/29.25 = { by axiom 4 (arity_RealDef__Oreal__Fields_Ofield) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 24 R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 25 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_Complex_Ocomplex)
% 229.81/29.25
% 229.81/29.25 Lemma 27: class_Groups_Omonoid__mult(tc_Complex_Ocomplex) = class_Fields_Ofield(tc_RealDef_Oreal).
% 229.81/29.25 Proof:
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
% 229.81/29.25 = { by axiom 5 (arity_Complex__Ocomplex__Groups_Omonoid__mult) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 24 R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 25 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 26 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_RealDef_Oreal)
% 229.81/29.25
% 229.81/29.25 Lemma 28: class_Groups_Omonoid__mult(tc_Int_Oint) = class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 229.81/29.25 Proof:
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Int_Oint)
% 229.81/29.25 = { by axiom 6 (arity_Int__Oint__Groups_Omonoid__mult) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 24 R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 25 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 26 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 27 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
% 229.81/29.25
% 229.81/29.25 Lemma 29: class_Groups_Omonoid__mult(tc_RealDef_Oreal) = class_Groups_Omonoid__mult(tc_Int_Oint).
% 229.81/29.25 Proof:
% 229.81/29.25 class_Groups_Omonoid__mult(tc_RealDef_Oreal)
% 229.81/29.25 = { by axiom 7 (arity_RealDef__Oreal__Groups_Omonoid__mult) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 24 R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 25 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 26 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 27 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 28 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Int_Oint)
% 229.81/29.25
% 229.81/29.25 Lemma 30: class_Int_Onumber__ring(tc_RealDef_Oreal) = class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 229.81/29.25 Proof:
% 229.81/29.25 class_Int_Onumber__ring(tc_RealDef_Oreal)
% 229.81/29.25 = { by axiom 9 (arity_RealDef__Oreal__Int_Onumber__ring) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 24 R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 25 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 26 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 27 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 28 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Int_Oint)
% 229.81/29.25 = { by lemma 29 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_RealDef_Oreal)
% 229.81/29.25
% 229.81/29.25 Lemma 31: class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) = class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 229.81/29.25 Proof:
% 229.81/29.25 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
% 229.81/29.25 = { by axiom 8 (arity_RealDef__Oreal__Rings_Ocomm__semiring__1) }
% 229.81/29.25 true2
% 229.81/29.25 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 24 R->L }
% 229.81/29.25 class_RealVector_Oreal__field(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 25 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 26 R->L }
% 229.81/29.25 class_Fields_Ofield(tc_RealDef_Oreal)
% 229.81/29.25 = { by lemma 27 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Complex_Ocomplex)
% 229.81/29.25 = { by lemma 28 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_Int_Oint)
% 229.81/29.25 = { by lemma 29 R->L }
% 229.81/29.25 class_Groups_Omonoid__mult(tc_RealDef_Oreal)
% 229.81/29.25
% 229.81/29.25 Goal 1 (conj_0): c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))).
% 229.81/29.25 Proof:
% 229.81/29.25 c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.25 = { by axiom 11 (fact_number__of__is__id) R->L }
% 229.81/29.25 c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 229.81/29.25 = { by axiom 14 (fact_double__number__of__Bit0) R->L }
% 229.81/29.25 c_NthRoot_Osqrt(fresh759(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.25 = { by lemma 30 R->L }
% 229.81/29.25 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.25 = { by lemma 29 }
% 229.81/29.25 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.25 = { by lemma 28 }
% 229.81/29.25 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.25 = { by lemma 27 }
% 229.81/29.25 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Fields_Ofield(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.25 = { by lemma 26 }
% 229.81/29.25 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Fields_Ofield(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.25 = { by lemma 25 }
% 229.81/29.25 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 24 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 229.81/29.26 c_NthRoot_Osqrt(fresh759(class_Int_Onumber__ring(tc_RealDef_Oreal), true2, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 23 (fact_double__number__of__Bit0) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 229.81/29.26 = { by axiom 22 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), true2, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 24 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 25 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Fields_Ofield(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 26 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Fields_Ofield(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 27 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 28 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 29 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 11 (fact_number__of__is__id) }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 31 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh850(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 13 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by axiom 15 (fact_mult__2__right) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 30 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 29 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 28 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 27 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Fields_Ofield(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 26 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), class_Fields_Ofield(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 25 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 24 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 229.81/29.26 c_NthRoot_Osqrt(fresh579(class_Int_Onumber__ring(tc_RealDef_Oreal), true2, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 21 (fact_mult__2__right) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by axiom 16 (fact_power__one__right) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by lemma 29 }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by lemma 28 }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by lemma 27 }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Fields_Ofield(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by lemma 26 }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Fields_Ofield(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by lemma 25 }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by lemma 24 }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, fresh12(class_Groups_Omonoid__mult(tc_RealDef_Oreal), true2, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by axiom 19 (fact_power__one__right) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by axiom 12 (fact_Numeral1__eq1__nat) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal, c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by axiom 20 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), true2, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 24 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_RealVector_Oreal__field(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 25 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Fields_Ofield(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 26 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Fields_Ofield(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 27 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Complex_Ocomplex), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 28 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 29 R->L }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by lemma 31 }
% 229.81/29.26 c_NthRoot_Osqrt(fresh861(class_Groups_Omonoid__mult(tc_RealDef_Oreal), class_Groups_Omonoid__mult(tc_RealDef_Oreal), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)), c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), tc_RealDef_Oreal))
% 229.81/29.26 = { by axiom 18 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 = { by axiom 12 (fact_Numeral1__eq1__nat) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 229.81/29.26 = { by axiom 10 (fact_One__nat__def) }
% 229.81/29.26 c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
% 229.81/29.26 = { by axiom 17 (fact_numeral__2__eq__2) R->L }
% 229.81/29.26 c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
% 229.81/29.26 % SZS output end Proof
% 229.81/29.26
% 229.81/29.26 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------