%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW256+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : Sat Jun 21 05:36:42 AM UTC 2025
% Result : Theorem 2.44s 2.61s
% Output : Proof 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW256+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:20:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.44/2.61 % SZS status Theorem
% 2.44/2.61 % SZS output start Proof
% 2.44/2.61 tff(c_Groups_Ozero__class_Ozero_type, type, (
% 2.44/2.61 c_Groups_Ozero__class_Ozero: $i > $i)).
% 2.44/2.61 tff(tc_Complex_Ocomplex_type, type, (
% 2.44/2.61 tc_Complex_Ocomplex: $i)).
% 2.44/2.61 tff(hAPP_type, type, (
% 2.44/2.61 hAPP: ( $i * $i ) > $i)).
% 2.44/2.61 tff(c_Polynomial_Opoly_type, type, (
% 2.44/2.61 c_Polynomial_Opoly: ( $i * $i ) > $i)).
% 2.44/2.61 tff(c_Polynomial_Osmult_type, type, (
% 2.44/2.61 c_Polynomial_Osmult: ( $i * $i * $i ) > $i)).
% 2.44/2.61 tff(v_q_____type, type, (
% 2.44/2.61 v_q____: $i)).
% 2.44/2.61 tff(c_Rings_Oinverse__class_Oinverse_type, type, (
% 2.44/2.61 c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i)).
% 2.44/2.61 tff(v_k_____type, type, (
% 2.44/2.61 v_k____: $i)).
% 2.44/2.61 tff(c_Power_Opower__class_Opower_type, type, (
% 2.44/2.61 c_Power_Opower__class_Opower: $i > $i)).
% 2.44/2.61 tff(tc_Nat_Onat_type, type, (
% 2.44/2.61 tc_Nat_Onat: $i)).
% 2.44/2.61 tff(class_Power_Opower_type, type, (
% 2.44/2.61 class_Power_Opower: $i > $o)).
% 2.44/2.61 tff(class_Rings_Omult__zero_type, type, (
% 2.44/2.61 class_Rings_Omult__zero: $i > $o)).
% 2.44/2.61 tff(class_Rings_Ozero__neq__one_type, type, (
% 2.44/2.61 class_Rings_Ozero__neq__one: $i > $o)).
% 2.44/2.61 tff(class_Rings_Ono__zero__divisors_type, type, (
% 2.44/2.61 class_Rings_Ono__zero__divisors: $i > $o)).
% 2.44/2.61 tff(c_Groups_Ominus__class_Ominus_type, type, (
% 2.44/2.61 c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i)).
% 2.44/2.61 tff(c_Groups_Oone__class_Oone_type, type, (
% 2.44/2.61 c_Groups_Oone__class_Oone: $i > $i)).
% 2.44/2.61 tff(c_Groups_Otimes__class_Otimes_type, type, (
% 2.44/2.61 c_Groups_Otimes__class_Otimes: $i > $i)).
% 2.44/2.61 tff(c_Nat_OSuc_type, type, (
% 2.44/2.61 c_Nat_OSuc: $i > $i)).
% 2.44/2.61 tff(tptp_fun_B_k_31_type, type, (
% 2.44/2.61 tptp_fun_B_k_31: $i)).
% 2.44/2.61 tff(c_Groups_Oplus__class_Oplus_type, type, (
% 2.44/2.61 c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i)).
% 2.44/2.61 tff(c_Polynomial_OpCons_type, type, (
% 2.44/2.61 c_Polynomial_OpCons: ( $i * $i * $i ) > $i)).
% 2.44/2.61 tff(tptp_fun_B_q_32_type, type, (
% 2.44/2.61 tptp_fun_B_q_32: $i)).
% 2.44/2.61 tff(tptp_fun_B_a_30_type, type, (
% 2.44/2.61 tptp_fun_B_a_30: $i)).
% 2.44/2.61 tff(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type, type, (
% 2.44/2.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i)).
% 2.44/2.61 tff(class_Groups_Omonoid__mult_type, type, (
% 2.44/2.61 class_Groups_Omonoid__mult: $i > $o)).
% 2.44/2.61 tff(1,plain,
% 2.44/2.61 (class_Power_Opower(tc_Complex_Ocomplex) <=> class_Power_Opower(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(2,axiom,(class_Power_Opower(tc_Complex_Ocomplex)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Power_Opower')).
