TSTP Solution File: LCL837-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 07:03:57 EDT 2023
% Result : Unsatisfiable 0.55s 1.05s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.17/0.18 % Problem : LCL837-1 : TPTP v8.1.2. Released v4.1.0.
% 0.19/0.19 % Command : do_cvc5 %s %d
% 0.19/0.40 % Computer : n028.cluster.edu
% 0.19/0.40 % Model : x86_64 x86_64
% 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40 % Memory : 8042.1875MB
% 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Thu Aug 24 17:25:50 EDT 2023
% 0.19/0.40 % CPUTime :
% 0.26/0.59 %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QrcoMGI35h/cvc5---1.0.5_24474.p...
% 0.26/0.71 ------- get file name : TPTP file name is LCL837-1
% 0.26/0.71 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24474.smt2...
% 0.26/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.55/1.05 % SZS status Unsatisfiable for LCL837-1
% 0.55/1.05 % SZS output start Proof for LCL837-1
% 0.55/1.07 (
% 0.55/1.07 (let ((_let_1 (tptp.c_List_Omap (tptp.c_COMBC (tptp.c_COMBC tptp.c_Lambda_Osubst tptp.v_u____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) tptp.v_i____ tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) tptp.v_as____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_3 (tptp.c_Suc tptp.v_i____))) (let ((_let_4 (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_r____))) (let ((_let_5 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift tptp.v_u____) _let_2)) _let_3)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_a____) tptp.v_u____) tptp.v_i____)) _let_2))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_5 _let_1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.hAPP (tptp.hAPP _let_4 tptp.v_a____) _let_2))) (let ((_let_9 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_8 tptp.v_as____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (let ((_let_10 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_9) tptp.v_u____) tptp.v_i____))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT _let_10)))) (let ((_let_12 (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_u) V_i) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i) (tptp.c_List_Omap (tptp.c_COMBC (tptp.c_COMBC tptp.c_Lambda_Osubst V_u tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) (let ((_let_13 (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_n) tptp.tc_nat)))) (let ((_let_14 (tptp.c_Suc _let_2))) (let ((_let_15 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_16 (tptp.hAPP _let_15 _let_2))) (let ((_let_17 (tptp.hAPP _let_16 _let_14))) (let ((_let_18 (tptp.hAPP (tptp.hAPP _let_15 _let_14) _let_2))) (let ((_let_19 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (let ((_let_20 (forall ((V_t $$unsorted) (V_v $$unsorted) (V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_Osubst V_t))) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_v) V_i)) (tptp.c_Suc V_j))) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_u) V_v) V_j)) V_i) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP _let_1 V_u) V_i)) V_v) V_j)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)) tptp.tc_nat))))))) (let ((_let_21 (tptp.c_HOL_Otimes__class_Otimes _let_19 _let_19 tptp.tc_nat))) (let ((_let_22 (forall ((V_n $$unsorted)) (= (tptp.c_Suc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))))) (let ((_let_23 (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_8) tptp.v_u____) tptp.v_i____))) (let ((_let_24 (= _let_10 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_23 _let_1 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (let ((_let_25 (= _let_5 _let_23))) (let ((_let_26 (ASSUME :args (_let_11)))) (let ((_let_27 (ASSUME :args (_let_7)))) (let ((_let_28 (_let_12))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 (tptp.hAPP (tptp.hAPP _let_15 tptp.v_i____) _let_19))) (let ((_let_31 (tptp.c_HOL_Oord__class_Oless _let_2 _let_30 tptp.tc_nat))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_25 _let_32))) (let ((_let_34 (_let_20))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (tptp.c_HOL_Oord__class_Oless _let_2 _let_3 tptp.tc_nat))) (let ((_let_37 (= _let_3 _let_30))) (let ((_let_38 (_let_13))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (_let_22))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (and _let_37 _let_36))) (let ((_let_43 (ASSUME :args (_let_36)))) (let ((_let_44 (ASSUME :args (_let_37)))) (let ((_let_45 (not _let_24))) (let ((_let_46 (not _let_25))) (let ((_let_47 (not _let_11))) (let ((_let_48 (REFL :args (tptp.tc_Lambda_OdB)))) (let ((_let_49 (ASSUME :args (_let_25)))) (let ((_let_50 (ASSUME :args (_let_24)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_27 _let_49 _let_50 _let_26) :args (_let_11 _let_7 _let_25 _let_24)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_26)) (CONG (CONG (REFL :args (tptp.c_InductTermi_OIT)) (TRANS (SYMM (SYMM _let_50)) (CONG (REFL :args (tptp.c_Lambda_OdB_OApp)) (SYMM _let_49) (REFL :args (_let_1)) _let_48 _let_48 :args (APPLY_UF tptp.c_List_Ofoldl))) :args (APPLY_UF tptp.hAPP)) :args (APPLY_UF tptp.hBOOL)) (FALSE_INTRO _let_27))) :args (_let_7 _let_25 _let_24 _let_11)) :args ((not (and _let_11 _let_7 _let_25 _let_24)) SB_LITERAL))) (CONG (REFL :args (_let_47)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) (REFL :args (_let_46)) (REFL :args (_let_45)) :args (or))) :args ((or _let_6 _let_47 _let_46 _let_45))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_25 _let_32 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_42)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_43 _let_44) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_2)) (SYMM _let_44) (REFL :args (tptp.tc_nat)) :args (APPLY_UF tptp.c_HOL_Oord__class_Oless)) (TRUE_INTRO _let_43))) :args (_let_36 _let_37))) :args (_let_37 _let_36))) :args (true _let_42)) :args ((or _let_31 (not _let_37) (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.v_i____ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Suc V_n)))) :args _let_40)) _let_41 :args (_let_37 false _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.v_i____ QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Suc V_n)))) :args _let_38)) _let_39 :args (_let_36 false _let_13)) :args (_let_31 false _let_37 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.v_r____ tptp.v_u____ _let_2 tptp.v_i____ tptp.v_a____ QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_v) V_i)) (tptp.c_Suc V_j))) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_u) V_v) V_j))))) :args _let_34)) _let_35 :args (_let_33 false _let_20)) :args (_let_25 false _let_31 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (_let_8 tptp.v_as____ tptp.v_u____ tptp.v_i____ QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_u) V_i)))) :args _let_28)) _let_29 :args (_let_24 false _let_12)) _let_27 _let_26 :args (false false _let_25 false _let_24 true _let_6 false _let_11)) :args ((forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_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 