TSTP Solution File: SWW256+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW256+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 20:58:05 EDT 2022
% Result : Theorem 89.41s 57.83s
% Output : Proof 89.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW256+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.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 13:29:35 EDT 2022
% 0.12/0.34 % 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.
% 89.41/57.83 % SZS status Theorem
% 89.41/57.83 % SZS output start Proof
% 89.41/57.83 tff(c_Groups_Ozero__class_Ozero_type, type, (
% 89.41/57.83 c_Groups_Ozero__class_Ozero: $i > $i)).
% 89.41/57.83 tff(tc_Complex_Ocomplex_type, type, (
% 89.41/57.83 tc_Complex_Ocomplex: $i)).
% 89.41/57.83 tff(c_Groups_Oone__class_Oone_type, type, (
% 89.41/57.83 c_Groups_Oone__class_Oone: $i > $i)).
% 89.41/57.83 tff(hAPP_type, type, (
% 89.41/57.83 hAPP: ( $i * $i ) > $i)).
% 89.41/57.83 tff(v_k_____type, type, (
% 89.41/57.83 v_k____: $i)).
% 89.41/57.83 tff(c_Power_Opower__class_Opower_type, type, (
% 89.41/57.83 c_Power_Opower__class_Opower: $i > $i)).
% 89.41/57.83 tff(tc_Nat_Onat_type, type, (
% 89.41/57.83 tc_Nat_Onat: $i)).
% 89.41/57.83 tff(class_Power_Opower_type, type, (
% 89.41/57.83 class_Power_Opower: $i > $o)).
% 89.41/57.83 tff(class_Rings_Omult__zero_type, type, (
% 89.41/57.83 class_Rings_Omult__zero: $i > $o)).
% 89.41/57.83 tff(class_Rings_Ozero__neq__one_type, type, (
% 89.41/57.83 class_Rings_Ozero__neq__one: $i > $o)).
% 89.41/57.83 tff(class_Rings_Ono__zero__divisors_type, type, (
% 89.41/57.83 class_Rings_Ono__zero__divisors: $i > $o)).
% 89.41/57.83 tff(c_Groups_Ominus__class_Ominus_type, type, (
% 89.41/57.83 c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i)).
% 89.41/57.83 tff(c_Groups_Otimes__class_Otimes_type, type, (
% 89.41/57.83 c_Groups_Otimes__class_Otimes: $i > $i)).
% 89.41/57.83 tff(c_Orderings_Oord__class_Oless_type, type, (
% 89.41/57.83 c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o)).
% 89.41/57.83 tff(c_Nat_OSuc_type, type, (
% 89.41/57.83 c_Nat_OSuc: $i > $i)).
% 89.41/57.83 tff(c_Orderings_Oord__class_Oless__eq_type, type, (
% 89.41/57.83 c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o)).
% 89.41/57.83 tff(class_Rings_Olinordered__semidom_type, type, (
% 89.41/57.83 class_Rings_Olinordered__semidom: $i > $o)).
% 89.41/57.83 tff(c_Groups_Oplus__class_Oplus_type, type, (
% 89.41/57.83 c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i)).
% 89.41/57.83 tff(class_Groups_Oordered__comm__monoid__add_type, type, (
% 89.41/57.83 class_Groups_Oordered__comm__monoid__add: $i > $o)).
% 89.41/57.83 tff(class_Groups_Omonoid__mult_type, type, (
% 89.41/57.83 class_Groups_Omonoid__mult: $i > $o)).
% 89.41/57.83 tff(tptp_fun_B_x_27_type, type, (
% 89.41/57.83 tptp_fun_B_x_27: $i)).
% 89.41/57.83 tff(c_Polynomial_Opoly_type, type, (
% 89.41/57.83 c_Polynomial_Opoly: ( $i * $i ) > $i)).
% 89.41/57.83 tff(c_Polynomial_OpCons_type, type, (
% 89.41/57.83 c_Polynomial_OpCons: ( $i * $i * $i ) > $i)).
% 89.41/57.83 tff(tptp_fun_B_q_30_type, type, (
% 89.41/57.83 tptp_fun_B_q_30: $i)).
% 89.41/57.83 tff(tptp_fun_B_a_28_type, type, (
% 89.41/57.83 tptp_fun_B_a_28: $i)).
% 89.41/57.83 tff(tptp_fun_B_k_29_type, type, (
% 89.41/57.83 tptp_fun_B_k_29: $i)).
% 89.41/57.83 tff(1,plain,
% 89.41/57.83 (class_Power_Opower(tc_Complex_Ocomplex) <=> class_Power_Opower(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(2,axiom,(class_Power_Opower(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Power_Opower')).
% 89.41/57.83 tff(3,plain,
% 89.41/57.83 (class_Power_Opower(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[2, 1])).
% 89.41/57.83 tff(4,plain,
% 89.41/57.83 (class_Rings_Omult__zero(tc_Complex_Ocomplex) <=> class_Rings_Omult__zero(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(5,axiom,(class_Rings_Omult__zero(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Omult__zero')).
% 89.41/57.83 tff(6,plain,
% 89.41/57.83 (class_Rings_Omult__zero(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[5, 4])).
% 89.41/57.83 tff(7,plain,
% 89.41/57.83 (class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) <=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(8,axiom,(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ozero__neq__one')).
