%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL848-1 : 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 07:04:00 EDT 2023

% Result   : Unsatisfiable 0.56s 0.98s
% Output   : Proof 0.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.18  % Problem    : LCL848-1 : TPTP v8.1.2. Released v4.1.0.
% 0.18/0.19  % 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   : Fri Aug 25 04:48:35 EDT 2023
% 0.19/0.40  % CPUTime    : 
% 0.26/0.59  %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.60  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2zYiPLd6B2/cvc5---1.0.5_2037.p...
% 0.26/0.71  ------- get file name : TPTP file name is LCL848-1
% 0.26/0.72  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2037.smt2...
% 0.26/0.72  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.56/0.98  % SZS status Unsatisfiable for LCL848-1
% 0.56/0.98  % SZS output start Proof for LCL848-1
% 0.56/0.99  (
% 0.56/0.99  (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_List_Olist_OCons (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift tptp.v_ta____) _let_1) (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar _let_1) _let_2 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.c_List_Olistsp tptp.c_InductTermi_OIT _let_2 tptp.tc_Lambda_OdB))) (let ((_let_6 (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)))))) (let ((_let_7 (not _let_5))) (let ((_let_8 (or _let_3 _let_7))) (let ((_let_9 (_let_6))) (let ((_let_10 (ASSUME :args _let_9))) (let ((_let_11 (not _let_8))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_10 :args (_let_1 _let_2 QUANTIFIERS_INST_E_MATCHING ((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)))) :args _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_3 _let_7 _let_11))) (ASSUME :args (_let_4)) (ASSUME :args (_let_5)) :args (_let_11 true _let_3 false _let_5)) _let_10 :args (false true _let_8 false _let_6)) :args ((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)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_c) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_n $$unsorted)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a _let_1 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((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 $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((T_a $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_j $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_j V_n tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((V_n $$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 $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (forall ((V_nat $$unsorted) (V_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 $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_l tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_N T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_b) V_a))) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_vs $$unsorted) (T_a $$unsorted) (V_us $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_x V_vs T_a) (tptp.c_List_Oappend V_x V_us T_a) T_a) (not (tptp.c_ListOrder_Ostep1 V_r V_vs V_us T_a)))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a)) (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys V_x T_a) (tptp.c_List_Oappend V_xs V_x T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_y $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_y (tptp.c_List_Olist_Olist__size V_f V_xs T_a) tptp.tc_nat) (not (tptp.c_lessequals V_y (tptp.hAPP V_f V_x) tptp.tc_nat)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_x $$unsorted)) (or (not (tptp.c_lessequals V_x V_x tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_Suc V_m) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_N T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat)))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_l tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_l tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Suc _let_1) tptp.tc_nat)) V_n) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Suc V_i) tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_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 $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_xa T_a) (not (tptp.c_in V_xa (tptp.c_List_Oset V_xs T_a) T_a)) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_xa T_a) (not (tptp.c_in V_xa (tptp.c_List_Oset V_ys T_a) T_a)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olength__unique (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_Suc (tptp.c_List_Olength__unique V_xs T_a))) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_in V_y (tptp.c_List_Oset V_xs T_a) T_a) (= V_y V_x) (not (tptp.c_in V_y (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a))) (forall ((V_x $$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_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_n $$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))))) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Suc _let_1) tptp.tc_nat) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus V_a V_b tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 (tptp.c_Suc V_n) T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_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_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_g V_xs T_b T_a))) (= (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_b) T_b)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_OCons V_x V_xa T_a) _let_1) (tptp.c_Suc (tptp.c_Nat_Osize__class_Osize V_xa _let_1))))) (forall ((V_xa $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Suc (tptp.c_Nat_Osize__class_Osize V_xa _let_1)) (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_OCons V_x V_xa T_a) _let_1)))) (forall ((V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_OCons V_x V_ys T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_ys _let_1) tptp.tc_nat)))) (forall ((T_a $$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_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ohd (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Ohd V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Ohd (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) T_a) (tptp.c_List_Ohd V_ys T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Otake V_n V_xs T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Odrop V_n V_xs T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (= (tptp.c_List_Onth (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_Suc V_n) T_a) (tptp.c_List_Onth V_xs V_n T_a))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake (tptp.c_Suc V_n) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Otake V_n