TSTP Solution File: ANA034-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ANA034-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 17:14:39 EDT 2023
% Result : Unsatisfiable 27.78s 27.99s
% Output : Proof 27.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.32 % Problem : ANA034-1 : TPTP v8.1.2. Released v3.2.0.
% 0.33/0.33 % Command : do_cvc5 %s %d
% 0.33/0.54 % Computer : n029.cluster.edu
% 0.33/0.54 % Model : x86_64 x86_64
% 0.33/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.33/0.54 % Memory : 8042.1875MB
% 0.33/0.54 % OS : Linux 3.10.0-693.el7.x86_64
% 0.33/0.54 % CPULimit : 300
% 0.33/0.54 % WCLimit : 300
% 0.33/0.54 % DateTime : Fri Aug 25 18:31:24 EDT 2023
% 0.33/0.55 % CPUTime :
% 0.75/0.95 %----Proving TF0_NAR, FOF, or CNF
% 0.75/0.95 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2bxjMsIOJQ/cvc5---1.0.5_22514.p...
% 0.79/1.24 ------- get file name : TPTP file name is ANA034-1
% 0.79/1.25 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22514.smt2...
% 0.79/1.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.27/11.45 --- Run --no-e-matching --full-saturate-quant at 5...
% 16.41/16.62 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 21.53/21.79 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.64/26.92 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.78/27.99 % SZS status Unsatisfiable for ANA034-1
% 27.78/27.99 % SZS output start Proof for ANA034-1
% 27.78/28.03 (
% 27.78/28.03 (let ((_let_1 (tptp.class_Ring__and__Field_Oordered__idom tptp.t_b))) (let ((_let_2 (tptp.v_g tptp.v_x))) (let ((_let_3 (tptp.v_f tptp.v_x))) (let ((_let_4 (tptp.c_times (tptp.c_times tptp.v_c tptp.v_ca tptp.t_b) (tptp.c_HOL_Oabs (tptp.c_times _let_3 _let_2 tptp.t_b) tptp.t_b) tptp.t_b))) (let ((_let_5 (tptp.v_b tptp.v_x))) (let ((_let_6 (tptp.v_a tptp.v_x))) (let ((_let_7 (tptp.c_HOL_Oabs (tptp.c_times _let_6 _let_5 tptp.t_b) tptp.t_b))) (let ((_let_8 (tptp.c_lessequals _let_7 _let_4 tptp.t_b))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.c_times tptp.v_ca (tptp.c_HOL_Oabs _let_2 tptp.t_b) tptp.t_b))) (let ((_let_11 (tptp.c_HOL_Oabs _let_3 tptp.t_b))) (let ((_let_12 (tptp.c_times tptp.v_c _let_11 tptp.t_b))) (let ((_let_13 (tptp.c_times _let_12 _let_10 tptp.t_b))) (let ((_let_14 (= _let_4 _let_13))) (let ((_let_15 (tptp.c_HOL_Oabs _let_5 tptp.t_b))) (let ((_let_16 (tptp.c_lessequals _let_15 _let_10 tptp.t_b))) (let ((_let_17 (tptp.c_HOL_Oabs _let_6 tptp.t_b))) (let ((_let_18 (tptp.c_lessequals _let_17 _let_12 tptp.t_b))) (let ((_let_19 (tptp.c_less tptp.c_0 tptp.v_c tptp.t_b))) (let ((_let_20 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (not (tptp.c_lessequals tptp.c_0 V_b T_a)) (not (tptp.c_lessequals tptp.c_0 V_a T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_times V_a V_b T_a) T_a))))) (let ((_let_21 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_lessequals tptp.c_0 V_c T_a)) (not (tptp.c_lessequals tptp.c_0 V_b T_a)) (tptp.c_lessequals (tptp.c_times V_a V_c T_a) (tptp.c_times V_b V_d T_a) T_a))))) (let ((_let_22 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs (tptp.c_times V_a V_b T_a) T_a) (tptp.c_times (tptp.c_HOL_Oabs V_a T_a) (tptp.c_HOL_Oabs V_b T_a) T_a)))))) (let ((_let_23 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_less V_x V_y T_a)) (tptp.c_lessequals V_x V_y T_a))))) (let ((_let_24 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Olordered__ab__group__abs T))))) (let ((_let_25 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Orderings_Oorder T))))) (let ((_let_26 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Opordered__semiring T))))) (let ((_let_27 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Opordered__cancel__semiring T))))) (let ((_let_28 (tptp.c_SetInterval_OlessThan tptp.c_0 tptp.tc_nat))) (let ((_let_29 (= _let_28 tptp.c_emptyset))) (let ((_let_30 (tptp.c_SetInterval_OatLeast tptp.c_0 tptp.tc_nat))) (let ((_let_31 (= _let_30 tptp.c_UNIV))) (let ((_let_32 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_HOL_Oabs V_a T_a) T_a))))) (let ((_let_33 (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) (let ((_let_34 (= (tptp.c_Numeral_Obin__pred tptp.c_Numeral_OPls) tptp.c_Numeral_OMin))) (let ((_let_35 (tptp.c_times tptp.c_1 tptp.c_1 tptp.tc_nat))) (let ((_let_36 (tptp.c_Suc tptp.c_0))) (let ((_let_37 (= (tptp.c_Numeral_Onumber__of _let_33 tptp.tc_nat) tptp.c_1))) (let ((_let_38 (tptp.c_IntDef_Oint tptp.c_0))) (let ((_let_39 (tptp.c_Nat_Osize tptp.c_Product__Type_OUnity tptp.tc_Product__Type_Ounit))) (let ((_let_40 (= _let_39 tptp.c_0))) (let ((_let_41 (tptp.c_times _let_17 _let_15 tptp.t_b))) (let ((_let_42 (= _let_7 _let_41))) (let ((_let_43 (tptp.c_lessequals _let_41 _let_13 tptp.t_b))) (let ((_let_44 (ASSUME :args (_let_14)))) (let ((_let_45 (ASSUME :args (_let_9)))) (let ((_let_46 (not _let_1))) (let ((_let_47 (or _let_46 _let_42))) (let ((_let_48 (_let_22))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (ASSUME :args (_let_1)))) (let ((_let_51 (tptp.c_lessequals _let_39 _let_12 tptp.t_b))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.c_lessequals _let_39 _let_15 tptp.t_b))) (let ((_let_54 (not _let_53))) (let ((_let_55 (not _let_18))) (let ((_let_56 (not _let_16))) (let ((_let_57 (tptp.class_Ring__and__Field_Opordered__semiring tptp.t_b))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56 _let_55 _let_54 _let_52 _let_43))) (let ((_let_60 (forall ((T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize tptp.c_Product__Type_OUnity tptp.tc_Product__Type_Ounit))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (tptp.c_lessequals (tptp.c_times V_a V_c T_a) (tptp.c_times V_b V_d T_a) T_a)))))) (let ((_let_61 (SYMM (ASSUME :args (_let_40))))) (let ((_let_62 (SYMM (ASSUME :args (_let_37))))) (let ((_let_63 (SYMM (ASSUME :args (_let_34))))) (let ((_let_64 (AND_INTRO _let_63 _let_62 _let_61))) (let ((_let_65 (EQ_RESOLVE (SYMM (ASSUME :args (_let_31))) (MACRO_SR_EQ_INTRO _let_64 :args ((= tptp.c_UNIV _let_30) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (AND_INTRO (EQ_RESOLVE (SYMM (ASSUME :args (_let_29))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_65 _let_63 _let_62 _let_61) :args ((= tptp.c_emptyset _let_28) SB_DEFAULT SBA_FIXPOINT))) _let_65 _let_63 _let_62 _let_61))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO _let_66 :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (tptp.class_OrderedGroup_Olordered__ab__group__abs tptp.t_b))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_53))) (let ((_let_71 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (tptp.c_lessequals (tptp.c_Nat_Osize tptp.c_Product__Type_OUnity tptp.tc_Product__Type_Ounit) (tptp.c_HOL_Oabs V_a T_a) T_a))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO _let_64 :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (_let_71))) (let ((_let_74 ((tptp.c_HOL_Oabs V_a T_a)))) (let ((_let_75 (or _let_46 _let_68))) (let ((_let_76 (_let_24))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_46 _let_68 (not _let_75)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.t_b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Oordered__idom T) false))))) :args _let_76)) _let_77 :args (_let_75 false _let_24)) :args (_let_68 false _let_1 false _let_75)))) (let ((_let_79 (tptp.c_lessequals _let_39 tptp.v_c tptp.t_b))) (let ((_let_80 (not _let_79))) (let ((_let_81 (tptp.c_lessequals _let_39 _let_11 tptp.t_b))) (let ((_let_82 (not _let_81))) (let ((_let_83 (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.t_b))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_84 _let_82 _let_80 _let_51))) (let ((_let_86 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osize tptp.c_Product__Type_OUnity tptp.tc_Product__Type_Ounit))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_lessequals _let_1 (tptp.c_times V_a V_b T_a) T_a)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO _let_66 :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (or _let_46 _let_83))) (let ((_let_89 (_let_27))) (let ((_let_90 (ASSUME :args _let_89))) (let ((_let_91 (tptp.c_less _let_39 tptp.v_c tptp.t_b))) (let ((_let_92 (not _let_91))) (let ((_let_93 (tptp.class_Orderings_Oorder tptp.t_b))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_94 _let_92 _let_79))) (let ((_let_96 (_let_23))) (let ((_let_97 (ASSUME :args _let_96))) (let ((_let_98 (or _let_46 _let_93))) (let ((_let_99 (_let_25))) (let ((_let_100 (ASSUME :args _let_99))) (let ((_let_101 (or _let_69 _let_81))) (let ((_let_102 (or _let_46 _let_57))) (let ((_let_103 (_let_26))) (let ((_let_104 (ASSUME :args _let_103))) (let ((_let_105 (not _let_43))) (let ((_let_106 (not _let_42))) (let ((_let_107 (not _let_14))) (let ((_let_108 (ASSUME :args (_let_43)))) (let ((_let_109 (ASSUME :args (_let_42)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_108 _let_109 _let_44 _let_45) :args (_let_14 _let_9 _let_42 _let_43)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_45)) (CONG (SYMM (SYMM _let_109)) (SYMM (SYMM _let_44)) (REFL :args (tptp.t_b)) :args (APPLY_UF tptp.c_lessequals)) (TRUE_INTRO _let_108))) :args (_let_43 _let_42 _let_14 _let_9)) :args ((not (and _let_14 _let_9 _let_42 _let_43)) SB_LITERAL))) (CONG (REFL :args (_let_107)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) (REFL :args (_let_106)) (REFL :args (_let_105)) :args (or))) :args ((or _let_8 _let_107 _let_106 _let_105))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_55 _let_56 _let_58 _let_52 _let_54 _let_43 (not _let_59)))) (ASSUME :args (_let_18)) (ASSUME :args (_let_16)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_46 _let_57 (not _let_102)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (tptp.t_b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Oordered__idom T) false))))) :args _let_103)) _let_104 :args (_let_102 false _let_26)) :args (_let_57 false _let_1 false _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_82 _let_80 _let_51 _let_84 (not _let_85)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_69 _let_81 (not _let_101)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.t_b _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_74)) :args _let_73)) _let_72 :args (_let_101 false _let_71)) :args (_let_81 false _let_68 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_92 _let_94 _let_79 (not _let_95)))) (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO _let_66 :args (_let_19 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_46 _let_93 (not _let_98)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (tptp.t_b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Oordered__idom T) false))))) :args _let_99)) _let_100 :args (_let_98 false _let_25)) :args (_let_93 false _let_1 false _let_98)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (tptp.t_b _let_39 tptp.v_c QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_less V_x V_y T_a) false))))) :args _let_96)) _let_97 :args (_let_95 false _let_23)) :args (_let_79 false _let_91 false _let_93 false _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_46 _let_83 (not _let_88)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (tptp.t_b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Oordered__idom T) false))))) :args _let_89)) _let_90 :args (_let_88 false _let_27)) :args (_let_83 false _let_1 false _let_88)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (tptp.t_b _let_11 tptp.v_c QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_times V_a V_b