% 89.41/57.83 tff(9,plain,
% 89.41/57.83 (class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[8, 7])).
% 89.41/57.83 tff(10,plain,
% 89.41/57.83 (class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) <=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(11,axiom,(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ono__zero__divisors')).
% 89.41/57.83 tff(12,plain,
% 89.41/57.83 (class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[11, 10])).
% 89.41/57.83 tff(13,plain,
% 89.41/57.83 (^[V_n_2: $i, V_aa_2: $i, T_a: $i] : refl(((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(14,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[13])).
% 89.41/57.83 tff(15,plain,
% 89.41/57.83 (^[V_n_2: $i, V_aa_2: $i, T_a: $i] : trans(monotonicity(trans(monotonicity(rewrite((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)) <=> (~((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))), ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) <=> (~(~((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))))), rewrite((~(~((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a)))), ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))))), rewrite(((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))), (((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> (((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), rewrite((((~class_Power_Opower(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))), (((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(16,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[15])).
% 89.41/57.83 tff(17,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(18,plain,
% 89.41/57.83 (^[V_n_2: $i, V_aa_2: $i, T_a: $i] : trans(monotonicity(trans(monotonicity(rewrite(((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) <=> (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a))), ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) <=> ((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)))), rewrite(((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) <=> (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))), ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) <=> (class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)))), (((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), rewrite(((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))), (((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(19,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[18])).
% 89.41/57.83 tff(20,axiom,(![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((((class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a)) & class_Rings_Ono__zero__divisors(T_a)) & class_Rings_Ozero__neq__one(T_a)) => ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_power__eq__0__iff')).
% 89.41/57.83 tff(21,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[20, 19])).
% 89.41/57.83 tff(22,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[21, 17])).
% 89.41/57.83 tff(23,plain,(
% 89.41/57.83 ![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~(class_Power_Opower(T_a) & class_Rings_Omult__zero(T_a) & class_Rings_Ono__zero__divisors(T_a) & class_Rings_Ozero__neq__one(T_a))) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> ((V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)) & (~(V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(skolemize,[status(sab)],[22])).
% 89.41/57.83 tff(24,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[23, 16])).
% 89.41/57.83 tff(25,plain,
% 89.41/57.83 (![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[24, 14])).
% 89.41/57.83 tff(26,plain,
% 89.41/57.83 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(27,plain,
% 89.41/57.83 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(28,plain,
% 89.41/57.83 (((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(29,plain,
% 89.41/57.83 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 89.41/57.83 inference(monotonicity,[status(thm)],[28])).
% 89.41/57.83 tff(30,plain,
% 89.41/57.83 (((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 89.41/57.83 inference(transitivity,[status(thm)],[29, 27])).
% 89.41/57.83 tff(31,plain,
% 89.41/57.83 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | ((~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(monotonicity,[status(thm)],[30])).
% 89.41/57.83 tff(32,plain,
% 89.41/57.83 (((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) <=> ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 89.41/57.83 inference(transitivity,[status(thm)],[31, 26])).
% 89.41/57.83 tff(33,plain,
% 89.41/57.83 ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~((~(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))),
% 89.41/57.83 inference(quant_inst,[status(thm)],[])).
% 89.41/57.83 tff(34,plain,
% 89.41/57.83 ((~![V_n_2: $i, V_aa_2: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~class_Rings_Ono__zero__divisors(T_a)) | (~class_Rings_Omult__zero(T_a)) | (~class_Rings_Ozero__neq__one(T_a)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_aa_2), V_n_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (~((~(V_aa_2 = c_Groups_Ozero__class_Ozero(T_a))) | (V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))) | (~class_Rings_Omult__zero(tc_Complex_Ocomplex)) | (~class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex)) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[33, 32])).
% 89.41/57.83 tff(35,plain,
% 89.41/57.83 ((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[34, 25, 12, 9, 6, 3])).
% 89.41/57.83 tff(36,plain,
% 89.41/57.83 ((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(37,axiom,(~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_kas_I2_J')).
% 89.41/57.83 tff(38,plain,
% 89.41/57.83 (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[37, 36])).
% 89.41/57.83 tff(39,plain,
% 89.41/57.83 ((~((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.83 inference(tautology,[status(thm)],[])).
% 89.41/57.83 tff(40,plain,
% 89.41/57.83 ((~((hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[39, 38])).
% 89.41/57.83 tff(41,plain,
% 89.41/57.83 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[40, 35])).
% 89.41/57.83 tff(42,plain,
% 89.41/57.83 (^[V_n_2: $i, V_m_2: $i] : refl(((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2))) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(43,plain,
% 89.41/57.83 (![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2))) <=> ![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2)))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[42])).
% 89.41/57.83 tff(44,plain,
% 89.41/57.83 (![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2))) <=> ![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(45,axiom,(![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_not__less__eq')).
% 89.41/57.83 tff(46,plain,
% 89.41/57.83 (![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[45, 44])).
% 89.41/57.83 tff(47,plain,(
% 89.41/57.83 ![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2)))),
% 89.41/57.83 inference(skolemize,[status(sab)],[46])).
% 89.41/57.83 tff(48,plain,
% 89.41/57.83 (![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[47, 43])).
