%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWW286+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n014.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 : Thu Sep 29 20:58:12 EDT 2022

% Result   : Theorem 0.78s 0.81s
% Output   : Proof 0.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWW286+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Sep  4 14:03:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.78/0.81  % SZS status Theorem
% 0.78/0.81  % SZS output start Proof
% 0.78/0.81  tff(c_Groups_Oone__class_Oone_type, type, (
% 0.78/0.81     c_Groups_Oone__class_Oone: $i > $i)).
% 0.78/0.81  tff(tc_Polynomial_Opoly_type, type, (
% 0.78/0.81     tc_Polynomial_Opoly: $i > $i)).
% 0.78/0.81  tff(tc_Complex_Ocomplex_type, type, (
% 0.78/0.81     tc_Complex_Ocomplex: $i)).
% 0.78/0.81  tff(hAPP_type, type, (
% 0.78/0.81     hAPP: ( $i * $i ) > $i)).
% 0.78/0.81  tff(c_Polynomial_OpCons_type, type, (
% 0.78/0.81     c_Polynomial_OpCons: ( $i * $i * $i ) > $i)).
% 0.78/0.81  tff(c_Groups_Ozero__class_Ozero_type, type, (
% 0.78/0.81     c_Groups_Ozero__class_Ozero: $i > $i)).
% 0.78/0.81  tff(c_Rings_Oinverse__class_Odivide_type, type, (
% 0.78/0.81     c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i)).
% 0.78/0.81  tff(v_k_____type, type, (
% 0.78/0.81     v_k____: $i)).
% 0.78/0.81  tff(tptp_fun_B_k_1_type, type, (
% 0.78/0.81     tptp_fun_B_k_1: $i)).
% 0.78/0.81  tff(c_Groups_Otimes__class_Otimes_type, type, (
% 0.78/0.81     c_Groups_Otimes__class_Otimes: $i > $i)).
% 0.78/0.81  tff(class_Rings_Ocomm__semiring__1_type, type, (
% 0.78/0.81     class_Rings_Ocomm__semiring__1: $i > $o)).
% 0.78/0.81  tff(c_Polynomial_Omonom_type, type, (
% 0.78/0.81     c_Polynomial_Omonom: ( $i * $i * $i ) > $i)).
% 0.78/0.81  tff(tc_Nat_Onat_type, type, (
% 0.78/0.81     tc_Nat_Onat: $i)).
% 0.78/0.81  tff(class_Groups_Ozero_type, type, (
% 0.78/0.81     class_Groups_Ozero: $i > $o)).
% 0.78/0.81  tff(c_Polynomial_Odegree_type, type, (
% 0.78/0.81     c_Polynomial_Odegree: ( $i * $i ) > $i)).
% 0.78/0.81  tff(c_Polynomial_Ocoeff_type, type, (
% 0.78/0.81     c_Polynomial_Ocoeff: ( $i * $i ) > $i)).
% 0.78/0.81  tff(c_Nat_OSuc_type, type, (
% 0.78/0.81     c_Nat_OSuc: $i > $i)).
% 0.78/0.81  tff(v_p_type, type, (
% 0.78/0.81     v_p: $i)).
% 0.78/0.81  tff(c_Rings_Oinverse__class_Oinverse_type, type, (
% 0.78/0.81     c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i)).
% 0.78/0.81  tff(class_Rings_Odivision__ring_type, type, (
% 0.78/0.81     class_Rings_Odivision__ring: $i > $o)).
% 0.78/0.81  tff(c_Polynomial_Osmult_type, type, (
% 0.78/0.81     c_Polynomial_Osmult: ( $i * $i * $i ) > $i)).
% 0.78/0.81  tff(class_Rings_Ocomm__semiring__0_type, type, (
% 0.78/0.81     class_Rings_Ocomm__semiring__0: $i > $o)).
% 0.78/0.81  tff(c_Groups_Oplus__class_Oplus_type, type, (
% 0.78/0.81     c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i)).
% 0.78/0.81  tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type, type, (
% 0.78/0.81     class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o)).
% 0.78/0.81  tff(class_Rings_Oidom_type, type, (
% 0.78/0.81     class_Rings_Oidom: $i > $o)).
% 0.78/0.81  tff(class_Rings_Omult__zero_type, type, (
% 0.78/0.81     class_Rings_Omult__zero: $i > $o)).
% 0.78/0.81  tff(v_q_type, type, (
% 0.78/0.81     v_q: $i)).
% 0.78/0.81  tff(c_Power_Opower__class_Opower_type, type, (
% 0.78/0.81     c_Power_Opower__class_Opower: $i > $i)).
% 0.78/0.81  tff(class_Power_Opower_type, type, (
% 0.78/0.81     class_Power_Opower: $i > $o)).
% 0.78/0.81  tff(1,plain,
% 0.78/0.81      (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  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')).
% 0.78/0.81  tff(3,plain,
% 0.78/0.81      (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[2, 1])).
% 0.78/0.81  tff(4,plain,
% 0.78/0.81      (^[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))))))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(5,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[4])).
% 0.78/0.81  tff(6,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(7,plain,
% 0.78/0.81      (^[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))))))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(8,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[7])).
% 0.78/0.81  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')).
% 0.78/0.81  tff(10,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[9, 8])).
% 0.78/0.81  tff(11,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[10, 6])).
% 0.78/0.81  tff(12,plain,(
% 0.78/0.81      ![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)))))),
% 0.78/0.81      inference(skolemize,[status(sab)],[11])).
% 0.78/0.81  tff(13,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[12, 5])).
% 0.78/0.81  tff(14,plain,
% 0.78/0.81      (((~![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)))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(15,plain,
% 0.78/0.81      ((~![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)))))),
% 0.78/0.81      inference(quant_inst,[status(thm)],[])).