V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_P $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_OtakeWhile V_P V_xs T_a) V_xs)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)) (not (tptp.c_List_Olistsp V_A V_xs T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oreplicate V_n V_y T_a) T_a) T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))) (or (= (tptp.c_List_Onth (tptp.c_List_Orev V_xs T_a) V_n T_a) (tptp.c_List_Onth V_xs (tptp.c_HOL_Ominus__class_Ominus _let_1 (tptp.c_Suc V_n) tptp.tc_nat) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_List_Onth V_xs V_i T_a) (tptp.c_List_Onth V_xs V_j T_a) T_a) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_j (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_List_Onth V_xs V_i T_a) (tptp.c_List_Onth V_xs V_j T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_j (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_Suc V_n) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Odrop V_n V_xs T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Otake V_n V_xs T_a) V_xs) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_OCons V_y V_zs T_a) T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_zs T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted _let_1 T_a)) (not (tptp.c_lessequals V_x V_y T_a))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Odrop V_n V_xs T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osize__class_Osize V_xs _let_1) V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_i $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_Suc V_i) V_y T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist__update V_xs V_i V_y T_a) T_a))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ohd (tptp.c_List_Oreplicate V_n V_x T_a) T_a) V_x) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.c_Suc V_n) V_x T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oreplicate V_n V_x T_a) T_a))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_xs) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_i tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize (tptp.c_List_OtakeWhile V_P V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast V_xs T_a) T_a) T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Otake V_m V_xs T_a) T_a) (tptp.c_List_Otake (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_List_Odrop V_n V_xs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_I $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Osublist V_xs V_I T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Osublist V_xs V_I T_a) T_a) T_a)) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_i (tptp.c_List_Oreplicate V_k V_x T_a) T_a) (tptp.c_List_Oreplicate (tptp.c_HOL_Ominus__class_Ominus V_k V_i tptp.tc_nat) V_x T_a))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_ys T_a))) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_List_Olinorder__class_Oinsort__key V_f V_x _let_1 T_a T_b) (tptp.c_List_Olist_OCons V_x _let_1 T_a)) (not (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_List_Olinorder__class_Oinsort__key V_f V_x (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a T_b) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olinorder__class_Oinsort__key V_f V_x V_ys T_a T_b) T_a)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y) T_b))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olinorder__class_Oinsort__key V_f V_x V_xs T_a T_b) _let_1) (tptp.c_Suc (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat))) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)) (= V_m V_n))) (forall ((T_a $$unsorted) (V_m $$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 ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_k tptp.tc_nat) V_j tptp.tc_nat))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_c tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_b V_c tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_c V_a tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_m))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= _let_1 V_n) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc V_k) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_k tptp.tc_nat))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Ominus__class_Ominus V_n V_i tptp.tc_nat) tptp.tc_nat) V_i) (not (tptp.c_lessequals V_i V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (= V_m _let_1) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m _let_1 tptp.tc_nat))))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a _let_2 T_a) (tptp.c_Power_Opower__class_Opower V_b _let_2 T_a))) (= V_a V_b) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_List_Ohd V_xs T_a) (tptp.c_List_Oset V_xs T_a) T_a) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a) (not (tptp.c_lessequals V_x V_y tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((V_x $$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 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$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 $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) _let_1)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) _let_1)) (= V_m V_n)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_lessequals V_n _let_1 tptp.tc_nat))))) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m V_m tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ohd (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) V_x)) (forall ((V_r $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_x V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a)))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_xa))) (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_x T_a) (tptp.c_List_Olist_OCons V_xa V_x T_a) T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (= V_xs V_ys) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_OCons V_y V_ys T_a) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Olist_ONil T_a) V_xs T_a))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_List_Onth V_xs V_j T_a) (tptp.c_List_Onth V_xs V_i T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_j (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Orev V_xs T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a) (tptp.c_in V_x (tptp.c_List_Oset V_xa T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a) (tptp.c_in V_x (tptp.c_List_Oset V_xb T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_a V_N T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_b V_x T_a) (tptp.c_Power_Opower__class_Opower V_b V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= V_ys V_xs) (= V_y V_x) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (= V_y V_x) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_r $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_r V_y) V_x)) (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= V_ys V_xs) (tptp.c_ListOrder_Ostep1 V_r V_ys V_xs T_a) (not (tptp.c_ListOrder_Ostep1 V_r (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) T_a))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ohd V_xs T_a) (tptp.c_List_Onth V_xs (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_OtakeWhile V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_r $$unsorted) (V_rs $$unsorted) (V_ss $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (not (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs V_ss tptp.tc_Lambda_OdB)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Olist_ONil T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Olist_ONil T_a)) (not (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat)))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= (tptp.c_List_Otake _let_2 V_xs_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0621) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1) _let_2 tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Otake (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) V_ys T_a) T_a))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= V_xs_092_060_094isub_0621 (tptp.c_List_Otake _let_2 V_ys_092_060_094isub_0621 T_a)) (not (tptp.c_lessequals _let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1) tptp.tc_nat)))))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= V_xs_092_060_094isub_0622 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_ys_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0622 T_a)) (not (tptp.c_lessequals _let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1) tptp.tc_nat)))))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_xs_092_060_094isub_0621 T_a) V_xs_092_060_094isub_0622 T_a) V_ys_092_060_094isub_0622) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1) _let_2 tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Odrop (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) V_ys T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast V_ys T_a) T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) T_a) T_a) (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Obutlast V_xs T_a) T_a) T_a)))) (forall ((V_as $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_List_Olast V_as T_a) (tptp.c_List_Oset V_as T_a) T_a) (= V_as (tptp.c_List_Olist_ONil T_a)))) (forall ((V_y $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y (tptp.c_List_Olist_Olist__size V_f V_xs T_a) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_y (tptp.hAPP V_f V_x) tptp.tc_nat)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_Otake V_n V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Onth V_xs V_n T_a))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Onth V_xs (tptp.c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 V_P V_n V_xs T_a) T_a)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ohd (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Olast V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Ohd V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olength__unique (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olength__unique V_xs T_a)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oappend (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Ohd (tptp.c_List_Odrop V_n V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Otake (tptp.c_Suc V_n) V_xs T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Omap V_f (tptp.c_List_Olinorder__class_Oinsort__key V_f V_x V_xs T_b T_a) T_b T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Omap V_f V_xs T_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Omap V_f (tptp.c_List_Olinorder__class_Oinsort__key V_f V_x V_xs T_b T_a) T_b T_a) T_a)))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist__update V_xs V_i V_x T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Obutlast V_xs T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_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_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Oreplicate V_n V_x T_a) T_a) V_x) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Odrop V_n V_xs T_a) T_a) (tptp.c_List_Odrop V_n (tptp.c_List_Obutlast V_xs T_a) T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Odrop V_n V_xs T_a) T_a) V_xs)) (forall ((T_a $$unsorted) (V_P $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs 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_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 $$unsorted) (V_a $$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 $$unsorted) (V_a $$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 $$unsorted) (V_x $$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 ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Odrop (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_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 ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_List_OtakeWhile V_P V_xs T_a))) (or (= (tptp.c_List_Onth _let_1 V_j T_a) (tptp.c_List_Onth V_xs V_j T_a)) (not (tptp.c_HOL_Oord__class_Oless V_j (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.tc_List_Olist T_a)) tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Obutlast V_xs T_a) T_a) (tptp.c_List_Obutlast (tptp.c_List_Odrop V_n V_xs T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a))) (= V_x V_y))) (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_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_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.c_in V_x V_S T_a)))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x V_S T_a) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_j $$unsorted)) (or (= (tptp.c_List_Onth (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_j T_a) (tptp.c_List_Onth V_xs V_j T_a)) (= V_i V_j))) (forall ((T_a $$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_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 ((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 ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_List_Onth (tptp.c_List_Otake V_n V_xs T_a) V_i T_a) (tptp.c_List_Onth V_xs V_i T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_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 ((V_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Otake V_n V_xs T_b) T_b T_a))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Odrop V_n V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((V_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst _let_1) V_s) V_k) _let_1) (= V_i V_k) (tptp.c_HOL_Oord__class_Oless V_k V_i tptp.tc_nat)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Olistsp V_A V_xs T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_A $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Olistsp V_A V_ys T_a) (not (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OAbs V_dB) T_a) (tptp.hAPP V_f3 V_dB))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP 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.