TSTP Solution File: SCT085-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SCT085-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 14:12:00 EDT 2023
% Result : Unsatisfiable 0.57s 1.44s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19 % Problem : SCT085-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.19 % Command : do_cvc5 %s %d
% 0.19/0.39 % Computer : n020.cluster.edu
% 0.19/0.39 % Model : x86_64 x86_64
% 0.19/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.39 % Memory : 8042.1875MB
% 0.19/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Thu Aug 24 15:25:30 EDT 2023
% 0.19/0.40 % CPUTime :
% 0.25/0.60 %----Proving TF0_NAR, FOF, or CNF
% 0.25/0.60 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.dmBC7FL1VD/cvc5---1.0.5_8675.p...
% 0.25/0.73 ------- get file name : TPTP file name is SCT085-1
% 0.25/0.73 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8675.smt2...
% 0.25/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.57/1.44 % SZS status Unsatisfiable for SCT085-1
% 0.57/1.44 % SZS output start Proof for SCT085-1
% 0.57/1.46 (
% 0.57/1.46 (let ((_let_1 (forall ((V_xa $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (let ((_let_5 (tptp.tc_fun _let_3 _let_4))) (let ((_let_6 (tptp.c_COMBC (tptp.c_COMBB _let_1 tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool))) (let ((_let_7 (tptp.c_HOL_OIf _let_3))) (let ((_let_8 (tptp.c_in _let_2))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.c_HOL_Oplus__class_Oplus V_xa (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_7 (tptp.hAPP _let_6 (tptp.hAPP tptp.v_x V_xa)) tptp.tc_bool _let_5 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))))))))) (let ((_let_2 (forall ((V_xa $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_2 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_3 (tptp.tc_fun _let_2 tptp.tc_bool))) (let ((_let_4 (tptp.tc_fun _let_3 _let_3))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in _let_2) (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_3) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_1 tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) (tptp.c_HOL_Oplus__class_Oplus V_xa (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) tptp.tc_bool (tptp.tc_fun _let_3 _let_4) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_4) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_3 _let_3) tptp.v_Lba____))))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.hAPP tptp.v_x V_xa)) V_xa)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)) tptp.tc_Arrow__Order__Mirabelle_Oindi)))))))))))) (let ((_let_3 (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_bool)))) (let ((_let_4 (tptp.c_Finite__Set_Ocard _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi))) (let ((_let_5 (tptp.v_sko__CHAINED__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____))) (let ((_let_6 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_6 _let_5) _let_4)))) (let ((_let_8 (forall ((V_i $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun _let_2 _let_2))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in _let_1) (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_2) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_i) tptp.tc_bool (tptp.tc_fun _let_2 _let_3) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_3) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_2) tptp.v_Lba____))))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_i) (tptp.v_sko__CHAINED__1 tptp.v_F tptp.v_Lab____ tptp.v_Lba____ tptp.v_a____ tptp.v_b____ tptp.v_h____))))))))))) (let ((_let_9 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_10 (tptp.tc_fun _let_9 tptp.tc_bool))) (let ((_let_11 (tptp.tc_fun _let_10 _let_10))) (let ((_let_12 (tptp.tc_fun _let_10 _let_11))) (let ((_let_13 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (let ((_let_14 (tptp.c_COMBC (tptp.c_COMBB _let_6 tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool))) (let ((_let_15 (tptp.c_HOL_OIf _let_10))) (let ((_let_16 (tptp.c_in _let_9))) (let ((_let_17 (tptp.hAPP _let_16 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (let ((_let_18 (tptp.hBOOL (tptp.hAPP _let_17 (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_15 (tptp.hAPP _let_14 (tptp.c_HOL_Oplus__class_Oplus _let_5 _let_13 tptp.tc_nat)) tptp.tc_bool _let_12 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_11) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_10) tptp.v_Lba____)))))) (let ((_let_19 (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_2) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_n) tptp.tc_bool (tptp.tc_fun _let_2 _let_3) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_3) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_2) tptp.v_Lba____)))) (let ((_let_5 (tptp.c_in _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) _let_4)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) _let_4))))))))))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP _let_17 (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_15 (tptp.hAPP _let_14 _let_4) tptp.tc_bool _let_12 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_11) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_10) tptp.v_Lba____)))))) (let ((_let_21 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_22 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_23 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_24 (tptp.hAPP tptp.v_x _let_5))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_22 _let_24) _let_5)))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_15 (tptp.hAPP _let_14 _let_24) tptp.tc_bool _let_12 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_11) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_10) tptp.v_Lba____)))) (let ((_let_28 (tptp.hBOOL (tptp.hAPP _let_17 _let_27)))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_26))) (let ((_let_31 (not _let_7))) (let ((_let_32 (not _let_18))) (let ((_let_33 (or _let_32 _let_25 _let_31))) (let ((_let_34 (_let_2))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (ASSUME :args (_let_7)))) (let ((_let_37 (ASSUME :args (_let_18)))) (let ((_let_38 (_let_8))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_16 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) _let_27)))) (let ((_let_41 (or _let_40 _let_28))) (let ((_let_42 (_let_19))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 (not _let_40))) (let ((_let_45 (or _let_32 _let_44 _let_31))) (let ((_let_46 (_let_1))) (let ((_let_47 (ASSUME :args _let_46))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_26 _let_29 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_28 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_32 _let_31 _let_44 (not _let_45)))) _let_37 _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Oplus__class_Oplus V_xa _let_13 tptp.tc_nat)))) :args _let_46)) _let_47 :args (_let_45 false _let_1)) :args (_let_44 false _let_18 false _let_7 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP _let_14 V_n)))) :args _let_42)) _let_43 :args (_let_41 false _let_19)) :args (_let_28 true _let_40 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP _let_14 V_i)))) :args _let_38)) _let_39 :args (_let_30 false _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_31 _let_25 (not _let_33)))) _let_37 _let_36 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Oplus__class_Oplus V_xa _let_13 tptp.tc_nat)))) :args _let_34)) _let_35 :args (_let_33 false _let_2)) :args (_let_25 false _let_18 false _let_7 false _let_33)) :args (false false _let_28 false _let_30 false _let_25)) :args ((forall ((T_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y)) (= V_x (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Orderings_Obot__class_Obot T_a)) V_x)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 V_A))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP _let_1 V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage V_R (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop T_a) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_A _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_1))) (= V_A V_B)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (tptp.c_Relation_Ototal__on (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_r T_a)) (forall ((T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_HOL_Ouminus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ouminus__class_Ouminus V_A (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP V_A tptp.v_x) T_b)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot T_a) T_a) (tptp.c_Orderings_Otop__class_Otop T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) (tptp.c_Orderings_Otop__class_Otop _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (= (tptp.hAPP _let_23 tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) tptp.v_x) _let_23)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_a V_b T_a T_b) V_c V_d T_a T_b) (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_m V_c V_d T_a T_b) V_a V_b T_a T_b)) (= V_a V_c))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) V_n T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_Relation_Orefl__on V_A (tptp.c_Relation_OId__on V_A T_a) T_a)) (forall ((T_a $$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 ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b T_b))) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a _let_2 tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_3) T_a) T_a T_b _let_3) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_HOL_Ouminus__class_Ouminus V_B _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b T_b))) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a _let_2 tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_3) T_a) T_a T_b _let_3) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A))))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_OId__on V_A T_a) T_a T_a) V_A)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (= (tptp.c_Fun_Ofun__upd (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_x V_z T_a T_b) (tptp.c_Fun_Ofun__upd V_f V_x V_z T_a T_b))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (tptp.c_Relation_Orefl__on V_A V_r T_a) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a))))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less__eq V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_less__eq $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_less V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a))))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_x))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_b T_a) V_f)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_x) V_y)) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_a T_b) V_f)) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_aa) V_x) V_y)) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_aa $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofun__upd V_f V_x (tptp.hAPP V_f V_x) T_aa T_a) V_f)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (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 ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_L $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x)) tptp.c_Arrow__Order__Mirabelle_OLin)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_L) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((V_L $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x)) tptp.c_Arrow__Order__Mirabelle_OLin)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_L) tptp.c_Arrow__Order__Mirabelle_OLin)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_y) V_x))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (= V_x V_y) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_y) V_x)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_b T_a) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_z $$unsorted)) (or (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_z) (tptp.hAPP V_f V_z)) (= V_z V_x))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_N T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_N)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_N T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_N)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_Orderings_Opreorder (tptp.c_lessequals T_a) (tptp.c_HOL_Oord__class_Oless T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) _let_1))))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_lessequals T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (= V_m V_n))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_OId__on V_A T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat))))))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_List_Oall__from__to__nat V_P V_i V_j) (not (tptp.hBOOL (tptp.hAPP V_P V_i))) (not (tptp.c_List_Oall__from__to__nat V_P (tptp.c_HOL_Oplus__class_Oplus V_i (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_j)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_L)) (= V_x V_z) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z))))))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (let ((_let_1 (= V_xa V_x))) (or _let_1 _let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_x V_z) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 V_b)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (= V_a V_b) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_a) V_b))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_less $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_3) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 V_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.hAPP _let_1 _let_2))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_a)))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (T_a $$unsorted)) (or (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_x) V_y)) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Fun_Ofun__upd V_f V_x V_y T_a T_b) V_f)) (= (tptp.hAPP V_f V_x) V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool))) (or (not (= (tptp.hAPP _let_1 V_R) (tptp.hAPP _let_1 V_S))) (= V_R V_S)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_A))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_w) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_1) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_w) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_w))) (not 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(tptp.hBOOL (tptp.hAPP _let_2 V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) V_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_2) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_1) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_c) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_2) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_b V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a)) _let_1))))))) (forall ((T_a $$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 $$unsorted) (V_n $$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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_List_Oall__from__to__nat V_P V_i V_j) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) V_j)))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) V_j))) (not (tptp.c_List_Oall__from__to__nat V_P V_i V_j)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_6 _let_21) _let_21))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) _let_1) V_n)) (= V_n _let_1)))) (forall ((V_m $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (tptp.c_Orderings_Opreorder (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) T_a) (not (tptp.c_Orderings_Opreorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (tptp.c_Orderings_Olinorder (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) T_a) (not (tptp.c_Orderings_Olinorder V_less__eq V_less T_a)))) (forall ((V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted)) (or (tptp.c_Orderings_Oorder (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) T_a) (not (tptp.c_Orderings_Oorder V_less__eq V_less T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a tptp.tc_nat))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) V_m)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (= (tptp.c_HOL_Oplus__class_Oplus _let_21 _let_21 tptp.tc_nat) _let_21) (forall ((V_x $$unsorted)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) V_n)) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_22 _let_21) _let_21)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) _let_1)))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_in _let_1))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_y V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_fun _let_1 tptp.tc_bool)) V_L) tptp.c_Arrow__Order__Mirabelle_OLin))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_in _let_1))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_y V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_fun _let_1 tptp.tc_bool)) V_L) tptp.c_Arrow__Order__Mirabelle_OLin))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_L $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.c_in _let_1))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_b V_a tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_a V_b tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) V_L))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_fun _let_1 tptp.tc_bool)) V_L) tptp.c_Arrow__Order__Mirabelle_OLin))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) V_x))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_x V_y) (= V_y V_z)))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_xa V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (or (= V_x V_y) (= V_y V_x) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omkbot V_L V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_L)) (= V_y V_z) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x))))) (forall ((V_x $$unsorted) (V_L $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_x tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_x))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_y V_z) (= V_x V_z)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_L $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) (tptp.c_Pair V_x V_y tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Arrow__Order__Mirabelle_Omktop V_L V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_L))) (= V_x V_y) (= V_x V_z)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofun__upd V_f V_a V_b tptp.t_a T_b) tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_HOL_OIf T_b) (tptp.c_fequal tptp.v_x V_a tptp.t_a)) V_b) (tptp.hAPP V_f tptp.v_x)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_b T_b))) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_2) T_a) T_a T_b _let_2) V_c) T_a T_b T_b) V_d) V_A T_a T_b) V_B) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) _let_1))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) _let_1) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_a T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) V_r)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Relation_Orefl__on V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (let ((_let_2 (tptp.c_in (tptp.tc_prod T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_xa V_x T_a T_a)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Pair V_x V_xa T_a T_a)) V_r)) (= V_x V_xa) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.c_Relation_Ototal__on V_A V_r T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b)))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ODomain V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ODomain V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_x T_a T_b)) V_r))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.c_Relation_ORange V_r T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Relation_ORange V_r T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_x V_a T_b T_a)) V_r))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_y) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) V_r))) (not (tptp.c_Equiv__Relations_Oequiv V_A V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_x T_a T_a)) (tptp.c_Relation_OId__on V_A T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Relation_OId__on V_A T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Relation_OImage V_r V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_b T_a)) (tptp.c_Pair V_x V_b T_b T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.c_Relation_OImage V_r V_A T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (let ((_let_2 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_y V_a T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Wellfounded_Oacc V_r T_a))) (let ((_let_2 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_a V_b T_a T_a)) V_r))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_b)) (tptp.c_Pair V_a V_b T_a T_b)) (tptp.c_Product__Type_OSigma V_A V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_b) (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a))) (let ((_let_2 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_Orderings_Opreorder (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_Orderings_Oorder (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_Orderings_Olinorder (tptp.c_COMBC (tptp.c_lessequals T_a) T_a T_a tptp.tc_bool) (tptp.c_COMBC (tptp.c_HOL_Oord__class_Oless T_a) T_a T_a tptp.tc_bool) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_a V_N T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_N)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (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.