% 0.78/0.81  tff(16,plain,
% 0.78/0.81      ((~![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))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.78/0.81  tff(17,plain,
% 0.78/0.81      (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)))),
% 0.78/0.81      inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 0.78/0.81  tff(18,plain,
% 0.78/0.81      (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))),
% 0.78/0.81      inference(symmetry,[status(thm)],[17])).
% 0.78/0.81  tff(19,plain,
% 0.78/0.81      (class_Groups_Ozero(tc_Complex_Ocomplex) <=> class_Groups_Ozero(tc_Complex_Ocomplex)),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(20,axiom,(class_Groups_Ozero(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Groups_Ozero')).
% 0.78/0.81  tff(21,plain,
% 0.78/0.81      (class_Groups_Ozero(tc_Complex_Ocomplex)),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[20, 19])).
% 0.78/0.81  tff(22,plain,
% 0.78/0.81      (^[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))))))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(23,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[22])).
% 0.78/0.81  tff(24,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(25,plain,
% 0.78/0.81      (^[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))))))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(26,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[25])).
% 0.78/0.81  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')).
% 0.78/0.81  tff(28,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[27, 26])).
% 0.78/0.81  tff(29,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[28, 24])).
% 0.78/0.81  tff(30,plain,(
% 0.78/0.81      ![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)))))),
% 0.78/0.81      inference(skolemize,[status(sab)],[29])).
% 0.78/0.81  tff(31,plain,
% 0.78/0.81      (![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)))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[30, 23])).
% 0.78/0.81  tff(32,plain,
% 0.78/0.81      (((~![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)))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(33,plain,
% 0.78/0.81      ((~![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)))))),
% 0.78/0.81      inference(quant_inst,[status(thm)],[])).
% 0.78/0.81  tff(34,plain,
% 0.78/0.81      ((~![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))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[33, 32])).
% 0.78/0.81  tff(35,plain,
% 0.78/0.81      (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)))),
% 0.78/0.81      inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.78/0.81  tff(36,plain,
% 0.78/0.81      (^[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)))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(37,plain,
% 0.78/0.81      (![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))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[36])).
% 0.78/0.81  tff(38,plain,
% 0.78/0.81      (![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))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(39,plain,
% 0.78/0.81      (^[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)))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(40,plain,
% 0.78/0.81      (![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))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[39])).
% 0.78/0.81  tff(41,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')).
% 0.78/0.81  tff(42,plain,
% 0.78/0.81      (![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))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.78/0.81  tff(43,plain,
% 0.78/0.81      (![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))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[42, 38])).
% 0.78/0.81  tff(44,plain,(
% 0.78/0.81      ![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))),
% 0.78/0.81      inference(skolemize,[status(sab)],[43])).
% 0.78/0.81  tff(45,plain,
% 0.78/0.81      (![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))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[44, 37])).
% 0.78/0.81  tff(46,plain,
% 0.78/0.81      (((~![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____)))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(47,plain,
% 0.78/0.81      ((~![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____)))),
% 0.78/0.81      inference(quant_inst,[status(thm)],[])).
% 0.78/0.81  tff(48,plain,
% 0.78/0.81      ((~![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____))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[47, 46])).
% 0.78/0.81  tff(49,plain,
% 0.78/0.81      (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____)),
% 0.78/0.81      inference(unit_resolution,[status(thm)],[48, 45, 21])).
% 0.78/0.81  tff(50,plain,
% 0.78/0.81      (^[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)))))))))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(51,plain,
% 0.78/0.81      (![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))))))))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[50])).
% 0.78/0.81  tff(52,plain,
% 0.78/0.81      (^[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)))))))))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(53,plain,
% 0.78/0.81      (![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))))))))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[52])).
% 0.78/0.81  tff(54,plain,
% 0.78/0.81      (![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))))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(55,plain,
% 0.78/0.81      (^[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))))))))),
% 0.78/0.81      inference(bind,[status(th)],[])).
% 0.78/0.81  tff(56,plain,
% 0.78/0.81      (![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))))))),
% 0.78/0.81      inference(quant_intro,[status(thm)],[55])).
% 0.78/0.81  tff(57,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')).
% 0.78/0.81  tff(58,plain,
% 0.78/0.81      (![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))))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[57, 56])).
% 0.78/0.81  tff(59,plain,
% 0.78/0.81      (![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))))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[58, 54])).
% 0.78/0.81  tff(60,plain,(
% 0.78/0.81      ![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))))))),
% 0.78/0.81      inference(skolemize,[status(sab)],[59])).
% 0.78/0.81  tff(61,plain,
% 0.78/0.81      (![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))))))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[60, 53])).
% 0.78/0.81  tff(62,plain,
% 0.78/0.81      (![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))))))))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[61, 51])).
% 0.78/0.81  tff(63,plain,
% 0.78/0.81      (((~![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)))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(64,plain,
% 0.78/0.81      (((~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)))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(65,plain,
% 0.78/0.81      (((~![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))))),
% 0.78/0.81      inference(monotonicity,[status(thm)],[64])).
% 0.78/0.81  tff(66,plain,
% 0.78/0.81      (((~![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)))),
% 0.78/0.81      inference(transitivity,[status(thm)],[65, 63])).
% 0.78/0.81  tff(67,plain,
% 0.78/0.81      ((~![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))))))))))),
% 0.78/0.81      inference(quant_inst,[status(thm)],[])).
% 0.78/0.81  tff(68,plain,
% 0.78/0.81      ((~![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))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[67, 66])).
% 0.78/0.81  tff(69,plain,
% 0.78/0.81      (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)),
% 0.78/0.81      inference(unit_resolution,[status(thm)],[68, 62, 21])).
