TSTP Solution File: LCL795-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LCL795-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:03:44 EDT 2023
% Result : Unsatisfiable 0.62s 1.33s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.20 % Problem : LCL795-1 : TPTP v8.1.2. Released v4.1.0.
% 0.19/0.21 % Command : do_cvc5 %s %d
% 0.20/0.43 % Computer : n016.cluster.edu
% 0.20/0.43 % Model : x86_64 x86_64
% 0.20/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.43 % Memory : 8042.1875MB
% 0.20/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.43 % CPULimit : 300
% 0.20/0.43 % WCLimit : 300
% 0.20/0.43 % DateTime : Fri Aug 25 06:48:40 EDT 2023
% 0.20/0.43 % CPUTime :
% 0.27/0.63 %----Proving TF0_NAR, FOF, or CNF
% 0.27/0.63 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.7P24BklQwO/cvc5---1.0.5_19067.p...
% 0.27/0.80 ------- get file name : TPTP file name is LCL795-1
% 0.27/0.81 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19067.smt2...
% 0.27/0.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.62/1.33 % SZS status Unsatisfiable for LCL795-1
% 0.62/1.33 % SZS output start Proof for LCL795-1
% 0.62/1.36 (
% 0.62/1.36 (let ((_let_1 (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun tptp.v_Ts____ tptp.v_T_H____ tptp.tc_Type_Otype tptp.tc_Type_Otype))) (let ((_let_2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun tptp.v_T_H_H____) _let_1))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_4 (tptp.c_Type_Otyping (tptp.c_Type_Oshift tptp.v_e____ _let_3 tptp.v_T_H_H____ tptp.tc_Type_Otype) (tptp.c_Lambda_Olift tptp.v_u____ _let_3) _let_2))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.c_Type_Otyping tptp.v_e____ tptp.v_u____ _let_2))) (let ((_let_7 (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) (tptp.c_Lambda_Olift V_t V_i) V_T) (not (tptp.c_Type_Otyping V_e V_t V_T)))))) (let ((_let_8 (tptp.c_Lambda_OdB_OVar tptp.v_n____))) (let ((_let_9 (tptp.c_Type_Oshift tptp.v_e____ tptp.v_i____ tptp.v_T____ tptp.tc_Type_Otype))) (let ((_let_10 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_11 (tptp.hAPP _let_10 _let_3))) (let ((_let_12 (tptp.c_Suc _let_3))) (let ((_let_13 (tptp.hAPP _let_11 _let_12))) (let ((_let_14 (tptp.hAPP (tptp.hAPP _let_10 _let_12) _let_3))) (let ((_let_15 (not _let_6))) (let ((_let_16 (or _let_4 _let_15))) (let ((_let_17 (_let_7))) (let ((_let_18 (ASSUME :args _let_17))) (let ((_let_19 (not _let_16))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (tptp.v_e____ _let_3 tptp.v_T_H_H____ tptp.v_u____ _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) (tptp.c_Lambda_Olift V_t V_i) V_T) true))))) :args _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_4 _let_15 _let_19))) (ASSUME :args (_let_5)) (ASSUME :args (_let_6)) :args (_let_19 true _let_4 false _let_6)) _let_18 :args (false true _let_16 false _let_7)) :args ((forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a)) V_c) V_d)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d))) (= V_c (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a)) V_d))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_u tptp.tc_nat)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_u tptp.tc_nat)) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_u tptp.tc_nat)) V_m) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_u tptp.tc_nat)) V_m) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a)) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n) (tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m))) (= (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_Suc (tptp.hAPP _let_1 V_n))))) (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 (tptp.c_Suc V_n) T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__Nat__Xnat__Xinduct__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omin V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a)) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a) (tptp.c_Orderings_Oord__class_Omin (tptp.c_HOL_Ominus__class_Ominus V_x V_z T_a) (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_z T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) V_m tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_j) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_m) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_k) 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)))) (= _let_14 _let_12) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_Osubst V_r V_t V_i) (tptp.c_Lambda_Osubst V_s V_t V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_z V_x T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_3 _let_1) _let_2) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1)))))) (forall ((V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_c tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_d tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_3 _let_1) _let_2) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1)))))) (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))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 _let_1) _let_2) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _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))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 _let_1) _let_2) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Orderings_Oord__class_Omax (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc (tptp.c_Orderings_Oord__class_Omax V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc _let_1) tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x _let_1 T_a) _let_1)))) (forall ((V_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Osubst _let_1 V_s V_k) _let_1) (= V_i V_k) (tptp.c_HOL_Oord__class_Oless V_k V_i tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_u tptp.tc_nat)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_u tptp.tc_nat)) V_m) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_b) V_a))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_b) V_x) V_b tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_b) V_d) V_b tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_d)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))) (forall ((V_k $$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 ((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 ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__Nat__Xnat__Xinducts__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_Suc V_n) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_a V_n T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_Suc V_n) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_Suc V_n) T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_Suc V_q) T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_Power_Opower__class_Opower V_x V_q T_a) T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l) 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 ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_x $$unsorted)) (or (not (tptp.c_lessequals V_x V_x tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum V_xs T_a) (tptp.c_List_Ofoldl (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) V_xs T_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))) (forall ((V_m $$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)) (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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_Suc V_m) tptp.tc_nat)) (forall ((T_a $$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_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) 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 $$unsorted) (V_x $$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 $$unsorted) (V_z $$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 ((V_e $$unsorted) (V_u $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_u (tptp.c_Type_Osko__Type__Xtyping__elims__2__1 V_T V_e V_t V_u)) (not (tptp.c_Type_Otyping V_e (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u) V_T)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_n)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 V_P) tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_m)) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_i)) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_x)) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat) (not (tptp.c_lessequals V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Onat_Onat__rec V_f1 V_f2 (tptp.c_Suc V_nat) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_nat) (tptp.c_Nat_Onat_Onat__rec V_f1 V_f2 V_nat T_a)))) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_mul $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_pwr (tptp.hAPP _let_1 V_p)) V_q) (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_p V_q tptp.tc_nat))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) V_x T_a) (tptp.c_Orderings_Oord__class_Omax (tptp.c_Orderings_Oord__class_Omin V_y V_x T_a) (tptp.c_Orderings_Oord__class_Omin V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) T_a) (tptp.c_Orderings_Oord__class_Omax (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) (tptp.c_Orderings_Oord__class_Omin V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__List__Xupt__Xinduct__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Type_Otype_OAtom V_nat) (tptp.c_Type_Otype_OAtom V_nat_H))) (= V_nat V_nat_H))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__List__Xreplicate__Xinduct__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_z tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_j) V_k tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_m) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_j) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a) (not (tptp.c_lessequals V_c (tptp.hAPP (tptp.hAPP _let_1 (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 $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals V_c (tptp.hAPP (tptp.hAPP _let_1 (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) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a)) V_c) V_d T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a)) V_c) V_d T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_l) (tptp.hAPP (tptp.hAPP _let_1 V_k) V_n))) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (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_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (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)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_OrderedGroup_Osemigroup__add T_a)) (= (tptp.c_List_Ofoldl _let_1 (tptp.hAPP _let_2 V_y) V_zs T_a T_a) (tptp.hAPP _let_2 (tptp.c_List_Ofoldl _let_1 V_y V_zs T_a T_a))))))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_l tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_n)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (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 $$unsorted) (V_a $$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_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_z V_y T_a) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_p T_a) (tptp.c_Power_Opower__class_Opower V_x V_q T_a) T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_p) V_q) T_a)))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Odrop V_n _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 V_P V_n) V_n tptp.tc_nat) (not (tptp.hBOOL (tptp.hAPP V_P V_n))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_mul $$unsorted) (V_pwr $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_p)) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_p) V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.c_lessequals V_j V_i tptp.tc_nat)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_u tptp.tc_nat)) V_m)))))) (forall ((V_n $$unsorted)) (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omin V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omin V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omin V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omin V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_List_Ofoldr _let_1 V_xs V_a T_a T_a) (tptp.c_List_Ofoldl _let_1 V_a V_xs T_a T_a))))) (forall ((V_nat $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.hAPP (tptp.hAPP _let_1 (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 $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.hAPP (tptp.hAPP _let_1 (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) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a)) V_c) V_d T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a)) V_c) V_d T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_d) T_a))))) (= tptp.v_n____ tptp.v_i____) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n))) (not (tptp.c_lessequals V_j V_i tptp.tc_nat)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_u tptp.tc_nat)) V_m) V_n)))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n))) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= V_m (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_u tptp.tc_nat)) V_n))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_z T_a) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_u tptp.tc_nat)) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n))))) (tptp.c_HOL_Oord__class_Oless _let_3 _let_12 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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) 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__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) 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__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _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_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_1) (= V_m _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_Suc _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_n _let_1)))) (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) (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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (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) (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat))))) (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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) T_a) (tptp.c_HOL_Otimes__class_Otimes (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)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_lessequals _let_1 V_n tptp.tc_nat) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_lessequals _let_1 V_m tptp.tc_nat) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Odrop (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) _let_1 T_a) _let_1))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.c_Suc V_n) V_x T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oreplicate V_n V_x T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 V_u))) (= (tptp.hAPP _let_2 V_z) V_u)))))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_j) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_m) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_k V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_lessequals V_x V_z tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_lessequals V_x V_y tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a) (tptp.c_Orderings_Oord__class_Omax (tptp.c_HOL_Ominus__class_Ominus V_x V_z T_a) (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a) T_a)))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 V_T V_e V_t V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (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_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 $$unsorted) (V_y $$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_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 ((V_P $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP V_P V_n)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 V_P) tptp.tc_nat) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((V_x $$unsorted) (V_s $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_x) V_s V_x) V_s))) (forall ((V_P $$unsorted) (V_T $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_T)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Osko__Type__Xtype__induct__1__1 V_P)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a) (tptp.c_Orderings_Oord__class_Omin V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a) (tptp.c_Orderings_Oord__class_Omin V_y (tptp.c_Orderings_Oord__class_Omin V_x V_z T_a) T_a)))) (= _let_12 _let_13) (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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) 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 ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_l tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_l 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 $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$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_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_k) tptp.tc_nat))) (forall ((T_a $$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_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat))) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a) V_x))) (forall ((V_k $$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_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_m _let_2))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((V_k $$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_f $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_OCons V_x V_xs T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.hAPP (tptp.hAPP V_f V_a) V_x) V_xs T_a T_b))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Suc V_m)) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.c_Suc V_n))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_Suc V_n) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Odrop V_n V_xs T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$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 $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_k $$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 ((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 ((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 $$unsorted) (V_a $$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_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__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 $$unsorted) (V_a $$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 ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (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_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_z T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) (tptp.c_Orderings_Oord__class_Omin V_y V_x T_a)))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j) V_u tptp.tc_nat)) V_k)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_e T_a)) V_c))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (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 ((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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$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_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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) _let_1 T_a))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs T_a) V_ys T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Nat_Onat_Onat__case V_f1 V_f2 (tptp.c_Suc V_xa) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f2 V_xa))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Nat_Onat_Onat__case V_f1 V_f2 (tptp.c_Suc V_nat) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f2 V_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_k (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (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 $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omin V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omin V_a V_b T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.c_List_Ofoldl _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) V_zs T_a T_a)) (tptp.c_List_Ofoldl _let_1 V_x V_zs T_a T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a) (not (tptp.c_lessequals V_z V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a) (not (tptp.c_lessequals V_z V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_a V_b T_a) V_x T_a)))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_j (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat) (not (tptp.c_lessequals V_j (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat)))) (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_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_y T_a) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.c_InductTermi_OIT V_s)) (not (tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_r V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((V_n $$unsorted) (V_ts $$unsorted) (V_r $$unsorted) (V_ss $$unsorted)) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Onat_Onat__case V_f1 V_f2 (tptp.c_Suc V_nat) T_a) (tptp.hAPP V_f2 V_nat))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_u tptp.tc_nat)) V_m) V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_u tptp.tc_nat)) V_m) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals V_m (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_u tptp.tc_nat)) V_n) tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_i V_u tptp.tc_nat)) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_j V_u tptp.tc_nat)) V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_u tptp.tc_nat)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_z T_a) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a)) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_w V_z T_a)) (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a)))) (= V_y V_z) (= V_w V_x)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_d T_a)) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))) (= V_c V_d) (= V_a V_b)))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c tptp.tc_nat)) (tptp.c_HOL_Otimes__class_Otimes V_b V_d tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_d tptp.tc_nat)) (tptp.c_HOL_Otimes__class_Otimes V_b V_c tptp.tc_nat)))) (= V_c V_d) (= V_a V_b)))) (forall ((V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_w V_y tptp.tc_nat)) (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_w V_z tptp.tc_nat)) (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_nat)))) (= V_y V_z) (= V_w V_x)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (forall ((V_nat $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H)))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1 T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_j) V_k tptp.tc_nat) (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat))) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_j) V_i) V_k tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) V_i)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (= (tptp.c_HOL_Otimes__class_Otimes _let_12 _let_12 tptp.tc_nat) _let_12) (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_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_j V_n tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_nat) T_a) (tptp.hAPP V_f1 V_nat))) (forall ((V_r $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Oreplicate (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x T_a))) (= _let_12 _let_14) (forall ((T_a $$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 ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (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 ((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_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_i))) (or (not (tptp.c_lessequals V_i _let_1 tptp.tc_nat)) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_i tptp.tc_nat) V_k)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omin V_x V_x T_a) V_x))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_Lambda_Osubst V_s V_t (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) tptp.tc_nat)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_x) tptp.tc_nat)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat)) V_m) (tptp.c_Orderings_Oord__class_Omax V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_List_Olistsum V_xs 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 ((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_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (= V_T V_U) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otyping V_e _let_1 V_T))))) (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_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_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (let ((_let_2 (tptp.c_List_Oreplicate V_k V_x T_a))) (= (tptp.c_List_Oappend _let_1 _let_2 T_a) (tptp.c_List_Oappend _let_2 _let_1 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_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 $$unsorted) (V_a $$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 $$unsorted) (V_b $$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 $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x V_x T_a) V_x))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_m $$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_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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((V_s $$unsorted) (V_ss $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1)) (= V_s _let_1)))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_k tptp.tc_nat) V_j tptp.tc_nat))) (forall ((T_a $$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 _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) 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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_c tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_b V_c tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_c V_a tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.c_HOL_Oord__class_Oless (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) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_m))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= _let_1 V_n) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x))) (or (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))) (= V_b V_c)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a))) (forall ((V_x $$unsorted) (V_xs1 $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs1 V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs1 T_a) V_zs T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a)) V_z) (tptp.c_Orderings_Oord__class_Omin (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z) T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_pwr $$unsorted) (V_mul $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_pwr (tptp.hAPP (tptp.hAPP V_mul V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_pwr V_x) V_q)) (tptp.hAPP (tptp.hAPP V_pwr V_y) V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_add $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_y) V_z)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_x) V_y) (tptp.hAPP (tptp.hAPP V_mul V_y) V_x)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_mul V_y) V_z)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_y)) V_z)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_r1 $$unsorted) (V_x $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r1) V_x) V_x) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_r0 $$unsorted) (V_x $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r0) V_x) V_r0) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_x) V_y) (tptp.hAPP (tptp.hAPP V_add V_y) V_x)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_y) V_z)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_y)) V_z)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_r0 $$unsorted) (V_x $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_r0) V_x) V_x) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_c) V_d)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_c)) V_d)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_a) V_c) (tptp.hAPP (tptp.hAPP V_add V_c) V_a)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_b)) V_c) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_c)) V_b)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (let ((_let_2 (tptp.hAPP V_add V_c))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_d)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_b)) V_c) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_b) V_c))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_b)) (tptp.hAPP (tptp.hAPP V_add V_c) V_d)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_c)) (tptp.hAPP (tptp.hAPP V_add V_b) V_d))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (let ((_let_2 (tptp.hAPP V_mul V_rx))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ry)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_ry))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_mul V_rx) V_ry)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_rx)) V_ry)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_ly)) V_rx) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_mul V_ly) V_rx))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_rx)) V_ly)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_mul V_lx) V_ly)))) (let ((_let_2 (tptp.hAPP V_mul V_rx))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ry)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_ry))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP V_mul V_rx) V_ry))) (let ((_let_2 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_2 V_ly)) _let_1) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP V_mul V_ly) _let_1))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_ly)) (tptp.hAPP (tptp.hAPP V_mul V_rx) V_ry)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_rx)) (tptp.hAPP (tptp.hAPP V_mul V_ly) V_ry))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_a) V_r1) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_r1 $$unsorted) (V_a $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r1) V_a) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_a $$unsorted) (V_r0 $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_a) V_r0) V_r0) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_r0 $$unsorted) (V_a $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r0) V_a) V_r0) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP (tptp.hAPP V_mul V_a) V_c)) (tptp.hAPP (tptp.hAPP V_mul V_b) V_c))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_a) V_b) (tptp.hAPP (tptp.hAPP V_mul V_b) V_a)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_r0 $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_a) V_r0) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_r0 $$unsorted) (V_a $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_r0) V_a) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_m $$unsorted) (V_mul $$unsorted) (V_r1 $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_m) V_m) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_r1) V_r1)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_m $$unsorted) (V_mul $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_m) (tptp.hAPP (tptp.hAPP V_mul V_a) V_m)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_r1)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_mul $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_r1 $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP (tptp.hAPP V_mul V_a) V_m)) V_m) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_r1)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_mul $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP (tptp.hAPP V_mul V_a) V_m)) (tptp.hAPP (tptp.hAPP V_mul V_b) V_m)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_b)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xc $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_xc) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_xc))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_nat) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_nat))))) (forall ((V_r $$unsorted) (V_ts $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_m _let_1) (= V_m _let_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc V_k) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_k tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.c_lessequals (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) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (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) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) T_a) (= V_y _let_1)))) (forall ((V_r $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r)) (not (tptp.c_InductTermi_OIT V_r)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))) (forall ((V_u $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_u))) (or (tptp.c_Lambda_Obeta (tptp.hAPP _let_1 V_s) (tptp.hAPP _let_1 V_t)) (not (tptp.c_Lambda_Obeta V_s V_t))))) (forall ((V_s $$unsorted) (V_u $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_u) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) (tptp.c_Orderings_Oord__class_Omax V_y V_x 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 ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_i (tptp.c_List_Oreplicate V_k V_x T_a) T_a) (tptp.c_List_Oreplicate (tptp.c_HOL_Ominus__class_Ominus V_k V_i tptp.tc_nat) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) (tptp.c_Orderings_Oord__class_Omin V_x V_z T_a) T_a) (tptp.c_Orderings_Oord__class_Omin V_x (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((V_nat $$unsorted)) (= (tptp.c_nat_Onat__size (tptp.c_Suc V_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_nat_Onat__size V_nat)) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Orderings_Oord__class_Omin V_x V_y T_a) T_a) V_x))) (forall ((V_m $$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 $$unsorted) (V_c $$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 ((V_n $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Ominus__class_Ominus V_n V_i tptp.tc_nat) tptp.tc_nat) V_i) (not (tptp.c_lessequals V_i V_n tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Olift _let_1 V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i) V_t))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) (tptp.c_Suc V_j) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (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 $$unsorted) (V_b $$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 $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$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_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_i) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= V_j (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_i)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) V_m) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) V_n) V_m) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_pwr $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_mul V_x) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.c_Suc V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_pwr $$unsorted) (V_x $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_q)) V_x) (tptp.hAPP _let_1 (tptp.c_Suc V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_q $$unsorted) (V_mul $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP _let_1 (tptp.c_Suc V_q)) (tptp.hAPP (tptp.hAPP V_mul V_x) (tptp.hAPP _let_1 V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_mul $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP V_mul V_x) (tptp.hAPP _let_1 V_n))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 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 ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i))) (or (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_j) V_k tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) V_i) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_j) V_i) V_k tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Odrop V_m V_xs T_a) T_a) (tptp.c_List_Odrop (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) V_xs T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals 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_lessequals (tptp.c_Power_Opower__class_Opower V_a _let_1 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_1 T_a) T_a))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) V_x T_a) (tptp.c_List_Oappend (tptp.c_List_Oreplicate V_n V_x T_a) (tptp.c_List_Oreplicate V_m 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_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$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_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_n V_x T_a) (tptp.c_List_Olist_ONil T_a))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_Power_Opower__class_Opower V_x V_q T_a) T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.c_Suc V_q) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_q T_a) V_x T_a) (tptp.c_Power_Opower__class_Opower V_x (tptp.c_Suc V_q) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Oreplicate V_n V_x T_a))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$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_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 ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_e $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otypings V_e V_ts (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 V_T V_e V_t V_ts)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless V_n (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_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_n tptp.tc_nat))) (forall ((V_m $$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_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_j))) (or (= (tptp.c_Lambda_Osubst _let_1 V_u V_i) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_j V_i tptp.tc_nat))))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_r (tptp.c_Lambda_OdB_OVar V_i) V_j)) (not (tptp.c_InductTermi_OIT V_r)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_j) V_i tptp.tc_nat))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_i) V_i tptp.tc_nat))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (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 ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_r V_c T_a)) (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_r V_d T_a)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x))) (or (not (= (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_r V_c tptp.tc_nat)) (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_r V_d tptp.tc_nat)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) _let_1)) (= V_y _let_1)))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) _let_1)) (= V_x _let_1)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) 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)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) 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_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (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.