% 89.41/57.83 tff(49,plain,
% 89.41/57.83 ((~![V_n_2: $i, V_m_2: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, c_Nat_OSuc(V_m_2)))) | ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____)))),
% 89.41/57.83 inference(quant_inst,[status(thm)],[])).
% 89.41/57.83 tff(50,plain,
% 89.41/57.83 ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[49, 48])).
% 89.41/57.83 tff(51,plain,
% 89.41/57.83 ((c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(52,axiom,(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_One__nat__def')).
% 89.41/57.83 tff(53,plain,
% 89.41/57.83 (c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[52, 51])).
% 89.41/57.83 tff(54,plain,
% 89.41/57.83 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)) <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(monotonicity,[status(thm)],[53])).
% 89.41/57.83 tff(55,plain,
% 89.41/57.83 (class_Rings_Olinordered__semidom(tc_Nat_Onat) <=> class_Rings_Olinordered__semidom(tc_Nat_Onat)),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(56,axiom,(class_Rings_Olinordered__semidom(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Nat__Onat__Rings_Olinordered__semidom')).
% 89.41/57.83 tff(57,plain,
% 89.41/57.83 (class_Rings_Olinordered__semidom(tc_Nat_Onat)),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[56, 55])).
% 89.41/57.83 tff(58,plain,
% 89.41/57.83 (^[T_a: $i] : refl(((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(59,plain,
% 89.41/57.83 (![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a))) <=> ![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[58])).
% 89.41/57.83 tff(60,plain,
% 89.41/57.83 (![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a))) <=> ![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(61,plain,
% 89.41/57.83 (^[T_a: $i] : rewrite((class_Rings_Olinordered__semidom(T_a) => c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(62,plain,
% 89.41/57.83 (![T_a: $i] : (class_Rings_Olinordered__semidom(T_a) => c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a))) <=> ![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[61])).
% 89.41/57.83 tff(63,axiom,(![T_a: $i] : (class_Rings_Olinordered__semidom(T_a) => c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_zero__le__one')).
% 89.41/57.83 tff(64,plain,
% 89.41/57.83 (![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[63, 62])).
% 89.41/57.83 tff(65,plain,
% 89.41/57.83 (![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[64, 60])).
% 89.41/57.83 tff(66,plain,(
% 89.41/57.83 ![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.83 inference(skolemize,[status(sab)],[65])).
% 89.41/57.83 tff(67,plain,
% 89.41/57.83 (![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[66, 59])).
% 89.41/57.83 tff(68,plain,
% 89.41/57.83 (((~![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))) | ((~class_Rings_Olinordered__semidom(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)))) <=> ((~![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))) | (~class_Rings_Olinordered__semidom(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(69,plain,
% 89.41/57.83 ((~![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))) | ((~class_Rings_Olinordered__semidom(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
% 89.41/57.83 inference(quant_inst,[status(thm)],[])).
% 89.41/57.83 tff(70,plain,
% 89.41/57.83 ((~![T_a: $i] : ((~class_Rings_Olinordered__semidom(T_a)) | c_Orderings_Oord__class_Oless__eq(T_a, c_Groups_Ozero__class_Ozero(T_a), c_Groups_Oone__class_Oone(T_a)))) | (~class_Rings_Olinordered__semidom(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[69, 68])).
% 89.41/57.83 tff(71,plain,
% 89.41/57.83 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat))),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 89.41/57.83 tff(72,plain,
% 89.41/57.83 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[71, 54])).
% 89.41/57.83 tff(73,plain,
% 89.41/57.83 (^[V_nat_H: $i] : refl((~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H))) <=> (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(74,plain,
% 89.41/57.83 (![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H))) <=> ![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H)))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[73])).
% 89.41/57.83 tff(75,plain,
% 89.41/57.83 (![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H))) <=> ![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(76,axiom,(![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_nat_Osimps_I2_J')).
% 89.41/57.83 tff(77,plain,
% 89.41/57.83 (![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[76, 75])).
% 89.41/57.83 tff(78,plain,(
% 89.41/57.83 ![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H)))),
% 89.41/57.83 inference(skolemize,[status(sab)],[77])).
% 89.41/57.83 tff(79,plain,
% 89.41/57.83 (![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H)))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[78, 74])).
% 89.41/57.83 tff(80,plain,
% 89.41/57.83 ((~![V_nat_H: $i] : (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(V_nat_H)))) | (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 89.41/57.83 inference(quant_inst,[status(thm)],[])).
% 89.41/57.83 tff(81,plain,
% 89.41/57.83 (~(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[80, 79])).
% 89.41/57.83 tff(82,plain,
% 89.41/57.83 (^[V_n: $i, V_m: $i] : refl((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)))) <=> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(83,plain,
% 89.41/57.83 (![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)))) <=> ![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[82])).
% 89.41/57.83 tff(84,plain,
% 89.41/57.83 (![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)))) <=> ![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(85,plain,
% 89.41/57.83 (^[V_n: $i, V_m: $i] : trans(monotonicity(rewrite(((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n)) => (V_m = c_Nat_OSuc(V_n))) <=> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)))), ((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)) => ((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n)) => (V_m = c_Nat_OSuc(V_n)))) <=> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)) => (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)))))), rewrite((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)) => (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)))) <=> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))), ((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)) => ((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n)) => (V_m = c_Nat_OSuc(V_n)))) <=> (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(86,plain,
% 89.41/57.83 (![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)) => ((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n)) => (V_m = c_Nat_OSuc(V_n)))) <=> ![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[85])).