% 0.78/0.81  tff(70,plain,
% 0.78/0.81      (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))),
% 0.78/0.81      inference(monotonicity,[status(thm)],[69])).
% 0.78/0.81  tff(71,plain,
% 0.78/0.81      (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_Odivide(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_k____)),
% 0.78/0.81      inference(transitivity,[status(thm)],[70, 49])).
% 0.78/0.81  tff(72,plain,
% 0.78/0.81      ((c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) <=> (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))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(73,plain,
% 0.78/0.81      ((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))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(74,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')).
% 0.78/0.81  tff(75,plain,
% 0.78/0.81      (c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[74, 73])).
% 0.78/0.81  tff(76,plain,
% 0.78/0.81      (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)),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[75, 72])).
% 0.78/0.81  tff(77,plain,
% 0.78/0.81      ((~![B_k: $i] : ((~(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, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~![B_k: $i] : ((~(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, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(78,plain,
% 0.78/0.81      ((~![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] : ((~(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, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(79,plain,
% 0.78/0.81      ((~![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))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(80,plain,
% 0.78/0.81      ((~![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))))),
% 0.78/0.81      inference(rewrite,[status(thm)],[])).
% 0.78/0.81  tff(81,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')).
% 0.78/0.81  tff(82,plain,
% 0.78/0.81      (~![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)))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[81, 80])).
% 0.78/0.81  tff(83,plain,
% 0.78/0.81      (~![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)))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[82, 79])).
% 0.78/0.81  tff(84,plain,
% 0.78/0.81      (~![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)))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[83, 79])).
% 0.78/0.81  tff(85,plain,
% 0.78/0.81      (~![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)))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[84, 79])).
% 0.78/0.81  tff(86,plain,
% 0.78/0.81      (~![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)))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[85, 79])).
% 0.78/0.81  tff(87,plain,
% 0.78/0.81      (~![B_k: $i] : ((~(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, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.78/0.81      inference(modus_ponens,[status(thm)],[86, 78])).
% 0.78/0.82  tff(88,plain,
% 0.78/0.82      (~![B_k: $i] : ((~(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, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[87, 77])).
% 0.78/0.82  tff(89,plain,
% 0.78/0.82      (~![B_k: $i] : ((~(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, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[88, 77])).
% 0.78/0.82  tff(90,plain,
% 0.78/0.82      (~![B_k: $i] : ((~(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, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))) | (B_k = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[89, 77])).
% 0.78/0.82  tff(91,plain,(
% 0.78/0.82      ~((~(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))))) | (B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.78/0.82      inference(skolemize,[status(sab)],[90])).
% 0.78/0.82  tff(92,plain,
% 0.78/0.82      (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)))),
% 0.78/0.82      inference(or_elim,[status(thm)],[91])).
% 0.78/0.82  tff(93,plain,
% 0.78/0.82      (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, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.78/0.82      inference(symmetry,[status(thm)],[92])).
% 0.78/0.82  tff(94,plain,
% 0.78/0.82      (c_Polynomial_Odegree(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_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[93])).
% 0.78/0.82  tff(95,plain,
% 0.78/0.82      (c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
% 0.78/0.82      inference(transitivity,[status(thm)],[94, 76])).
% 0.78/0.82  tff(96,plain,
% 0.78/0.82      (hAPP(c_Polynomial_Ocoeff(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_Odegree(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_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[95])).
% 0.78/0.82  tff(97,plain,
% 0.78/0.82      (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, 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, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.78/0.82      inference(symmetry,[status(thm)],[96])).
% 0.78/0.82  tff(98,plain,
% 0.78/0.82      (((~![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, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = B_k!1))) <=> ((~![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, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = B_k!1))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(99,plain,
% 0.78/0.82      ((~![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, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = B_k!1))),
% 0.78/0.82      inference(quant_inst,[status(thm)],[])).
% 0.78/0.82  tff(100,plain,
% 0.78/0.82      ((~![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, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = B_k!1)),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[99, 98])).
% 0.78/0.82  tff(101,plain,
% 0.78/0.82      (hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = B_k!1),
% 0.78/0.82      inference(unit_resolution,[status(thm)],[100, 45, 21])).
% 0.78/0.82  tff(102,plain,
% 0.78/0.82      (B_k!1 = hAPP(c_Polynomial_Ocoeff(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 0.78/0.82      inference(symmetry,[status(thm)],[101])).
% 0.78/0.82  tff(103,plain,
% 0.78/0.82      (B_k!1 = hAPP(c_Polynomial_Ocoeff(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_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))),
% 0.78/0.82      inference(transitivity,[status(thm)],[102, 97])).
% 0.78/0.82  tff(104,plain,
% 0.78/0.82      (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, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[103])).
% 0.78/0.82  tff(105,plain,
% 0.78/0.82      (hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(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_Odegree(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_Complex_Ocomplex), B_k!1)),
% 0.78/0.82      inference(symmetry,[status(thm)],[104])).
% 0.78/0.82  tff(106,plain,
% 0.78/0.82      (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Ocoeff(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_Odegree(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_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____))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[105, 71])).
% 0.78/0.82  tff(107,plain,
% 0.78/0.82      (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)))))),
% 0.78/0.82      inference(symmetry,[status(thm)],[70])).
% 0.78/0.82  tff(108,plain,
% 0.78/0.82      (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))),
% 0.78/0.82      inference(symmetry,[status(thm)],[49])).
% 0.78/0.82  tff(109,plain,
% 0.78/0.82      (class_Rings_Odivision__ring(tc_Complex_Ocomplex) <=> class_Rings_Odivision__ring(tc_Complex_Ocomplex)),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(110,axiom,(class_Rings_Odivision__ring(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Odivision__ring')).
