%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW286+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:36:46 AM UTC 2025
% Result : Theorem 0.63s 0.81s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW286+1 : TPTP v9.0.0. Released v5.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 11:24:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.63/0.81 % SZS status Theorem
% 0.63/0.81 % SZS output start Proof
% 0.63/0.81 tff(c_Groups_Oone__class_Oone_type, type, (
% 0.63/0.81 c_Groups_Oone__class_Oone: $i > $i)).
% 0.63/0.81 tff(tc_Polynomial_Opoly_type, type, (
% 0.63/0.81 tc_Polynomial_Opoly: $i > $i)).
% 0.63/0.81 tff(tc_Complex_Ocomplex_type, type, (
% 0.63/0.81 tc_Complex_Ocomplex: $i)).
% 0.63/0.81 tff(hAPP_type, type, (
% 0.63/0.81 hAPP: ( $i * $i ) > $i)).
% 0.63/0.81 tff(c_Polynomial_OpCons_type, type, (
% 0.63/0.81 c_Polynomial_OpCons: ( $i * $i * $i ) > $i)).
% 0.63/0.81 tff(c_Groups_Ozero__class_Ozero_type, type, (
% 0.63/0.81 c_Groups_Ozero__class_Ozero: $i > $i)).
% 0.63/0.81 tff(c_Rings_Oinverse__class_Odivide_type, type, (
% 0.63/0.81 c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i)).
% 0.63/0.81 tff(v_k_____type, type, (
% 0.63/0.81 v_k____: $i)).
% 0.63/0.81 tff(c_Groups_Otimes__class_Otimes_type, type, (
% 0.63/0.81 c_Groups_Otimes__class_Otimes: $i > $i)).
% 0.63/0.81 tff(class_Rings_Ocomm__semiring__1_type, type, (
% 0.63/0.81 class_Rings_Ocomm__semiring__1: $i > $o)).
% 0.63/0.81 tff(c_Polynomial_Omonom_type, type, (
% 0.63/0.81 c_Polynomial_Omonom: ( $i * $i * $i ) > $i)).
% 0.63/0.81 tff(tc_Nat_Onat_type, type, (
% 0.63/0.81 tc_Nat_Onat: $i)).
% 0.63/0.81 tff(class_Groups_Ozero_type, type, (
% 0.63/0.81 class_Groups_Ozero: $i > $o)).
% 0.63/0.81 tff(tptp_fun_B_k_1_type, type, (
% 0.63/0.81 tptp_fun_B_k_1: $i)).
% 0.63/0.81 tff(c_Polynomial_Odegree_type, type, (
% 0.63/0.81 c_Polynomial_Odegree: ( $i * $i ) > $i)).
% 0.63/0.81 tff(c_Polynomial_Ocoeff_type, type, (
% 0.63/0.81 c_Polynomial_Ocoeff: ( $i * $i ) > $i)).
% 0.63/0.81 tff(c_Nat_OSuc_type, type, (
% 0.63/0.81 c_Nat_OSuc: $i > $i)).
% 0.63/0.81 tff(v_p_type, type, (
% 0.63/0.81 v_p: $i)).
% 0.63/0.81 tff(c_Rings_Oinverse__class_Oinverse_type, type, (
% 0.63/0.81 c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i)).
% 0.63/0.81 tff(class_Rings_Odivision__ring_type, type, (
% 0.63/0.81 class_Rings_Odivision__ring: $i > $o)).
% 0.63/0.81 tff(c_Polynomial_Osmult_type, type, (
% 0.63/0.81 c_Polynomial_Osmult: ( $i * $i * $i ) > $i)).
% 0.63/0.81 tff(class_Rings_Ocomm__semiring__0_type, type, (
% 0.63/0.81 class_Rings_Ocomm__semiring__0: $i > $o)).
% 0.63/0.81 tff(c_Groups_Oplus__class_Oplus_type, type, (
% 0.63/0.81 c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i)).
% 0.63/0.81 tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type, type, (
% 0.63/0.81 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o)).
% 0.63/0.81 tff(class_Rings_Oidom_type, type, (
% 0.63/0.81 class_Rings_Oidom: $i > $o)).
% 0.63/0.81 tff(class_Rings_Omult__zero_type, type, (
% 0.63/0.81 class_Rings_Omult__zero: $i > $o)).
% 0.63/0.81 tff(v_q_type, type, (
% 0.63/0.81 v_q: $i)).
% 0.63/0.81 tff(c_Power_Opower__class_Opower_type, type, (
% 0.63/0.81 c_Power_Opower__class_Opower: $i > $i)).
% 0.63/0.81 tff(class_Power_Opower_type, type, (
% 0.63/0.81 class_Power_Opower: $i > $o)).
% 0.63/0.81 tff(1,plain,
% 0.63/0.81 (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2,axiom,(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ocomm__semiring__1')).
% 0.63/0.81 tff(3,plain,
% 0.63/0.81 (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.63/0.81 tff(4,plain,
% 0.63/0.81 (^[T_a: $i] : refl(((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(5,plain,
% 0.63/0.81 (![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[4])).
% 0.63/0.81 tff(6,plain,
% 0.63/0.81 (![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(7,plain,
% 0.63/0.81 (^[T_a: $i] : rewrite((class_Rings_Ocomm__semiring__1(T_a) => (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(8,plain,
% 0.63/0.81 (![T_a: $i] : (class_Rings_Ocomm__semiring__1(T_a) => (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[7])).
% 0.63/0.81 tff(9,axiom,(![T_a: $i] : (class_Rings_Ocomm__semiring__1(T_a) => (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_one__poly__def')).
% 0.63/0.81 tff(10,plain,
% 0.63/0.81 (![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.63/0.81 tff(11,plain,
% 0.63/0.81 (![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.63/0.81 tff(12,plain,(
% 0.63/0.81 ![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.81 inference(skolemize,[status(sab)],[11])).