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Olist__update V_xs V_i (tptp.c_List_Onth V_xs V_i T_a) T_a) V_xs))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olist__update V_xs V_i V_a T_a) (tptp.c_List_Oappend (tptp.c_List_Otake V_i V_xs T_a) (tptp.c_List_Olist_OCons V_a (tptp.c_List_Odrop (tptp.c_Suc V_i) V_xs T_a) T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (T_a $$unsorted)) (or (= V_xs (tptp.c_List_Oappend (tptp.c_List_Otake V_i V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Onth V_xs V_i T_a) (tptp.c_List_Odrop (tptp.c_Suc V_i) V_xs T_a) T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Otake (tptp.c_Suc V_i) V_xs T_a) (tptp.c_List_Oappend (tptp.c_List_Otake V_i V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Onth V_xs V_i T_a) (tptp.c_List_Olist_ONil T_a) T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_u) V_i) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_u) V_i) (tptp.c_List_Omap (tptp.c_COMBC (tptp.c_COMBC tptp.c_Lambda_Osubst V_u tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB (tptp.tc_fun tptp.tc_nat tptp.tc_Lambda_OdB)) V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (forall ((V_rs $$unsorted) (V_n $$unsorted) (V_v $$unsorted)) (or (tptp.c_ListOrder_Ostep1 tptp.c_Lambda_Obeta V_rs (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (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)) V_v))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_Otake V_n V_xs T_a)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Onth V_xs (tptp.c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 V_P V_n V_xs T_a) T_a)))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_Otake V_n V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Onth V_xs V_n T_a))) (tptp.c_HOL_Oord__class_Oless (tptp.c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 V_P V_n V_xs T_a) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Ohd (tptp.c_List_Odrop V_n V_xs T_a) T_a) (tptp.c_List_Onth V_xs V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olist_OCons (tptp.c_List_Onth V_xs V_i T_a) (tptp.c_List_Odrop (tptp.c_Suc V_i) V_xs T_a) T_a) (tptp.c_List_Odrop V_i V_xs T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Odrop V_i V_xs T_a) T_a) (tptp.c_List_Otake (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_i tptp.tc_nat) (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Otake V_i V_xs T_a) T_a) (tptp.c_List_Odrop (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_i tptp.tc_nat) (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_Otake V_n V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Onth V_xs V_n T_a))) (tptp.c_HOL_Oord__class_Oless (tptp.c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 V_P V_n V_xs T_a) V_n tptp.tc_nat))) (forall ((V_xs_092_060_094isub_0621 $$unsorted) (T_a $$unsorted) (V_ys_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (or (not (= V_xs_092_060_094isub_0621 (tptp.c_List_Otake _let_2 V_ys_092_060_094isub_0621 T_a))) (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_ys_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0622 T_a) T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a)) (not (tptp.c_lessequals _let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1) tptp.tc_nat)))))) (forall ((V_ys_092_060_094isub_0621 $$unsorted) (T_a $$unsorted) (V_xs_092_060_094isub_0621 $$unsorted) (V_xs_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Otake _let_2 V_xs_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0621)) (tptp.c_lessequals (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1) _let_2 tptp.tc_nat) (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 V_xs_092_060_094isub_0622 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_xs_092_060_094isub_0621 T_a) V_xs_092_060_094isub_0622 T_a) T_a)))))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_Otake V_n V_xs T_a)) (tptp.c_HOL_Oord__class_Oless V_n _let_1 tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless (tptp.c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 V_P V_n V_xs T_a) _let_1 tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P V_xs T_a) (tptp.c_List_Otake V_n V_xs T_a)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless (tptp.c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 V_P V_n V_xs T_a) V_n tptp.tc_nat))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))) (or (= (tptp.c_List_Olist__update (tptp.c_List_Oappend V_xs V_ys T_a) V_n V_x T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist__update V_ys (tptp.c_HOL_Ominus__class_Ominus V_n _let_1 tptp.tc_nat) V_x T_a) T_a)) (tptp.c_HOL_Oord__class_Oless V_n _let_1 tptp.tc_nat)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))) (or (= (tptp.c_List_Onth (tptp.c_List_Oappend V_xs V_ys T_a) V_n T_a) (tptp.c_List_Onth V_ys (tptp.c_HOL_Ominus__class_Ominus V_n _let_1 tptp.tc_nat) T_a)) (tptp.c_HOL_Oord__class_Oless V_n _let_1 tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Olist__update V_xs V_n V_x T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_xs $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_List_Onth V_xs V_n T_a) (tptp.c_List_Oset V_xs T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_xa $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_xa (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (tptp.c_in (tptp.c_List_Onth V_xs V_xa T_a) (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (= V_a V_b) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_N T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_k $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist__update V_xs V_k V_y T_b) T_b T_a) (tptp.c_List_Olist__update (tptp.c_List_Omap V_f V_xs T_b T_a) V_k (tptp.hAPP V_f V_y) T_a))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_xs)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Onth V_xs V_i T_a) V_x))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_s)) (tptp.c_Lambda_OdB_OAbs V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 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 ((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 $$unsorted) (V_a $$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)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (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))) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_1 