% 0.78/0.82  tff(111,plain,
% 0.78/0.82      (class_Rings_Odivision__ring(tc_Complex_Ocomplex)),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[110, 109])).
% 0.78/0.82  tff(112,plain,
% 0.78/0.82      (^[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))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(113,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[112])).
% 0.78/0.82  tff(114,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(115,plain,
% 0.78/0.82      (^[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)))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(116,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[115])).
% 0.78/0.82  tff(117,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')).
% 0.78/0.82  tff(118,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[117, 116])).
% 0.78/0.82  tff(119,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[118, 114])).
% 0.78/0.82  tff(120,plain,(
% 0.78/0.82      ![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)))),
% 0.78/0.82      inference(skolemize,[status(sab)],[119])).
% 0.78/0.82  tff(121,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[120, 113])).
% 0.78/0.82  tff(122,plain,
% 0.78/0.82      ((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(123,axiom,(~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_k_I2_J')).
% 0.78/0.82  tff(124,plain,
% 0.78/0.82      (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[123, 122])).
% 0.78/0.82  tff(125,plain,
% 0.78/0.82      (((~![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____)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(126,plain,
% 0.78/0.82      (((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____)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(127,plain,
% 0.78/0.82      (((~![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____))))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[126])).
% 0.78/0.82  tff(128,plain,
% 0.78/0.82      (((~![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____)))),
% 0.78/0.82      inference(transitivity,[status(thm)],[127, 125])).
% 0.78/0.82  tff(129,plain,
% 0.78/0.82      ((~![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)))),
% 0.78/0.82      inference(quant_inst,[status(thm)],[])).
% 0.78/0.82  tff(130,plain,
% 0.78/0.82      ((~![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____))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[129, 128])).
% 0.78/0.82  tff(131,plain,
% 0.78/0.82      (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____)),
% 0.78/0.82      inference(unit_resolution,[status(thm)],[130, 124, 121, 111])).
% 0.78/0.82  tff(132,plain,
% 0.78/0.82      (^[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)) | ((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)))))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(133,plain,
% 0.78/0.82      (![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))))))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[132])).
% 0.78/0.82  tff(134,plain,
% 0.78/0.82      (^[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)) | ((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)))))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(135,plain,
% 0.78/0.82      (![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))))))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[134])).
% 0.78/0.82  tff(136,plain,
% 0.78/0.82      (![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))))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(137,plain,
% 0.78/0.82      (^[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)) | ((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)))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(138,plain,
% 0.78/0.82      (![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))))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[137])).
% 0.78/0.82  tff(139,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')).
% 0.78/0.82  tff(140,plain,
% 0.78/0.82      (![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))))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[139, 138])).
% 0.78/0.82  tff(141,plain,
% 0.78/0.82      (![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))))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[140, 136])).
% 0.78/0.82  tff(142,plain,(
% 0.78/0.82      ![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))))),
% 0.78/0.82      inference(skolemize,[status(sab)],[141])).
% 0.78/0.82  tff(143,plain,
% 0.78/0.82      (![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))))))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[142, 135])).
% 0.78/0.82  tff(144,plain,
% 0.78/0.82      (![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))))))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[143, 133])).
% 0.78/0.82  tff(145,plain,
% 0.78/0.82      (((~![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))))))) | ((~class_Groups_Ozero(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_k____ = B_k!1)))) <=> ((~![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))))))) | (~class_Groups_Ozero(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_k____ = B_k!1)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(146,plain,
% 0.78/0.82      (((~class_Groups_Ozero(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_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)))))))) <=> ((~class_Groups_Ozero(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_k____ = B_k!1)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(147,plain,
% 0.78/0.82      (((~![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))))))) | ((~class_Groups_Ozero(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_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))))))))) <=> ((~![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))))))) | ((~class_Groups_Ozero(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_k____ = B_k!1))))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[146])).
% 0.78/0.82  tff(148,plain,
% 0.78/0.82      (((~![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))))))) | ((~class_Groups_Ozero(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_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))))))))) <=> ((~![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))))))) | (~class_Groups_Ozero(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_k____ = B_k!1)))),
% 0.78/0.82      inference(transitivity,[status(thm)],[147, 145])).
% 0.78/0.82  tff(149,plain,
% 0.78/0.82      ((~![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))))))) | ((~class_Groups_Ozero(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_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))))))))),
% 0.78/0.82      inference(quant_inst,[status(thm)],[])).
% 0.78/0.82  tff(150,plain,
% 0.78/0.82      ((~![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))))))) | (~class_Groups_Ozero(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_k____ = B_k!1))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[149, 148])).
% 0.78/0.82  tff(151,plain,
% 0.78/0.82      ((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)),
% 0.78/0.82      inference(unit_resolution,[status(thm)],[150, 144, 21])).
% 0.78/0.82  tff(152,plain,
% 0.78/0.82      ((~((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))))) | (v_k____ = B_k!1)),
% 0.78/0.82      inference(tautology,[status(thm)],[])).
% 0.78/0.82  tff(153,plain,
% 0.78/0.82      ((~((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))) | (v_k____ = B_k!1)),
% 0.78/0.82      inference(unit_resolution,[status(thm)],[152, 92])).
% 0.78/0.82  tff(154,plain,
% 0.78/0.82      (v_k____ = B_k!1),
% 0.78/0.82      inference(unit_resolution,[status(thm)],[153, 151])).
% 0.78/0.82  tff(155,plain,
% 0.78/0.82      (B_k!1 = v_k____),
% 0.78/0.82      inference(symmetry,[status(thm)],[154])).