% 89.41/57.83 tff(87,axiom,(![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n)) => ((~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n)) => (V_m = c_Nat_OSuc(V_n))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_le__SucE')).
% 89.41/57.83 tff(88,plain,
% 89.41/57.83 (![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[87, 86])).
% 89.41/57.83 tff(89,plain,
% 89.41/57.83 (![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[88, 84])).
% 89.41/57.83 tff(90,plain,(
% 89.41/57.83 ![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))),
% 89.41/57.83 inference(skolemize,[status(sab)],[89])).
% 89.41/57.83 tff(91,plain,
% 89.41/57.83 (![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[90, 83])).
% 89.41/57.83 tff(92,plain,
% 89.41/57.83 (((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | ((c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <=> ((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(93,plain,
% 89.41/57.83 ((c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(94,plain,
% 89.41/57.83 (((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | ((c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 89.41/57.83 inference(monotonicity,[status(thm)],[93])).
% 89.41/57.83 tff(95,plain,
% 89.41/57.83 (((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) <=> ((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(transitivity,[status(thm)],[94, 92])).
% 89.41/57.83 tff(96,plain,
% 89.41/57.83 ((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),
% 89.41/57.83 inference(quant_inst,[status(thm)],[])).
% 89.41/57.83 tff(97,plain,
% 89.41/57.83 ((~![V_n: $i, V_m: $i] : (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, V_n) | (V_m = c_Nat_OSuc(V_n)) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, V_m, c_Nat_OSuc(V_n))))) | (c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[96, 95])).
% 89.41/57.83 tff(98,plain,
% 89.41/57.83 (c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[97, 91, 81, 72])).
% 89.41/57.83 tff(99,plain,
% 89.41/57.83 (^[V_i: $i, V_j: $i] : refl((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i)) <=> (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i)))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(100,plain,
% 89.41/57.83 (![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i)) <=> ![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[99])).
% 89.41/57.83 tff(101,plain,
% 89.41/57.83 (![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i)) <=> ![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(102,axiom,(![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_not__add__less2')).
% 89.41/57.83 tff(103,plain,
% 89.41/57.83 (![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[102, 101])).
% 89.41/57.83 tff(104,plain,(
% 89.41/57.83 ![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i))),
% 89.41/57.83 inference(skolemize,[status(sab)],[103])).
% 89.41/57.83 tff(105,plain,
% 89.41/57.83 (![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[104, 100])).
% 89.41/57.83 tff(106,plain,
% 89.41/57.83 ((~![V_i: $i, V_j: $i] : (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j, V_i), V_i))) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.83 inference(quant_inst,[status(thm)],[])).
% 89.41/57.83 tff(107,plain,
% 89.41/57.83 (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.83 inference(unit_resolution,[status(thm)],[106, 105])).
% 89.41/57.83 tff(108,plain,
% 89.41/57.83 (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) <=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(109,axiom,(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Nat__Onat__Groups_Oordered__comm__monoid__add')).
% 89.41/57.83 tff(110,plain,
% 89.41/57.83 (class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[109, 108])).
% 89.41/57.83 tff(111,plain,
% 89.41/57.83 (^[V_b: $i, V_a: $i, T_a: $i] : refl((c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)))) <=> (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(112,plain,
% 89.41/57.83 (![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)))) <=> ![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[111])).
% 89.41/57.83 tff(113,plain,
% 89.41/57.83 (![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)))) <=> ![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.83 inference(rewrite,[status(thm)],[])).
% 89.41/57.83 tff(114,plain,
% 89.41/57.83 (^[V_b: $i, V_a: $i, T_a: $i] : trans(monotonicity(trans(monotonicity(rewrite((c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)) => c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a))) <=> ((~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))) | c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)))), ((c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => (c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)) => c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)))) <=> (c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => ((~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))) | c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)))))), rewrite((c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => ((~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))) | c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)))) <=> (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))), ((c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => (c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)) => c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)))) <=> (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)))))), ((class_Groups_Oordered__comm__monoid__add(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => (c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)) => c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a))))) <=> (class_Groups_Oordered__comm__monoid__add(T_a) => (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))))), rewrite((class_Groups_Oordered__comm__monoid__add(T_a) => (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) <=> (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))), ((class_Groups_Oordered__comm__monoid__add(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => (c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)) => c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a))))) <=> (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))))),
% 89.41/57.83 inference(bind,[status(th)],[])).
% 89.41/57.83 tff(115,plain,
% 89.41/57.83 (![V_b: $i, V_a: $i, T_a: $i] : (class_Groups_Oordered__comm__monoid__add(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => (c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)) => c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a))))) <=> ![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.83 inference(quant_intro,[status(thm)],[114])).
% 89.41/57.83 tff(116,axiom,(![V_b: $i, V_a: $i, T_a: $i] : (class_Groups_Oordered__comm__monoid__add(T_a) => (c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a)) => (c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a)) => c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_add__neg__nonpos')).
% 89.41/57.83 tff(117,plain,
% 89.41/57.83 (![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[116, 115])).
% 89.41/57.83 tff(118,plain,
% 89.41/57.83 (![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[117, 113])).