% 0.63/0.81 tff(13,plain,
% 0.63/0.81 (![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.63/0.81 tff(14,plain,
% 0.63/0.81 (((~![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | ((~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> ((~![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(15,plain,
% 0.63/0.81 ((~![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | ((~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(16,plain,
% 0.63/0.82 ((~![T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a, c_Groups_Oone__class_Oone(T_a), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.63/0.82 tff(17,plain,
% 0.63/0.82 (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 0.63/0.82 tff(18,plain,
% 0.63/0.82 (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.82 inference(symmetry,[status(thm)],[17])).
% 0.63/0.82 tff(19,plain,
% 0.63/0.82 (class_Groups_Ozero(tc_Complex_Ocomplex) <=> class_Groups_Ozero(tc_Complex_Ocomplex)),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(20,axiom,(class_Groups_Ozero(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Groups_Ozero')).
% 0.63/0.82 tff(21,plain,
% 0.63/0.82 (class_Groups_Ozero(tc_Complex_Ocomplex)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.63/0.82 tff(22,plain,
% 0.63/0.82 (^[V_a: $i, T_a: $i] : refl(((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(23,plain,
% 0.63/0.82 (![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[22])).
% 0.63/0.82 tff(24,plain,
% 0.63/0.82 (![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(25,plain,
% 0.63/0.82 (^[V_a: $i, T_a: $i] : rewrite((class_Groups_Ozero(T_a) => (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(26,plain,
% 0.63/0.82 (![V_a: $i, T_a: $i] : (class_Groups_Ozero(T_a) => (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[25])).
% 0.63/0.82 tff(27,axiom,(![V_a: $i, T_a: $i] : (class_Groups_Ozero(T_a) => (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_monom__0')).
% 0.63/0.82 tff(28,plain,
% 0.63/0.82 (![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.63/0.82 tff(29,plain,
% 0.63/0.82 (![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.63/0.82 tff(30,plain,(
% 0.63/0.82 ![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.82 inference(skolemize,[status(sab)],[29])).
% 0.63/0.82 tff(31,plain,
% 0.63/0.82 (![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.63/0.82 tff(32,plain,
% 0.63/0.82 (((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> ((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(33,plain,
% 0.63/0.82 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(34,plain,
% 0.63/0.82 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.63/0.82 tff(35,plain,
% 0.63/0.82 (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.63/0.82 tff(36,plain,
% 0.63/0.82 (^[V_a: $i, V_p: $i, T_a: $i] : refl(((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))))) <=> ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(37,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))))) <=> ![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[36])).
% 0.63/0.82 tff(38,plain,
% 0.63/0.82 (^[V_a: $i, V_p: $i, T_a: $i] : rewrite(((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))) <=> ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(39,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))) <=> ![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[38])).
% 0.63/0.82 tff(40,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))) <=> ![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(41,plain,
% 0.63/0.82 (^[V_a: $i, V_p: $i, T_a: $i] : trans(monotonicity(rewrite((((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))) <=> (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))), ((class_Groups_Ozero(T_a) => (((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))) <=> (class_Groups_Ozero(T_a) => (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))))), rewrite((class_Groups_Ozero(T_a) => (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))) <=> ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))), ((class_Groups_Ozero(T_a) => (((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))) <=> ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(42,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : (class_Groups_Ozero(T_a) => (((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p)))))) <=> ![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[41])).
% 0.63/0.82 tff(43,axiom,(![V_a: $i, V_p: $i, T_a: $i] : (class_Groups_Ozero(T_a) => (((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) => (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_degree__pCons__eq__if')).
% 0.63/0.82 tff(44,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.63/0.82 tff(45,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.63/0.82 tff(46,plain,(
% 0.63/0.82 ![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) & ((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))),
% 0.63/0.82 inference(skolemize,[status(sab)],[45])).
% 0.63/0.82 tff(47,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.63/0.82 tff(48,plain,
% 0.63/0.82 (![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[47, 37])).
% 0.63/0.82 tff(49,plain,
% 0.63/0.82 (((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <=> ((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(50,plain,
% 0.63/0.82 (((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~((~((~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Nat_OSuc(c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))))))) <=> ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(51,plain,
% 0.63/0.82 (((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~((~((~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Nat_OSuc(c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))))))) <=> ((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[50])).
% 0.63/0.82 tff(52,plain,
% 0.63/0.82 (((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~((~((~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Nat_OSuc(c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))))))) <=> ((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[51, 49])).
% 0.63/0.82 tff(53,plain,
% 0.63/0.82 ((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~((~((~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Nat_OSuc(c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(54,plain,
% 0.63/0.82 ((~![V_a: $i, V_p: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~((~((~(V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | (~((V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) | (c_Polynomial_Odegree(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a, V_p))))))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.63/0.82 tff(55,plain,
% 0.63/0.82 (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[54, 48, 21])).
% 0.63/0.82 tff(56,plain,
% 0.63/0.82 (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[55])).
% 0.63/0.82 tff(57,plain,
% 0.63/0.82 (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.82 inference(symmetry,[status(thm)],[56])).
% 0.63/0.82 tff(58,plain,
% 0.63/0.82 (^[V_p: $i, V_a: $i, T_a: $i] : refl(((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)) <=> ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(59,plain,
% 0.63/0.82 (![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)) <=> ![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[58])).
% 0.63/0.82 tff(60,plain,
% 0.63/0.82 (![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)) <=> ![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(61,plain,
% 0.63/0.82 (^[V_p: $i, V_a: $i, T_a: $i] : rewrite((class_Groups_Ozero(T_a) => (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)) <=> ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(62,plain,
% 0.63/0.82 (![V_p: $i, V_a: $i, T_a: $i] : (class_Groups_Ozero(T_a) => (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a)) <=> ![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[61])).