% 0.78/0.82  tff(156,plain,
% 0.78/0.82      (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1) = c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, v_k____)),
% 0.78/0.82      inference(monotonicity,[status(thm)],[155])).
% 0.78/0.82  tff(157,plain,
% 0.78/0.82      (c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, B_k!1) = 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)))))),
% 0.78/0.82      inference(transitivity,[status(thm)],[156, 131, 108, 107])).
% 0.78/0.82  tff(158,plain,
% 0.78/0.82      (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, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), c_Polynomial_Odegree(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_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))))))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[104, 157])).
% 0.78/0.82  tff(159,plain,
% 0.78/0.82      (^[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))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(160,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[159])).
% 0.78/0.82  tff(161,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(162,plain,
% 0.78/0.82      (^[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)))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(163,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[162])).
% 0.78/0.82  tff(164,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')).
% 0.78/0.82  tff(165,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[164, 163])).
% 0.78/0.82  tff(166,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[165, 161])).
% 0.78/0.82  tff(167,plain,(
% 0.78/0.82      ![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)))),
% 0.78/0.82      inference(skolemize,[status(sab)],[166])).
% 0.78/0.82  tff(168,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[167, 160])).
% 0.78/0.82  tff(169,plain,
% 0.78/0.82      (~(B_k!1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 0.78/0.82      inference(or_elim,[status(thm)],[91])).
% 0.78/0.82  tff(170,plain,
% 0.78/0.82      (((~![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)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(171,plain,
% 0.78/0.82      (((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)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(172,plain,
% 0.78/0.82      (((~![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))))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[171])).
% 0.78/0.82  tff(173,plain,
% 0.78/0.82      (((~![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)))),
% 0.78/0.82      inference(transitivity,[status(thm)],[172, 170])).
% 0.78/0.82  tff(174,plain,
% 0.78/0.82      ((~![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)))),
% 0.78/0.82      inference(quant_inst,[status(thm)],[])).
% 0.78/0.82  tff(175,plain,
% 0.78/0.82      ((~![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))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[174, 173])).
% 0.78/0.82  tff(176,plain,
% 0.78/0.82      (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)),
% 0.78/0.82      inference(unit_resolution,[status(thm)],[175, 169, 168, 111])).
% 0.78/0.82  tff(177,plain,
% 0.78/0.82      (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))),
% 0.78/0.82      inference(symmetry,[status(thm)],[176])).
% 0.78/0.82  tff(178,plain,
% 0.78/0.82      (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____))),
% 0.78/0.82      inference(transitivity,[status(thm)],[177, 158, 106])).
% 0.78/0.82  tff(179,plain,
% 0.78/0.82      (c_Polynomial_Omonom(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_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))),
% 0.78/0.82      inference(monotonicity,[status(thm)],[178])).
% 0.78/0.82  tff(180,plain,
% 0.78/0.82      (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))),
% 0.78/0.82      inference(symmetry,[status(thm)],[179])).
% 0.78/0.82  tff(181,plain,
% 0.78/0.82      (class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) <=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(182,axiom,(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ocomm__semiring__0')).
% 0.78/0.82  tff(183,plain,
% 0.78/0.82      (class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[182, 181])).
% 0.78/0.82  tff(184,plain,
% 0.78/0.82      (^[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))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(185,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[184])).
% 0.78/0.82  tff(186,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(187,plain,
% 0.78/0.82      (^[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))))),
% 0.78/0.82      inference(bind,[status(th)],[])).
% 0.78/0.82  tff(188,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(quant_intro,[status(thm)],[187])).
% 0.78/0.82  tff(189,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')).
% 0.78/0.82  tff(190,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[189, 188])).
% 0.78/0.82  tff(191,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[190, 186])).
% 0.78/0.82  tff(192,plain,(
% 0.78/0.82      ![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)))),
% 0.78/0.82      inference(skolemize,[status(sab)],[191])).
% 0.78/0.82  tff(193,plain,
% 0.78/0.82      (![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)))),
% 0.78/0.82      inference(modus_ponens,[status(thm)],[192, 185])).
% 0.78/0.82  tff(194,plain,
% 0.78/0.82      (((~![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))))),
% 0.78/0.82      inference(rewrite,[status(thm)],[])).
% 0.78/0.82  tff(195,plain,
% 0.78/0.82      ((~![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))))),
% 0.78/0.83      inference(quant_inst,[status(thm)],[])).
% 0.78/0.83  tff(196,plain,
% 0.78/0.83      ((~![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)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[195, 194])).
% 0.78/0.83  tff(197,plain,
% 0.78/0.83      (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))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[196, 193, 183])).
% 0.78/0.83  tff(198,plain,
% 0.78/0.83      (((~![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)))))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(199,plain,
% 0.78/0.83      ((~![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)))))),
% 0.78/0.83      inference(quant_inst,[status(thm)],[])).
% 0.78/0.83  tff(200,plain,
% 0.78/0.83      ((~![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))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[199, 198])).
% 0.78/0.83  tff(201,plain,
% 0.78/0.83      (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)))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[200, 31, 21])).
% 0.78/0.83  tff(202,plain,
% 0.78/0.83      (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))))),
% 0.78/0.83      inference(monotonicity,[status(thm)],[201])).
% 0.78/0.83  tff(203,plain,
% 0.78/0.83      (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)))),
% 0.78/0.83      inference(symmetry,[status(thm)],[202])).
% 0.78/0.83  tff(204,plain,
% 0.78/0.83      (^[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))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(205,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[204])).
% 0.78/0.83  tff(206,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(207,plain,
% 0.78/0.83      (^[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))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(208,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[207])).
% 0.78/0.83  tff(209,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')).
% 0.78/0.83  tff(210,plain,
% 0.78/0.83      (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[209, 208])).