% 89.41/57.83 tff(119,plain,(
% 89.41/57.83 ![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.83 inference(skolemize,[status(sab)],[118])).
% 89.41/57.83 tff(120,plain,
% 89.41/57.83 (![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.83 inference(modus_ponens,[status(thm)],[119, 112])).
% 89.41/57.83 tff(121,plain,
% 89.41/57.83 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(122,plain,
% 89.41/57.84 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) <=> ((~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(123,plain,
% 89.41/57.84 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 89.41/57.84 inference(monotonicity,[status(thm)],[122])).
% 89.41/57.84 tff(124,plain,
% 89.41/57.84 (((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.84 inference(transitivity,[status(thm)],[123, 121])).
% 89.41/57.84 tff(125,plain,
% 89.41/57.84 ((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
% 89.41/57.84 inference(quant_inst,[status(thm)],[])).
% 89.41/57.84 tff(126,plain,
% 89.41/57.84 ((~![V_b: $i, V_a: $i, T_a: $i] : (c_Orderings_Oord__class_Oless(T_a, c_Groups_Oplus__class_Oplus(T_a, V_a, V_b), c_Groups_Ozero__class_Ozero(T_a)) | (~class_Groups_Oordered__comm__monoid__add(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, V_a, c_Groups_Ozero__class_Ozero(T_a))) | (~c_Orderings_Oord__class_Oless__eq(T_a, V_b, c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[125, 124])).
% 89.41/57.84 tff(127,plain,
% 89.41/57.84 ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (~c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 89.41/57.84 inference(unit_resolution,[status(thm)],[126, 120, 110, 107])).
% 89.41/57.84 tff(128,plain,
% 89.41/57.84 (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 89.41/57.84 inference(unit_resolution,[status(thm)],[127, 98])).
% 89.41/57.84 tff(129,plain,
% 89.41/57.84 ((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____)))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, v_k____, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))),
% 89.41/57.84 inference(tautology,[status(thm)],[])).
% 89.41/57.84 tff(130,plain,
% 89.41/57.84 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))),
% 89.41/57.84 inference(unit_resolution,[status(thm)],[129, 128, 50])).
% 89.41/57.84 tff(131,plain,
% 89.41/57.84 (^[V_m: $i, V_n: $i] : refl((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)))) <=> (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(132,plain,
% 89.41/57.84 (![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)))) <=> ![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[131])).
% 89.41/57.84 tff(133,plain,
% 89.41/57.84 (![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)))) <=> ![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(134,plain,
% 89.41/57.84 (^[V_m: $i, V_n: $i] : trans(monotonicity(rewrite((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)) => (V_m = V_n)) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))) | (V_m = V_n))), (((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m)) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)) => (V_m = V_n))) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m)) => ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))) | (V_m = V_n))))), rewrite(((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m)) => ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))) | (V_m = V_n))) <=> (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))), (((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m)) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)) => (V_m = V_n))) <=> (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(135,plain,
% 89.41/57.84 (![V_m: $i, V_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m)) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)) => (V_m = V_n))) <=> ![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[134])).
% 89.41/57.84 tff(136,axiom,(![V_m: $i, V_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m)) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m)) => (V_m = V_n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_less__antisym')).
% 89.41/57.84 tff(137,plain,
% 89.41/57.84 (![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[136, 135])).
% 89.41/57.84 tff(138,plain,
% 89.41/57.84 (![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[137, 133])).
% 89.41/57.84 tff(139,plain,(
% 89.41/57.84 ![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))),
% 89.41/57.84 inference(skolemize,[status(sab)],[138])).
% 89.41/57.84 tff(140,plain,
% 89.41/57.84 (![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[139, 132])).
% 89.41/57.84 tff(141,plain,
% 89.41/57.84 (((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))))) <=> ((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(142,plain,
% 89.41/57.84 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____)))) <=> ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(143,plain,
% 89.41/57.84 (((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))))) <=> ((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____)))))),
% 89.41/57.84 inference(monotonicity,[status(thm)],[142])).
% 89.41/57.84 tff(144,plain,
% 89.41/57.84 (((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))))) <=> ((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))))),
% 89.41/57.84 inference(transitivity,[status(thm)],[143, 141])).
% 89.41/57.84 tff(145,plain,
% 89.41/57.84 ((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____))))),
% 89.41/57.84 inference(quant_inst,[status(thm)],[])).
% 89.41/57.84 tff(146,plain,
% 89.41/57.84 ((~![V_m: $i, V_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, V_m) | (V_m = V_n) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n, c_Nat_OSuc(V_m))))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____)))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[145, 144])).
% 89.41/57.84 tff(147,plain,
% 89.41/57.84 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(v_k____)))),
% 89.41/57.84 inference(unit_resolution,[status(thm)],[146, 38, 140])).
% 89.41/57.84 tff(148,plain,
% 89.41/57.84 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)),
% 89.41/57.84 inference(unit_resolution,[status(thm)],[147, 130])).
% 89.41/57.84 tff(149,plain,
% 89.41/57.84 (class_Groups_Omonoid__mult(tc_Complex_Ocomplex) <=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex)),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(150,axiom,(class_Groups_Omonoid__mult(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Groups_Omonoid__mult')).
% 89.41/57.84 tff(151,plain,
% 89.41/57.84 (class_Groups_Omonoid__mult(tc_Complex_Ocomplex)),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[150, 149])).