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_a)))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omeasure V_f T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omeasure V_f T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted) (V_R $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)) (tptp.c_Wellfounded_Omlex__prod V_f V_R T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a)) (tptp.c_Power_Opower__class_Opower V_a V_N T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_N)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_f $$unsorted) (V_R $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in (tptp.tc_prod T_a T_a)) (tptp.c_Pair V_x V_y T_a T_a)))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Wellfounded_Omlex__prod V_f V_R T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_R))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) (tptp.hAPP V_f V_x)) (tptp.hAPP V_f V_y))))))) (forall ((V_P $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_List_Oall__from__to__nat V_P (tptp.c_HOL_Oplus__class_Oplus V_i (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_j) (not (tptp.hBOOL (tptp.hAPP V_P V_i))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i) V_j))) (not (tptp.c_List_Oall__from__to__nat V_P V_i V_j)))) (tptp.c_Fun_Oinj__on tptp.v_h____ _let_3 tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_in T_b))) (let ((_let_2 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun T_b T_b))) (or (= (tptp.c_Set_Ovimage (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf T_b) (tptp.hAPP (tptp.c_COMBC (tptp.c_in T_a) T_a _let_2 tptp.tc_bool) V_B) tptp.tc_bool (tptp.tc_fun T_b _let_3) T_a) T_a T_b _let_3) V_c) T_a T_b T_b) V_d) V_A T_a T_b) (tptp.c_Orderings_Otop__class_Otop _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_d) V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_A)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Power_Opower__class_Opower V_b V_x T_a)) (tptp.c_Power_Opower__class_Opower V_b V_y T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) (tptp.c_Power_Opower__class_Opower V_a V_m T_a)) (tptp.c_Power_Opower__class_Opower V_a V_n T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_fun tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1)) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_1) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_n) tptp.tc_bool (tptp.tc_fun _let_1 _let_2) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 _let_2) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 _let_1) tptp.v_Lba____)) tptp.c_Arrow__Order__Mirabelle_OProf))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.tc_fun (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt) tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun _let_1 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in _let_1) (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_1) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_n) tptp.tc_bool (tptp.tc_fun _let_1 _let_2) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 _let_2) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_1 _let_1) tptp.v_Lba____))) tptp.c_Arrow__Order__Mirabelle_OLin))))) (not (tptp.hBOOL (tptp.hAPP _let_17 (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB _let_15 (tptp.hAPP _let_14 _let_21) tptp.tc_bool _let_12 tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_11) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_10 _let_10) tptp.v_Lba____))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_z) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) V_n))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_j))))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a)))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a_H $$unsorted) (V_b_H $$unsorted)) (or (not (= (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Pair V_a_H V_b_H T_a T_b))) (= V_b V_b_H))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_b) V_a))) (= V_a V_b))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_j V_i tptp.tc_nat)) V_i)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat)) V_i)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) (tptp.c_Orderings_Otop__class_Otop T_a))))) _let_20 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_m) V_n))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_y))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_l tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Otop T_b)) (= (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Otop__class_Otop T_b)))) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_m) (tptp.c_HOL_Oplus__class_Oplus V_m V_x tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_n) (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_n) V_n)))) (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_x T_a)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_l tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_j tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_j V_m tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat)) V_k)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat)) (tptp.c_HOL_Oplus__class_Oplus V_j V_l tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oplus__class_Oplus V_a V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_u T_a))) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) V_u))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_j tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_i))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_j V_m tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat)) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_lessequals tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat)) V_n)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_lessequals tptp.tc_nat) V_x))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_y) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_x) V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_y) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_x V_z tptp.tc_nat))) (= V_y V_z))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat))) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a))) (= V_y V_z))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_lessequals T_a) V_c) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))) _let_20 (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt))) (let ((_let_2 (tptp.tc_fun _let_1 tptp.tc_bool))) (let ((_let_3 (tptp.tc_fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP tptp.v_F (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_OIf _let_2) (tptp.hAPP (tptp.c_COMBC (tptp.c_COMBB (tptp.c_HOL_Oord__class_Oless tptp.tc_nat) tptp.v_h____ tptp.tc_nat (tptp.tc_fun tptp.tc_nat tptp.tc_bool) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi tptp.tc_nat tptp.tc_bool) V_n) tptp.tc_bool (tptp.tc_fun _let_2 _let_3) tptp.tc_Arrow__Order__Mirabelle_Oindi) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_3) tptp.v_Lab____) tptp.tc_Arrow__Order__Mirabelle_Oindi _let_2 _let_2) tptp.v_Lba____)))) (let ((_let_5 (tptp.c_in _let_1))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.c_Pair tptp.v_a____ tptp.v_b____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) _let_4))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_5 (tptp.c_Pair tptp.v_b____ tptp.v_a____ tptp.tc_Arrow__Order__Mirabelle_Oalt tptp.tc_Arrow__Order__Mirabelle_Oalt)) _let_4)))))))))) _let_19 _let_18 _let_8 _let_7 _let_2 _let_1 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Ouminus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ouminus T_1)))) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ouminus tptp.tc_bool) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_fequal V_x V_x T_a))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.hBOOL (tptp.c_fequal V_X V_Y T_a)))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.57/1.46 )
% 0.57/1.46 % SZS output end Proof for SCT085-1
% 0.57/1.47 % cvc5---1.0.5 exiting
% 0.57/1.47 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------