TSTP Solution File: ALG424-1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG424-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 : Wed Aug 30 16:09:35 EDT 2023
% Result : Unsatisfiable 0.68s 1.21s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.22 % Problem : ALG424-1 : TPTP v8.1.2. Released v4.1.0.
% 0.16/0.23 % Command : do_cvc5 %s %d
% 0.23/0.44 % Computer : n019.cluster.edu
% 0.23/0.44 % Model : x86_64 x86_64
% 0.23/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.44 % Memory : 8042.1875MB
% 0.23/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.23/0.44 % CPULimit : 300
% 0.23/0.44 % WCLimit : 300
% 0.23/0.44 % DateTime : Mon Aug 28 05:02:58 EDT 2023
% 0.23/0.45 % CPUTime :
% 0.30/0.67 %----Proving TF0_NAR, FOF, or CNF
% 0.30/0.68 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.psSfcP1nPT/cvc5---1.0.5_27790.p...
% 0.61/0.83 ------- get file name : TPTP file name is ALG424-1
% 0.61/0.84 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27790.smt2...
% 0.61/0.84 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.68/1.21 % SZS status Unsatisfiable for ALG424-1
% 0.68/1.21 % SZS output start Proof for ALG424-1
% 0.68/1.23 (
% 0.68/1.23 (let ((_let_1 (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (let ((_let_3 (tptp.c_Ring__and__Field_Odvd__class_Odvd tptp.v_pa____ (tptp.c_Power_Opower__class_Opower tptp.v_qa____ tptp.v_na____ _let_2) _let_2))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_6 (tptp.c_Polynomial_Oorder tptp.v_a____ tptp.v_pa____ tptp.tc_Complex_Ocomplex))) (let ((_let_7 (or _let_3 (= _let_6 _let_5)))) (let ((_let_8 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_9 (tptp.c_Polynomial_Opoly tptp.v_pa____ tptp.v_a____ tptp.tc_Complex_Ocomplex))) (let ((_let_10 (= _let_9 _let_8))) (let ((_let_11 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_Polynomial_Oorder V_a V_p T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= V_p (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Opoly V_p V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (let ((_let_12 (= tptp.v_pa____ (tptp.c_HOL_Ozero__class_Ozero _let_2)))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (let ((_let_15 (tptp.c_HOL_Otimes__class_Otimes _let_14 _let_14 tptp.tc_nat))) (let ((_let_16 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Polynomial_Oorder V_a V_p T_a))) (= V_p (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Opoly V_p V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (let ((_let_17 (= _let_8 _let_9))) (let ((_let_18 (not _let_17))) (let ((_let_19 (= _let_5 _let_6))) (let ((_let_20 (not _let_19))) (let ((_let_21 (not _let_1))) (let ((_let_22 (or _let_21 _let_20 _let_12 _let_18))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (not _let_22))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.tc_Complex_Ocomplex tptp.v_a____ tptp.v_pa____ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Polynomial_Oorder V_a V_p T_a)))) :args (_let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_12 _let_18 _let_20 _let_21 _let_24))) (ASSUME :args (_let_13)) (SYMM (ASSUME :args (_let_10))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_4)) :args (_let_19 true _let_3)) (ASSUME :args (_let_1)) :args (_let_24 true _let_12 false _let_17 false _let_19 false _let_1)) _let_23 :args (false true _let_22 false _let_16)) :args ((forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Polynomial_Osmult V_a V_p T_a) T_a) (tptp.c_Polynomial_Odegree V_p T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_d $$unsorted) (V_x $$unsorted) (V_k $$unsorted) (V_D $$unsorted) (V_t $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_x (tptp.c_HOL_Otimes__class_Otimes V_k V_D T_a) T_a) V_t T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus V_x V_t T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_D T_a)))) (forall ((T_a $$unsorted) (V_d $$unsorted) (V_x $$unsorted) (V_t $$unsorted) (V_k $$unsorted) (V_D $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus V_x V_t T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_x (tptp.c_HOL_Otimes__class_Otimes V_k V_D T_a) T_a) V_t T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_d V_D T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero _let_1))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) _let_2 _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p _let_2 _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_j tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_d T_a) T_a))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) V_h T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_h T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_m _let_1 tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n _let_1 tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a) _let_1)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) (tptp.c_Divides_Odiv__class_Odiv V_w V_z T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_x V_w T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_w T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_z V_w T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_w T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Polynomial_Opoly__gcd _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_lessequals V_n _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_b_H T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a) (not (tptp.c_lessequals V_x V_y tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_lessequals V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) _let_1)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_m T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_l tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_k V_l tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_m $$unsorted)) (tptp.c_lessequals V_m (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_HOL_Otimes__class_Otimes V_m V_m tptp.tc_nat) tptp.tc_nat) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oone__class_Oone T_a) V_p T_a) V_p))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_3 T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= V_a _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_x T_a) V_y T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (= _let_14 _let_15) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_x V_z T_a) (tptp.c_Divides_Odiv__class_Odiv V_y V_z T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Olordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_lessequals V_c _let_1 T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) V_x))) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_n tptp.tc_nat) V_n)) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_n)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a))) (= V_y V_z))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_b V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_N T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_Polynomial_Osmult V_a V_p T_a) _let_1)) (= V_p _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_u T_a))) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) V_u))) (forall ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_h $$unsorted)) (or (not (tptp.class_RealVector_Oreal__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) V_h T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) V_h T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) V_h T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a))) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a))) (= V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_N T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_N T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) V_n T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_2 T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_c T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_d T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_2 T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Polynomial_Opoly__gcd V_x (tptp.c_Polynomial_Opoly__gcd V_y V_z T_a) T_a) (tptp.c_Polynomial_Opoly__gcd V_y (tptp.c_Polynomial_Opoly__gcd V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Polynomial_Opoly__gcd (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) V_z T_a) (tptp.c_Polynomial_Opoly__gcd V_x (tptp.c_Polynomial_Opoly__gcd V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (let ((_let_2 (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_1 T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oplus__class_Oplus V_a V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_x V_n T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_x V_n T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus V_y V_b T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_e T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_x _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ominus__class_Ominus V_b V_b_H T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_b T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a_H T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (= V_m V_n) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_m V_m T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) V_m T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_lessequals (tptp.c_Polynomial_Odegree V_p T_a) (tptp.c_Polynomial_Odegree V_q T_a) tptp.tc_nat) (= V_q (tptp.c_HOL_Ozero__class_Ozero _let_1)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_d T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))) (= V_c V_d) (= V_a V_b))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a))) (= V_y V_z) (= V_w V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= V_m (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_m _let_1 tptp.tc_nat) _let_1))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) _let_1))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_n T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) V_m T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_y T_a) V_x T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ominus__class_Ominus V_c V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) V_a T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_r T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a) (= V_x _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Odegree (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Osmult V_a V_p T_a) V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Polynomial_Opoly V_p V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (= V_a V_b) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y)) (= V_x (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted)) (tptp.c_lessequals V_m (tptp.c_HOL_Otimes__class_Otimes V_m V_m tptp.tc_nat) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) V_y T_a)))) (= _let_15 _let_14) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_a T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_j tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_Polynomial_Osmult V_b V_p T_a) T_a) (tptp.c_Polynomial_Osmult (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_p T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_a V_r T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_r T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) V_q _let_1)) (= V_q (tptp.c_HOL_Ozero__class_Ozero _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_m V_n))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) (tptp.c_Polynomial_Opoly__gcd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (not (tptp.c_HOL_Oord__class_Oless _let_5 _let_5 tptp.tc_nat)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oinverse__class_Oinverse V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Osmult V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_N T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.c_lessequals _let_5 _let_5 tptp.tc_nat) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_lessequals (tptp.c_Polynomial_Odegree (tptp.c_Power_Opower__class_Opower V_p V_n (tptp.tc_Polynomial_Opoly T_a)) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Polynomial_Odegree V_p T_a) V_n tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_a V_r T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_m _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (tptp.c_lessequals (tptp.c_Polynomial_Odegree (tptp.c_Polynomial_Osmult V_a V_p T_a) T_a) (tptp.c_Polynomial_Odegree V_p T_a) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_l T_a) (tptp.c_HOL_Oabs__class_Oabs V_k T_a))) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_l V_k T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_Power_Opower__class_Opower V_a V_m T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_a V_m T_a) V_b T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_a V_n T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_d T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_b T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_y _let_1)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_x _let_1))))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_y _let_1)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_x _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) V_x (tptp.tc_Polynomial_Opoly T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) V_y (tptp.tc_Polynomial_Opoly T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_m T_a) T_a) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m (tptp.c_HOL_Oabs__class_Oabs V_k T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m (tptp.c_HOL_Oabs__class_Oabs V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oabs__class_Oabs V_m T_a) V_k T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oabs__class_Oabs V_m T_a) V_k T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) V_n T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_y _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) _let_1))))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_x _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Polynomial_Opoly__gcd V_x V_y T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1)))) (not (= tptp.v_na____ _let_5)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= V_a _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (= (tptp.c_Polynomial_Odegree tptp.v_pa____ tptp.tc_Complex_Ocomplex) tptp.v_na____) (forall ((V_q $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree V_p tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (not (= (tptp.c_Polynomial_Opoly V_q (tptp.v_sko__local__XIH__1 V_p V_q) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (tptp.c_HOL_Oord__class_Oless _let_1 tptp.v_na____ tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Power_Opower__class_Opower V_q _let_1 _let_2) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree V_p tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Polynomial_Opoly V_p (tptp.v_sko__local__XIH__1 V_p V_q) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (tptp.c_HOL_Oord__class_Oless _let_1 tptp.v_na____ tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Power_Opower__class_Opower V_q _let_1 _let_2) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_q T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_q T_a) (tptp.c_Power_Opower__class_Opower V_y V_q T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) _let_13 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (not (= (tptp.c_Polynomial_Opoly tptp.v_pa____ V_x tptp.tc_Complex_Ocomplex) _let_1)) (= (tptp.c_Polynomial_Opoly tptp.v_qa____ V_x tptp.tc_Complex_Ocomplex) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b (tptp.c_HOL_Otimes__class_Otimes V_b V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Polynomial_Osmult V_a V_p T_a) V_q _let_1))))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_p V_q _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_Power_Opower__class_Opower V_x V_p T_a) V_q T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Otimes__class_Otimes V_p V_q tptp.tc_nat) T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Power_Opower__class_Opower V_p V_n (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_Polynomial_Opoly V_p V_x T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) _let_13 (forall ((T_a $$unsorted) (V_p $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Opoly V_p V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Oorder V_a V_p T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) _let_11 _let_10 _let_7 _let_4 (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Divides_Osemiring__div tptp.tc_nat) (tptp.class_Ring__and__Field_Odvd tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_HOL_Ozero tptp.tc_nat) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__ring tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__field tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring tptp.tc_Complex_Ocomplex) _let_1 (tptp.class_Ring__and__Field_Odvd tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) (tptp.class_HOL_Ozero tptp.tc_Complex_Ocomplex) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__group__add__abs (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__ring__abs (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semidom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__idom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Osemiring__0 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__zero (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Osemiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oabs__if (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Divides_Osemiring__div (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ofield T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oidom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Odvd (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Divides_Oring__div (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ofield T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Int_Onumber__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Power_Opower (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_HOL_Ozero (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_HOL_Ozero T_1)))))))))))))))))))))))))))))))
% 0.68/1.23 )
% 0.68/1.24 % SZS output end Proof for ALG424-1
% 0.68/1.24 % cvc5---1.0.5 exiting
% 0.68/1.24 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------