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Suc V_m) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a)) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_e T_a)) V_c))))) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_s) V_j)) V_i) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) V_i)) _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_i _let_1 tptp.tc_nat))))) (forall ((V_env $$unsorted) (V_x $$unsorted)) (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OVar V_x) (tptp.hAPP V_env V_x))) (forall ((V_n $$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 $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_b V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) V_a T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) V_b) V_c T_a))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_s $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_x)) V_s) V_x) V_s))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Divides_Odiv__class_Omod V_m V_n 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 ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1)))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.c_Lambda_OdB_OVar V_i)) V_k) (tptp.c_Lambda_OdB_OVar (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))) (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 V_u))) (= (tptp.hAPP _let_2 V_z) V_u)))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_m $$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_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((T_a $$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_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a (tptp.c_Suc V_n) T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_Suc V_q) T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_Power_Opower__class_Opower V_x V_q T_a) T_a)))) (forall ((T_a $$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 $$unsorted) (V_a $$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_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 $$unsorted) (V_x $$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_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_1) V_s) V_k) _let_1) (= V_i V_k) (tptp.c_HOL_Oord__class_Oless V_k V_i tptp.tc_nat)))) (forall ((V_m $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_m tptp.tc_nat))) (forall ((V_m $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_m tptp.tc_nat) V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 _let_1) _let_2) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_c T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_d T_a))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 _let_1) _let_2) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1))))))) (forall ((V_x $$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 ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_3 _let_1) _let_2) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1)))))) _let_22 (forall ((V_n $$unsorted)) (= (tptp.c_Suc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)) V_n))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_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_Power_Opower__class_Opower V_m V_n tptp.tc_nat) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) V_n T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b (tptp.c_HOL_Otimes__class_Otimes V_b V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_n tptp.tc_nat) V_n)) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_n)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) V_n tptp.tc_nat) V_m) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat) V_n tptp.tc_nat) V_m) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (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_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) V_z T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_x V_z T_a)) (tptp.c_Divides_Odiv__class_Odiv V_y V_z T_a))) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) 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))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c))))) (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_nat $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__size (tptp.c_Lambda_OdB_OVar V_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_N T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat)))) (forall ((V_x $$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 $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_m T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Suc (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat)) V_k tptp.tc_nat) _let_1) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_k tptp.tc_nat))))) (= _let_19 _let_21) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Osubstn (tptp.c_Lambda_OdB_OAbs V_t) V_s V_k) (tptp.c_Lambda_OdB_OAbs (tptp.c_Lambda_Osubstn V_t V_s (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))))) (forall ((T_a $$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 ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((V_e $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$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 $$unsorted) (V_x $$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 ((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_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (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_2 V_m) V_m) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_2 _let_1) _let_1) V_m T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) tptp.tc_nat))))) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_19 _let_19 tptp.tc_nat) (forall ((V_x $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) (tptp.c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero 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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) T_a) (= V_x _let_1)))) (forall ((T_a $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))) (forall ((V_dB $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_Lambda_OdB_OAbs V_dB) tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize V_dB tptp.tc_Lambda_OdB)) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (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 ((V_n $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Oliftn V_n _let_1 V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_c) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (= _let_21 _let_19) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) V_a T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Odiv V_b V_a T_a) T_a) V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift _let_1) V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((V_x $$unsorted) (V_s $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (= (tptp.c_Lambda_Osubstn (tptp.c_Lambda_OdB_OVar V_x) V_s V_x) (tptp.c_Lambda_Oliftn V_x