% 0.78/0.83  tff(211,plain,
% 0.78/0.83      (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[210, 206])).
% 0.78/0.83  tff(212,plain,(
% 0.78/0.83      ![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.78/0.83      inference(skolemize,[status(sab)],[211])).
% 0.78/0.83  tff(213,plain,
% 0.78/0.83      (![T_1: $i] : (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Oidom(T_1)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[212, 205])).
% 0.78/0.83  tff(214,plain,
% 0.78/0.83      (class_Rings_Oidom(tc_Complex_Ocomplex) <=> class_Rings_Oidom(tc_Complex_Ocomplex)),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(215,axiom,(class_Rings_Oidom(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Oidom')).
% 0.78/0.83  tff(216,plain,
% 0.78/0.83      (class_Rings_Oidom(tc_Complex_Ocomplex)),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[215, 214])).
% 0.78/0.83  tff(217,plain,
% 0.78/0.83      (((~![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)))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(218,plain,
% 0.78/0.83      ((~![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)))),
% 0.78/0.83      inference(quant_inst,[status(thm)],[])).
% 0.78/0.83  tff(219,plain,
% 0.78/0.83      ((~![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))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[218, 217])).
% 0.78/0.83  tff(220,plain,
% 0.78/0.83      (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[219, 216, 213])).
% 0.78/0.83  tff(221,plain,
% 0.78/0.83      (^[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)))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(222,plain,
% 0.78/0.83      (![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))))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[221])).
% 0.78/0.83  tff(223,plain,
% 0.78/0.83      (![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))))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(224,plain,
% 0.78/0.83      (^[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)))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(225,plain,
% 0.78/0.83      (![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))))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[224])).
% 0.78/0.83  tff(226,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')).
% 0.78/0.83  tff(227,plain,
% 0.78/0.83      (![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))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[226, 225])).
% 0.78/0.83  tff(228,plain,
% 0.78/0.83      (![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))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[227, 223])).
% 0.78/0.83  tff(229,plain,(
% 0.78/0.83      ![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))))),
% 0.78/0.83      inference(skolemize,[status(sab)],[228])).
% 0.78/0.83  tff(230,plain,
% 0.78/0.83      (![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))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[229, 222])).
% 0.78/0.83  tff(231,plain,
% 0.78/0.83      (((~![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)))))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(232,plain,
% 0.78/0.83      ((~![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)))))),
% 0.78/0.83      inference(quant_inst,[status(thm)],[])).
% 0.78/0.83  tff(233,plain,
% 0.78/0.83      ((~![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))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[232, 231])).
% 0.78/0.83  tff(234,plain,
% 0.78/0.83      ((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)))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[233, 230, 220])).
% 0.78/0.83  tff(235,plain,
% 0.78/0.83      (^[V_pa_2: $i, V_a_2: $i, T_a: $i] : refl(((~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)))))))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(236,plain,
% 0.78/0.83      (![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))))))))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[235])).
% 0.78/0.83  tff(237,plain,
% 0.78/0.83      (^[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)))))))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(238,plain,
% 0.78/0.83      (![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))))))))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[237])).
% 0.78/0.83  tff(239,plain,
% 0.78/0.83      (![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))))))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(240,plain,
% 0.78/0.83      (^[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)))))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(241,plain,
% 0.78/0.83      (![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))))))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[240])).
% 0.78/0.83  tff(242,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')).
% 0.78/0.83  tff(243,plain,
% 0.78/0.83      (![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))))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[242, 241])).
% 0.78/0.83  tff(244,plain,
% 0.78/0.83      (![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))))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[243, 239])).
% 0.78/0.83  tff(245,plain,(
% 0.78/0.83      ![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))))))),
% 0.78/0.83      inference(skolemize,[status(sab)],[244])).
% 0.78/0.83  tff(246,plain,
% 0.78/0.83      (![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))))))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[245, 238])).
% 0.78/0.83  tff(247,plain,
% 0.78/0.83      (![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))))))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[246, 236])).
% 0.78/0.83  tff(248,plain,
% 0.78/0.83      (((~![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))))))))) | ((~class_Groups_Ozero(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)))))) <=> ((~![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))))))))) | (~class_Groups_Ozero(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)))))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(249,plain,
% 0.78/0.83      (((~class_Groups_Ozero(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_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)))))))) <=> ((~class_Groups_Ozero(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)))))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(250,plain,
% 0.78/0.83      (((~![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))))))))) | ((~class_Groups_Ozero(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_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))))))))) <=> ((~![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))))))))) | ((~class_Groups_Ozero(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))))))),
% 0.78/0.83      inference(monotonicity,[status(thm)],[249])).
% 0.78/0.83  tff(251,plain,
% 0.78/0.83      (((~![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))))))))) | ((~class_Groups_Ozero(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_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))))))))) <=> ((~![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))))))))) | (~class_Groups_Ozero(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)))))),
% 0.78/0.83      inference(transitivity,[status(thm)],[250, 248])).
% 0.78/0.83  tff(252,plain,
% 0.78/0.83      ((~![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))))))))) | ((~class_Groups_Ozero(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_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))))))))),
% 0.78/0.83      inference(quant_inst,[status(thm)],[])).
% 0.78/0.83  tff(253,plain,
% 0.78/0.83      ((~![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))))))))) | (~class_Groups_Ozero(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))))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[252, 251])).
% 0.78/0.83  tff(254,plain,
% 0.78/0.83      ((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)))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[253, 247, 21])).
% 0.78/0.83  tff(255,plain,
% 0.78/0.83      (^[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))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(256,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[255])).
% 0.78/0.83  tff(257,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(258,plain,
% 0.78/0.83      (^[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))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(259,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[258])).