T_a)))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_51 false _let_81 false _let_79 false _let_83 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_53 (not _let_70)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.t_b _let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_74)) :args _let_73)) _let_72 :args (_let_70 false _let_71)) :args (_let_53 false _let_68 false _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.t_b _let_15 _let_10 _let_17 _let_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_60))) _let_67 :args (_let_59 false _let_60)) :args (_let_43 false _let_18 false _let_16 false _let_57 false _let_51 false _let_53 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_42 (not _let_47)))) _let_50 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.t_b _let_6 _let_5 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oabs (tptp.c_times V_a V_b T_a) T_a)))) :args _let_48)) _let_49 :args (_let_47 false _let_22)) :args (_let_42 false _let_1 false _let_47)) _let_45 _let_44 :args (false false _let_43 false _let_42 true _let_8 false _let_14)) :args ((forall ((T_a $$unsorted) (V_b $$unsorted) (V_C $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_HOL_Oplus T_a)) (not (tptp.c_in V_b V_C T_a)) (tptp.c_in (tptp.c_plus V_a V_b T_a) (tptp.c_SetsAndFunctions_Oelt__set__plus V_a V_C T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_D $$unsorted) (V_a $$unsorted) (V_C $$unsorted)) (or (not (tptp.class_HOL_Oplus T_a)) (not (tptp.c_in V_b V_D T_a)) (not (tptp.c_in V_a V_C T_a)) (tptp.c_in (tptp.c_plus V_a V_b T_a) (tptp.c_plus V_C V_D (tptp.tc_set T_a)) T_a))) (forall ((T_a $$unsorted) (V_E $$unsorted) (V_F $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.class_HOL_Oplus T_a)) (not (tptp.c_lessequals V_E V_F _let_1)) (not (tptp.c_lessequals V_C V_D _let_1)) 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(or (not (tptp.class_HOL_Otimes T_a)) (not (tptp.c_in V_a V_C T_a)) (tptp.c_lessequals (tptp.c_SetsAndFunctions_Oelt__set__times V_a V_D T_a) (tptp.c_times V_C V_D _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (not (tptp.c_in V_a V_C T_a)) (tptp.c_lessequals (tptp.c_SetsAndFunctions_Oelt__set__times V_a V_D T_a) (tptp.c_times V_D V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.class_HOL_Otimes T_a)) (not (tptp.c_lessequals V_C V_D _let_1)) (tptp.c_lessequals (tptp.c_SetsAndFunctions_Oelt__set__times V_a V_C T_a) (tptp.c_SetsAndFunctions_Oelt__set__times V_a V_D T_a) _let_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__semigroup__add (tptp.tc_fun T_2 T_1)) (not (tptp.class_OrderedGroup_Oab__group__add 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tptp.c_emptyset)) (= V_xo tptp.c_Datatype_Ooption_ONone))) (forall ((T_a $$unsorted)) (= (tptp.c_Datatype_Oo2s tptp.c_Datatype_Ooption_ONone T_a) tptp.c_emptyset)) (forall ((V_a_H $$unsorted) (T_a $$unsorted)) (not (= tptp.c_Datatype_Ooption_ONone (tptp.c_Datatype_Ooption_OSome V_a_H T_a)))) (forall ((V_a_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Datatype_Ooption_OSome V_a_H T_a) tptp.c_Datatype_Ooption_ONone))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted)) (or (not (= (tptp.c_Datatype_Ooption_OSome V_a T_a) (tptp.c_Datatype_Ooption_OSome V_a_H T_a))) (= V_a V_a_H))) (forall ((T_a $$unsorted)) (= (tptp.c_Nat_Osize tptp.c_Datatype_Ooption_ONone (tptp.tc_Datatype_Ooption T_a)) tptp.c_0)) (forall ((V_a $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_Datatype_Ooption_OSome V_a T_a) (tptp.tc_Datatype_Ooption T_a)) tptp.c_0)) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_Pair V_a V_b T_a T_b) (tptp.tc_prod T_a T_b)) tptp.c_0)) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_Sum__Type_OInl V_a T_a T_b) (tptp.tc_sum T_a T_b)) tptp.c_0)) (forall ((V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_Sum__Type_OInr V_b T_b T_a) (tptp.tc_sum T_a T_b)) tptp.c_0)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Datatype_Othe (tptp.c_Datatype_Ooption_OSome V_y T_a) T_a) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Datatype_Ounit_Ounit__case V_y tptp.c_Product__Type_OUnity T_a) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Datatype_Ounit_Ounit__rec V_y tptp.c_Product__Type_OUnity T_a) V_y)) _let_40 (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OAtom V_a T_a T_b) (tptp.c_Datatype__Universe_OAtom V_b T_a T_b))) (= V_a V_b))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_OAtom V_a T_a T_b) (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (= (tptp.c_Relation_ODomain (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Ouprod (tptp.c_Relation_ODomain V_r _let_1 _let_1) (tptp.c_Relation_ODomain V_s _let_1 _let_1) T_a T_b)))) (forall ((V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (= (tptp.c_Relation_ODomain (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Ousum (tptp.c_Relation_ODomain V_r _let_1 _let_1) (tptp.c_Relation_ODomain V_s _let_1 _let_1) T_a T_b)))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_N $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn0 V_N T_a T_b))) (= V_M V_N))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b)))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_N $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OIn1 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b))) (= V_M V_N))) (forall ((V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted)) (not (= (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b) (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b) (tptp.c_Datatype__Universe_ONumb V_k T_a T_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b) (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b)))) (forall ((V_k $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Datatype__Universe_ONumb V_k T_a T_b) (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b)))) (forall ((V_k $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (not (= (tptp.c_Datatype__Universe_ONumb V_k T_a T_b) (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b)))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M_H $$unsorted) (V_N_H $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OScons V_M_H V_N_H T_a T_b))) (= V_M V_M_H))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M_H $$unsorted) (V_N_H $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OScons V_M_H V_N_H T_a T_b))) (= V_N V_N_H))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OAtom V_a T_a T_b)))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b)))) (forall ((V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_ONumb V_k T_a T_b)))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Datatype__Universe_Ontrunc tptp.c_0 V_M T_a T_b) tptp.c_emptyset)) (forall ((V_k $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Datatype__Universe_OAtom V_a T_a T_b))) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc V_k) _let_1 T_a T_b) _let_1))) (forall ((V_k $$unsorted) (V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc _let_1) (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn0 (tptp.c_Datatype__Universe_Ontrunc _let_1 V_M T_a T_b) T_a T_b)))) (forall ((V_k $$unsorted) (V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc _let_1) (tptp.c_Datatype__Universe_OIn1 V_M T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn1 (tptp.c_Datatype__Universe_Ontrunc _let_1 V_M T_a T_b) T_a T_b)))) (forall ((V_k $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Datatype__Universe_OLeaf V_a T_a T_b))) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc V_k) _let_1 T_a T_b) _let_1))) (forall ((V_k $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Datatype__Universe_ONumb V_i T_a T_b))) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc V_k) _let_1 T_a T_b) _let_1))) (forall ((V_k $$unsorted) (V_M $$unsorted) (V_N $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc V_k) (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OScons (tptp.c_Datatype__Universe_Ontrunc V_k V_M T_a T_b) (tptp.c_Datatype__Universe_Ontrunc V_k V_N T_a T_b) T_a T_b))) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc tptp.c_0) (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) T_a T_b) tptp.c_emptyset)) (forall ((V_M $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Datatype__Universe_Ontrunc (tptp.c_Suc tptp.c_0) (tptp.c_Datatype__Universe_OIn1 V_M T_a T_b) T_a T_b) tptp.c_emptyset)) (forall ((V_a $$unsorted)) (= (tptp.c_div V_a tptp.c_0 tptp.tc_nat) tptp.c_0)) (forall ((V_y $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_y tptp.c_0 tptp.tc_nat) V_y)) (forall ((V_m $$unsorted)) (= (tptp.c_div tptp.c_0 V_m tptp.tc_nat) tptp.c_0)) (forall ((V_y $$unsorted)) (= (tptp.c_div V_y (tptp.c_Suc tptp.c_0) tptp.tc_nat) V_y)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_div V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (= (tptp.c_div V_m V_n tptp.tc_nat) tptp.c_0))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_m tptp.tc_nat)) (not (tptp.c_less tptp.c_1 V_n tptp.tc_nat)) (tptp.c_less (tptp.c_div V_m V_n tptp.tc_nat) V_m tptp.tc_nat))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_c tptp.tc_nat)) (= (tptp.c_div (tptp.c_times V_c V_a tptp.tc_nat) (tptp.c_times V_c V_b tptp.tc_nat) tptp.tc_nat) (tptp.c_div V_a V_b tptp.tc_nat)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_c tptp.tc_nat)) (= (tptp.c_div (tptp.c_times V_a V_c tptp.tc_nat) (tptp.c_times V_b V_c tptp.tc_nat) tptp.tc_nat) (tptp.c_div V_a V_b tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (= (tptp.c_div (tptp.c_plus V_m (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_plus V_k (tptp.c_div V_m V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (= (tptp.c_div (tptp.c_times V_n V_y tptp.tc_nat) V_n tptp.tc_nat) V_y))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (= (tptp.c_div (tptp.c_plus V_m (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_plus V_k (tptp.c_div V_m V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (= (tptp.c_div (tptp.c_times V_y V_n tptp.tc_nat) V_n tptp.tc_nat) V_y))) (forall ((V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (= (tptp.c_div V_n V_n tptp.tc_nat) tptp.c_1))) (forall ((V_m $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd tptp.c_0 V_m tptp.tc_nat)) (= V_m tptp.c_0))) (tptp.c_Divides_Oop_Advd tptp.c_0 tptp.c_0 tptp.tc_nat) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Suc tptp.c_0))) (or (not (tptp.c_Divides_Oop_Advd V_m _let_1 tptp.tc_nat)) (= V_m _let_1)))) (tptp.c_Divides_Oop_Advd _let_36 _let_36 tptp.tc_nat) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_m V_m tptp.tc_nat)) (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Oop_Amod tptp.c_0 V_m tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_m (tptp.c_Suc tptp.c_0) tptp.tc_nat) tptp.c_0)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_plus V_n V_m tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_plus V_m V_n tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_lessequals (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat) V_n tptp.tc_nat))) (forall ((V_y $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less V_y V_n tptp.tc_nat)) (= (tptp.c_Divides_Oop_Amod V_y V_n tptp.tc_nat) V_y))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_less (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat) V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_plus V_m (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_times V_n V_m tptp.tc_nat) V_n tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_plus V_m (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_times V_m V_n tptp.tc_nat) V_n tptp.tc_nat) tptp.c_0)) (forall ((V_n $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_n V_n tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_div (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat) V_n tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Divides_Oop_Amod V_m V_n tptp.tc_nat))) (= (tptp.c_Divides_Oop_Amod _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_Equiv__Relations_Oquotient V_A V_r T_a))) (= V_A tptp.c_emptyset))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= tptp.c_emptyset (tptp.c_Equiv__Relations_Oquotient tptp.c_emptyset V_r T_a))) (forall ((V_A $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Equiv__Relations_Oquotient V_A V_r T_a) tptp.c_emptyset)) (= V_A tptp.c_emptyset))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Equiv__Relations_Oquotient tptp.c_emptyset V_r T_a) tptp.c_emptyset)) (forall ((V_y $$unsorted) (V_f2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Extraction_Osumbool_Osumbool__case V_y V_f2 tptp.c_Extraction_Osumbool_OLeft T_a) V_y)) (forall ((V_f1 $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Extraction_Osumbool_Osumbool__case V_f1 V_y tptp.c_Extraction_Osumbool_ORight T_a) V_y)) (not (= tptp.c_Extraction_Osumbool_OLeft tptp.c_Extraction_Osumbool_ORight)) (not (= tptp.c_Extraction_Osumbool_ORight tptp.c_Extraction_Osumbool_OLeft)) (forall ((V_y $$unsorted) (V_f2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Extraction_Osumbool_Osumbool__rec V_y V_f2 tptp.c_Extraction_Osumbool_OLeft T_a) V_y)) (forall ((V_f1 $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Extraction_Osumbool_Osumbool__rec V_f1 V_y tptp.c_Extraction_Osumbool_ORight T_a) V_y)) (= (tptp.c_Nat_Osize tptp.c_Extraction_Osumbool_OLeft tptp.tc_Extraction_Osumbool) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_Extraction_Osumbool_ORight tptp.tc_Extraction_Osumbool) tptp.c_0) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_lessequals V_x (tptp.c_Finite__Set_OMax V_A T_a) T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Finite__Set_OMax V_A T_a) V_A T_a) (= V_A tptp.c_emptyset))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_b))) (= V_A tptp.c_emptyset) (= (tptp.c_Finite__Set_OMax (tptp.c_insert V_x V_A T_b) T_b) (tptp.c_Orderings_Omax V_x (tptp.c_Finite__Set_OMax V_A T_b) T_b)))) (forall ((T_a $$unsorted) (V_U $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_U V_A T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_lessequals (tptp.c_Finite__Set_OMax V_A T_a) V_x T_a)) (tptp.c_lessequals V_U V_x T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Main_OMax__le__iff__1 V_A V_x T_a) V_A T_a) (tptp.c_lessequals (tptp.c_Finite__Set_OMax V_A T_a) V_x T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_lessequals (tptp.c_Main_OMax__le__iff__1 V_A V_x T_a) V_x T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_OMax V_A T_a) V_x T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_U $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_U V_A T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_less (tptp.c_Finite__Set_OMax V_A T_a) V_x T_a)) (tptp.c_less V_U V_x T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Main_OMax__less__iff__1 V_A V_x T_a) V_A T_a) (tptp.c_less (tptp.c_Finite__Set_OMax V_A T_a) V_x T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_less (tptp.c_Main_OMax__less__iff__1 V_A V_x T_a) V_x T_a)) (tptp.c_less (tptp.c_Finite__Set_OMax V_A T_a) V_x T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_OMax (tptp.c_insert V_y tptp.c_emptyset T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_U $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_U V_A T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_lessequals V_x (tptp.c_Finite__Set_OMin V_A T_a) T_a)) (tptp.c_lessequals V_x V_U T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Main_OMin__ge__iff__1 V_A V_x T_a) V_A T_a) (tptp.c_lessequals V_x (tptp.c_Finite__Set_OMin V_A T_a) T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_lessequals V_x (tptp.c_Main_OMin__ge__iff__1 V_A V_x T_a) T_a)) (tptp.c_lessequals V_x (tptp.c_Finite__Set_OMin V_A T_a) T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_U $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_U V_A T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_less V_x (tptp.c_Finite__Set_OMin V_A T_a) T_a)) (tptp.c_less V_x V_U T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Main_OMin__gr__iff__1 V_A V_x T_a) V_A T_a) (tptp.c_less V_x (tptp.c_Finite__Set_OMin V_A T_a) T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (tptp.c_less V_x (tptp.c_Main_OMin__gr__iff__1 V_A V_x T_a) T_a)) (tptp.c_less V_x (tptp.c_Finite__Set_OMin V_A T_a) T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_in (tptp.c_Finite__Set_OMin V_A T_a) V_A T_a) (= V_A tptp.c_emptyset))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_b))) (= V_A tptp.c_emptyset) (= (tptp.c_Finite__Set_OMin (tptp.c_insert V_x V_A T_b) T_b) (tptp.c_Orderings_Omin V_x (tptp.c_Finite__Set_OMin V_A T_b) T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_lessequals (tptp.c_Finite__Set_OMin V_A T_a) V_x T_a) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_OMin (tptp.c_insert V_y tptp.c_emptyset T_a) T_a) V_y))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (not (= (tptp.c_Finite__Set_Ocard V_A T_a) tptp.c_0)) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted)) (or (not (tptp.c_in tptp.c_emptyset tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (= (tptp.c_Finite__Set_Ocard tptp.c_emptyset T_a) tptp.c_0))) (forall ((T_a $$unsorted)) (= (tptp.c_Finite__Set_Ocard tptp.c_emptyset T_a) tptp.c_0)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a)) (= (tptp.c_Finite__Set_Ocard V_A T_a) tptp.c_0))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (tptp.c_in V_x V_A T_a) (= (tptp.c_Finite__Set_Ocard (tptp.c_insert V_x V_A T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard V_A T_a))))) (forall ((V_B $$unsorted) (T_a $$unsorted) (V_Ba $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_B tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_minus V_B V_Ba _let_1) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_minus V_A (tptp.c_insert V_a V_B T_a) _let_1) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_minus V_A V_B _let_1) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_minus V_A V_B _let_1) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_minus V_A (tptp.c_insert V_a V_B T_a) _let_1) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_Pow V_A T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))) (tptp.c_in V_A tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_Pow V_A T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_union V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in V_F tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_F $$unsorted) (V_G $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_union V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in V_G tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_G tptp.c_Finite__Set_OFinites _let_1)) (not (tptp.c_in V_F tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_union V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Relation_Oconverse V_r T_b T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_a T_b)))) (tptp.c_in V_r tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_b T_a))))) (forall ((V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_r tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_b T_a)))) (tptp.c_in (tptp.c_Relation_Oconverse V_r T_b T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set (tptp.tc_prod T_a T_b))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in (tptp.c_insert V_a V_A T_a) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in V_A tptp.c_Finite__Set_OFinites _let_1)))) (forall ((T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_b))) (tptp.c_lessequals (tptp.c_Finite__Set_OMin V_A T_b) (tptp.c_Finite__Set_OMax V_A T_b) T_b) (= V_A tptp.c_emptyset))) (forall ((T_b $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_in V_y V_A T_b)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_b))) (= V_A tptp.c_emptyset) (= (tptp.c_Orderings_Omin V_y (tptp.c_Finite__Set_OMax V_A T_b) T_b) V_y))) (forall ((T_b $$unsorted) (V_y $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_in V_y V_A T_b)) (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set T_b))) (= V_A tptp.c_emptyset) (= (tptp.c_Orderings_Omax V_y (tptp.c_Finite__Set_OMin V_A T_b) T_b) V_y))) (forall ((V_y $$unsorted)) (= (tptp.c_NatArith_Oof__nat V_y tptp.tc_nat) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Oid V_y T_a) V_y)) (forall ((V_y $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair V_y tptp.c_0 tptp.tc_nat tptp.tc_nat)) V_y)) (forall ((V_y $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair tptp.c_0 V_y tptp.tc_nat tptp.tc_nat)) V_y)) (forall ((V_m $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair V_m (tptp.c_Suc tptp.c_0) tptp.tc_nat tptp.tc_nat)) tptp.c_1)) (forall ((V_m $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair (tptp.c_Suc tptp.c_0) V_m tptp.tc_nat tptp.tc_nat)) tptp.c_1)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair (tptp.c_plus V_m V_n tptp.tc_nat) V_n tptp.tc_nat tptp.tc_nat)) (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair V_m (tptp.c_plus V_m V_n tptp.tc_nat) tptp.tc_nat tptp.tc_nat)) (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair V_m (tptp.c_plus V_n V_m tptp.tc_nat) tptp.tc_nat tptp.tc_nat)) (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_k (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) tptp.tc_nat)) (tptp.c_Divides_Oop_Advd V_k V_m tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_k (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) tptp.tc_nat)) (tptp.c_Divides_Oop_Advd V_k V_n tptp.tc_nat))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_k V_n tptp.tc_nat)) (not (tptp.c_Divides_Oop_Advd V_k V_m tptp.tc_nat)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) tptp.tc_nat))) (forall ((V_y $$unsorted) (V_n $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair V_y (tptp.c_times V_y V_n tptp.tc_nat) tptp.tc_nat tptp.tc_nat)) V_y)) (forall ((V_y $$unsorted)) (= (tptp.c_GCD_Ogcd (tptp.c_Pair V_y V_y tptp.tc_nat tptp.tc_nat)) V_y)) (not (tptp.c_in tptp.c_UNIV tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs (tptp.c_Nat_Opower (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) V_n T_a) T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_Numeral_Onumber__of V_y T_a) T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add tptp.c_Numeral_OPls (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add tptp.c_Numeral_OPls (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a)) (tptp.c_less tptp.c_0 (tptp.c_Numeral_Onumber__of V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_1 (tptp.c_Numeral_Onumber__of V_y T_a) T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a)) (tptp.c_less tptp.c_1 (tptp.c_Numeral_Onumber__of V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_0 T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OPls)) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OPls)) T_a) T_a)) (tptp.c_less (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_1 T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) T_a) T_a)) (tptp.c_less (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_1 T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_y (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OPls)) T_a) T_a)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_Numeral_Onumber__of V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_y (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OPls)) T_a) T_a) (tptp.c_lessequals tptp.c_0 (tptp.c_Numeral_Onumber__of V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_y (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) T_a) T_a)) (not (tptp.c_lessequals tptp.c_1 (tptp.c_Numeral_Onumber__of V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_y (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) T_a) T_a) (tptp.c_lessequals tptp.c_1 (tptp.c_Numeral_Onumber__of V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add tptp.c_Numeral_OPls (tptp.c_Numeral_Obin__minus V_x)) T_a) T_a)) (not (tptp.c_lessequals (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add tptp.c_Numeral_OPls (tptp.c_Numeral_Obin__minus V_x)) T_a) T_a) (tptp.c_lessequals (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_Obin__minus V_x)) T_a) T_a)) (not (tptp.c_lessequals (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_1 T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_Obin__minus V_x)) T_a) T_a) (tptp.c_lessequals (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_1 T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_plus tptp.c_1 tptp.c_1 T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_plus tptp.c_1 (tptp.c_Numeral_Onumber__of V_w T_a) T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) V_w) T_a)))) (forall ((T_a $$unsorted) (V_v $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_plus (tptp.c_Numeral_Onumber__of V_v T_a) tptp.c_1 T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1)) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_minus tptp.c_1 (tptp.c_Numeral_Onumber__of V_w T_a) T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_Obin__minus V_w)) T_a)))) (forall ((T_a $$unsorted) (V_v $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_minus (tptp.c_Numeral_Onumber__of V_v T_a) tptp.c_1 T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (= tptp.c_0 (tptp.c_Numeral_Onumber__of V_y T_a))) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add tptp.c_Numeral_OPls (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add tptp.c_Numeral_OPls (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a)) (= tptp.c_0 (tptp.c_Numeral_Onumber__of V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (= tptp.c_1 (tptp.c_Numeral_Onumber__of V_y T_a))) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a)) (= tptp.c_1 (tptp.c_Numeral_Onumber__of V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (= (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_0)) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OPls)) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OPls)) T_a) T_a)) (= (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (= (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_1)) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1))) T_a) T_a)) (= (tptp.c_Numeral_Onumber__of V_x T_a) tptp.c_1))) (forall ((V_m $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (= (tptp.c_IntDef_Oint V_m) _let_1)) (= V_m (tptp.c_IntDef_Onat _let_1))))) (forall ((V_m $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (= (tptp.c_IntDef_Oint V_m) _let_1)) (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint)))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_IntDef_Oint (tptp.c_IntDef_Onat _let_1)) _let_1)))) (= (tptp.c_IntDef_Onat tptp.c_1) _let_36) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_IntDef_Oof__int (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin tptp.tc_IntDef_Oint) T_a) (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a)))) (forall ((V_z $$unsorted)) (or (not (tptp.c_less (tptp.c_Suc tptp.c_0) (tptp.c_IntDef_Onat V_z) tptp.tc_nat)) (tptp.c_less tptp.c_1 V_z tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted)) (or (not (tptp.c_less tptp.c_1 V_z tptp.tc_IntDef_Oint)) (tptp.c_less (tptp.c_Suc tptp.c_0) (tptp.c_IntDef_Onat V_z) tptp.tc_nat))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (= (tptp.c_plus V_z (tptp.c_uminus V_w tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_minus V_z V_w tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted)) (or (not (tptp.c_less (tptp.c_HOL_Oabs V_z tptp.tc_IntDef_Oint) tptp.c_1 tptp.tc_IntDef_Oint)) (= V_z tptp.c_0))) (tptp.c_less (tptp.c_HOL_Oabs tptp.c_0 tptp.tc_IntDef_Oint) tptp.c_1 tptp.tc_IntDef_Oint) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.c_less V_w (tptp.c_plus V_z tptp.c_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_lessequals V_w V_z tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.c_lessequals V_w V_z tptp.tc_IntDef_Oint)) (tptp.c_less V_w (tptp.c_plus V_z tptp.c_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.c_lessequals V_w (tptp.c_minus V_z tptp.c_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_less V_w V_z tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.c_less V_w V_z tptp.tc_IntDef_Oint)) (tptp.c_lessequals V_w (tptp.c_minus V_z tptp.c_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_prod tptp.tc_nat tptp.tc_nat)))) (or (not (tptp.c_in V_y tptp.c_IntDef_OInteg _let_1)) (not (tptp.c_in V_x tptp.c_IntDef_OInteg _let_1)) (not (= (tptp.c_IntDef_OAbs__Integ V_x) (tptp.c_IntDef_OAbs__Integ V_y))) (= V_x V_y)))) (forall ((V_y $$unsorted)) (or (not (tptp.c_in V_y tptp.c_IntDef_OInteg (tptp.tc_set (tptp.tc_prod tptp.tc_nat tptp.tc_nat)))) (= (tptp.c_IntDef_ORep__Integ (tptp.c_IntDef_OAbs__Integ V_y)) V_y))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_in tptp.c_0 tptp.c_IntDef_OInts T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_in tptp.c_1 tptp.c_IntDef_OInts T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (not (tptp.c_in V_b tptp.c_IntDef_OInts T_a)) (not (tptp.c_in V_a tptp.c_IntDef_OInts T_a)) (tptp.c_in (tptp.c_plus V_a V_b T_a) tptp.c_IntDef_OInts T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (not (tptp.c_in V_b tptp.c_IntDef_OInts T_a)) (not (tptp.c_in V_a tptp.c_IntDef_OInts T_a)) (tptp.c_in (tptp.c_minus V_a V_b T_a) tptp.c_IntDef_OInts T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (not (tptp.c_in V_a tptp.c_IntDef_OInts T_a)) (tptp.c_in (tptp.c_uminus V_a T_a) tptp.c_IntDef_OInts T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (not (tptp.c_in V_b tptp.c_IntDef_OInts T_a)) (not (tptp.c_in V_a tptp.c_IntDef_OInts T_a)) (tptp.c_in (tptp.c_times V_a V_b T_a) tptp.c_IntDef_OInts T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (tptp.c_in tptp.c_0 tptp.c_IntDef_ONats T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (tptp.c_in tptp.c_1 tptp.c_IntDef_ONats T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (not (tptp.c_in V_b tptp.c_IntDef_ONats T_a)) (not (tptp.c_in V_a tptp.c_IntDef_ONats T_a)) (tptp.c_in (tptp.c_plus V_a V_b T_a) tptp.c_IntDef_ONats T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (not (tptp.c_in V_b tptp.c_IntDef_ONats T_a)) (not (tptp.c_in V_a tptp.c_IntDef_ONats T_a)) (tptp.c_in (tptp.c_times V_a V_b T_a) tptp.c_IntDef_ONats T_a))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_IntDef_Oint V_m))) (= (tptp.c_HOL_Oabs _let_1 tptp.tc_IntDef_Oint) _let_1))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_nat tptp.tc_nat))) (or (not (= (tptp.c_Relation_OImage tptp.c_IntDef_Ointrel (tptp.c_insert V_x tptp.c_emptyset _let_1) _let_1 _let_1) (tptp.c_Relation_OImage tptp.c_IntDef_Ointrel (tptp.c_insert V_y tptp.c_emptyset _let_1) _let_1 _let_1))) (tptp.c_in (tptp.c_Pair V_x V_y _let_1 _let_1) tptp.c_IntDef_Ointrel (tptp.tc_prod _let_1 _let_1))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_nat tptp.tc_nat))) (or (not (tptp.c_in (tptp.c_Pair V_x V_y _let_1 _let_1) tptp.c_IntDef_Ointrel (tptp.tc_prod _let_1 _let_1))) (= (tptp.c_Relation_OImage tptp.c_IntDef_Ointrel (tptp.c_insert V_x tptp.c_emptyset _let_1) _let_1 _let_1) (tptp.c_Relation_OImage tptp.c_IntDef_Ointrel (tptp.c_insert V_y tptp.c_emptyset _let_1) _let_1 _let_1))))) (not (= tptp.c_0 tptp.c_1)) (= (tptp.c_IntDef_Oint tptp.c_1) tptp.c_1) (forall ((V_m $$unsorted)) (= (tptp.c_IntDef_Oint (tptp.c_Suc V_m)) (tptp.c_plus tptp.c_1 (tptp.c_IntDef_Oint V_m) tptp.tc_IntDef_Oint))) (forall ((V_n $$unsorted)) (or (not (= (tptp.c_IntDef_Oint V_n) tptp.c_0)) (= V_n tptp.c_0))) (= _let_38 tptp.c_0) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_IntDef_Oint V_m) (tptp.c_IntDef_Oint V_n))) (= V_m V_n))) (forall ((V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_IntDef_Oint V_n) tptp.c_0 tptp.tc_IntDef_Oint)) (= V_n tptp.c_0))) (tptp.c_lessequals _let_38 tptp.c_0 tptp.tc_IntDef_Oint) (forall ((V_k $$unsorted)) (not (tptp.c_less (tptp.c_IntDef_Oint V_k) tptp.c_0 tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted)) (or (not (tptp.c_lessequals tptp.c_0 V_z tptp.tc_IntDef_Oint)) (= (tptp.c_IntDef_Oint (tptp.c_IntDef_Onat V_z)) V_z))) (forall ((V_z $$unsorted)) (or (tptp.c_lessequals tptp.c_0 V_z tptp.tc_IntDef_Oint) (= (tptp.c_IntDef_Oint (tptp.c_IntDef_Onat V_z)) tptp.c_0))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_nat tptp.tc_nat))) (tptp.c_in (tptp.c_Relation_OImage tptp.c_IntDef_Ointrel (tptp.c_insert (tptp.c_Pair V_x V_y tptp.tc_nat tptp.tc_nat) tptp.c_emptyset _let_1) _let_1 _let_1) tptp.c_IntDef_OInteg (tptp.tc_set _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_u $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_nat tptp.tc_nat))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_Pair V_x V_y tptp.tc_nat tptp.tc_nat) (tptp.c_Pair V_u V_v tptp.tc_nat tptp.tc_nat) _let_1 _let_1) tptp.c_IntDef_Ointrel (tptp.tc_prod _let_1 _let_1))) (= (tptp.c_plus V_x V_v tptp.tc_nat) (tptp.c_plus V_u V_y tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_prod tptp.tc_nat tptp.tc_nat))) (or (not (= (tptp.c_plus V_x V_v tptp.tc_nat) (tptp.c_plus V_u V_y tptp.tc_nat))) (tptp.c_in (tptp.c_Pair (tptp.c_Pair V_x V_y tptp.tc_nat tptp.tc_nat) (tptp.c_Pair V_u V_v tptp.tc_nat tptp.tc_nat) _let_1 _let_1) tptp.c_IntDef_Ointrel (tptp.tc_prod _let_1 _let_1))))) (forall ((V_y $$unsorted)) (= (tptp.c_IntDef_Onat (tptp.c_IntDef_Oint V_y)) V_y)) (forall ((V_z $$unsorted)) (or (not (tptp.c_lessequals V_z tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_IntDef_Onat V_z) tptp.c_0))) (= (tptp.c_IntDef_Onat tptp.c_0) tptp.c_0) (forall ((V_n $$unsorted)) (= (tptp.c_IntDef_Onat (tptp.c_uminus (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint)) tptp.c_0)) (forall ((V_n $$unsorted)) (tptp.c_IntDef_Oneg (tptp.c_uminus (tptp.c_IntDef_Oint (tptp.c_Suc V_n)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (= (tptp.c_uminus (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oint V_m))) (= V_n tptp.c_0))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (= (tptp.c_uminus (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oint V_m))) (= V_m tptp.c_0))) (= (tptp.c_uminus _let_38 tptp.tc_IntDef_Oint) _let_38) (forall ((V_n $$unsorted) (V_m $$unsorted)) (not (tptp.c_less (tptp.c_IntDef_Oint V_n) (tptp.c_uminus (tptp.c_IntDef_Oint V_m) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_n $$unsorted)) (not (tptp.c_IntDef_Oneg (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint))) (forall ((V_n $$unsorted)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_uminus (tptp.c_IntDef_Oint (tptp.c_Suc V_n)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= tptp.c_0 (tptp.c_IntDef_Oof__int V_z T_a))) (= tptp.c_0 V_z))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= tptp.c_0 (tptp.c_IntDef_Oof__int tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_IntDef_Oof__int V_z T_a) T_a)) (tptp.c_lessequals tptp.c_0 V_z tptp.tc_IntDef_Oint))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals tptp.c_0 V_z tptp.tc_IntDef_Oint)) (tptp.c_lessequals tptp.c_0 (tptp.c_IntDef_Oof__int V_z T_a) T_a))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_IntDef_Oof__int V_z T_a) T_a)) (tptp.c_less tptp.c_0 V_z tptp.tc_IntDef_Oint))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 V_z tptp.tc_IntDef_Oint)) (tptp.c_less tptp.c_0 (tptp.c_IntDef_Oof__int V_z T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_IntDef_Oof__int tptp.c_1 T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_IntDef_Oof__int (tptp.c_plus V_w V_z tptp.tc_IntDef_Oint) T_a) (tptp.c_plus (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_IntDef_Oof__int (tptp.c_minus V_w V_z tptp.tc_IntDef_Oint) T_a) (tptp.c_minus (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_IntDef_Oof__int V_w T_a) tptp.c_0)) (= V_w tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_IntDef_Oof__int tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a))) (= V_w V_z))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_IntDef_Oof__int (tptp.c_IntDef_Oint V_n) T_a) (tptp.c_NatArith_Oof__nat V_n T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.c_IntDef_Oof__int V_w T_a) tptp.c_0 T_a)) (tptp.c_lessequals V_w tptp.c_0 tptp.tc_IntDef_Oint))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals V_w tptp.c_0 tptp.tc_IntDef_Oint)) (tptp.c_lessequals (tptp.c_IntDef_Oof__int V_w T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a) T_a)) (tptp.c_lessequals V_w V_z tptp.tc_IntDef_Oint))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals V_w V_z tptp.tc_IntDef_Oint)) (tptp.c_lessequals (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less (tptp.c_IntDef_Oof__int V_w T_a) tptp.c_0 T_a)) (tptp.c_less V_w tptp.c_0 tptp.tc_IntDef_Oint))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less V_w tptp.c_0 tptp.tc_IntDef_Oint)) (tptp.c_less (tptp.c_IntDef_Oof__int V_w T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a) T_a)) (tptp.c_less V_w V_z tptp.tc_IntDef_Oint))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less V_w V_z tptp.tc_IntDef_Oint)) (tptp.c_less (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a) T_a))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_IntDef_Oof__int (tptp.c_uminus V_z tptp.tc_IntDef_Oint) T_a) (tptp.c_uminus (tptp.c_IntDef_Oof__int V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_IntDef_Oof__int (tptp.c_times V_w V_z tptp.tc_IntDef_Oint) T_a) (tptp.c_times (tptp.c_IntDef_Oof__int V_w T_a) (tptp.c_IntDef_Oof__int V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_IntDef_Oof__int (tptp.c_NatArith_Oof__nat V_n tptp.tc_IntDef_Oint) T_a) (tptp.c_NatArith_Oof__nat V_n T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (tptp.c_in (tptp.c_NatArith_Oof__nat V_n T_a) tptp.c_IntDef_ONats T_a))) (forall ((V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint)) (tptp.c_less tptp.c_0 V_n tptp.tc_nat))) (forall ((V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_IntDef_Onat V_z) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_z tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_z tptp.tc_IntDef_Oint)) (tptp.c_less tptp.c_0 (tptp.c_IntDef_Onat V_z) tptp.tc_nat))) (forall ((V_n $$unsorted)) (tptp.c_lessequals tptp.c_0 (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_IntDef_Oint V_m) (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (tptp.c_lessequals (tptp.c_IntDef_Oint V_m) (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_IntDef_Oint V_m) (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (tptp.c_less (tptp.c_IntDef_Oint V_m) (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.c_less (tptp.c_IntDef_Onat V_w) (tptp.c_IntDef_Onat V_z) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_z tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.c_less (tptp.c_IntDef_Onat V_w) (tptp.c_IntDef_Onat V_z) tptp.tc_nat)) (tptp.c_less V_w V_z tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.c_less V_w V_z tptp.tc_IntDef_Oint)) (not (tptp.c_less tptp.c_0 V_z tptp.tc_IntDef_Oint)) (tptp.c_less (tptp.c_IntDef_Onat V_w) (tptp.c_IntDef_Onat V_z) tptp.tc_nat))) (forall ((V_y $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_y tptp.c_0 tptp.tc_IntDef_Oint) V_y)) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less _let_2 tptp.c_0 tptp.tc_IntDef_Oint)) (not (tptp.c_lessequals _let_1 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_div _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_fst (tptp.c_IntDiv_OnegateSnd (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair (tptp.c_uminus _let_2 tptp.tc_IntDef_Oint) (tptp.c_uminus _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_less _let_2 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_div _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_fst (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair _let_2 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_less _let_1 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_div tptp.c_1 _let_1 tptp.tc_IntDef_Oint) (tptp.c_fst (tptp.c_IntDiv_OnegateSnd (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair (tptp.c_uminus tptp.c_1 tptp.tc_IntDef_Oint) (tptp.c_uminus _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_2 tptp.tc_IntDef_Oint)) (not (tptp.c_less _let_1 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_div _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_fst (tptp.c_IntDiv_OnegateSnd (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair (tptp.c_uminus _let_2 tptp.tc_IntDef_Oint) (tptp.c_uminus _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_div tptp.c_1 _let_1 tptp.tc_IntDef_Oint) (tptp.c_fst (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair tptp.c_1 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_2 tptp.tc_IntDef_Oint)) (not (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_div _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_fst (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair _let_2 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_z (tptp.c_uminus V_w tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd V_z (tptp.c_uminus V_w tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_div (tptp.c_Divides_Oop_Amod V_a V_b tptp.tc_IntDef_Oint) V_b tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Oop_Amod V_a V_b tptp.tc_IntDef_Oint))) (= (tptp.c_Divides_Oop_Amod _let_1 V_b tptp.tc_IntDef_Oint) _let_1))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less _let_2 tptp.c_0 tptp.tc_IntDef_Oint)) (not (tptp.c_lessequals _let_1 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_snd (tptp.c_IntDiv_OnegateSnd (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair (tptp.c_uminus _let_2 tptp.tc_IntDef_Oint) (tptp.c_uminus _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_less _let_2 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_snd (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair _let_2 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_less _let_1 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod tptp.c_1 _let_1 tptp.tc_IntDef_Oint) (tptp.c_snd (tptp.c_IntDiv_OnegateSnd (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair (tptp.c_uminus tptp.c_1 tptp.tc_IntDef_Oint) (tptp.c_uminus _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_2 tptp.tc_IntDef_Oint)) (not (tptp.c_less _let_1 tptp.c_0 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_snd (tptp.c_IntDiv_OnegateSnd (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair (tptp.c_uminus _let_2 tptp.tc_IntDef_Oint) (tptp.c_uminus _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod tptp.c_1 _let_1 tptp.tc_IntDef_Oint) (tptp.c_snd (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair tptp.c_1 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_2 tptp.tc_IntDef_Oint)) (not (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod _let_2 _let_1 tptp.tc_IntDef_Oint) (tptp.c_snd (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair _let_2 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_plus tptp.c_1 _let_1 tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_lessequals tptp.c_0 _let_2 tptp.tc_IntDef_Oint)) (= (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair tptp.c_1 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_Pair (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin tptp.tc_IntDef_Oint) _let_2 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (tptp.c_lessequals tptp.c_0 (tptp.c_plus tptp.c_1 _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair tptp.c_1 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_IntDiv_Oadjust _let_1 (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair tptp.c_1 (tptp.c_times (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_3 (tptp.c_plus _let_2 _let_1 tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_lessequals tptp.c_0 _let_3 tptp.tc_IntDef_Oint)) (= (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair _let_2 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_Pair (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin tptp.tc_IntDef_Oint) _let_3 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (tptp.c_lessequals tptp.c_0 (tptp.c_plus _let_2 _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair _let_2 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_IntDiv_Oadjust _let_1 (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair _let_2 (tptp.c_times (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))))) (forall ((V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin tptp.tc_IntDef_Oint))) (= (tptp.c_IntDiv_OnegDivAlg (tptp.c_Pair _let_1 V_b tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_Pair _let_1 (tptp.c_minus V_b tptp.c_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_less V_b tptp.c_0 tptp.tc_IntDef_Oint)) (tptp.c_less V_b (tptp.c_Divides_Oop_Amod V_a V_b tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_less V_b tptp.c_0 tptp.tc_IntDef_Oint)) (tptp.c_lessequals (tptp.c_Divides_Oop_Amod V_a V_b tptp.tc_IntDef_Oint) tptp.c_0 tptp.tc_IntDef_Oint))) (forall ((V_q $$unsorted) (V_r $$unsorted)) (= (tptp.c_IntDiv_OnegateSnd (tptp.c_Pair V_q V_r tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_Pair V_q (tptp.c_uminus V_r tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) (forall ((V_b $$unsorted)) (= (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair tptp.c_0 V_b tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_Pair tptp.c_0 tptp.c_0 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_less tptp.c_1 _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair tptp.c_1 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_Pair tptp.c_0 tptp.c_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (tptp.c_less tptp.c_1 _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair tptp.c_1 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_IntDiv_Oadjust _let_1 (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair tptp.c_1 (tptp.c_times (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint))))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_2 tptp.tc_IntDef_Oint)) (not (tptp.c_less _let_1 _let_2 tptp.tc_IntDef_Oint)) (= (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair _let_1 _let_2 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_Pair tptp.c_0 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (tptp.c_less _let_2 _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair _let_2 _let_1 tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)) (tptp.c_IntDiv_Oadjust _let_1 (tptp.c_IntDiv_OposDivAlg (tptp.c_Pair _let_2 (tptp.c_times (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint tptp.tc_IntDef_Oint)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_b tptp.tc_IntDef_Oint)) (tptp.c_less (tptp.c_Divides_Oop_Amod V_a V_b tptp.tc_IntDef_Oint) V_b tptp.tc_IntDef_Oint))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_b tptp.tc_IntDef_Oint)) (tptp.c_lessequals tptp.c_0 (tptp.c_Divides_Oop_Amod V_a V_b tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_p $$unsorted)) (= (tptp.c_Nat_Opower V_p tptp.c_0 tptp.tc_IntDef_Oint) tptp.c_1)) (forall ((V_p $$unsorted) (V_n $$unsorted)) (= (tptp.c_Nat_Opower V_p (tptp.c_Suc V_n) tptp.tc_IntDef_Oint) (tptp.c_times V_p (tptp.c_Nat_Opower V_p V_n tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted)) (= (tptp.c_div V_y tptp.c_1 tptp.tc_IntDef_Oint) V_y)) (forall ((V_a $$unsorted)) (= (tptp.c_div V_a (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_uminus V_a tptp.tc_IntDef_Oint))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (= (tptp.c_div (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_v tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_div (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_w $$unsorted) (V_v $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (not (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_div (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_v V_b) tptp.tc_IntDef_Oint) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_div (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) _let_1 tptp.tc_IntDef_Oint))))) (forall ((V_w $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint))) (or (tptp.c_lessequals tptp.c_0 _let_1 tptp.tc_IntDef_Oint) (= V_b tptp.c_Numeral_Obit_OB0) (= (tptp.c_div (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_v V_b) tptp.tc_IntDef_Oint) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_div (tptp.c_plus (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.c_1 tptp.tc_IntDef_Oint) _let_1 tptp.tc_IntDef_Oint))))) (forall ((V_a $$unsorted)) (or (= V_a tptp.c_0) (= (tptp.c_div V_a V_a tptp.tc_IntDef_Oint) tptp.c_1))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (= V_a tptp.c_0) (= (tptp.c_div (tptp.c_plus V_a V_b tptp.tc_IntDef_Oint) V_a tptp.tc_IntDef_Oint) (tptp.c_plus (tptp.c_div V_b V_a tptp.tc_IntDef_Oint) tptp.c_1 tptp.tc_IntDef_Oint)))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (= V_a tptp.c_0) (= (tptp.c_div (tptp.c_plus V_b V_a tptp.tc_IntDef_Oint) V_a tptp.tc_IntDef_Oint) (tptp.c_plus (tptp.c_div V_b V_a tptp.tc_IntDef_Oint) tptp.c_1 tptp.tc_IntDef_Oint)))) (forall ((V_b $$unsorted)) (= (tptp.c_div tptp.c_0 V_b tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_div (tptp.c_uminus V_a tptp.tc_IntDef_Oint) (tptp.c_uminus V_b tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_div V_a V_b tptp.tc_IntDef_Oint))) (forall ((V_b $$unsorted) (V_y $$unsorted)) (or (= V_b tptp.c_0) (= (tptp.c_div (tptp.c_times V_y V_b tptp.tc_IntDef_Oint) V_b tptp.tc_IntDef_Oint) V_y))) (forall ((V_b $$unsorted) (V_y $$unsorted)) (or (= V_b tptp.c_0) (= (tptp.c_div (tptp.c_times V_b V_y tptp.tc_IntDef_Oint) V_b tptp.tc_IntDef_Oint) V_y))) (forall ((V_m $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd tptp.c_0 V_m tptp.tc_IntDef_Oint)) (= V_m tptp.c_0))) (tptp.c_Divides_Oop_Advd tptp.c_0 tptp.c_0 tptp.tc_IntDef_Oint) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_x tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_y tptp.tc_IntDef_Oint))) (or (not (tptp.c_Divides_Oop_Advd _let_1 _let_2 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod _let_2 _let_1 tptp.tc_IntDef_Oint) tptp.c_0))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_y tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_x tptp.tc_IntDef_Oint))) (or (not (= (tptp.c_Divides_Oop_Amod _let_1 _let_2 tptp.tc_IntDef_Oint) tptp.c_0)) (tptp.c_Divides_Oop_Advd _let_2 _let_1 tptp.tc_IntDef_Oint))))) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_m V_m tptp.tc_IntDef_Oint)) (forall ((V_x $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs V_x tptp.tc_IntDef_Oint) V_n tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (forall ((V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs tptp.c_0 tptp.tc_IntDef_Oint) V_n tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= V_n tptp.c_0))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs V_x tptp.tc_IntDef_Oint) V_n tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= V_x tptp.c_0))) (forall ((V_x $$unsorted)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs V_x tptp.tc_IntDef_Oint) tptp.c_0 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd (tptp.c_uminus V_z tptp.tc_IntDef_Oint) V_w tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_Divides_Oop_Advd V_z V_w tptp.tc_IntDef_Oint)) (tptp.c_Divides_Oop_Advd (tptp.c_uminus V_z tptp.tc_IntDef_Oint) V_w tptp.tc_IntDef_Oint))) (forall ((V_a $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_a tptp.c_1 tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((V_a $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_a (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((V_a $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_a V_a tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_plus V_a V_b tptp.tc_IntDef_Oint) V_a tptp.tc_IntDef_Oint) (tptp.c_Divides_Oop_Amod V_b V_a tptp.tc_IntDef_Oint))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_plus V_b V_a tptp.tc_IntDef_Oint) V_a tptp.tc_IntDef_Oint) (tptp.c_Divides_Oop_Amod V_b V_a tptp.tc_IntDef_Oint))) (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Oop_Amod tptp.c_0 V_b tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_uminus V_a tptp.tc_IntDef_Oint) (tptp.c_uminus V_b tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_uminus (tptp.c_Divides_Oop_Amod V_a V_b tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_times V_a V_b tptp.tc_IntDef_Oint) V_b tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Oop_Amod (tptp.c_times V_b V_a tptp.tc_IntDef_Oint) V_b tptp.tc_IntDef_Oint) tptp.c_0)) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_LOrder_Ojoin__semilorder T_a)) (= (tptp.c_LOrder_Ojoin V_y V_y T_a) V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_LOrder_Omeet__semilorder T_a)) (= (tptp.c_LOrder_Omeet V_y V_y T_a) V_y))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) (tptp.c_List_Olex V_r T_a) (tptp.tc_prod _let_1 _let_1))) (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)) (= V_x V_y)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olex V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a)) (tptp.c_in (tptp.c_Pair V_xs V_ys _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) (tptp.c_List_Olex V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_x V_y) (= (tptp.c_Nat_Osize V_xs _let_1) (tptp.c_Nat_Osize V_ys _let_1))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olex V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair V_xs V_ys _let_1 _let_1) _let_3 _let_2) (= (tptp.c_Nat_Osize V_xs _let_1) (tptp.c_Nat_Osize V_ys _let_1))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))) (not (= (tptp.c_Nat_Osize V_xs _let_1) (tptp.c_Nat_Osize V_ys _let_1))) (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) (tptp.c_List_Olex V_r T_a) (tptp.tc_prod _let_1 _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olex V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs V_ys _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_x V_ys T_a) _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.c_in (tptp.c_Pair V_xs tptp.c_List_Olist_ONil _let_1 _let_1) (tptp.c_List_Olex V_r T_a) (tptp.tc_prod _let_1 _let_1))))) (forall ((V_U $$unsorted) (V_xss $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in V_U (tptp.c_List_Oset V_xss _let_1) _let_1)) (not (= tptp.c_List_Olist_ONil (tptp.c_List_Oconcat V_xss T_a))) (= V_U tptp.c_List_Olist_ONil)))) (forall ((V_xss $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (tptp.c_in (tptp.c_Main_ONil__eq__concat__conv__1 V_xss T_a) (tptp.c_List_Oset V_xss _let_1) _let_1) (= tptp.c_List_Olist_ONil (tptp.c_List_Oconcat V_xss T_a))))) (forall ((V_xss $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Main_ONil__eq__concat__conv__1 V_xss T_a) tptp.c_List_Olist_ONil)) (= tptp.c_List_Olist_ONil (tptp.c_List_Oconcat V_xss T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_List_Olist_ONil (tptp.c_append V_xs V_ys T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_List_Olist_ONil (tptp.c_append V_xs V_ys T_a))) (= V_ys tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= tptp.c_List_Olist_ONil (tptp.c_append tptp.c_List_Olist_ONil tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_List_Olist_ONil (tptp.c_List_Orev V_xs T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= tptp.c_List_Olist_ONil (tptp.c_List_Orev tptp.c_List_Olist_ONil T_a))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.c_in (tptp.c_Pair tptp.c_List_Olist_ONil V_ys _let_1 _let_1) (tptp.c_List_Olex V_r T_a) (tptp.tc_prod _let_1 _let_1))))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_append V_ys (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a))) (= V_xs V_ys))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_append V_ys (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a))) (= V_x V_y))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_append (tptp.c_append V_xs V_ys T_a) V_zs T_a) (tptp.c_append V_xs (tptp.c_append V_ys V_zs T_a) T_a))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (or (= V_y tptp.c_List_Olist_ONil) (= (tptp.c_append (tptp.c_List_Obutlast V_y T_a) (tptp.c_List_Olist_OCons (tptp.c_List_Olast V_y T_a) tptp.c_List_Olist_ONil T_a) T_a) V_y))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_us $$unsorted) (V_vs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize V_xs _let_1) (tptp.c_Nat_Osize V_ys _let_1))) (not (= (tptp.c_append V_xs V_us T_a) (tptp.c_append V_ys V_vs T_a))) (= V_xs V_ys)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_us $$unsorted) (V_vs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize V_xs _let_1) (tptp.c_Nat_Osize V_ys _let_1))) (not (= (tptp.c_append V_xs V_us T_a) (tptp.c_append V_ys V_vs T_a))) (= V_us V_vs)))) (forall ((V_us $$unsorted) (T_a $$unsorted) (V_vs $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize V_us _let_1) (tptp.c_Nat_Osize V_vs _let_1))) (not (= (tptp.c_append V_xs V_us T_a) (tptp.c_append V_ys V_vs T_a))) (= V_xs V_ys)))) (forall ((V_us $$unsorted) (T_a $$unsorted) (V_vs $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize V_us _let_1) (tptp.c_Nat_Osize V_vs _let_1))) (not (= (tptp.c_append V_xs V_us T_a) (tptp.c_append V_ys V_vs T_a))) (= V_us V_vs)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in (tptp.c_append V_xs V_ys T_a) _let_2 _let_1)) (tptp.c_in V_xs _let_2 _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in (tptp.c_append V_xs V_ys T_a) _let_2 _let_1)) (tptp.c_in V_ys _let_2 _let_1))))) (forall ((V_ys $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in V_ys _let_2 _let_1)) (not (tptp.c_in V_xs _let_2 _let_1)) (tptp.c_in (tptp.c_append V_xs V_ys T_a) _let_2 _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) tptp.c_List_Olist_ONil)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) tptp.c_List_Olist_ONil)) (= V_ys tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_append tptp.c_List_Olist_ONil tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_append V_ys V_xs T_a) (tptp.c_append V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) V_ys)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_append tptp.c_List_Olist_ONil V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) V_xs)) (= V_ys tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_append V_xs tptp.c_List_Olist_ONil T_a) V_xs)) (forall ((V_n $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_append (tptp.c_List_Otake V_n V_y T_a) (tptp.c_List_Odrop V_n V_y T_a) T_a) V_y)) (forall ((T_a__1 $$unsorted)) (= (tptp.c_List_Obutlast tptp.c_List_Olist_ONil T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_x $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a__1) T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a__1 $$unsorted)) (or (= V_xs tptp.c_List_Olist_ONil) (= (tptp.c_List_Obutlast (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Obutlast V_xs T_a__1) T_a__1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Obutlast (tptp.c_append V_y (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a) T_a) T_a) V_y)) (forall ((V_nibble1 $$unsorted) (V_nibble2 $$unsorted) (V_nibble1_H $$unsorted) (V_nibble2_H $$unsorted)) (or (not (= (tptp.c_List_Ochar_OChar V_nibble1 V_nibble2) (tptp.c_List_Ochar_OChar V_nibble1_H V_nibble2_H))) (= V_nibble1 V_nibble1_H))) (forall ((V_nibble1 $$unsorted) (V_nibble2 $$unsorted) (V_nibble1_H $$unsorted) (V_nibble2_H $$unsorted)) (or (not (= (tptp.c_List_Ochar_OChar V_nibble1 V_nibble2) (tptp.c_List_Ochar_OChar V_nibble1_H V_nibble2_H))) (= V_nibble2 V_nibble2_H))) (forall ((V_nibble1 $$unsorted) (V_nibble2 $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_List_Ochar_OChar V_nibble1 V_nibble2) tptp.tc_List_Ochar) tptp.c_0)) (forall ((T_a__1 $$unsorted)) (= (tptp.c_List_Oconcat tptp.c_List_Olist_ONil T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Oconcat (tptp.c_List_Olist_OCons V_x V_xs (tptp.tc_List_Olist T_a__1)) T_a__1) (tptp.c_append V_x (tptp.c_List_Oconcat V_xs T_a__1) T_a__1))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oconcat (tptp.c_append V_xs V_ys (tptp.tc_List_Olist T_a)) T_a) (tptp.c_append (tptp.c_List_Oconcat V_xs T_a) (tptp.c_List_Oconcat V_ys T_a) T_a))) (forall ((V_U $$unsorted) (V_xss $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in V_U (tptp.c_List_Oset V_xss _let_1) _let_1)) (not (= (tptp.c_List_Oconcat V_xss T_a) tptp.c_List_Olist_ONil)) (= V_U tptp.c_List_Olist_ONil)))) (forall ((V_xss $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (tptp.c_in (tptp.c_Main_Oconcat__eq__Nil__conv__1 V_xss T_a) (tptp.c_List_Oset V_xss _let_1) _let_1) (= (tptp.c_List_Oconcat V_xss T_a) tptp.c_List_Olist_ONil)))) (forall ((V_xss $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Main_Oconcat__eq__Nil__conv__1 V_xss T_a) tptp.c_List_Olist_ONil)) (= (tptp.c_List_Oconcat V_xss T_a) tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_List_Orotate1 V_xs T_a) T_a)) (tptp.c_List_Odistinct V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_List_Odistinct (tptp.c_List_Orotate1 V_xs T_a) T_a))) (forall ((T_a__1 $$unsorted)) (tptp.c_List_Odistinct tptp.c_List_Olist_ONil T_a__1)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1)) (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a__1) T_a__1)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1)) (tptp.c_List_Odistinct V_xs T_a__1))) (forall ((V_xs $$unsorted) (T_a__1 $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a__1)) (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a__1) T_a__1))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_append V_xs V_ys T_a) T_a)) (tptp.c_List_Odistinct V_xs T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_append V_xs V_ys T_a) T_a)) (tptp.c_List_Odistinct V_ys T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_append V_xs V_ys T_a) T_a)) (= (tptp.c_inter (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset V_ys T_a) T_a) tptp.c_emptyset))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (not (tptp.c_List_Odistinct V_ys T_a)) (not (tptp.c_List_Odistinct V_xs T_a)) (not (= (tptp.c_inter (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset V_ys T_a) T_a) tptp.c_emptyset)) (tptp.c_List_Odistinct (tptp.c_append V_xs V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_List_Odistinct (tptp.c_List_Odrop V_i V_xs T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_List_Odistinct (tptp.c_List_Oremove1 V_x V_xs T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_List_Orev V_xs T_a) T_a)) (tptp.c_List_Odistinct V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_List_Odistinct (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_List_Odistinct (tptp.c_List_Orotate V_n V_xs T_a) T_a)) (tptp.c_List_Odistinct V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_List_Odistinct (tptp.c_List_Orotate V_n V_xs T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_I $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_List_Odistinct (tptp.c_List_Osublist V_xs V_I T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.c_List_Odistinct (tptp.c_List_Otake V_i V_xs T_a) T_a))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Oupt V_i V_j) tptp.tc_nat)) (forall ((V_n $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Odrop V_n tptp.c_List_Olist_ONil T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop tptp.c_0 V_y T_a) V_y)) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_2 tptp.c_0)) (= (tptp.c_List_Odrop _let_2 _let_1 T_a) _let_1))))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (= (tptp.c_List_Odrop _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Odrop (tptp.c_minus _let_1 tptp.c_1 tptp.tc_nat) V_xs T_a)) (= _let_1 tptp.c_0)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop (tptp.c_Suc V_n) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Odrop V_n V_xs T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_append V_xs V_ys T_a) T_a) (tptp.c_append (tptp.c_List_Odrop V_n V_xs T_a) (tptp.c_List_Odrop (tptp.c_minus V_n (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) V_ys T_a) T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_n (tptp.c_List_Odrop V_m V_xs T_a) T_a) (tptp.c_List_Odrop (tptp.c_plus V_n V_m tptp.tc_nat) V_xs T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Odrop V_n V_xs T_a) tptp.c_List_Olist_ONil)) (tptp.c_lessequals (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat)) (= (tptp.c_List_Odrop V_n V_xs T_a) tptp.c_List_Olist_ONil))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Odrop V_i (tptp.c_List_Oreplicate V_k V_x T_a) T_a) (tptp.c_List_Oreplicate (tptp.c_minus V_k V_i tptp.tc_nat) V_x T_a))) (forall ((V_m $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (= (tptp.c_List_Odrop V_m (tptp.c_List_Oupt V_i V_j) tptp.tc_nat) (tptp.c_List_Oupt (tptp.c_plus V_i V_m tptp.tc_nat) V_j))) (forall ((V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Ohd (tptp.c_List_Olist_OCons V_y V_xs T_a) T_a) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (or (= V_y tptp.c_List_Olist_ONil) (= (tptp.c_List_Olist_OCons (tptp.c_List_Ohd V_y T_a) (tptp.c_List_Otl V_y T_a) T_a) V_y))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= V_xs tptp.c_List_Olist_ONil) (= (tptp.c_List_Ohd (tptp.c_append V_xs V_ys T_a) T_a) (tptp.c_List_Ohd V_xs T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_List_Ohd V_xs T_a) (tptp.c_List_Oset V_xs T_a) T_a) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_n $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (= V_n tptp.c_0) (= (tptp.c_List_Ohd (tptp.c_List_Oreplicate V_n V_y T_a) T_a) V_y))) (forall ((V_y $$unsorted) (V_j $$unsorted)) (or (not (tptp.c_less V_y V_j tptp.tc_nat)) (= (tptp.c_List_Ohd (tptp.c_List_Oupt V_y V_j) tptp.tc_nat) V_y))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oitrev V_xs V_x T_a) (tptp.c_append (tptp.c_List_Orev V_xs T_a) V_x T_a))) (forall ((V_y $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Oitrev tptp.c_List_Olist_ONil V_y T_a__1) V_y)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oitrev (tptp.c_List_Olist_OCons V_x V_xs T_a__1) V_ys T_a__1) (tptp.c_List_Oitrev V_xs (tptp.c_List_Olist_OCons V_x V_ys T_a__1) T_a__1))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a) T_a) V_x)) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= V_xs tptp.c_List_Olist_ONil) (= (tptp.c_List_Olast (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olast V_xs T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_append V_xs tptp.c_List_Olist_ONil T_a) T_a) (tptp.c_List_Olast V_xs T_a))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= V_ys tptp.c_List_Olist_ONil) (= (tptp.c_List_Olast (tptp.c_append V_xs V_ys T_a) T_a) (tptp.c_List_Olast V_ys T_a)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_less V_n (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Olast (tptp.c_List_Odrop V_n V_xs T_a) T_a) (tptp.c_List_Olast V_xs T_a)))) (forall ((V_as $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_List_Olast V_as T_a) (tptp.c_List_Oset V_as T_a) T_a) (= V_as tptp.c_List_Olist_ONil))) (forall ((V_n $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (= V_n tptp.c_0) (= (tptp.c_List_Olast (tptp.c_List_Oreplicate V_n V_y T_a) T_a) V_y))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olast (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a) T_a) V_y)) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.c_less V_i V_j tptp.tc_nat)) (= (tptp.c_List_Olast (tptp.c_List_Oupt V_i V_j) tptp.tc_nat) (tptp.c_minus V_j tptp.c_1 tptp.tc_nat)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.c_0)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_Nat_Osize tptp.c_List_Olist_ONil (tptp.tc_List_Olist T_a)) tptp.c_0)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_append V_xs V_ys T_a) _let_1) (tptp.c_plus (tptp.c_Nat_Osize V_xs _let_1) (tptp.c_Nat_Osize V_ys _let_1) tptp.tc_nat)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Obutlast V_xs T_a) _let_1) (tptp.c_minus (tptp.c_Nat_Osize V_xs _let_1) tptp.c_1 tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Odrop V_n V_xs T_a) _let_1) (tptp.c_minus (tptp.c_Nat_Osize V_xs _let_1) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted)) (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Osize tptp.c_List_Olist_ONil (tptp.tc_List_Olist T_a)) tptp.tc_nat))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_less tptp.c_0 (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Olist__update V_xs V_i V_x T_a) _let_1) (tptp.c_Nat_Osize V_xs _let_1)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oremdups V_xs T_a))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize _let_1 _let_2) (tptp.c_Nat_Osize V_xs _let_2))) (= _let_1 V_xs))))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Oremdups