tptp.tc_nat)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (forall ((V_m $$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 $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_xs T_a) V_xs)) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Oreplicate _let_1 V_x T_a) (tptp.c_List_Oreplicate _let_1 V_y T_a)))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_x V_y) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Onth (tptp.c_List_Olist_OCons V_x V_xs T_a) _let_1 T_a) V_x)))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Odrop _let_2 _let_1 T_a) _let_1))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Osplice (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_OCons V_y (tptp.c_List_Osplice V_xs V_ys T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_zs $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_y V_zs T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted _let_1 T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs T_a) V_ys T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xa T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xa T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_xa) (tptp.c_List_Omap V_f V_xb T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_xa V_xb T_b) T_b T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Olist_OCons V_x V_xs T_b) T_b T_a) (tptp.c_List_Olist_OCons (tptp.hAPP V_f V_x) (tptp.c_List_Omap V_f V_xs T_b T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a))) (forall ((V_x $$unsorted) (V_xs1 $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs1 V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs1 T_a) V_zs T_a))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted V_xs T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_OtakeWhile V_P V_xs T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_ONil T_a) (tptp.tc_List_Olist T_a)) tptp.tc_nat))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) V_x)) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) V_xs)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a)))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Oappend (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Olist_ONil T_a) T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (forall ((V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_i V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_x _let_1 T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_f $$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)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Obutlast _let_1 T_a) _let_1))) (forall ((V_P $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_OtakeWhile V_P _let_1 T_a) _let_1))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Osplice V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Osplice (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Odrop V_n _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f V_xs T_b T_a))) (= V_xs (tptp.c_List_Olist_ONil T_b)))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Otake V_n _let_1 T_a) _let_1))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_List_Olistsp V_A (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_f $$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 $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Osublist _let_1 V_A T_a) _let_1))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_k V_x T_a) _let_1))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_i V_y T_a) _let_1))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__update _let_1 V_i V_v T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Omap V_f (tptp.c_List_Olist_ONil T_b) T_b T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Olist__update V_xs V_k V_x T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum V_xs T_a) (tptp.c_List_Ofoldl (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) V_xs T_a T_a)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u)) V_s) V_k) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_t) V_s) V_k)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_u) V_s) V_k)))) (forall ((V_dB1 $$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 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_xb $$unsorted) (V_xc $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_xb) V_xc) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_xb) V_xc))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP V_f2 V_dB1) V_dB2))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_dB1) V_dB2) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_dB1) V_dB2))) (forall ((V_u $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Lambda_OdB_OApp V_u))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP _let_1 V_s)) (tptp.hAPP _let_1 V_t))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t)))))) (forall ((V_s $$unsorted) (V_u $$unsorted) (V_t $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_s) V_u)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_s) V_t))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_OrderedGroup_Osemigroup__add T_a)) (= (tptp.c_List_Ofoldl _let_1 (tptp.hAPP _let_2 V_y) V_zs T_a T_a) (tptp.hAPP _let_2 (tptp.c_List_Ofoldl _let_1 V_y V_zs T_a T_a))))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Oappend V_xs V_ys T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.c_List_Ofoldl V_f V_a V_xs T_a T_b) V_ys T_a T_b))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_xd $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OVar V_xd) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_xd))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_nat $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OVar V_nat) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f1 V_nat))))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k)) V_u) V_k) V_u)) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i)) V_t)))) (forall ((V_nat $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Orev V_xs T_b) T_b T_a))) (forall ((V_m $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_m V_x T_a) (tptp.c_List_Oreplicate V_n V_y T_a))) (= V_m V_n))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Otake V_n V_xs T_a) T_a) (not (tptp.c_List_Olinorder__class_Osorted V_xs T_a)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onth (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x V_ys T_a) T_a) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) T_a) V_x)) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_OtakeWhile V_P V_xs T_a))) (= _let_1 (tptp.c_List_Otake (tptp.c_Nat_Osize__class_Osize _let_1 (tptp.tc_List_Olist T_a)) V_xs