% 89.41/57.84 tff(152,plain,
% 89.41/57.84 (^[V_x: $i, V_n: $i, T_a: $i] : refl(((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n))) <=> ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(153,plain,
% 89.41/57.84 (![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n))) <=> ![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[152])).
% 89.41/57.84 tff(154,plain,
% 89.41/57.84 (![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n))) <=> ![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(155,plain,
% 89.41/57.84 (^[V_x: $i, V_n: $i, T_a: $i] : trans(monotonicity(rewrite((c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n))) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)))), ((class_Groups_Omonoid__mult(T_a) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)))) <=> (class_Groups_Omonoid__mult(T_a) => ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)))))), rewrite((class_Groups_Omonoid__mult(T_a) => ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)))) <=> ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))), ((class_Groups_Omonoid__mult(T_a) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)))) <=> ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(156,plain,
% 89.41/57.84 (![V_x: $i, V_n: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)))) <=> ![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[155])).
% 89.41/57.84 tff(157,axiom,(![V_x: $i, V_n: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_realpow__minus__mult')).
% 89.41/57.84 tff(158,plain,
% 89.41/57.84 (![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[157, 156])).
% 89.41/57.84 tff(159,plain,
% 89.41/57.84 (![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[158, 154])).
% 89.41/57.84 tff(160,plain,(
% 89.41/57.84 ![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))),
% 89.41/57.84 inference(skolemize,[status(sab)],[159])).
% 89.41/57.84 tff(161,plain,
% 89.41/57.84 (![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[160, 153])).
% 89.41/57.84 tff(162,plain,
% 89.41/57.84 (((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)))) <=> ((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(163,plain,
% 89.41/57.84 (((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____))) <=> ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(164,plain,
% 89.41/57.84 (((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)))) <=> ((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____))))),
% 89.41/57.84 inference(monotonicity,[status(thm)],[163])).
% 89.41/57.84 tff(165,plain,
% 89.41/57.84 (((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)))) <=> ((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)))),
% 89.41/57.84 inference(transitivity,[status(thm)],[164, 162])).
% 89.41/57.84 tff(166,plain,
% 89.41/57.84 ((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)))),
% 89.41/57.84 inference(quant_inst,[status(thm)],[])).
% 89.41/57.84 tff(167,plain,
% 89.41/57.84 ((~![V_x: $i, V_n: $i, T_a: $i] : ((hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_x), V_n)) | (~class_Groups_Omonoid__mult(T_a)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n)))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), v_k____)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[166, 165])).
% 89.41/57.84 tff(168,plain,
% 89.41/57.84 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), v_k____)),
% 89.41/57.84 inference(unit_resolution,[status(thm)],[167, 161, 151, 148])).
% 89.41/57.84 tff(169,plain,
% 89.41/57.84 (^[V_n: $i, V_a: $i, T_a: $i] : refl(((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)))) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(170,plain,
% 89.41/57.84 (![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)))) <=> ![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[169])).
% 89.41/57.84 tff(171,plain,
% 89.41/57.84 (![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)))) <=> ![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(172,plain,
% 89.41/57.84 (^[V_n: $i, V_a: $i, T_a: $i] : rewrite((class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)))) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(173,plain,
% 89.41/57.84 (![V_n: $i, V_a: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)))) <=> ![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[172])).
% 89.41/57.84 tff(174,axiom,(![V_n: $i, V_a: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_power__commutes')).
% 89.41/57.84 tff(175,plain,
% 89.41/57.84 (![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[174, 173])).
% 89.41/57.84 tff(176,plain,
% 89.41/57.84 (![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[175, 171])).
% 89.41/57.84 tff(177,plain,(
% 89.41/57.84 ![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))),
% 89.41/57.84 inference(skolemize,[status(sab)],[176])).
% 89.41/57.84 tff(178,plain,
% 89.41/57.84 (![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[177, 170])).
% 89.41/57.84 tff(179,plain,
% 89.41/57.84 (((~![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) <=> ((~![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(180,plain,
% 89.41/57.84 ((~![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 89.41/57.84 inference(quant_inst,[status(thm)],[])).
% 89.41/57.84 tff(181,plain,
% 89.41/57.84 ((~![V_n: $i, V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n)), V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_a), V_n))))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[180, 179])).
% 89.41/57.84 tff(182,plain,
% 89.41/57.84 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 89.41/57.84 inference(unit_resolution,[status(thm)],[181, 178, 151])).
% 89.41/57.84 tff(183,plain,
% 89.41/57.84 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 89.41/57.84 inference(symmetry,[status(thm)],[182])).
% 89.41/57.84 tff(184,plain,
% 89.41/57.84 (^[B_x: $i, B_y: $i] : refl((hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(185,plain,
% 89.41/57.84 (![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) <=> ![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[184])).
% 89.41/57.84 tff(186,plain,
% 89.41/57.84 (^[B_x: $i, B_y: $i] : rewrite((~(~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 89.41/57.84 inference(bind,[status(th)],[])).
% 89.41/57.84 tff(187,plain,
% 89.41/57.84 (![B_x: $i, B_y: $i] : (~(~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) <=> ![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.84 inference(quant_intro,[status(thm)],[186])).