% 0.63/0.82 tff(63,axiom,(![V_p: $i, V_a: $i, T_a: $i] : (class_Groups_Ozero(T_a) => (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_coeff__pCons__0')).
% 0.63/0.82 tff(64,plain,
% 0.63/0.82 (![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.63/0.82 tff(65,plain,
% 0.63/0.82 (![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.63/0.82 tff(66,plain,(
% 0.63/0.82 ![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))),
% 0.63/0.82 inference(skolemize,[status(sab)],[65])).
% 0.63/0.82 tff(67,plain,
% 0.63/0.82 (![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.63/0.82 tff(68,plain,
% 0.63/0.82 (((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)))) <=> ((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(69,plain,
% 0.63/0.82 ((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(70,plain,
% 0.63/0.82 ((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.63/0.82 tff(71,plain,
% 0.63/0.82 (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[70, 67, 21])).
% 0.63/0.82 tff(72,plain,
% 0.63/0.82 (c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.82 inference(symmetry,[status(thm)],[71])).
% 0.63/0.82 tff(73,plain,
% 0.63/0.82 (c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[72, 57])).
% 0.63/0.82 tff(74,plain,
% 0.63/0.82 ((c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(75,axiom,(c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_dp')).
% 0.63/0.82 tff(76,plain,
% 0.63/0.82 (c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.63/0.82 tff(77,plain,
% 0.63/0.82 ((v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) <=> (v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(78,axiom,(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_k_I1_J')).
% 0.63/0.82 tff(79,plain,
% 0.63/0.82 (v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.63/0.82 tff(80,plain,
% 0.63/0.82 (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p),
% 0.63/0.82 inference(symmetry,[status(thm)],[79])).
% 0.63/0.82 tff(81,plain,
% 0.63/0.82 (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)),
% 0.63/0.82 inference(monotonicity,[status(thm)],[80])).
% 0.63/0.82 tff(82,plain,
% 0.63/0.82 (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.63/0.82 inference(transitivity,[status(thm)],[81, 76])).
% 0.63/0.82 tff(83,plain,
% 0.63/0.82 (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[82])).
% 0.63/0.82 tff(84,plain,
% 0.63/0.82 (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.82 inference(symmetry,[status(thm)],[83])).
% 0.63/0.82 tff(85,plain,
% 0.63/0.82 (((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = v_k____))) <=> ((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = v_k____))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(86,plain,
% 0.63/0.82 ((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = v_k____))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(87,plain,
% 0.63/0.82 ((~![V_p: $i, V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (hAPP(c_Polynomial_Ocoeff(T_a, c_Polynomial_OpCons(T_a, V_a, V_p)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = v_k____)),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.63/0.82 tff(88,plain,
% 0.63/0.82 (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = v_k____),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[87, 67, 21])).
% 0.63/0.82 tff(89,plain,
% 0.63/0.82 (v_k____ = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.82 inference(symmetry,[status(thm)],[88])).
% 0.63/0.82 tff(90,plain,
% 0.63/0.82 (^[V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : refl(((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2))))) <=> ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(91,plain,
% 0.63/0.82 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2))))) <=> ![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[90])).
% 0.63/0.82 tff(92,plain,
% 0.63/0.82 (^[V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : rewrite(((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2)))) <=> ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(93,plain,
% 0.63/0.82 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2)))) <=> ![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[92])).
% 0.63/0.82 tff(94,plain,
% 0.63/0.82 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2)))) <=> ![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(95,plain,
% 0.63/0.83 (^[V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : rewrite((class_Groups_Ozero(T_a) => ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2)))) <=> ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(96,plain,
% 0.63/0.83 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : (class_Groups_Ozero(T_a) => ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2)))) <=> ![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[95])).
% 0.63/0.83 tff(97,axiom,(![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : (class_Groups_Ozero(T_a) => ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_pCons__eq__iff')).
% 0.63/0.83 tff(98,plain,
% 0.63/0.83 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.63/0.83 tff(99,plain,
% 0.63/0.83 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.63/0.83 tff(100,plain,(
% 0.63/0.83 ![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)) <=> ((V_a_2 = V_b_2) & (V_pa_2 = V_qa_2))))),
% 0.63/0.83 inference(skolemize,[status(sab)],[99])).
% 0.63/0.83 tff(101,plain,
% 0.63/0.83 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.63/0.83 tff(102,plain,
% 0.63/0.83 (![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.63/0.83 tff(103,plain,
% 0.63/0.83 (((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> ((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(104,plain,
% 0.63/0.83 (((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(v_k____ = B_k!1)) | (~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(105,plain,
% 0.63/0.83 (((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(v_k____ = B_k!1)) | (~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))))) <=> ((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[104])).
% 0.63/0.83 tff(106,plain,
% 0.63/0.83 (((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(v_k____ = B_k!1)) | (~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))))) <=> ((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[105, 103])).
% 0.63/0.83 tff(107,plain,
% 0.63/0.83 ((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(v_k____ = B_k!1)) | (~(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(108,plain,
% 0.63/0.83 ((~![V_qa_2: $i, V_b_2: $i, V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = V_b_2)) | (~(V_pa_2 = V_qa_2))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Polynomial_OpCons(T_a, V_b_2, V_qa_2)))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.63/0.83 tff(109,plain,
% 0.63/0.83 ((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[108, 102, 21])).
% 0.63/0.83 tff(110,plain,
% 0.63/0.83 ((~![B_k: $i] : ((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~![B_k: $i] : ((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(111,plain,
% 0.63/0.83 ((~![B_k: $i] : ((v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) => (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~![B_k: $i] : ((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(112,axiom,(~![B_k: $i] : ((v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) => (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact__096_B_Bthesis_O_A_I_B_Bk_O_A_091_124_Ap_A_061_A_091_058k_058_093_059_Ak_A_126_061_A0_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096')).