% 2.44/2.61 tff(3,plain,
% 2.44/2.61 (class_Power_Opower(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[2, 1])).
% 2.44/2.61 tff(4,plain,
% 2.44/2.61 (class_Rings_Omult__zero(tc_Complex_Ocomplex) <=> class_Rings_Omult__zero(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(5,axiom,(class_Rings_Omult__zero(tc_Complex_Ocomplex)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Omult__zero')).
% 2.44/2.61 tff(6,plain,
% 2.44/2.61 (class_Rings_Omult__zero(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.44/2.61 tff(7,plain,
% 2.44/2.61 (class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) <=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8,axiom,(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ozero__neq__one')).
% 2.44/2.61 tff(9,plain,
% 2.44/2.61 (class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8, 7])).
% 2.44/2.61 tff(10,plain,
% 2.44/2.61 (class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) <=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(11,axiom,(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ono__zero__divisors')).
% 2.44/2.61 tff(12,plain,
% 2.44/2.61 (class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[11, 10])).
% 2.44/2.61 tff(13,plain,
% 2.44/2.61 (^[V_n_2: $i, V_aa_2: $i, T_a: $i] : refl(((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(14,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[13])).
% 2.44/2.61 tff(15,plain,
% 2.44/2.61 (^[V_n_2: $i, V_aa_2: $i, T_a: $i] : trans(monotonicity(trans(monotonicity(rewrite((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)) <=> (~((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))), ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) <=> (~(~((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))))), rewrite((~(~((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a)))), ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))), trans(trans(monotonicity(rewrite(((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), (((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))), rewrite(((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a))))), (((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))), rewrite((~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))) <=> (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a))))), (((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))), (((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> (((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a))))))), rewrite((((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))), (((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(16,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[15])).
% 2.44/2.61 tff(17,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(18,plain,
% 2.44/2.61 (^[V_n_2: $i, V_aa_2: $i, T_a: $i] : trans(monotonicity(trans(monotonicity(rewrite(((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) <=> (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a))), ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) <=> ((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)))), rewrite(((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) <=> (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))), ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) <=> (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)))), (((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), rewrite(((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))), (((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))),
% 2.44/2.61 inference(bind,[status(th)],[])).
% 2.44/2.61 tff(19,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.44/2.61 inference(quant_intro,[status(thm)],[18])).
% 2.44/2.61 tff(20,axiom,(![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_power__eq__0__iff')).
% 2.44/2.61 tff(21,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.44/2.61 tff(22,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[21, 17])).
% 2.44/2.61 tff(23,plain,(
% 2.44/2.61 ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.44/2.61 inference(skolemize,[status(sab)],[22])).
% 2.44/2.61 tff(24,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[23, 16])).
% 2.44/2.61 tff(25,plain,
% 2.44/2.61 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[24, 14])).
% 2.44/2.61 tff(26,plain,
% 2.44/2.61 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(27,plain,
% 2.44/2.61 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(28,plain,
% 2.44/2.61 ((~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(29,plain,
% 2.44/2.61 ((((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(30,plain,
% 2.44/2.61 ((~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[29])).
% 2.44/2.61 tff(31,plain,
% 2.44/2.61 ((~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[30, 28])).
% 2.44/2.61 tff(32,plain,
% 2.44/2.61 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[31])).
% 2.44/2.61 tff(33,plain,
% 2.44/2.61 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[32, 27])).
% 2.44/2.61 tff(34,plain,
% 2.44/2.61 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[33])).
% 2.44/2.61 tff(35,plain,
% 2.44/2.61 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[34, 26])).
% 2.44/2.61 tff(36,plain,
% 2.44/2.61 ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(37,plain,
% 2.44/2.61 ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[36, 35])).
% 2.44/2.62 tff(38,plain,
% 2.44/2.62 (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[37, 25, 12, 9, 6, 3])).
% 2.44/2.62 tff(39,plain,
% 2.44/2.62 ((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(40,axiom,(~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_kas_I2_J')).
% 2.44/2.62 tff(41,plain,
% 2.44/2.62 (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.44/2.62 tff(42,plain,
% 2.44/2.62 (((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.44/2.62 inference(tautology,[status(thm)],[])).
% 2.44/2.62 tff(43,plain,
% 2.44/2.62 (((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[42, 41])).
% 2.44/2.62 tff(44,plain,
% 2.44/2.62 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[43, 38])).