T_a)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize (tptp.c_List_OtakeWhile V_P V_xs T_a) _let_1))) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_List_Onth V_xs _let_2 T_a)))) (not (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_Nat_Osize__class_Osize V_xs _let_1) tptp.tc_nat)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Orev (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_ys T_a) T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_xs T_a) T_a) V_xs)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= (tptp.c_List_Oappend (tptp.c_List_Obutlast V_xs T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Olast V_xs T_a) _let_1 T_a) T_a) V_xs) (= V_xs _let_1)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= V_xs (tptp.c_List_Otake (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_b)))) (forall ((V_f $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Oreplicate V_n V_x T_b) T_b T_a) (tptp.c_List_Oreplicate V_n (tptp.hAPP V_f V_x) T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_List_Onth (tptp.c_List_Oappend V_xs V_ys T_a) V_n T_a) (tptp.c_List_Onth V_xs V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Onth (tptp.c_List_Olist__update V_xs V_x V_xa T_a) V_x T_a) V_xa))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Onth (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_i T_a) V_x) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Odrop V_n V_xs T_a) T_a) (tptp.c_List_Olast V_xs T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (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 ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Otake V_n (tptp.c_List_Obutlast V_xs T_a) T_a) (tptp.c_List_Otake V_n V_xs T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_b))) (or (not (= (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a))) (= (tptp.c_Nat_Osize__class_Osize V_xs _let_1) (tptp.c_Nat_Osize__class_Osize V_ys _let_1))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)))) (or (not (= V_xs (tptp.c_List_Otake _let_1 V_zs T_a))) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Odrop _let_1 V_zs T_a) T_a) V_zs)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_List_Olist__update (tptp.c_List_Oappend V_xs V_ys T_a) V_n V_x T_a) (tptp.c_List_Oappend (tptp.c_List_Olist__update V_xs V_n V_x T_a) V_ys T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_i $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_List_Olist__update (tptp.c_List_Oappend V_xs V_ys T_a) V_i V_x T_a) (tptp.c_List_Oappend (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_ys T_a)) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_List_Onth (tptp.c_List_Oreplicate V_n V_x T_a) V_i T_a) V_x) (not (tptp.c_HOL_Oord__class_Oless V_i V_n tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_xs $$unsorted) (V_x $$unsorted) (V_l $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x V_l T_a) T_a) T_a) (tptp.c_List_OtakeWhile V_P V_xs T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (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_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Olast V_ys T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t)) (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_s) V_t) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$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 $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_List_Olistsum V_xs T_a))))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Omap V_f (tptp.c_List_Oappend V_xs V_ys T_b) T_b T_a) (tptp.c_List_Oappend (tptp.c_List_Omap V_f V_xs T_b T_a) (tptp.c_List_Omap V_f V_ys T_b T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((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 $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_y $$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 ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (let ((_let_2 (tptp.c_List_Oreplicate V_k V_x T_a))) (= (tptp.c_List_Oappend _let_1 _let_2 T_a) (tptp.c_List_Oappend _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_f $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_List_Onth (tptp.c_List_Omap V_f V_xs T_a T_b) V_n T_b) (tptp.hAPP V_f (tptp.c_List_Onth V_xs V_n T_a))) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_a))) (= V_xs V_ys))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olast V_xs T_a))) (forall ((T_a $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_List_Olistsum (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Olistsum V_xs T_a)))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Olistsp V_A (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (not (tptp.c_List_Olistsp V_A V_ys T_a)) (not (tptp.c_List_Olistsp V_A V_xs T_a)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Oreplicate V_n V_x T_a) (tptp.tc_List_Olist T_a)) V_n)) (forall ((V_xs $$unsorted) (V_i $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist__update V_xs V_i (tptp.c_List_Onth V_xs V_i T_a) T_a) V_xs)) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_j))) (or (= (tptp.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 ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_dB $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OAbs V_dB) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f3 V_dB))))) (forall ((V_P $$unsorted) (V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_xa $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OAbs V_xa) tptp.t_a)))) (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP V_f3 V_xa))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x V_ys T_a) T_a) (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) V_y T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= (tptp.c_List_Onth V_xs V_n T_a) V_y))) (forall ((V_ys_092_060_094isub_0621 $$unsorted) (T_a $$unsorted) (V_xs_092_060_094isub_0621 $$unsorted) (V_ys_092_060_094isub_0622 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_Nat_Osize__class_Osize V_xs_092_060_094isub_0621 _let_1))) (let ((_let_3 (tptp.c_List_Oappend (tptp.c_List_Odrop _let_2 V_ys_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0622 T_a))) (let ((_let_4 (tptp.c_Nat_Osize__class_Osize V_ys_092_060_094isub_0621 _let_1))) (or (not (= (tptp.c_List_Oappend (tptp.c_List_Odrop _let_4 V_xs_092_060_094isub_0621 T_a) _let_3 T_a) V_ys_092_060_094isub_0622)) (not (= (tptp.c_List_Otake _let_4 V_xs_092_060_094isub_0621 T_a) V_ys_092_060_094isub_0621)) (not (= V_xs_092_060_094isub_0621 (tptp.c_List_Otake _let_2 V_ys_092_060_094isub_0621 T_a))) (= (tptp.c_List_Oappend V_xs_092_060_094isub_0621 _let_3 T_a) (tptp.c_List_Oappend V_ys_092_060_094isub_0621 V_ys_092_060_094isub_0622 T_a)))))))) (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.