% 0.63/0.83 tff(113,plain,
% 0.63/0.83 (~![B_k: $i] : ((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.63/0.83 tff(114,plain,
% 0.63/0.83 (~![B_k: $i] : ((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.63/0.83 tff(115,plain,
% 0.63/0.83 (~![B_k: $i] : ((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.63/0.83 tff(116,plain,
% 0.63/0.83 (~![B_k: $i] : ((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[115, 110])).
% 0.63/0.83 tff(117,plain,(
% 0.63/0.83 ~((~(v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[116])).
% 0.63/0.83 tff(118,plain,
% 0.63/0.83 (v_p = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(or_elim,[status(thm)],[117])).
% 0.63/0.83 tff(119,plain,
% 0.63/0.83 (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[80, 118])).
% 0.63/0.83 tff(120,plain,
% 0.63/0.83 ((~((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) | (v_k____ = B_k!1) | (~(c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.83 inference(tautology,[status(thm)],[])).
% 0.63/0.83 tff(121,plain,
% 0.63/0.83 ((~((v_k____ = B_k!1) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) | (v_k____ = B_k!1)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.63/0.83 tff(122,plain,
% 0.63/0.83 (v_k____ = B_k!1),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[121, 109])).
% 0.63/0.83 tff(123,plain,
% 0.63/0.83 (B_k!1 = v_k____),
% 0.63/0.83 inference(symmetry,[status(thm)],[122])).
% 0.63/0.83 tff(124,plain,
% 0.63/0.83 (B_k!1 = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[123, 89, 84])).
% 0.63/0.83 tff(125,plain,
% 0.63/0.83 (hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[124])).
% 0.63/0.83 tff(126,plain,
% 0.63/0.83 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[125, 73])).
% 0.63/0.83 tff(127,plain,
% 0.63/0.83 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____))),
% 0.63/0.83 inference(symmetry,[status(thm)],[126])).
% 0.63/0.83 tff(128,plain,
% 0.63/0.83 (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____)),
% 0.63/0.83 inference(monotonicity,[status(thm)],[123])).
% 0.63/0.83 tff(129,plain,
% 0.63/0.83 (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)),
% 0.63/0.83 inference(symmetry,[status(thm)],[128])).
% 0.63/0.83 tff(130,plain,
% 0.63/0.83 (class_Rings_Odivision__ring(tc_Complex_Ocomplex) <=> class_Rings_Odivision__ring(tc_Complex_Ocomplex)),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(131,axiom,(class_Rings_Odivision__ring(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Odivision__ring')).
% 0.63/0.83 tff(132,plain,
% 0.63/0.83 (class_Rings_Odivision__ring(tc_Complex_Ocomplex)),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.63/0.83 tff(133,plain,
% 0.63/0.83 (^[V_a: $i, T_a: $i] : refl(((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(134,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a))) <=> ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[133])).
% 0.63/0.83 tff(135,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a))) <=> ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(136,plain,
% 0.63/0.83 (^[V_a: $i, T_a: $i] : trans(monotonicity(rewrite(((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)))), ((class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)))) <=> (class_Rings_Odivision__ring(T_a) => ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)))))), rewrite((class_Rings_Odivision__ring(T_a) => ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))), ((class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(137,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : (class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)))) <=> ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[136])).
% 0.63/0.83 tff(138,axiom,(![V_a: $i, T_a: $i] : (class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_nonzero__inverse__eq__divide')).
% 0.63/0.83 tff(139,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.63/0.83 tff(140,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.63/0.83 tff(141,plain,(
% 0.63/0.83 ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[140])).
% 0.63/0.83 tff(142,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.63/0.83 tff(143,plain,
% 0.63/0.83 ((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(144,axiom,(~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_k_I2_J')).
% 0.63/0.83 tff(145,plain,
% 0.63/0.83 (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.63/0.83 tff(146,plain,
% 0.63/0.83 (((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)))) <=> ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(147,plain,
% 0.63/0.83 (((v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex))) <=> ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(148,plain,
% 0.63/0.83 (((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)))) <=> ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[147])).
% 0.63/0.83 tff(149,plain,
% 0.63/0.83 (((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)))) <=> ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[148, 146])).
% 0.63/0.83 tff(150,plain,
% 0.63/0.83 ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(151,plain,
% 0.63/0.83 ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (c_Rings_Oinverse__class_Oinverse(T_a, V_a) = c_Rings_Oinverse__class_Odivide(T_a, c_Groups_Oone__class_Oone(T_a), V_a)) | (~class_Rings_Odivision__ring(T_a)))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.63/0.83 tff(152,plain,
% 0.63/0.83 (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____) = c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[151, 145, 142, 132])).
% 0.63/0.83 tff(153,plain,
% 0.63/0.83 (c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____)),
% 0.63/0.83 inference(symmetry,[status(thm)],[152])).
% 0.63/0.83 tff(154,plain,
% 0.63/0.83 (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)),
% 0.63/0.83 inference(transitivity,[status(thm)],[56, 71, 153, 129])).
% 0.63/0.83 tff(155,plain,
% 0.63/0.83 (hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1)),
% 0.63/0.83 inference(symmetry,[status(thm)],[125])).
% 0.63/0.83 tff(156,plain,
% 0.63/0.83 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[155, 154])).
% 0.63/0.83 tff(157,plain,
% 0.63/0.83 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))), hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.83 inference(symmetry,[status(thm)],[156])).
% 0.63/0.83 tff(158,plain,
% 0.63/0.83 (^[V_a: $i, T_a: $i] : refl(((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(159,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a))) <=> ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[158])).
% 0.63/0.83 tff(160,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a))) <=> ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(161,plain,
% 0.63/0.83 (^[V_a: $i, T_a: $i] : trans(monotonicity(rewrite(((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)))), ((class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)))) <=> (class_Rings_Odivision__ring(T_a) => ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)))))), rewrite((class_Rings_Odivision__ring(T_a) => ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))), ((class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)))) <=> ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(162,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : (class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)))) <=> ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[161])).