V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_s) V_j)) V_i) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) _let_1)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) V_i)) V_j)) (not (tptp.c_HOL_Oord__class_Oless V_j _let_1 tptp.tc_nat))))) (forall ((V_t $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_Olift V_t))) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.hAPP _let_1 V_i)) (tptp.c_Suc V_k)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.hAPP _let_1 V_k)) V_i)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_k (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (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 $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_j tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_m $$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 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_a V_c tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Odiv V_b V_c tptp.tc_nat))) (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Omod V_b V_c tptp.tc_nat)) V_c tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_i $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_i V_m tptp.tc_nat) (tptp.c_Power_Opower__class_Opower V_i V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_i tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv (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_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (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.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i) V_T))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) T_a)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat)) V_m) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_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_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Otimes__class_Otimes V_n (tptp.c_Suc (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$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_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_x _let_1 tptp.tc_nat) tptp.tc_nat))) (forall ((V_s $$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_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_P $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat)) V_j) V_k tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_j)))) (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_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_x tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$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)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (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_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 V_a T_a) _let_1)))) (forall ((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 $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_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 ((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_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_x V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_nat))))) (forall ((V_m $$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 $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_P $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat)) V_j) V_k tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_i)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) V_n T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Power_Opower__class_Opower V_x V_n T_a) (tptp.c_Power_Opower__class_Opower V_y V_n T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((V_e $$unsorted) (V_x $$unsorted) (V_T $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Type_Oshift V_e V_x V_T T_a) V_x) V_T)) (forall ((V_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Osubstn _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 ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_dB $$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 ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat)) V_m)) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.c_Suc V_m) V_n tptp.tc_nat))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= V_m (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_lx $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$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)) V_m) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_m T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a)) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_m T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_k) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_k) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_k V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) V_m) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_x $$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 $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_n $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_Lambda_Oliftn V_n (tptp.c_Lambda_OdB_OVar V_i) V_k) (tptp.c_Lambda_OdB_OVar (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_n))) (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_n $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Oliftn V_n (tptp.c_Lambda_OdB_OAbs V_s) V_k) (tptp.c_Lambda_OdB_OAbs (tptp.c_Lambda_Oliftn V_n V_s (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)) (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n V_m tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat)))) (forall ((V_n $$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_x $$unsorted) (V_y $$unsorted)) (or (= V_x V_y) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_a tptp.tc_nat)) (= V_a V_b) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_a tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b tptp.tc_nat)) (= V_a V_b))) (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 $$unsorted) (V_y $$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_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 $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_n V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)))) (forall ((T_a $$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__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 ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_a T_a))) (forall ((V_x $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_x tptp.tc_nat)) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a (tptp.c_Suc V_n) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i) V_t))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_Ring__and__Field_Odvd__class_Odvd (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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_b tptp.tc_nat) V_c tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Odiv V_b V_c tptp.tc_nat) tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c tptp.tc_nat) tptp.tc_nat) V_c tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$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_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_x V_y T_a) (tptp.c_Divides_Odiv__class_Odiv V_w V_z T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_x V_w T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_w T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a)))) (forall ((V_x $$unsorted) (V_n $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_xb $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.c_HOL_Otimes__class_Otimes V_n V_xa tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 V_y) (tptp.c_HOL_Otimes__class_Otimes V_n V_xb tptp.tc_nat)))) (= (tptp.c_Divides_Odiv__class_Omod V_x V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod V_y 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 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)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_m V_n))) (forall ((V_p $$unsorted)) (= (tptp.c_Power_Opower__class_Opower V_p (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$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 $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= V_a _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (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))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_n))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_n)))) (forall ((V_m $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xlexn__Xinduct__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_P $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1 V_P)))) (not (tptp.hBOOL (tptp.hAPP V_P V_k))))) (not (tptp.c_HOL_Oord__class_Oless _let_2 _let_2 tptp.tc_nat)) (forall ((V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Oliftn (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_t V_k) V_t)) (forall ((V_P $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv V_m _let_1 tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP V_P _let_1))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv V_n _let_1 tptp.tc_nat)))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv V_n _let_1 tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P _let_1))))) (forall ((V_n $$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 ((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_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 $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (= V_m V_n) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_x $$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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xreplicate__Xinduct__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__Nat__Xnat__Xinducts__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (= (tptp.hAPP _let_16 _let_2) _let_2) (forall ((V_P $$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 $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (tptp.hBOOL (tptp.hAPP V_P (tptp.v_sko__List__Xupt__Xinduct__1 V_P))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_x $$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_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 $$unsorted) (V_m $$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_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_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat))) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$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 $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.c_Suc (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)) V_n tptp.tc_nat))) (forall ((V_i $$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 ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_n) 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 ((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_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)) (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 ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)))) (or (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Suc V_m) V_n tptp.tc_nat) _let_1) (= _let_1 V_n)))) (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_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_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 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_x $$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 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_dB1 $$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 $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)))) (forall ((V_nat $$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 ((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 ((V_n $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Oliftn V_n (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_Oliftn V_n V_s V_k)) (tptp.c_Lambda_Oliftn V_n V_t V_k)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Osubstn (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_Osubstn V_t V_s V_k)) (tptp.c_Lambda_Osubstn V_u V_s V_k)))) (forall ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (= (tptp.c_Lambda_Osubstn V_t V_s V_n) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) (tptp.c_Lambda_Oliftn V_n V_s (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) V_n))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Olist_ONil T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f V_xs T_b T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (= V_T V_U) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otyping V_e _let_1 V_T))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_r) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (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_m $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_s $$unsorted) (V_ss $$unsorted) (V_r $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_Lambda_OdB_OAbs V_r))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_m) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_OrderedGroup_Osemigroup__add T_a)) (= (tptp.c_List_Ofoldl _let_1 (tptp.hAPP _let_2 V_y) V_zs T_a T_a) (tptp.hAPP _let_2 (tptp.c_List_Ofoldl _let_1 V_y V_zs T_a T_a))))))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k)) V_u) V_k) V_u)) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_r) V_t) V_i) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_s) V_t) V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv (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_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) tptp.tc_nat) _let_1))) (forall ((T_a $$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_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((V_e $$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 ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_Suc V_n) tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c tptp.tc_nat) tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Omod (tptp.c_Divides_Odiv__class_Odiv V_a V_b tptp.tc_nat) V_c