% 2.44/2.62 tff(45,plain,
% 2.44/2.62 (^[V_m: $i, V_n: $i, T_a: $i] : refl(((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))) <=> ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(46,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[45])).
% 2.44/2.62 tff(47,plain,
% 2.44/2.62 (^[V_m: $i, V_n: $i, T_a: $i] : rewrite(((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(48,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[47])).
% 2.44/2.62 tff(49,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(50,plain,
% 2.44/2.62 (^[V_m: $i, V_n: $i, T_a: $i] : trans(monotonicity(rewrite((((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) <=> (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))), ((class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> (class_Power_Opower(T_a) => (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))), rewrite((class_Power_Opower(T_a) => (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))), ((class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.44/2.62 inference(bind,[status(th)],[])).
% 2.44/2.62 tff(51,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : (class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.44/2.62 inference(quant_intro,[status(thm)],[50])).
% 2.44/2.62 tff(52,axiom,(![V_m: $i, V_n: $i, T_a: $i] : (class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_realpow__num__eq__if')).
% 2.44/2.62 tff(53,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[52, 51])).
% 2.44/2.62 tff(54,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.44/2.62 tff(55,plain,(
% 2.44/2.62 ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.44/2.62 inference(skolemize,[status(sab)],[54])).
% 2.44/2.62 tff(56,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[55, 48])).
% 2.44/2.62 tff(57,plain,
% 2.44/2.62 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[56, 46])).
% 2.44/2.62 tff(58,plain,
% 2.46/2.62 (((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) <=> ((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(59,plain,
% 2.46/2.62 ((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.46/2.62 inference(quant_inst,[status(thm)],[])).
% 2.46/2.62 tff(60,plain,
% 2.46/2.62 ((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))),
% 2.46/2.62 inference(modus_ponens,[status(thm)],[59, 58])).
% 2.46/2.62 tff(61,plain,
% 2.46/2.62 (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.46/2.62 inference(unit_resolution,[status(thm)],[60, 57, 3])).
% 2.46/2.62 tff(62,plain,
% 2.46/2.62 (((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 2.46/2.62 inference(tautology,[status(thm)],[])).
% 2.46/2.62 tff(63,plain,
% 2.46/2.62 ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.46/2.62 inference(unit_resolution,[status(thm)],[62, 61])).
% 2.46/2.62 tff(64,plain,
% 2.46/2.62 ((~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.46/2.62 inference(tautology,[status(thm)],[])).
% 2.46/2.62 tff(65,plain,
% 2.46/2.62 ((~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.46/2.62 inference(unit_resolution,[status(thm)],[64, 41])).
% 2.46/2.62 tff(66,plain,
% 2.46/2.62 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 2.46/2.62 inference(unit_resolution,[status(thm)],[65, 63])).
% 2.46/2.62 tff(67,plain,
% 2.46/2.62 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)),
% 2.46/2.62 inference(symmetry,[status(thm)],[66])).
% 2.46/2.62 tff(68,plain,
% 2.46/2.62 ((c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(69,axiom,(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_One__nat__def')).
% 2.46/2.62 tff(70,plain,
% 2.46/2.62 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 2.46/2.62 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.46/2.62 tff(71,plain,
% 2.46/2.62 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 2.46/2.62 inference(monotonicity,[status(thm)],[70])).
% 2.46/2.62 tff(72,plain,
% 2.46/2.62 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 2.46/2.62 inference(monotonicity,[status(thm)],[71])).
% 2.46/2.62 tff(73,plain,
% 2.46/2.62 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
% 2.46/2.62 inference(symmetry,[status(thm)],[72])).
% 2.46/2.62 tff(74,plain,
% 2.46/2.62 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(75,plain,
% 2.46/2.62 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(76,plain,
% 2.46/2.62 ((~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(77,plain,
% 2.46/2.62 ((((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> ((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(78,plain,
% 2.46/2.62 ((~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.46/2.62 inference(monotonicity,[status(thm)],[77])).
% 2.46/2.62 tff(79,plain,
% 2.46/2.62 ((~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.46/2.62 inference(transitivity,[status(thm)],[78, 76])).
% 2.46/2.62 tff(80,plain,
% 2.46/2.62 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.46/2.62 inference(monotonicity,[status(thm)],[79])).
% 2.46/2.62 tff(81,plain,
% 2.46/2.62 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.46/2.62 inference(transitivity,[status(thm)],[80, 75])).