% 0.63/0.83 tff(163,axiom,(![V_a: $i, T_a: $i] : (class_Rings_Odivision__ring(T_a) => ((~(V_a = c_Groups_Ozero__class_Ozero(T_a))) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_right__inverse')).
% 0.63/0.83 tff(164,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.63/0.83 tff(165,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.63/0.83 tff(166,plain,(
% 0.63/0.83 ![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(skolemize,[status(sab)],[165])).
% 0.63/0.83 tff(167,plain,
% 0.63/0.83 (![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.63/0.83 tff(168,plain,
% 0.63/0.83 (~(B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 0.63/0.83 inference(or_elim,[status(thm)],[117])).
% 0.63/0.83 tff(169,plain,
% 0.63/0.83 (((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) <=> ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | (B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(170,plain,
% 0.63/0.83 (((B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex))) <=> ((B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(171,plain,
% 0.63/0.83 (((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)))) <=> ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[170])).
% 0.63/0.83 tff(172,plain,
% 0.63/0.83 (((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)))) <=> ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | (B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(transitivity,[status(thm)],[171, 169])).
% 0.63/0.83 tff(173,plain,
% 0.63/0.83 ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | ((B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(174,plain,
% 0.63/0.83 ((~![V_a: $i, T_a: $i] : ((V_a = c_Groups_Ozero__class_Ozero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Rings_Oinverse__class_Oinverse(T_a, V_a)) = c_Groups_Oone__class_Oone(T_a)) | (~class_Rings_Odivision__ring(T_a)))) | (B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~class_Rings_Odivision__ring(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.63/0.83 tff(175,plain,
% 0.63/0.83 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[174, 168, 167, 132])).
% 0.63/0.83 tff(176,plain,
% 0.63/0.83 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1))),
% 0.63/0.83 inference(symmetry,[status(thm)],[175])).
% 0.63/0.83 tff(177,plain,
% 0.63/0.83 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____))),
% 0.63/0.83 inference(transitivity,[status(thm)],[176, 157, 127])).
% 0.63/0.83 tff(178,plain,
% 0.63/0.83 (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_Omonom(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[177])).
% 0.63/0.84 tff(179,plain,
% 0.63/0.84 (c_Polynomial_Omonom(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.84 inference(symmetry,[status(thm)],[178])).
% 0.63/0.84 tff(180,plain,
% 0.63/0.84 (class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) <=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(181,axiom,(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ocomm__semiring__0')).
% 0.63/0.84 tff(182,plain,
% 0.63/0.84 (class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.63/0.84 tff(183,plain,
% 0.63/0.84 (^[V_n: $i, V_b: $i, V_a: $i, T_a: $i] : refl(((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n))) <=> ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(184,plain,
% 0.63/0.84 (![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n))) <=> ![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[183])).
% 0.63/0.84 tff(185,plain,
% 0.63/0.84 (![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n))) <=> ![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(186,plain,
% 0.63/0.84 (^[V_n: $i, V_b: $i, V_a: $i, T_a: $i] : rewrite((class_Rings_Ocomm__semiring__0(T_a) => (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n))) <=> ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(187,plain,
% 0.63/0.84 (![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : (class_Rings_Ocomm__semiring__0(T_a) => (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n))) <=> ![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[186])).
% 0.63/0.84 tff(188,axiom,(![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : (class_Rings_Ocomm__semiring__0(T_a) => (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_smult__monom')).
% 0.63/0.84 tff(189,plain,
% 0.63/0.84 (![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.63/0.84 tff(190,plain,
% 0.63/0.84 (![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.63/0.84 tff(191,plain,(
% 0.63/0.84 ![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))),
% 0.63/0.84 inference(skolemize,[status(sab)],[190])).
% 0.63/0.84 tff(192,plain,
% 0.63/0.84 (![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.63/0.84 tff(193,plain,
% 0.63/0.84 (((~![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))) | ((~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Polynomial_Omonom(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((~![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Polynomial_Omonom(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(194,plain,
% 0.63/0.84 ((~![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))) | ((~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Polynomial_Omonom(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(195,plain,
% 0.63/0.84 ((~![V_n: $i, V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (c_Polynomial_Osmult(T_a, V_a, c_Polynomial_Omonom(T_a, V_b, V_n)) = c_Polynomial_Omonom(T_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b), V_n)))) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Polynomial_Omonom(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.63/0.84 tff(196,plain,
% 0.63/0.84 (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Polynomial_Omonom(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_k!1), c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[195, 192, 182])).
% 0.63/0.84 tff(197,plain,
% 0.63/0.84 (((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> ((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(198,plain,
% 0.63/0.84 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(199,plain,
% 0.63/0.84 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (c_Polynomial_Omonom(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a, V_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.63/0.84 tff(200,plain,
% 0.63/0.84 (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[199, 31, 21])).
% 0.63/0.84 tff(201,plain,
% 0.63/0.84 (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[200])).
% 0.63/0.84 tff(202,plain,
% 0.63/0.84 (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 0.63/0.84 inference(symmetry,[status(thm)],[201])).
% 0.63/0.84 tff(203,plain,
% 0.63/0.84 (^[T_1: $i] : refl((class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1))) <=> (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(204,plain,
% 0.63/0.84 (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1))) <=> ![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[203])).
% 0.63/0.84 tff(205,plain,
% 0.63/0.84 (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1))) <=> ![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(206,plain,
% 0.63/0.84 (^[T_1: $i] : rewrite((class_Rings_Oidom(T_1) => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))) <=> (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(207,plain,
% 0.63/0.84 (![T_1: $i] : (class_Rings_Oidom(T_1) => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))) <=> ![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[206])).
% 0.63/0.84 tff(208,axiom,(![T_1: $i] : (class_Rings_Oidom(T_1) => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct')).