tptp.tc_nat) tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Omod V_a V_b tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_j))) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_1) V_u) V_i) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_j V_i tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_N T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((V_i $$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_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c tptp.tc_nat) tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Odiv V_a V_b tptp.tc_nat) V_c tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_d T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((V_b $$unsorted) (V_q $$unsorted) (V_c $$unsorted) (V_r $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Omod V_q V_c tptp.tc_nat) tptp.tc_nat)) V_r) (tptp.c_HOL_Otimes__class_Otimes V_b V_c tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_r V_b tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_c tptp.tc_nat)))) (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 $$unsorted) (V_y $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a)) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a)) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_e $$unsorted) (V_t_H $$unsorted) (V_T $$unsorted) (V_t $$unsorted)) (or (tptp.c_Type_Otyping V_e V_t_H V_T) (not (tptp.c_Lambda_Obeta V_t V_t_H)) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_Suc V_n) tptp.tc_nat) tptp.tc_nat T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat) tptp.tc_nat T_a)) (tptp.hAPP V_f V_n))) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat) V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_d $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_d V_x tptp.tc_nat) V_d tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OVar V_nat_H))) (= V_nat V_nat_H))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (= V_m _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m _let_1 tptp.tc_nat))))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a)) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.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_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_x V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))))) (forall ((V_nat $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_Lambda_OdB_OVar V_nat) tptp.tc_Lambda_OdB) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_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 $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c 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_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 V_b) V_c T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat) tptp.tc_nat T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP V_f V_m)) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_Suc V_m) V_n tptp.tc_nat) tptp.tc_nat T_a))) (not (tptp.c_HOL_Oord__class_Oless 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.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)))) (tptp.c_Type_Otyping tptp.v_e____ tptp.v_u____ tptp.v_T____) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a)))) (forall ((V_s $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.c_Lambda_OdB_OAbs V_s)) V_k) (tptp.c_Lambda_OdB_OAbs (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))))) (forall ((V_dB $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__size (tptp.c_Lambda_OdB_OAbs V_dB)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Lambda_OdB_OdB__size V_dB)) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a)) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a)))))) (forall ((V_e $$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.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i) V_T) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (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_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_z V_y tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_z tptp.tc_nat)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_y V_x tptp.tc_nat) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y tptp.tc_nat)))) (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_t $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OAbs V_t)) V_s) V_k) (tptp.c_Lambda_OdB_OAbs (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat)))))) _let_20 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ua______)) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_r) V_i) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_T_H $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_a____) V_u) V_i))) (not (tptp.c_Type_Otyping V_e V_u tptp.v_T____)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i tptp.v_T____ tptp.tc_Type_Otype) tptp.v_a____ V_T_H)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (not (= (tptp.hAPP V_f _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_Suc _let_1) V_k tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_k tptp.tc_nat) tptp.tc_nat T_a))))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Lambda_OdB_OdB__size (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lambda_OdB_OdB__size V_dB1)) (tptp.c_Lambda_OdB_OdB__size V_dB2))) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Nat_Osize__class_Osize (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) tptp.tc_Lambda_OdB) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Nat_Osize__class_Osize V_dB1 tptp.tc_Lambda_OdB)) (tptp.c_Nat_Osize__class_Osize V_dB2 tptp.tc_Lambda_OdB))) (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_s) V_t) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_rs $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT V_rs tptp.tc_Lambda_OdB)))) (tptp.c_Type_Otyping (tptp.c_Type_Oshift tptp.v_e____ tptp.v_i____ tptp.v_T____ tptp.tc_Type_Otype) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs tptp.v_r____)) tptp.v_a____) tptp.v_as____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.v_T_H____) (forall ((T_a $$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 ((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 ((V_y $$unsorted)) (or (= V_y (tptp.c_Suc (tptp.c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1 V_y))) (= V_y (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) (tptp.c_Suc _let_1))) (= V_m _let_1) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (= _let_17 _let_14) (forall ((V_P $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1 V_P)))) (not (tptp.hBOOL (tptp.hAPP V_P V_k))))) (forall ((V_x $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= (tptp.c_Power_Opower__class_Opower V_x V_m tptp.tc_nat) _let_2)) (= V_x _let_2) (= V_m _let_1))))) (= _let_14 _let_18) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__List__Xlexn__Xinduct__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Omod V_m (tptp.c_Suc _let_1) tptp.tc_nat) _let_1))) (= (tptp.c_HOL_Otimes__class_Otimes _let_14 _let_14 tptp.tc_nat) _let_14) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_14 _let_14 tptp.tc_nat) (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 ((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)))) (tptp.c_HOL_Oord__class_Oless _let_2 _let_14 tptp.tc_nat) (= _let_19 _let_14) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (T_a $$unsorted) (V_T $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Type_Oshift (tptp.c_Type_Oshift V_e V_i V_U T_a) _let_1 V_T T_a) (tptp.c_Type_Oshift (tptp.c_Type_Oshift V_e _let_1 V_T T_a) (tptp.c_Suc V_i) V_U T_a)))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_n)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__List__Xreplicate__Xinduct__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__List__Xupt__Xinduct__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_v $$unsorted)) (or (= V_v (tptp.c_Suc (tptp.c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1 V_v))) (= V_v (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Power_Opower__class_Opower V_x _let_1 tptp.tc_nat) (tptp.c_Suc _let_1)))) (forall ((V_P $$unsorted) (V_nat $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Suc (tptp.v_sko__Nat__Xnat__Xinduct__1 V_P))))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (= _let_18 _let_14) (forall ((V_n $$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 ((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 ((V_n $$unsorted)) (or (= V_n (tptp.c_Suc (tptp.c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1 V_n))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_k $$unsorted)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_k tptp.tc_nat)) (= _let_14 _let_17) (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))))) _let_13 (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_Suc (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)) V_n)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$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)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (= (tptp.c_Power_Opower__class_Opower _let_1 V_m tptp.tc_nat) _let_1))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (= V_m _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_m _let_1 tptp.tc_nat))))) (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv V_m (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat) V_m)) (forall ((T_a $$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 ((V_t $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Lambda_Osubstn V_t V_s _let_1) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_s) _let_1)))) (forall ((V_r $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (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_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_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_t)))) (forall ((V_s $$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 ((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_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 $$unsorted) (V_ss $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_m $$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_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) (tptp.c_Lambda_OdB_OVar V_i)))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_e $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted) (V_T $$unsorted)) (or (tptp.c_Type_Otypings V_e (tptp.c_List_Omap (tptp.c_COMBC (tptp.c_COMBC tptp.c_Lambda_Osubst V_u tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_Ts) (not (tptp.c_Type_Otypings (tptp.c_Type_Oshift V_e V_i V_T tptp.tc_Type_Otype) V_ts V_Ts)) (not (tptp.c_Type_Otyping V_e V_u V_T)))) (forall ((V_n $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Oliftn (tptp.c_Suc V_n) V_t V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.c_Lambda_Oliftn V_n V_t V_k)) V_k))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_r) (tptp.c_Lambda_OdB_OVar V_i)) V_j))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_U $$unsorted) (V_ts $$unsorted) (V_Ts $$unsorted)) (or (tptp.c_Type_Otypings (tptp.c_Type_Oshift V_e V_i V_U tptp.tc_Type_Otype) (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) V_Ts) (not (tptp.c_Type_Otypings V_e V_ts V_Ts)))) (forall ((V_u $$unsorted) (V_i $$unsorted) (V_e $$unsorted) (V_T_H $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst tptp.v_r____) tptp.v_a____) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.v_as____ tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_1) V_u) V_i))) (not (tptp.c_Type_Otyping V_e V_u tptp.v_T____)) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_u))) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_e V_i tptp.v_T____ tptp.tc_Type_Otype) _let_1 V_T_H))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r)) V_s) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_s))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_r) V_s) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))))) (forall ((V_ts $$unsorted)) (or (tptp.c_List_Olistsp tptp.c_InductTermi_OIT (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) (not (tptp.c_List_Olistsp tptp.c_InductTermi_OIT V_ts tptp.tc_Lambda_OdB)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_a____)) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP 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.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_s) V_k)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_u) V_s) V_k)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT _let_9)) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_i) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i) (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1_H) V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP 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.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) V_k)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_k)))) _let_12 (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 $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_r $$unsorted) (V_ts $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_u____)) (forall ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_k)) V_s) V_k) V_t)) _let_11 _let_7 (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)))) (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_Oordered__semiring__strict 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_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__zero tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Divides_Osemiring__div tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Odvd tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted)) (= (tptp.c_COMBB V_P V_Q V_R T_b T_a T_c) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.55/1.07 )
% 0.55/1.07 % SZS output end Proof for LCL837-1
% 0.55/1.07 % cvc5---1.0.5 exiting
% 0.55/1.08 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------