% 2.46/2.62 tff(82,plain,
% 2.46/2.62 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))))),
% 2.46/2.62 inference(monotonicity,[status(thm)],[81])).
% 2.46/2.62 tff(83,plain,
% 2.46/2.62 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.46/2.62 inference(transitivity,[status(thm)],[82, 74])).
% 2.46/2.62 tff(84,plain,
% 2.46/2.62 ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.46/2.62 inference(quant_inst,[status(thm)],[])).
% 2.46/2.62 tff(85,plain,
% 2.46/2.62 ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | (~(((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.46/2.62 inference(modus_ponens,[status(thm)],[84, 83])).
% 2.46/2.62 tff(86,plain,
% 2.46/2.62 (~((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.46/2.62 inference(unit_resolution,[status(thm)],[85, 25, 12, 9, 6, 3])).
% 2.46/2.62 tff(87,plain,
% 2.46/2.62 (((~(B_a!30 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z)))))) <=> ((~(B_a!30 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z)))))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(88,plain,
% 2.46/2.62 (((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z))))) <=> ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z)))))),
% 2.46/2.62 inference(rewrite,[status(thm)],[])).
% 2.46/2.62 tff(89,plain,
% 2.46/2.62 (((~(B_a!30 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z)))))) <=> ((~(B_a!30 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z))))))),
% 2.46/2.62 inference(monotonicity,[status(thm)],[88])).
% 2.46/2.62 tff(90,plain,
% 2.46/2.62 (((~(B_a!30 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z)))))) <=> ((~(B_a!30 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z)))))),
% 2.46/2.63 inference(transitivity,[status(thm)],[89, 87])).
% 2.46/2.63 tff(91,plain,
% 2.46/2.63 (?[B_k: $i, B_a: $i] : ((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z)))))) <=> ?[B_k: $i, B_a: $i] : ((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z))))))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(92,plain,
% 2.46/2.63 (^[B_k: $i, B_a: $i] : rewrite((((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z)))))) <=> ((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z)))))))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(93,plain,
% 2.46/2.63 (?[B_k: $i, B_a: $i] : (((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z)))))) <=> ?[B_k: $i, B_a: $i] : ((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z))))))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[92])).
% 2.46/2.63 tff(94,axiom,(?[B_k: $i, B_a: $i] : (((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096')).
% 2.46/2.63 tff(95,plain,
% 2.46/2.63 (?[B_k: $i, B_a: $i] : ((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z))))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.46/2.63 tff(96,plain,
% 2.46/2.63 (?[B_k: $i, B_a: $i] : ((~(B_a = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ?[B_q: $i] : ((c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q), B_k), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a, B_q)), B_z))))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[95, 91])).
% 2.46/2.63 tff(97,plain,
% 2.46/2.63 ((~(B_a!30 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) & (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & (c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, B_q!32), B_k!31), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____))) & ![B_z: $i] : (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), B_z) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), B_k!31)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!30, B_q!32)), B_z))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[96, 90])).
% 2.46/2.63 tff(98,plain,
% 2.46/2.63 (~(B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 2.46/2.63 inference(and_elim,[status(thm)],[97])).
% 2.46/2.63 tff(99,plain,
% 2.46/2.63 (((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(tautology,[status(thm)],[])).
% 2.46/2.63 tff(100,plain,
% 2.46/2.63 (((B_k!31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(unit_resolution,[status(thm)],[99, 98])).
% 2.46/2.63 tff(101,plain,
% 2.46/2.63 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 2.46/2.63 inference(unit_resolution,[status(thm)],[100, 86])).
% 2.46/2.63 tff(102,plain,
% 2.46/2.63 (hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)) = hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(monotonicity,[status(thm)],[101])).
% 2.46/2.63 tff(103,plain,
% 2.46/2.63 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 2.46/2.63 inference(monotonicity,[status(thm)],[102])).
% 2.46/2.63 tff(104,plain,
% 2.46/2.63 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
% 2.46/2.63 inference(transitivity,[status(thm)],[103, 73])).
% 2.46/2.63 tff(105,plain,
% 2.46/2.63 (hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(monotonicity,[status(thm)],[101])).
% 2.46/2.63 tff(106,plain,
% 2.46/2.63 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 2.46/2.63 inference(monotonicity,[status(thm)],[105, 104])).