% 0.78/0.83  tff(260,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')).
% 0.78/0.83  tff(261,plain,
% 0.78/0.83      (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[260, 259])).
% 0.78/0.83  tff(262,plain,
% 0.78/0.83      (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[261, 257])).
% 0.78/0.83  tff(263,plain,(
% 0.78/0.83      ![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.78/0.83      inference(skolemize,[status(sab)],[262])).
% 0.78/0.83  tff(264,plain,
% 0.78/0.83      (![T_1: $i] : (class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__0(T_1)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[263, 256])).
% 0.78/0.83  tff(265,plain,
% 0.78/0.83      (((~![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)))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(266,plain,
% 0.78/0.83      ((~![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)))),
% 0.78/0.83      inference(quant_inst,[status(thm)],[])).
% 0.78/0.83  tff(267,plain,
% 0.78/0.83      ((~![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))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[266, 265])).
% 0.78/0.83  tff(268,plain,
% 0.78/0.83      (class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[267, 183, 264])).
% 0.78/0.83  tff(269,plain,
% 0.78/0.83      (^[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))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(270,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[269])).
% 0.78/0.83  tff(271,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(272,plain,
% 0.78/0.83      (^[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))))),
% 0.78/0.83      inference(bind,[status(th)],[])).
% 0.78/0.83  tff(273,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(quant_intro,[status(thm)],[272])).
% 0.78/0.83  tff(274,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')).
% 0.78/0.83  tff(275,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[274, 273])).
% 0.78/0.83  tff(276,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[275, 271])).
% 0.78/0.83  tff(277,plain,(
% 0.78/0.83      ![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)))),
% 0.78/0.83      inference(skolemize,[status(sab)],[276])).
% 0.78/0.83  tff(278,plain,
% 0.78/0.83      (![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)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[277, 270])).
% 0.78/0.83  tff(279,plain,
% 0.78/0.83      (((~![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))))),
% 0.78/0.83      inference(rewrite,[status(thm)],[])).
% 0.78/0.83  tff(280,plain,
% 0.78/0.83      ((~![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))))),
% 0.78/0.83      inference(quant_inst,[status(thm)],[])).
% 0.78/0.83  tff(281,plain,
% 0.78/0.83      ((~![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)))),
% 0.78/0.83      inference(modus_ponens,[status(thm)],[280, 279])).
% 0.78/0.83  tff(282,plain,
% 0.78/0.83      (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))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[281, 278, 268])).
% 0.78/0.83  tff(283,plain,
% 0.78/0.83      ((~((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))) | (~(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))))),
% 0.78/0.83      inference(tautology,[status(thm)],[])).
% 0.78/0.83  tff(284,plain,
% 0.78/0.83      (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))),
% 0.78/0.83      inference(unit_resolution,[status(thm)],[283, 282, 254])).
% 0.78/0.83  tff(285,plain,
% 0.78/0.83      ((~((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))))),
% 0.78/0.84      inference(tautology,[status(thm)],[])).
% 0.78/0.84  tff(286,plain,
% 0.78/0.84      (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))))))),
% 0.78/0.84      inference(unit_resolution,[status(thm)],[285, 284, 234])).
% 0.78/0.84  tff(287,plain,
% 0.78/0.84      (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))))),
% 0.78/0.84      inference(symmetry,[status(thm)],[286])).
% 0.78/0.84  tff(288,plain,
% 0.78/0.84      (^[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))))))),
% 0.78/0.84      inference(bind,[status(th)],[])).
% 0.78/0.84  tff(289,plain,
% 0.78/0.84      (![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)))))),
% 0.78/0.84      inference(quant_intro,[status(thm)],[288])).
% 0.78/0.84  tff(290,plain,
% 0.78/0.84      (![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)))))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(291,plain,
% 0.78/0.84      (^[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))))))),
% 0.78/0.84      inference(bind,[status(th)],[])).
% 0.78/0.84  tff(292,plain,
% 0.78/0.84      (![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)))))),
% 0.78/0.84      inference(quant_intro,[status(thm)],[291])).
% 0.78/0.84  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')).
% 0.78/0.84  tff(294,plain,
% 0.78/0.84      (![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)))))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[293, 292])).
% 0.78/0.84  tff(295,plain,
% 0.78/0.84      (![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)))))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[294, 290])).
% 0.78/0.84  tff(296,plain,(
% 0.78/0.84      ![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)))))),
% 0.78/0.84      inference(skolemize,[status(sab)],[295])).
% 0.78/0.84  tff(297,plain,
% 0.78/0.84      (![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)))))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[296, 289])).
% 0.78/0.84  tff(298,plain,
% 0.78/0.84      (((~![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))))))))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(299,plain,
% 0.78/0.84      ((~![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))))))))),
% 0.78/0.84      inference(quant_inst,[status(thm)],[])).
% 0.78/0.84  tff(300,plain,
% 0.78/0.84      ((~![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)))))))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[299, 298])).
% 0.78/0.84  tff(301,plain,
% 0.78/0.84      (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))))))),
% 0.78/0.84      inference(unit_resolution,[status(thm)],[300, 297, 183])).
% 0.78/0.84  tff(302,plain,
% 0.78/0.84      (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_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.78/0.84      inference(transitivity,[status(thm)],[301, 287, 203, 197, 180, 35, 18])).
% 0.78/0.84  tff(303,plain,
% 0.78/0.84      ((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, 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)), 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_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.78/0.84      inference(commutativity,[status(thm)],[])).
% 0.78/0.84  tff(304,plain,
% 0.78/0.84      (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)), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_k____, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.78/0.84      inference(monotonicity,[status(thm)],[93])).