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_t) V_t_H))) (not (tptp.c_Type_Otyping V_e V_t V_T)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted V_xs T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((T_a $$unsorted) (V_ys $$unsorted) (V_xs $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted V_ys T_a) (not (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_i_H $$unsorted) (V_x_H $$unsorted)) (or (= (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_i_H V_x_H T_a) (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i_H V_x_H T_a) V_i V_x T_a)) (= V_i V_i_H))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Oappend _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend _let_1 V_xs T_a) T_a)))) (forall ((V_n $$unsorted) (V_f $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Omap V_f V_xs T_b T_a) T_a) (tptp.c_List_Omap V_f (tptp.c_List_Odrop V_n V_xs T_b) T_b T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Orev V_xs T_a) _let_1) (tptp.c_Nat_Osize__class_Osize V_xs _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Obutlast (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Obutlast V_ys T_a) T_a)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum (tptp.c_List_Oappend V_xs V_ys T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_List_Olistsum V_xs T_a)) (tptp.c_List_Olistsum V_ys T_a))))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_j $$unsorted)) (or (= (tptp.c_List_Onth (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_j T_a) (tptp.c_List_Onth V_xs V_j T_a)) (= V_i V_j) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_i V_y T_a) (tptp.c_List_Olist__update V_xs V_i V_y T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_ys T_a) V_zs T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_ys V_zs T_a) T_a))) (forall ((V_xs $$unsorted) (V_xs1 $$unsorted) (V_us $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_xs1 V_us T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_xs1 T_a) V_us T_a))) (forall ((V_zs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_zs V_x T_a) V_ys T_a) (tptp.c_List_Oappend V_zs (tptp.c_List_Oappend V_x V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_x V_ts T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_x T_a) V_ts T_a))) (forall ((T_a $$unsorted) (V_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 $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_e $$unsorted) (V_i $$unsorted) (V_T $$unsorted)) (or (= (tptp.hAPP V_e V_i) V_T) (not (tptp.c_Type_Otyping V_e (tptp.c_Lambda_OdB_OVar V_i) V_T)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_nat $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__case V_f1 V_f2 V_f3 (tptp.c_Lambda_OdB_OVar V_nat) T_a) (tptp.hAPP V_f1 V_nat))) (forall ((V_env $$unsorted) (V_x $$unsorted)) (tptp.c_Type_Otyping V_env (tptp.c_Lambda_OdB_OVar V_x) (tptp.hAPP V_env V_x))) (forall ((V_ts $$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_s____)) (forall ((V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_t $$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)) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_r) V_i)) (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_s) V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (= (tptp.c_List_Osublist _let_1 V_A T_a) _let_1) (not (tptp.c_in (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_A tptp.tc_nat))))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_List_Otake _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a))))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (= (tptp.c_List_Osublist (tptp.c_List_Olist_OCons V_x _let_1 T_a) V_A T_a) _let_1) (tptp.c_in (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_A tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_n $$unsorted) (V_rs $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_n))) (or (= V_v (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 V_n V_rs V_v) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_rs tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_v)))))) (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_i) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift V_t) V_i) (tptp.c_List_Omap (tptp.c_COMBC tptp.c_Lambda_Olift V_i tptp.tc_Lambda_OdB tptp.tc_nat tptp.tc_Lambda_OdB) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_List_Olistsum (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onth (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) V_x)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Odrop (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) _let_1 T_a) _let_1))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_y T_a) (tptp.c_List_Olist_OCons V_y V_xs T_a))) (forall ((V_fa $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__size V_fa (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_f $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_Olist__size V_f (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Nat_Osize__class_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Oreplicate V_n V_x T_a))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oreplicate V_n V_x T_a) (tptp.c_List_Olist_ONil T_a))) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_xs T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Oreplicate (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x T_a))) (forall ((T_a $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_List_Olist_ONil T_a) (tptp.tc_List_Olist T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Otake V_n V_xs T_a) _let_1)) (= V_xs _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Olength__unique (tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_x T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_x V_y)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_xs V_ys)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_List_Olinorder__class_Oinsort__key V_f V_x _let_1 T_a T_b) (tptp.c_List_Olist_OCons V_x _let_1 T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Obutlast V_xs T_a) T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a) V_x)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) _let_1))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Osplice _let_1 (tptp.c_List_Olist_ONil T_a) T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_OtakeWhile V_P (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a)) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olast V_xs T_a)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_List_Olinorder__class_Osorted (tptp.c_List_Olist_OCons V_x (tptp.c_List_Olist_ONil T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_zs $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.c_List_Ofoldl _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) V_zs T_a T_a)) (tptp.c_List_Ofoldl _let_1 V_x V_zs T_a T_a))))) (forall ((V_nat $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize (tptp.c_Lambda_OdB_OVar V_nat) tptp.tc_Lambda_OdB) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_nat $$unsorted)) (= (tptp.c_Lambda_OdB_OdB__size (tptp.c_Lambda_OdB_OVar V_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((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.hBOOL (tptp.hAPP (tptp.hAPP 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.