% 2.46/2.63 tff(107,plain,
% 2.46/2.63 (^[B_x: $i, B_y: $i] : refl((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(108,plain,
% 2.46/2.63 (![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[107])).
% 2.46/2.63 tff(109,plain,
% 2.46/2.63 ((~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))) <=> (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(110,axiom,(~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_0')).
% 2.46/2.63 tff(111,plain,
% 2.46/2.63 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[110, 109])).
% 2.46/2.63 tff(112,plain,
% 2.46/2.63 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[111, 109])).
% 2.46/2.63 tff(113,plain,
% 2.46/2.63 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[112, 109])).
% 2.46/2.63 tff(114,plain,
% 2.46/2.63 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[113, 109])).
% 2.46/2.63 tff(115,plain,
% 2.46/2.63 (^[B_x: $i, B_y: $i] : refl($oeq((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(116,plain,(
% 2.46/2.63 ![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.46/2.63 inference(nnf-neg,[status(sab)],[114, 115])).
% 2.46/2.63 tff(117,plain,
% 2.46/2.63 (![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[116, 108])).
% 2.46/2.63 tff(118,plain,
% 2.46/2.63 ((~![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.46/2.63 inference(quant_inst,[status(thm)],[])).
% 2.46/2.63 tff(119,plain,
% 2.46/2.63 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 2.46/2.63 inference(unit_resolution,[status(thm)],[118, 117])).
% 2.46/2.63 tff(120,plain,
% 2.46/2.63 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), B_k!31)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 2.46/2.63 inference(symmetry,[status(thm)],[119])).
% 2.46/2.63 tff(121,plain,
% 2.46/2.63 (class_Groups_Omonoid__mult(tc_Complex_Ocomplex) <=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex)),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(122,axiom,(class_Groups_Omonoid__mult(tc_Complex_Ocomplex)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Groups_Omonoid__mult')).
% 2.46/2.63 tff(123,plain,
% 2.46/2.63 (class_Groups_Omonoid__mult(tc_Complex_Ocomplex)),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[122, 121])).
% 2.46/2.63 tff(124,plain,
% 2.46/2.63 (^[V_a: $i, T_a: $i] : refl(((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(125,plain,
% 2.46/2.63 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[124])).
% 2.46/2.63 tff(126,plain,
% 2.46/2.63 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(127,plain,
% 2.46/2.63 (^[V_a: $i, T_a: $i] : rewrite((class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(128,plain,
% 2.46/2.63 (![V_a: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[127])).
% 2.46/2.63 tff(129,axiom,(![V_a: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_mult__1__left')).
% 2.46/2.63 tff(130,plain,
% 2.46/2.63 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[129, 128])).
% 2.46/2.63 tff(131,plain,
% 2.46/2.63 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[130, 126])).
% 2.46/2.63 tff(132,plain,(
% 2.46/2.63 ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 2.46/2.63 inference(skolemize,[status(sab)],[131])).
% 2.46/2.63 tff(133,plain,
% 2.46/2.63 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[132, 125])).
% 2.46/2.63 tff(134,plain,
% 2.46/2.63 (((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) <=> ((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(135,plain,
% 2.46/2.63 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 2.46/2.63 inference(quant_inst,[status(thm)],[])).
% 2.46/2.63 tff(136,plain,
% 2.46/2.63 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[135, 134])).
% 2.46/2.63 tff(137,plain,
% 2.46/2.63 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 2.46/2.63 inference(unit_resolution,[status(thm)],[136, 133, 123])).
% 2.46/2.63 tff(138,plain,
% 2.46/2.63 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 2.46/2.63 inference(symmetry,[status(thm)],[137])).
% 2.46/2.63 tff(139,plain,
% 2.46/2.63 (^[V_n: $i, T_a: $i] : refl(((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(140,plain,
% 2.46/2.63 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[139])).
% 2.46/2.63 tff(141,plain,
% 2.46/2.63 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(142,plain,
% 2.46/2.63 (^[V_n: $i, T_a: $i] : rewrite((class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(143,plain,
% 2.46/2.63 (![V_n: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[142])).
% 2.46/2.63 tff(144,axiom,(![V_n: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_power__one')).
% 2.46/2.63 tff(145,plain,
% 2.46/2.63 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[144, 143])).
% 2.46/2.63 tff(146,plain,
% 2.46/2.63 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[145, 141])).