% 89.41/57.84 tff(188,plain,
% 89.41/57.84 ((~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) <=> (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(189,plain,
% 89.41/57.84 ((~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))) <=> (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(190,plain,
% 89.41/57.84 ((~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))) <=> (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))),
% 89.41/57.84 inference(rewrite,[status(thm)],[])).
% 89.41/57.84 tff(191,axiom,(~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 89.41/57.84 tff(192,plain,
% 89.41/57.84 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.84 inference(modus_ponens,[status(thm)],[191, 190])).
% 89.41/57.84 tff(193,plain,
% 89.41/57.84 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[192, 190])).
% 89.41/57.85 tff(194,plain,
% 89.41/57.85 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[193, 190])).
% 89.41/57.85 tff(195,plain,
% 89.41/57.85 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[194, 190])).
% 89.41/57.85 tff(196,plain,
% 89.41/57.85 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[195, 190])).
% 89.41/57.85 tff(197,plain,
% 89.41/57.85 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[196, 190])).
% 89.41/57.85 tff(198,plain,
% 89.41/57.85 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[197, 190])).
% 89.41/57.85 tff(199,plain,
% 89.41/57.85 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[198, 189])).
% 89.41/57.85 tff(200,plain,
% 89.41/57.85 (~?[B_x: $i, B_y: $i] : (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[199, 188])).
% 89.41/57.85 tff(201,plain,
% 89.41/57.85 (^[B_x: $i, B_y: $i] : refl($oeq((~(~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))), (~(~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))),
% 89.41/57.85 inference(bind,[status(th)],[])).
% 89.41/57.85 tff(202,plain,(
% 89.41/57.85 ![B_x: $i, B_y: $i] : (~(~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))),
% 89.41/57.85 inference(nnf-neg,[status(sab)],[200, 201])).
% 89.41/57.85 tff(203,plain,
% 89.41/57.85 (![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[202, 187])).
% 89.41/57.85 tff(204,plain,
% 89.41/57.85 (![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[203, 185])).
% 89.41/57.85 tff(205,plain,
% 89.41/57.85 ((~![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.85 inference(quant_inst,[status(thm)],[])).
% 89.41/57.85 tff(206,plain,
% 89.41/57.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 89.41/57.85 inference(unit_resolution,[status(thm)],[205, 204])).
% 89.41/57.85 tff(207,plain,
% 89.41/57.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 89.41/57.85 inference(symmetry,[status(thm)],[206])).
% 89.41/57.85 tff(208,plain,
% 89.41/57.85 ((~![B_x: $i, B_y: $i] : (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_x), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_y), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_y), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.85 inference(quant_inst,[status(thm)],[])).
% 89.41/57.85 tff(209,plain,
% 89.41/57.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 89.41/57.85 inference(unit_resolution,[status(thm)],[208, 204])).
% 89.41/57.85 tff(210,plain,
% 89.41/57.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_x!27), B_k!29)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, B_a!28, B_q!30)), B_x!27)))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 89.41/57.85 inference(symmetry,[status(thm)],[209])).
% 89.41/57.85 tff(211,plain,
% 89.41/57.85 (^[V_a: $i, T_a: $i] : refl(((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)))),
% 89.41/57.85 inference(bind,[status(th)],[])).
% 89.41/57.85 tff(212,plain,
% 89.41/57.85 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 89.41/57.85 inference(quant_intro,[status(thm)],[211])).
% 89.41/57.85 tff(213,plain,
% 89.41/57.85 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 89.41/57.85 inference(rewrite,[status(thm)],[])).
% 89.41/57.85 tff(214,plain,
% 89.41/57.85 (^[V_a: $i, T_a: $i] : rewrite((class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)))),
% 89.41/57.85 inference(bind,[status(th)],[])).
% 89.41/57.85 tff(215,plain,
% 89.41/57.85 (![V_a: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a)) <=> ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 89.41/57.85 inference(quant_intro,[status(thm)],[214])).
% 89.41/57.85 tff(216,axiom,(![V_a: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_mult__1__left')).
% 89.41/57.85 tff(217,plain,
% 89.41/57.85 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[216, 215])).
% 89.41/57.85 tff(218,plain,
% 89.41/57.85 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[217, 213])).
% 89.41/57.85 tff(219,plain,(
% 89.41/57.85 ![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 89.41/57.85 inference(skolemize,[status(sab)],[218])).
% 89.41/57.85 tff(220,plain,
% 89.41/57.85 (![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[219, 212])).
% 89.41/57.85 tff(221,plain,
% 89.41/57.85 (((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) <=> ((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.85 inference(rewrite,[status(thm)],[])).
% 89.41/57.85 tff(222,plain,
% 89.41/57.85 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 89.41/57.85 inference(quant_inst,[status(thm)],[])).
% 89.41/57.85 tff(223,plain,
% 89.41/57.85 ((~![V_a: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Oone__class_Oone(T_a)), V_a) = V_a))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[222, 221])).
% 89.41/57.85 tff(224,plain,
% 89.41/57.85 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
% 89.41/57.85 inference(unit_resolution,[status(thm)],[223, 220, 151])).
% 89.41/57.85 tff(225,plain,
% 89.41/57.85 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 89.41/57.85 inference(symmetry,[status(thm)],[224])).