% 0.78/0.84  tff(305,plain,
% 0.78/0.84      (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)), c_Polynomial_OpCons(tc_Complex_Ocomplex, B_k!1, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.78/0.84      inference(symmetry,[status(thm)],[304])).
% 0.78/0.84  tff(306,plain,
% 0.78/0.84      (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, 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))))),
% 0.78/0.84      inference(monotonicity,[status(thm)],[305])).
% 0.78/0.84  tff(307,plain,
% 0.78/0.84      (^[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))))),
% 0.78/0.84      inference(bind,[status(th)],[])).
% 0.78/0.84  tff(308,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(quant_intro,[status(thm)],[307])).
% 0.78/0.84  tff(309,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(310,plain,
% 0.78/0.84      (^[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))))),
% 0.78/0.84      inference(bind,[status(th)],[])).
% 0.78/0.84  tff(311,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(quant_intro,[status(thm)],[310])).
% 0.78/0.84  tff(312,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')).
% 0.78/0.84  tff(313,plain,
% 0.78/0.84      (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[312, 311])).
% 0.78/0.84  tff(314,plain,
% 0.78/0.84      (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[313, 309])).
% 0.78/0.84  tff(315,plain,(
% 0.78/0.84      ![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.78/0.84      inference(skolemize,[status(sab)],[314])).
% 0.78/0.84  tff(316,plain,
% 0.78/0.84      (![T_1: $i] : (class_Power_Opower(tc_Polynomial_Opoly(T_1)) | (~class_Rings_Ocomm__semiring__1(T_1)))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[315, 308])).
% 0.78/0.84  tff(317,plain,
% 0.78/0.84      (((~![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)))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(318,plain,
% 0.78/0.84      ((~![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)))),
% 0.78/0.84      inference(quant_inst,[status(thm)],[])).
% 0.78/0.84  tff(319,plain,
% 0.78/0.84      ((~![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))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[318, 317])).
% 0.78/0.84  tff(320,plain,
% 0.78/0.84      (class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),
% 0.78/0.84      inference(unit_resolution,[status(thm)],[319, 3, 316])).
% 0.78/0.84  tff(321,plain,
% 0.78/0.84      (^[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))))),
% 0.78/0.84      inference(bind,[status(th)],[])).
% 0.78/0.84  tff(322,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(quant_intro,[status(thm)],[321])).
% 0.78/0.84  tff(323,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(324,plain,
% 0.78/0.84      (^[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))))),
% 0.78/0.84      inference(bind,[status(th)],[])).
% 0.78/0.84  tff(325,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(quant_intro,[status(thm)],[324])).
% 0.78/0.84  tff(326,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')).
% 0.78/0.84  tff(327,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[326, 325])).
% 0.78/0.84  tff(328,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[327, 323])).
% 0.78/0.84  tff(329,plain,(
% 0.78/0.84      ![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)))),
% 0.78/0.84      inference(skolemize,[status(sab)],[328])).
% 0.78/0.84  tff(330,plain,
% 0.78/0.84      (![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)))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[329, 322])).
% 0.78/0.84  tff(331,plain,
% 0.78/0.84      (((~![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))))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(332,plain,
% 0.78/0.84      ((~![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))))),
% 0.78/0.84      inference(quant_inst,[status(thm)],[])).
% 0.78/0.84  tff(333,plain,
% 0.78/0.84      ((~![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)))),
% 0.78/0.84      inference(modus_ponens,[status(thm)],[332, 331])).
% 0.78/0.84  tff(334,plain,
% 0.78/0.84      ((~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)))),
% 0.78/0.84      inference(unit_resolution,[status(thm)],[333, 330])).
% 0.78/0.84  tff(335,plain,
% 0.78/0.84      (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))),
% 0.78/0.84      inference(unit_resolution,[status(thm)],[334, 320])).
% 0.78/0.84  tff(336,plain,
% 0.78/0.84      ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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)) = 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)))))),
% 0.78/0.84      inference(monotonicity,[status(thm)],[335, 306])).
% 0.78/0.84  tff(337,plain,
% 0.78/0.84      ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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, 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_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.78/0.84      inference(transitivity,[status(thm)],[336, 303])).
% 0.78/0.84  tff(338,plain,
% 0.78/0.84      ((~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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, 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_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),
% 0.78/0.84      inference(monotonicity,[status(thm)],[337])).
% 0.78/0.84  tff(339,plain,
% 0.78/0.84      ((~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), 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(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_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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))))))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(340,plain,
% 0.78/0.84      ((~(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, c_Polynomial_OpCons(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))))))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(341,plain,
% 0.78/0.84      ((~(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))))))),
% 0.78/0.84      inference(rewrite,[status(thm)],[])).
% 0.78/0.84  tff(342,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')).
% 0.78/0.84  tff(343,plain,
% 0.78/0.84      (~(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)))))),
% 0.88/0.89      inference(modus_ponens,[status(thm)],[342, 341])).
% 0.88/0.89  tff(344,plain,
% 0.88/0.89      (~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), 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(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)))))),
% 0.88/0.89      inference(modus_ponens,[status(thm)],[343, 340])).
% 0.88/0.89  tff(345,plain,
% 0.88/0.89      (~(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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)))))),
% 0.88/0.89      inference(modus_ponens,[status(thm)],[344, 339])).
% 0.88/0.89  tff(346,plain,
% 0.88/0.89      (~(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_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))),
% 0.88/0.89      inference(modus_ponens,[status(thm)],[345, 338])).
% 0.88/0.89  tff(347,plain,
% 0.88/0.89      ($false),
% 0.88/0.89      inference(unit_resolution,[status(thm)],[346, 302])).
% 0.88/0.89  % SZS output end Proof
%------------------------------------------------------------------------------