% 0.63/0.84 tff(209,plain,
% 0.63/0.84 (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.63/0.84 tff(210,plain,
% 0.63/0.84 (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.63/0.84 tff(211,plain,(
% 0.63/0.84 ![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.63/0.84 inference(skolemize,[status(sab)],[210])).
% 0.63/0.84 tff(212,plain,
% 0.63/0.84 (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.63/0.84 tff(213,plain,
% 0.63/0.84 (class_Rings_Oidom(tc_Complex_Ocomplex) <=> class_Rings_Oidom(tc_Complex_Ocomplex)),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(214,axiom,(class_Rings_Oidom(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Oidom')).
% 0.63/0.84 tff(215,plain,
% 0.63/0.84 (class_Rings_Oidom(tc_Complex_Ocomplex)),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.63/0.84 tff(216,plain,
% 0.63/0.84 (((~![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))) | (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Oidom(tc_Complex_Ocomplex)))) <=> ((~![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))) | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Oidom(tc_Complex_Ocomplex)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(217,plain,
% 0.63/0.84 ((~![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))) | (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Oidom(tc_Complex_Ocomplex)))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(218,plain,
% 0.63/0.84 ((~![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))) | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Oidom(tc_Complex_Ocomplex))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.63/0.84 tff(219,plain,
% 0.63/0.84 (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[218, 215, 212])).
% 0.63/0.84 tff(220,plain,
% 0.63/0.84 (^[V_a_2: $i, V_b_2: $i, T_a: $i] : refl(((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) <=> ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(221,plain,
% 0.63/0.84 (![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[220])).
% 0.63/0.84 tff(222,plain,
% 0.63/0.84 (![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(223,plain,
% 0.63/0.84 (^[V_a_2: $i, V_b_2: $i, T_a: $i] : rewrite((class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) => ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) <=> ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(224,plain,
% 0.63/0.84 (![V_a_2: $i, V_b_2: $i, T_a: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) => ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[223])).
% 0.63/0.84 tff(225,axiom,(![V_a_2: $i, V_b_2: $i, T_a: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) => ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_add__0__iff')).
% 0.63/0.84 tff(226,plain,
% 0.63/0.84 (![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.63/0.84 tff(227,plain,
% 0.63/0.84 (![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.63/0.84 tff(228,plain,(
% 0.63/0.84 ![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.84 inference(skolemize,[status(sab)],[227])).
% 0.63/0.84 tff(229,plain,
% 0.63/0.84 (![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.63/0.84 tff(230,plain,
% 0.63/0.84 (((~![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | ((c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> ((~![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | ((c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(231,plain,
% 0.63/0.84 ((~![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | ((c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(232,plain,
% 0.63/0.84 ((~![V_a_2: $i, V_b_2: $i, T_a: $i] : ((~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)) | ((V_b_2 = c_Groups_Oplus__class_Oplus(T_a, V_b_2, V_a_2)) <=> (V_a_2 = c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | ((c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.63/0.84 tff(233,plain,
% 0.63/0.84 ((c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[232, 229, 219])).
% 0.63/0.84 tff(234,plain,
% 0.63/0.84 (^[V_pa_2: $i, V_a_2: $i, T_a: $i] : refl(((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) <=> ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(235,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) <=> ![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[234])).
% 0.63/0.84 tff(236,plain,
% 0.63/0.84 (^[V_pa_2: $i, V_a_2: $i, T_a: $i] : rewrite(((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) <=> ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(237,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) <=> ![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[236])).
% 0.63/0.84 tff(238,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) <=> ![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(239,plain,
% 0.63/0.84 (^[V_pa_2: $i, V_a_2: $i, T_a: $i] : rewrite((class_Groups_Ozero(T_a) => ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) <=> ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(240,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : (class_Groups_Ozero(T_a) => ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))))) <=> ![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[239])).
% 0.63/0.84 tff(241,axiom,(![V_pa_2: $i, V_a_2: $i, T_a: $i] : (class_Groups_Ozero(T_a) => ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_pCons__eq__0__iff')).
% 0.63/0.84 tff(242,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.63/0.84 tff(243,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.63/0.84 tff(244,plain,(
% 0.63/0.84 ![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | ((c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) <=> ((V_a_2 = c_Groups_Ozero__class_Ozero(T_a)) & (V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(skolemize,[status(sab)],[243])).
% 0.63/0.84 tff(245,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.63/0.84 tff(246,plain,
% 0.63/0.84 (![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[245, 235])).
% 0.63/0.84 tff(247,plain,
% 0.63/0.84 (((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> ((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(248,plain,
% 0.63/0.84 (((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(249,plain,
% 0.63/0.84 (((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> ((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[248])).
% 0.63/0.84 tff(250,plain,
% 0.63/0.84 (((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> ((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.85 inference(transitivity,[status(thm)],[249, 247])).
% 0.63/0.85 tff(251,plain,
% 0.63/0.85 ((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | ((~class_Groups_Ozero(tc_Complex_Ocomplex)) | (~(((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(252,plain,
% 0.63/0.85 ((~![V_pa_2: $i, V_a_2: $i, T_a: $i] : ((~class_Groups_Ozero(T_a)) | (~(((~(V_a_2 = c_Groups_Ozero__class_Ozero(T_a))) | (~(V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))) <=> (c_Polynomial_OpCons(T_a, V_a_2, V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))))) | (~class_Groups_Ozero(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.63/0.85 tff(253,plain,
% 0.63/0.85 ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[252, 246, 21])).
% 0.63/0.85 tff(254,plain,
% 0.63/0.85 (^[T_1: $i] : refl((class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1))) <=> (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(255,plain,
% 0.63/0.85 (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1))) <=> ![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[254])).