% 89.41/57.85 tff(226,plain,
% 89.41/57.85 (^[V_n: $i, T_a: $i] : refl(((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))))),
% 89.41/57.85 inference(bind,[status(th)],[])).
% 89.41/57.85 tff(227,plain,
% 89.41/57.85 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.85 inference(quant_intro,[status(thm)],[226])).
% 89.41/57.85 tff(228,plain,
% 89.41/57.85 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.85 inference(rewrite,[status(thm)],[])).
% 89.41/57.85 tff(229,plain,
% 89.41/57.85 (^[V_n: $i, T_a: $i] : rewrite((class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))))),
% 89.41/57.85 inference(bind,[status(th)],[])).
% 89.41/57.85 tff(230,plain,
% 89.41/57.85 (![V_n: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a))) <=> ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.85 inference(quant_intro,[status(thm)],[229])).
% 89.41/57.85 tff(231,axiom,(![V_n: $i, T_a: $i] : (class_Groups_Omonoid__mult(T_a) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_power__one')).
% 89.41/57.85 tff(232,plain,
% 89.41/57.85 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[231, 230])).
% 89.41/57.85 tff(233,plain,
% 89.41/57.85 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[232, 228])).
% 89.41/57.85 tff(234,plain,(
% 89.41/57.85 ![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.85 inference(skolemize,[status(sab)],[233])).
% 89.41/57.85 tff(235,plain,
% 89.41/57.85 (![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[234, 227])).
% 89.41/57.85 tff(236,plain,
% 89.41/57.85 (((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) <=> ((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 89.41/57.85 inference(rewrite,[status(thm)],[])).
% 89.41/57.85 tff(237,plain,
% 89.41/57.85 ((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | ((~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 89.41/57.85 inference(quant_inst,[status(thm)],[])).
% 89.41/57.85 tff(238,plain,
% 89.41/57.85 ((~![V_n: $i, T_a: $i] : ((~class_Groups_Omonoid__mult(T_a)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), c_Groups_Oone__class_Oone(T_a)), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~class_Groups_Omonoid__mult(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[237, 236])).
% 89.41/57.85 tff(239,plain,
% 89.41/57.85 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
% 89.41/57.85 inference(unit_resolution,[status(thm)],[238, 235, 151])).
% 89.41/57.85 tff(240,plain,
% 89.41/57.85 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
% 89.41/57.85 inference(symmetry,[status(thm)],[239])).
% 89.41/57.85 tff(241,plain,
% 89.41/57.85 (c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 89.41/57.85 inference(transitivity,[status(thm)],[240, 225, 210, 207, 183, 168, 41])).
% 89.41/57.85 tff(242,plain,
% 89.41/57.85 (^[T_a: $i] : refl(((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 89.41/57.85 inference(bind,[status(th)],[])).
% 89.41/57.85 tff(243,plain,
% 89.41/57.85 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.85 inference(quant_intro,[status(thm)],[242])).
% 89.41/57.85 tff(244,plain,
% 89.41/57.85 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.85 inference(rewrite,[status(thm)],[])).
% 89.41/57.85 tff(245,plain,
% 89.41/57.85 (^[T_a: $i] : rewrite((class_Rings_Ozero__neq__one(T_a) => (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 89.41/57.85 inference(bind,[status(th)],[])).
% 89.41/57.85 tff(246,plain,
% 89.41/57.85 (![T_a: $i] : (class_Rings_Ozero__neq__one(T_a) => (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.85 inference(quant_intro,[status(thm)],[245])).
% 89.41/57.85 tff(247,axiom,(![T_a: $i] : (class_Rings_Ozero__neq__one(T_a) => (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_one__neq__zero')).
% 89.41/57.85 tff(248,plain,
% 89.41/57.85 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[247, 246])).
% 89.41/57.85 tff(249,plain,
% 89.41/57.85 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[248, 244])).
% 89.41/57.85 tff(250,plain,(
% 89.41/57.85 ![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.85 inference(skolemize,[status(sab)],[249])).
% 89.41/57.85 tff(251,plain,
% 89.41/57.85 (![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))),
% 89.41/57.85 inference(modus_ponens,[status(thm)],[250, 243])).
% 89.41/57.85 tff(252,plain,
% 89.41/57.85 (((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 89.45/57.92 inference(rewrite,[status(thm)],[])).
% 89.45/57.92 tff(253,plain,
% 89.45/57.92 ((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | ((~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 89.45/57.92 inference(quant_inst,[status(thm)],[])).
% 89.45/57.92 tff(254,plain,
% 89.45/57.92 ((~![T_a: $i] : ((~class_Rings_Ozero__neq__one(T_a)) | (~(c_Groups_Oone__class_Oone(T_a) = c_Groups_Ozero__class_Ozero(T_a))))) | (~class_Rings_Ozero__neq__one(tc_Complex_Ocomplex)) | (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 89.45/57.92 inference(modus_ponens,[status(thm)],[253, 252])).
% 89.45/57.92 tff(255,plain,
% 89.45/57.92 (~(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 89.45/57.92 inference(unit_resolution,[status(thm)],[254, 251, 9])).
% 89.45/57.92 tff(256,plain,
% 89.45/57.92 ($false),
% 89.45/57.92 inference(unit_resolution,[status(thm)],[255, 241])).
% 89.45/57.92 % SZS output end Proof
%------------------------------------------------------------------------------