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Obeta V_r) V_s))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_r $$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_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Osubst V_r) (tptp.c_Lambda_OdB_OVar V_i)) V_j))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_r))))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_Olift _let_1) V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB))) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ts (tptp.c_List_Oappend (tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 V_r V_s V_t V_ts) (tptp.c_List_Olist_OCons V_s _let_1 tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB)) (= V_ts _let_1)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_ONil T_a))) (forall ((V_T $$unsorted) (V_U $$unsorted) (V_e $$unsorted) (V_i $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_i) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (or (= V_T V_U) (not (tptp.c_Type_Otyping V_e _let_1 V_U)) (not (tptp.c_Type_Otyping V_e _let_1 V_T))))) (forall ((V_n $$unsorted) (V_ts $$unsorted) (V_r $$unsorted) (V_ss $$unsorted)) (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_r) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted) (V_ss $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s)) V_t) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OVar V_n) V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_r $$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_r $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_ts $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 V_r V_s V_t V_ts) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) (= V_ts (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_s $$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 $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OAbs V_r))) (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) _let_1))) _let_6 (forall ((V_x $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB))) (let ((_let_2 (tptp.c_List_Oappend V_x (tptp.c_List_Olist_OCons V_s _let_1 tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB))) (or (= _let_2 _let_1) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_x tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_s) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t _let_2 tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))))) (forall ((V_t $$unsorted) (V_ts $$unsorted) (V_u $$unsorted)) (= (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)) V_u) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_List_Oappend V_ts (tptp.c_List_Olist_OCons V_u (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (or (not (= V_r (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 V_xa tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_s (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))))) (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_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 $$unsorted) (V_rs $$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_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_r $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_r) V_s))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_t (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_t)))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((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_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (or (not (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= _let_1 V_s)))) (forall ((V_nat $$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_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_f $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_ONil T_b) T_a T_b) V_a)) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n)))) (forall ((V_s $$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)))) (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT tptp.v_ta____)) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_m))) (= _let_1 (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp _let_1 (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB) tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ofoldl V_f V_a (tptp.c_List_Olist_OCons V_x V_xs T_b) T_a T_b) (tptp.c_List_Ofoldl V_f (tptp.hAPP (tptp.hAPP V_f V_a) V_x) V_xs T_a T_b))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_r $$unsorted) (V_ts $$unsorted) (V_s $$unsorted)) (or (not (= (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_r V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ts tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_r V_s))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_m $$unsorted) (V_s $$unsorted) (V_ss $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_m) (tptp.c_List_Ofoldl tptp.c_Lambda_OdB_OApp V_s V_ss tptp.tc_Lambda_OdB tptp.tc_Lambda_OdB))) (= V_ss (tptp.c_List_Olist_ONil tptp.tc_Lambda_OdB)))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT (tptp.hAPP (tptp.hAPP tptp.c_Lambda_OdB_OApp V_t) (tptp.c_Lambda_OdB_OVar V_i)))) (not (tptp.hBOOL (tptp.hAPP tptp.c_InductTermi_OIT V_t))))) (forall ((V_dB1_H $$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)))) _let_5 _let_4 (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_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_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__add 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_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_Int_Onumber tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Osemigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_Int_Oint) (tptp.class_Nat_Osemiring__char__0 tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (tptp.class_Power_Opower tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (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))))))))))))))))))
% 0.56/0.99  )
% 0.56/1.00  % SZS output end Proof for LCL848-1
% 0.56/1.00  % cvc5---1.0.5 exiting
% 0.56/1.00  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------