% 0.63/0.85 tff(256,plain,
% 0.63/0.85 (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1))) <=> ![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(257,plain,
% 0.63/0.85 (^[T_1: $i] : rewrite((class_Rings_Ocomm__semiring__0(T_1) => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))) <=> (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(258,plain,
% 0.63/0.85 (![T_1: $i] : (class_Rings_Ocomm__semiring__0(T_1) => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))) <=> ![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[257])).
% 0.63/0.85 tff(259,axiom,(![T_1: $i] : (class_Rings_Ocomm__semiring__0(T_1) => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Polynomial__Opoly__Rings_Omult__zero')).
% 0.63/0.85 tff(260,plain,
% 0.63/0.85 (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.63/0.85 tff(261,plain,
% 0.63/0.85 (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.63/0.85 tff(262,plain,(
% 0.63/0.85 ![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.63/0.85 inference(skolemize,[status(sab)],[261])).
% 0.63/0.85 tff(263,plain,
% 0.63/0.85 (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.63/0.85 tff(264,plain,
% 0.63/0.85 (((~![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))) | (class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)))) <=> ((~![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))) | class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(265,plain,
% 0.63/0.85 ((~![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))) | (class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(266,plain,
% 0.63/0.85 ((~![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))) | class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.63/0.85 tff(267,plain,
% 0.63/0.85 (class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[266, 182, 263])).
% 0.63/0.85 tff(268,plain,
% 0.63/0.85 (^[V_a: $i, T_a: $i] : refl(((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a))) <=> ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(269,plain,
% 0.63/0.85 (![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[268])).
% 0.63/0.85 tff(270,plain,
% 0.63/0.85 (![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(271,plain,
% 0.63/0.85 (^[V_a: $i, T_a: $i] : rewrite((class_Rings_Omult__zero(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a))) <=> ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(272,plain,
% 0.63/0.85 (![V_a: $i, T_a: $i] : (class_Rings_Omult__zero(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[271])).
% 0.63/0.85 tff(273,axiom,(![V_a: $i, T_a: $i] : (class_Rings_Omult__zero(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_mult__zero__left')).
% 0.63/0.85 tff(274,plain,
% 0.63/0.85 (![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.63/0.85 tff(275,plain,
% 0.63/0.85 (![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.63/0.85 tff(276,plain,(
% 0.63/0.85 ![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))),
% 0.63/0.85 inference(skolemize,[status(sab)],[275])).
% 0.63/0.85 tff(277,plain,
% 0.63/0.85 (![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.63/0.85 tff(278,plain,
% 0.63/0.85 (((~![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))) | ((~class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> ((~![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))) | (~class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(279,plain,
% 0.63/0.85 ((~![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))) | ((~class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(280,plain,
% 0.63/0.85 ((~![V_a: $i, T_a: $i] : ((~class_Rings_Omult__zero(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ozero__class_Ozero(T_a)), V_a) = c_Groups_Ozero__class_Ozero(T_a)))) | (~class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.63/0.85 tff(281,plain,
% 0.63/0.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[280, 277, 267])).
% 0.63/0.85 tff(282,plain,
% 0.63/0.85 ((~((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) | (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(283,plain,
% 0.63/0.85 ((~((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.63/0.85 tff(284,plain,
% 0.63/0.85 (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[283, 253])).
% 0.63/0.85 tff(285,plain,
% 0.63/0.85 ((~((c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) <=> (c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))) | (~(c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(286,plain,
% 0.63/0.85 (c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[285, 284, 233])).
% 0.63/0.85 tff(287,plain,
% 0.63/0.85 (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(symmetry,[status(thm)],[286])).
% 0.63/0.85 tff(288,plain,
% 0.63/0.85 (^[V_q: $i, V_p: $i, V_a: $i, T_a: $i] : refl(((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q))))) <=> ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q))))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(289,plain,
% 0.63/0.85 (![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q))))) <=> ![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[288])).
% 0.63/0.85 tff(290,plain,
% 0.63/0.85 (![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q))))) <=> ![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(291,plain,
% 0.63/0.85 (^[V_q: $i, V_p: $i, V_a: $i, T_a: $i] : rewrite((class_Rings_Ocomm__semiring__0(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q))))) <=> ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q))))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(292,plain,
% 0.63/0.85 (![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : (class_Rings_Ocomm__semiring__0(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q))))) <=> ![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[291])).
% 0.63/0.85 tff(293,axiom,(![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : (class_Rings_Ocomm__semiring__0(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_mult__pCons__left')).
% 0.63/0.85 tff(294,plain,
% 0.63/0.85 (![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.63/0.85 tff(295,plain,
% 0.63/0.85 (![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.63/0.85 tff(296,plain,(
% 0.63/0.85 ![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))),
% 0.63/0.85 inference(skolemize,[status(sab)],[295])).
% 0.63/0.85 tff(297,plain,
% 0.63/0.85 (![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[296, 289])).
% 0.63/0.85 tff(298,plain,
% 0.63/0.85 (((~![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))) | ((~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))))) <=> ((~![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(299,plain,
% 0.63/0.85 ((~![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))) | ((~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(300,plain,
% 0.63/0.85 ((~![V_q: $i, V_p: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__0(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), c_Polynomial_OpCons(T_a, V_a, V_p)), V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a), c_Polynomial_Osmult(T_a, V_a, V_q), c_Polynomial_OpCons(T_a, c_Groups_Ozero__class_Ozero(T_a), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)), V_p), V_q)))))) | (~class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.63/0.85 tff(301,plain,
% 0.63/0.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, B_k!1, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[300, 297, 182])).
% 0.63/0.85 tff(302,plain,
% 0.63/0.85 (c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = v_p),
% 0.63/0.85 inference(symmetry,[status(thm)],[118])).
% 0.63/0.85 tff(303,plain,
% 0.63/0.85 (hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p)),
% 0.63/0.85 inference(monotonicity,[status(thm)],[302])).
% 0.63/0.85 tff(304,plain,
% 0.63/0.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[303])).