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) 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)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 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 $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (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.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals _let_1 V_n tptp.tc_nat)) (not (tptp.c_lessequals _let_1 V_m tptp.tc_nat))))) (forall ((T_a $$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_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 $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not 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(tptp.c_Orderings_Oord__class_Omin (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc (tptp.c_Orderings_Oord__class_Omin V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (= V_m _let_1) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m _let_1 tptp.tc_nat))))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_m $$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) 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$$unsorted) (V_j $$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_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_k $$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 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(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_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__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 $$unsorted) (V_c $$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 ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a)) V_z) (tptp.c_Orderings_Oord__class_Omax (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z) T_a))))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) (tptp.c_Lambda_OdB_OVar V_i))) (not (tptp.c_InductTermi_OIT V_t)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a _let_2 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_2 T_a))) (= V_a V_b) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((V_i $$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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) V_z T_a) (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Orderings_Oord__class_Omax V_y V_z T_a) T_a) (tptp.c_Orderings_Oord__class_Omax V_y (tptp.c_Orderings_Oord__class_Omax V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a)) (tptp.c_HOL_Otimes__class_Otimes V_b V_m T_a)) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_m T_a))))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) T_a)))))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_s) (tptp.c_Lambda_OdB_OAbs V_t)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x _let_1 T_a) _let_1)))) (forall ((V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_i V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_x _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$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 ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) V_n tptp.tc_nat) V_m)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) V_n tptp.tc_nat) V_m)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) V_b T_a) V_a))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Oappend V_xs V_ys T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.c_List_Ofoldl V_f V_a V_xs T_a T_b) V_ys T_a T_b))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.c_Type_Otype_OAtom V_nat) T_a) (tptp.hAPP V_f1 V_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) 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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_x) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x 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) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _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))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) 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 _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_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_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_T $$unsorted) (V_e $$unsorted) (V_t $$unsorted)) (or (= V_T (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xtyping__elims__3__1 V_T V_e V_t)) (tptp.c_Type_Osko__Type__Xtyping__elims__3__2 V_T V_e V_t))) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OAbs V_t) V_T)))) (forall ((T_a $$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_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_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_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 $$unsorted) (V_b $$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 ((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_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)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1)) (= V_a _let_1)))) (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_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 $$unsorted) (V_a $$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 $$unsorted) (V_x $$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 $$unsorted) (V_x $$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) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1)))) (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_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 $$unsorted) (V_a $$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_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (tptp.c_lessequals _let_3 _let_3 tptp.tc_nat) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_m _let_1 tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n _let_1 tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat)))) (not (tptp.c_HOL_Oord__class_Oless _let_3 _let_3 tptp.tc_nat)) (forall ((V_n $$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)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x 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) (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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_c) T_a))))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k) V_u V_k) V_u)) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_rs V_ss))) (forall ((V_m $$unsorted) (V_rs $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_m) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_m V_n))) (forall ((V_dB_H $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)))) (forall ((V_m $$unsorted) (V_i $$unsorted) (V_n $$unsorted)) (= (tptp.c_Orderings_Oord__class_Omin (tptp.c_HOL_Ominus__class_Ominus V_m V_i tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_i tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Orderings_Oord__class_Omin V_m V_n tptp.tc_nat) V_i tptp.tc_nat))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus V_a V_b tptp.tc_nat)))))) (= _let_13 _let_12) (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 ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not 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(or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_i $$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 $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend _let_1 V_xs T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1))))) (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 $$unsorted) (V_b $$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_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_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u) V_s V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_t V_s V_k)) (tptp.c_Lambda_Osubst V_u V_s V_k)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat))) (= V_m V_n)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Suc _let_1) tptp.tc_nat)) V_n) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a) (tptp.c_Orderings_Oord__class_Omin (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) (tptp.c_Orderings_Oord__class_Omax V_x V_z T_a) T_a) T_a))) (forall ((T_a $$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 $$unsorted) (V_x $$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_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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((T_a $$unsorted) (V_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_xs $$unsorted) (V_ys $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_List_Olistsum V_xs T_a)) (tptp.c_List_Olistsum V_ys T_a))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) V_m) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Suc V_i) tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_xs V_ys)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_x V_y)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) (tptp.c_Suc _let_1))) (= V_m _let_1) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) V_x T_a) (tptp.c_Orderings_Oord__class_Omin (tptp.c_Orderings_Oord__class_Omax V_y V_x T_a) (tptp.c_Orderings_Oord__class_Omax V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Omax V_x (tptp.c_Orderings_Oord__class_Omin V_y V_z T_a) T_a) (tptp.c_Orderings_Oord__class_Omin (tptp.c_Orderings_Oord__class_Omax V_x V_y T_a) (tptp.c_Orderings_Oord__class_Omax V_x V_z T_a) 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 $$unsorted) (V_b $$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_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 ((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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$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 $$unsorted) (V_a $$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 $$unsorted) (V_a $$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)) (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a))) (forall ((T_a $$unsorted) (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 $$unsorted) (V_b $$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 $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_ys T_a) V_zs T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_ys V_zs T_a) T_a))) (forall ((V_m $$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 ((V_xs $$unsorted) (V_xs1 $$unsorted) (V_us $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_xs1 V_us T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_xs1 T_a) V_us T_a))) (forall ((V_zs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_zs V_x T_a) V_ys T_a) (tptp.c_List_Oappend V_zs (tptp.c_List_Oappend V_x V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_x V_ts T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_x T_a) V_ts 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_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)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) V_k tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat)) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_k (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 (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))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a)) (tptp.c_HOL_Otimes__class_Otimes V_x V_z 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_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 ((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 $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$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 $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Onat_Onat__rec V_f1 V_f2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) V_f1)) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 V_P V_n))) (not (tptp.hBOOL (tptp.hAPP V_P V_n))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) _let_1)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) _let_1)) (= V_m V_n)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_lessequals V_n _let_1 tptp.tc_nat))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_n)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_m $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_m _let_1)))) (forall ((V_x $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Onat_Onat__case V_x V_f (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) V_x)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Onat_Onat__case V_f1 V_f2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) V_f1)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Orderings_Oord__class_Omin V_n _let_1 tptp.tc_nat) _let_1))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Orderings_Oord__class_Omin _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_m $$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 ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m V_m tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) V_m)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xreplicate__Xinduct__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Nat_Onat_Onat__case V_f1 V_f2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P V_f1)))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Nat__Xnat__Xinducts__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_x $$unsorted)) (= (tptp.c_Nitpick_Onat__gcd V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_x)) (= (tptp.c_nat_Onat__size _let_3) _let_3) (forall ((V_c $$unsorted)) (= (tptp.c_String_Ochar_Ochar__size V_c) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP _let_11 _let_3) _let_3) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Nat__Xnat__Xinduct__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_m $$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 $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (= (tptp.c_Orderings_Obot__class_Obot tptp.tc_nat) _let_3) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xupt__Xinduct__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_xs T_a) V_xs)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_n)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 V_P)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (forall ((V_c $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize V_c tptp.tc_String_Ochar) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Oreplicate _let_1 V_x T_a) (tptp.c_List_Oreplicate _let_1 V_y T_a)))) (forall ((V_n $$unsorted)) (= (tptp.c_Orderings_Oord__class_Omax V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n)) (forall ((V_n $$unsorted)) (= (tptp.c_Orderings_Oord__class_Omax (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) V_n)) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_x V_y) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_x $$unsorted)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n) V_n)) (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_m)) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_r1 $$unsorted) (V_add $$unsorted) (V_mul $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_pwr V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_r1) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum V_xs T_a) (tptp.c_List_Ofoldr (tptp.c_HOL_Oplus__class_Oplus T_a) V_xs (tptp.c_HOL_Ozero__class_Ozero T_a) T_a T_a)))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Ofoldl _let_2 _let_1 V_xs T_a T_a) (tptp.c_List_Ofoldr _let_2 V_xs _let_1 T_a T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Ofoldl _let_1 V_a V_xs T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_List_Ofoldr _let_1 V_xs (tptp.c_HOL_Ozero__class_Ozero T_a) T_a T_a)))))) (tptp.c_Type_Otypings _let_9 tptp.v_as____ tptp.v_Ts____) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t_H V_T) (not (tptp.c_Lambda_Obeta V_t V_t_H)) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted)) (or (= (tptp.hAPP V_e V_i) V_T) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OVar V_i) V_T)))) (forall ((V_env $$unsorted) (V_x $$unsorted)) (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OVar V_x) (tptp.hAPP V_env V_x))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Type_Osko__Type__Xabs__typeE__1__1 V_e V_t) tptp.tc_Type_Otype) V_t (tptp.c_Type_Osko__Type__Xabs__typeE__1__2 V_e V_t)) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OAbs V_t) V_T)))) (forall ((V_e $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Type_Osko__Type__Xtyping__elims__3__1 V_T V_e V_t) tptp.tc_Type_Otype) V_t (tptp.c_Type_Osko__Type__Xtyping__elims__3__2 V_T V_e V_t)) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OAbs V_t) V_T)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_u $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xtyping__elims__2__1 V_T V_e V_t V_u)) V_T)) (not (tptp.c_Type_Otyping V_e (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u) V_T)))) (forall ((V_type1_H $$unsorted) (V_type2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H) (tptp.c_Type_Otype_OAtom V_nat)))) (forall ((V_P $$unsorted) (V_T1 $$unsorted) (V_T2 $$unsorted) (V_T $$unsorted)) (or (not (= (tptp.c_Type_Osko__Type__Xtype__induct__1__1 V_P) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1) V_T2))) (tptp.hBOOL (tptp.hAPP V_P V_T)) (tptp.hBOOL (tptp.hAPP V_P V_T2)))) (forall ((V_P $$unsorted) (V_T1a $$unsorted) (V_x $$unsorted) (V_T $$unsorted)) (or (not (= (tptp.c_Type_Osko__Type__Xtype__induct__1__1 V_P) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1a) V_x))) (tptp.hBOOL (tptp.hAPP V_P V_T)) (tptp.hBOOL (tptp.hAPP V_P V_T1a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_type1 $$unsorted) (V_type2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f2 V_type1) V_type2) (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 V_type1 T_a)) (tptp.c_Type_Otype_Otype__rec V_f1 V_f2 V_type2 T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_type1 $$unsorted) (V_type2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_type1) V_type2))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_xa) V_xb) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_xa) V_xb))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_type1 $$unsorted) (V_type2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Type_Otype_Otype__case V_f1 V_f2 (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_type1) V_type2))))) (forall ((V_nat $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (not (= (tptp.c_Type_Otype_OAtom V_nat) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_OCons V_x V_xs T_b) V_a T_b T_a) (tptp.hAPP (tptp.hAPP V_f V_x) (tptp.c_List_Ofoldr V_f V_xs V_a T_b T_a)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Oappend V_xs V_ys T_b) V_a T_b T_a) (tptp.c_List_Ofoldr V_f V_xs (tptp.c_List_Ofoldr V_f V_ys V_a T_b T_a) T_b T_a))) (forall ((V_f $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldr V_f (tptp.c_List_Olist_ONil T_b) V_a T_b T_a) V_a)) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift V_t V_i)) (not (tptp.c_InductTermi_OIT V_t)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift V_s V_k)) (tptp.c_Lambda_Olift V_t V_k)))) (forall ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_Olift V_t V_k) V_s V_k) V_t)) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_Olift V_r V_i) (tptp.c_Lambda_Olift V_s V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1) V_T2))) (tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_t V_u V_i)) (not (tptp.c_Type_Otyping V_e V_u V_T2)) (not (tptp.c_InductTermi_OIT V_u)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_T2 tptp.tc_Type_Otype) V_t V_Ta)) (not (tptp.c_InductTermi_OIT V_t)))) (forall ((V_T1 $$unsorted) (V_T2 $$unsorted) (V_t $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_Ta $$unsorted)) (or (not (= tptp.v_T____ (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T1) V_T2))) (tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_t V_u V_i)) (not (tptp.c_Type_Otyping V_e V_u V_T1)) (not (tptp.c_InductTermi_OIT V_u)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i V_T1 tptp.tc_Type_Otype) V_t V_Ta)) (not (tptp.c_InductTermi_OIT V_t)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted) (T_a $$unsorted) (V_j $$unsorted)) (or (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_i V_T T_a) V_j) (tptp.hAPP V_e V_j)) (not (tptp.c_HOL_Oord__class_Oless V_j V_i tptp.tc_nat)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xlist__app__typeE__1__1 V_T V_e V_t V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_ts $$unsorted) (V_T $$unsorted) (V_Ts $$unsorted)) (or (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)) (not (tptp.c_Type_Otyping V_e V_t (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun V_Ts V_T tptp.tc_Type_Otype tptp.tc_Type_Otype))))) (forall ((V_e $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t (tptp.c_List_Ofoldr tptp.c_Type_Otype_OFun (tptp.c_Type_Osko__Type__Xlist__app__typeD__1__1 V_T V_e V_t V_ts) V_T tptp.tc_Type_Otype tptp.tc_Type_Otype)) (not (tptp.c_Type_Otyping V_e (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_T)))) (tptp.c_Type_Otyping _let_9 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp _let_8) tptp.v_a____) _let_1) (tptp.c_InductTermi_OIT tptp.v_u____) (tptp.c_Type_Otyping _let_9 tptp.v_a____ tptp.v_T_H_H____) (forall ((T_a $$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_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_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)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (T_a $$unsorted) (V_T $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Type_Oshift (tptp.c_Type_Oshift V_e V_i V_U T_a) _let_1 V_T T_a) (tptp.c_Type_Oshift (tptp.c_Type_Oshift V_e _let_1 V_T T_a) (tptp.c_Suc V_i) V_U T_a)))) (forall ((V_env $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_U $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_t) V_U) (not (tptp.c_Type_Otyping V_env V_t V_T)) (not (tptp.c_Type_Otyping V_env V_s (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T) V_U))))) (forall ((V_e_H $$unsorted) (V_u $$unsorted) (V_U $$unsorted) (V_i $$unsorted) (V_t $$unsorted) (V_T $$unsorted)) (or (not (tptp.c_Type_Otyping V_e_H V_u V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e_H V_i V_U tptp.tc_Type_Otype) V_t V_T)) (tptp.c_Type_Otyping V_e_H (tptp.c_Lambda_Osubst V_t V_u V_i) V_T))) (tptp.c_Type_Otyping _let_9 _let_8 _let_2) (tptp.c_Type_Otyping tptp.v_e____ tptp.v_u____ tptp.v_T____) (forall ((V_env $$unsorted) (V_t $$unsorted) (V_T $$unsorted) (V_U $$unsorted)) (or (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OAbs V_t) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_T) V_U)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_env (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_T tptp.tc_Type_Otype) V_t V_U)))) (= tptp.v_T____ _let_2) _let_7 (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H))) (= V_type1 V_type1_H))) (forall ((V_type1 $$unsorted) (V_type2 $$unsorted) (V_type1_H $$unsorted) (V_type2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1) V_type2) (tptp.hAPP (tptp.hAPP tptp.c_Type_Otype_OFun V_type1_H) V_type2_H))) (= V_type2 V_type2_H))) _let_6 (forall ((V_e $$unsorted) (V_x $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_x V_T T_a) V_x) V_T)) _let_5 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (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_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_OrderedGroup_Osemigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 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_Nat_Osemiring__char__0 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_Orderings_Obot tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a))))))))))))))))))))))))))
% 0.62/1.37 )
% 0.62/1.37 % SZS output end Proof for LCL795-1
% 0.62/1.37 % cvc5---1.0.5 exiting
% 0.62/1.37 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------