% 2.46/2.63 tff(147,plain,(
% 2.46/2.63 ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 2.46/2.63 inference(skolemize,[status(sab)],[146])).
% 2.46/2.63 tff(148,plain,
% 2.46/2.63 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[147, 140])).
% 2.46/2.63 tff(149,plain,
% 2.46/2.63 (((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) <=> ((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(150,plain,
% 2.46/2.63 ((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 2.46/2.63 inference(quant_inst,[status(thm)],[])).
% 2.46/2.63 tff(151,plain,
% 2.46/2.63 ((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.46/2.63 tff(152,plain,
% 2.46/2.63 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
% 2.46/2.63 inference(unit_resolution,[status(thm)],[151, 148, 123])).
% 2.46/2.63 tff(153,plain,
% 2.46/2.63 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 2.46/2.63 inference(symmetry,[status(thm)],[152])).
% 2.46/2.63 tff(154,plain,
% 2.46/2.63 ((hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) <=> (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(155,axiom,(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_r01')).
% 2.46/2.63 tff(156,plain,
% 2.46/2.63 (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
% 2.46/2.63 inference(modus_ponens,[status(thm)],[155, 154])).
% 2.46/2.63 tff(157,plain,
% 2.46/2.63 (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 2.46/2.63 inference(transitivity,[status(thm)],[156, 153, 138, 120, 106, 67, 44])).
% 2.46/2.63 tff(158,plain,
% 2.46/2.63 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(symmetry,[status(thm)],[156])).
% 2.46/2.63 tff(159,plain,
% 2.46/2.63 ((c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.63 inference(monotonicity,[status(thm)],[158])).
% 2.46/2.63 tff(160,plain,
% 2.46/2.63 ((~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> (~(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.46/2.63 inference(monotonicity,[status(thm)],[159])).
% 2.46/2.63 tff(161,plain,
% 2.46/2.63 (^[T_a: $i] : refl(((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(162,plain,
% 2.46/2.63 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[161])).
% 2.46/2.63 tff(163,plain,
% 2.46/2.63 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.46/2.63 inference(rewrite,[status(thm)],[])).
% 2.46/2.63 tff(164,plain,
% 2.46/2.63 (^[T_a: $i] : rewrite((class_Rings_Ozero__neq__one(T_a) => (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 2.46/2.63 inference(bind,[status(th)],[])).
% 2.46/2.63 tff(165,plain,
% 2.46/2.63 (![T_a: $i] : (class_Rings_Ozero__neq__one(T_a) => (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.46/2.63 inference(quant_intro,[status(thm)],[164])).
% 2.46/2.63 tff(166,axiom,(![T_a: $i] : (class_Rings_Ozero__neq__one(T_a) => (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_one__neq__zero')).
% 2.46/2.70 tff(167,plain,
% 2.46/2.70 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.46/2.70 inference(modus_ponens,[status(thm)],[166, 165])).
% 2.46/2.70 tff(168,plain,
% 2.46/2.70 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.46/2.70 inference(modus_ponens,[status(thm)],[167, 163])).
% 2.46/2.70 tff(169,plain,(
% 2.46/2.70 ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.46/2.70 inference(skolemize,[status(sab)],[168])).
% 2.46/2.70 tff(170,plain,
% 2.46/2.70 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.46/2.70 inference(modus_ponens,[status(thm)],[169, 162])).
% 2.46/2.70 tff(171,plain,
% 2.46/2.70 (((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.46/2.70 inference(rewrite,[status(thm)],[])).
% 2.46/2.70 tff(172,plain,
% 2.46/2.70 ((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.46/2.70 inference(quant_inst,[status(thm)],[])).
% 2.46/2.70 tff(173,plain,
% 2.46/2.70 ((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.46/2.70 inference(modus_ponens,[status(thm)],[172, 171])).
% 2.46/2.70 tff(174,plain,
% 2.46/2.70 (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.70 inference(unit_resolution,[status(thm)],[173, 170, 9])).
% 2.46/2.70 tff(175,plain,
% 2.46/2.70 (~(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.46/2.70 inference(modus_ponens,[status(thm)],[174, 160])).
% 2.46/2.70 tff(176,plain,
% 2.46/2.70 ($false),
% 2.46/2.70 inference(unit_resolution,[status(thm)],[175, 157])).
% 2.46/2.70 % SZS output end Proof
% 2.46/2.70 % E exiting
%------------------------------------------------------------------------------