% 0.63/0.85 tff(305,plain,
% 0.63/0.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(symmetry,[status(thm)],[304])).
% 0.63/0.85 tff(306,plain,
% 0.63/0.85 (hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p)),
% 0.63/0.85 inference(monotonicity,[status(thm)],[80])).
% 0.63/0.85 tff(307,plain,
% 0.63/0.85 (hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p) = hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(symmetry,[status(thm)],[306])).
% 0.63/0.85 tff(308,plain,
% 0.63/0.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[307])).
% 0.63/0.85 tff(309,plain,
% 0.63/0.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.85 inference(symmetry,[status(thm)],[308])).
% 0.63/0.85 tff(310,plain,
% 0.63/0.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.85 inference(transitivity,[status(thm)],[309, 305, 301, 287, 202, 196, 179, 35, 18])).
% 0.63/0.85 tff(311,plain,
% 0.63/0.85 ((c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.85 inference(commutativity,[status(thm)],[])).
% 0.63/0.85 tff(312,plain,
% 0.63/0.85 (^[T_1: $i] : refl((class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1))) <=> (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(313,plain,
% 0.63/0.85 (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1))) <=> ![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[312])).
% 0.63/0.85 tff(314,plain,
% 0.63/0.85 (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1))) <=> ![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(315,plain,
% 0.63/0.85 (^[T_1: $i] : rewrite((class_Rings_Ocomm__semiring__1(T_1) => class_Power_Opower(tc_Polynomial_Opoly(T_1))) <=> (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(316,plain,
% 0.63/0.85 (![T_1: $i] : (class_Rings_Ocomm__semiring__1(T_1) => class_Power_Opower(tc_Polynomial_Opoly(T_1))) <=> ![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[315])).
% 0.63/0.85 tff(317,axiom,(![T_1: $i] : (class_Rings_Ocomm__semiring__1(T_1) => class_Power_Opower(tc_Polynomial_Opoly(T_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Polynomial__Opoly__Power_Opower')).
% 0.63/0.86 tff(318,plain,
% 0.63/0.86 (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.63/0.86 tff(319,plain,
% 0.63/0.86 (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.63/0.86 tff(320,plain,(
% 0.63/0.86 ![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.63/0.86 inference(skolemize,[status(sab)],[319])).
% 0.63/0.86 tff(321,plain,
% 0.63/0.86 (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.63/0.86 tff(322,plain,
% 0.63/0.86 (((~![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))) | (class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)))) <=> ((~![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))) | class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(323,plain,
% 0.63/0.86 ((~![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))) | (class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(324,plain,
% 0.63/0.86 ((~![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))) | class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.63/0.86 tff(325,plain,
% 0.63/0.86 (class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[324, 3, 321])).
% 0.63/0.86 tff(326,plain,
% 0.63/0.86 (^[V_a: $i, T_a: $i] : refl(((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(327,plain,
% 0.63/0.86 (![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[326])).
% 0.63/0.86 tff(328,plain,
% 0.63/0.86 (![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(329,plain,
% 0.63/0.86 (^[V_a: $i, T_a: $i] : rewrite((class_Power_Opower(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))))),
% 0.63/0.86 inference(bind,[status(th)],[])).
% 0.63/0.86 tff(330,plain,
% 0.63/0.86 (![V_a: $i, T_a: $i] : (class_Power_Opower(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))),
% 0.63/0.86 inference(quant_intro,[status(thm)],[329])).
% 0.63/0.86 tff(331,axiom,(![V_a: $i, T_a: $i] : (class_Power_Opower(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_power__0')).
% 0.63/0.86 tff(332,plain,
% 0.63/0.86 (![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.63/0.86 tff(333,plain,
% 0.63/0.86 (![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[332, 328])).
% 0.63/0.86 tff(334,plain,(
% 0.63/0.86 ![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))),
% 0.63/0.86 inference(skolemize,[status(sab)],[333])).
% 0.63/0.86 tff(335,plain,
% 0.63/0.86 (![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[334, 327])).
% 0.63/0.86 tff(336,plain,
% 0.63/0.86 (((~![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))) | ((~class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> ((~![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))) | (~class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(337,plain,
% 0.63/0.86 ((~![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))) | ((~class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(338,plain,
% 0.63/0.86 ((~![V_a: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)))) | (~class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.63/0.86 tff(339,plain,
% 0.63/0.86 ((~class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[338, 335])).
% 0.63/0.86 tff(340,plain,
% 0.63/0.86 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[339, 325])).
% 0.63/0.86 tff(341,plain,
% 0.63/0.86 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[76])).
% 0.63/0.86 tff(342,plain,
% 0.63/0.86 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.63/0.86 inference(transitivity,[status(thm)],[341, 340])).
% 0.63/0.86 tff(343,plain,
% 0.63/0.86 ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[342, 308])).
% 0.63/0.86 tff(344,plain,
% 0.63/0.86 ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.63/0.86 inference(transitivity,[status(thm)],[343, 311])).
% 0.63/0.86 tff(345,plain,
% 0.63/0.86 ((~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[344])).
% 0.63/0.86 tff(346,plain,
% 0.63/0.86 ((~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) <=> (~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.76/0.91 inference(rewrite,[status(thm)],[])).
% 0.76/0.91 tff(347,axiom,(~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 0.76/0.91 tff(348,plain,
% 0.76/0.91 (~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_p), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.76/0.91 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.76/0.91 tff(349,plain,
% 0.76/0.91 (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.76/0.91 inference(modus_ponens,[status(thm)],[348, 345])).
% 0.76/0.91 tff(350,plain,
% 0.76/0.91 ($false),
% 0.76/0.91 inference(unit_resolution,[status(thm)],[349, 310])).
% 0.76/0.91 % SZS output end Proof
% 0.76/0.92 % E exiting
%------------------------------------------------------------------------------