V_xs T_a))) (or (not (= _let_2 V_xs)) (= (tptp.c_Nat_Osize _let_2 _let_1) (tptp.c_Nat_Osize V_xs _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_List_Oreplicate V_y V_x T_a) (tptp.tc_List_Olist T_a)) V_y)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Orev V_xs T_a) _let_1) (tptp.c_Nat_Osize V_xs _let_1)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Orotate1 V_xs T_a) _let_1) (tptp.c_Nat_Osize V_xs _let_1)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Orotate V_n V_xs T_a) _let_1) (tptp.c_Nat_Osize V_xs _let_1)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Otake V_n V_xs T_a) _let_1) (tptp.c_Orderings_Omin (tptp.c_Nat_Osize V_xs _let_1) V_n tptp.tc_nat)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Otl V_xs T_a) _let_1) (tptp.c_minus (tptp.c_Nat_Osize V_xs _let_1) tptp.c_1 tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_List_Oupt V_i V_j) (tptp.tc_List_Olist tptp.tc_nat)) (tptp.c_minus V_j V_i tptp.tc_nat))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Nat_Osize (tptp.c_List_Ozip V_xs V_ys T_a T_b) (tptp.tc_List_Olist (tptp.tc_prod T_a T_b))) (tptp.c_Orderings_Omin (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize V_ys (tptp.tc_List_Olist T_b)) tptp.tc_nat))) (forall ((V_r $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Olexn V_r tptp.c_0 T_a__1) tptp.c_emptyset)) (forall ((V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair tptp.c_List_Olist_ONil V_y _let_1 _let_1) (tptp.c_List_Olexord V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_y (tptp.c_List_Olist_OCons (tptp.c_Main_Olexord__Nil__left__1 V_y T_a) (tptp.c_Main_Olexord__Nil__left__2 V_y T_a) T_a))))) (forall ((V_U $$unsorted) (V_V $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_in (tptp.c_Pair tptp.c_List_Olist_ONil (tptp.c_List_Olist_OCons V_U V_V T_a) _let_1 _let_1) (tptp.c_List_Olexord V_r T_a) (tptp.tc_prod _let_1 _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (not (tptp.c_in (tptp.c_Pair V_x tptp.c_List_Olist_ONil _let_1 _let_1) (tptp.c_List_Olexord V_r T_a) (tptp.tc_prod _let_1 _let_1))))) (forall ((V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_a V_x T_a) (tptp.c_List_Olist_OCons V_b V_y T_a) _let_1 _let_1) (tptp.c_List_Olexord V_r T_a) (tptp.tc_prod _let_1 _let_1))) (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)) (= V_a V_b)))) (forall ((V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (V_y $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olexord V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_a V_x T_a) (tptp.c_List_Olist_OCons V_b V_y T_a) _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a)) (tptp.c_in (tptp.c_Pair V_x V_y _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) V_r (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_a V_x T_a) (tptp.c_List_Olist_OCons V_b V_y T_a) _let_1 _let_1) (tptp.c_List_Olexord V_r T_a) (tptp.tc_prod _let_1 _let_1))))) (forall ((V_xa $$unsorted) (V_y $$unsorted) (T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olexord V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xa V_y _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_OCons V_x V_y T_a) _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= tptp.c_List_Olist_ONil (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((V_a_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) tptp.c_List_Olist_ONil))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (= (tptp.c_Nat_Osize (tptp.c_List_Olist_OCons V_a V_list T_a) _let_1) (tptp.c_plus (tptp.c_Nat_Osize V_list _let_1) (tptp.c_Suc tptp.c_0) tptp.tc_nat)))) (forall ((V_bs $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Olist__inter tptp.c_List_Olist_ONil V_bs T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_a $$unsorted) (V_bs $$unsorted) (T_a__1 $$unsorted) (V_as $$unsorted)) (or (not (tptp.c_in V_a (tptp.c_List_Oset V_bs T_a__1) T_a__1)) (= (tptp.c_List_Olist__inter (tptp.c_List_Olist_OCons V_a V_as T_a__1) V_bs T_a__1) (tptp.c_List_Olist_OCons V_a (tptp.c_List_Olist__inter V_as V_bs T_a__1) T_a__1)))) (forall ((V_a $$unsorted) (V_bs $$unsorted) (T_a__1 $$unsorted) (V_as $$unsorted)) (or (tptp.c_in V_a (tptp.c_List_Oset V_bs T_a__1) T_a__1) (= (tptp.c_List_Olist__inter (tptp.c_List_Olist_OCons V_a V_as T_a__1) V_bs T_a__1) (tptp.c_List_Olist__inter V_as V_bs T_a__1)))) (forall ((V_i $$unsorted) (V_v $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Olist__update tptp.c_List_Olist_ONil V_i V_v T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_y $$unsorted) (T_a $$unsorted) (V_i $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Nat_Osize V_y (tptp.tc_List_Olist T_a)) V_i tptp.tc_nat)) (= (tptp.c_List_Olist__update V_y V_i V_x T_a) V_y))) (forall ((V_i $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_less V_i (tptp.c_Nat_Osize V_y (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Olist__update V_y V_i (tptp.c_List_Onth V_y V_i T_a) T_a) V_y))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Olist__update (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_x V_ys T_a) T_a) (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) V_y T_a) (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_less V_i (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Olist__update (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_i V_y T_a) (tptp.c_List_Olist__update V_xs V_i V_y T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_insert tptp.c_List_Olist_ONil tptp.c_emptyset _let_1))) (= (tptp.c_Relation_OImage (tptp.c_List_Olistrel V_r T_a) _let_2 _let_1 _let_1) _let_2)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olists (tptp.c_inter V_A V_B T_a) T_a) (tptp.c_inter (tptp.c_List_Olists V_A T_a) (tptp.c_List_Olists V_B T_a) (tptp.tc_List_Olist T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Olists tptp.c_UNIV T_a) tptp.c_UNIV)) (forall ((T_a__1 $$unsorted)) (= (tptp.c_List_Olistset tptp.c_List_Olist_ONil T_a__1) (tptp.c_insert tptp.c_List_Olist_ONil tptp.c_emptyset (tptp.tc_List_Olist T_a__1)))) (forall ((V_A $$unsorted) (V_As $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Olistset (tptp.c_List_Olist_OCons V_A V_As (tptp.tc_set T_a__1)) T_a__1) (tptp.c_List_Oset__Cons V_A (tptp.c_List_Olistset V_As T_a__1) T_a__1))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_y $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_y V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble9 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_y $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_y V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibbleA T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_y $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_y V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibbleB T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_y $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_y V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibbleC T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_y $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_y V_f15 V_f16 tptp.c_List_Onibble_ONibbleD T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_y $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_y V_f16 tptp.c_List_Onibble_ONibbleE T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_y tptp.c_List_Onibble_ONibbleF T_a) V_y)) (forall ((V_y $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_y V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble0 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_y $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_y V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble1 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_y $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_y V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble2 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_y $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_y V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble3 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_y $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_y V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble4 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_y $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_y V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble5 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_y $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_y V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble6 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_y $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_y V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble7 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_y $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_y V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble8 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_y $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_y V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble9 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_y $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_y V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibbleA T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_y $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_y V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibbleB T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_y $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_y V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibbleC T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_y $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_y V_f15 V_f16 tptp.c_List_Onibble_ONibbleD T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_y $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_y V_f16 tptp.c_List_Onibble_ONibbleE T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_y tptp.c_List_Onibble_ONibbleF T_a) V_y)) (forall ((V_y $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_y V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble0 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_y $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_y V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble1 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_y $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_y V_f4 V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble2 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_y $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_y V_f5 V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble3 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_y $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_y V_f6 V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble4 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_y $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_y V_f7 V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble5 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_y $$unsorted) (V_f8 $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_y V_f8 V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble6 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_y $$unsorted) (V_f9 $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_y V_f9 V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble7 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_y $$unsorted) (V_f10 $$unsorted) (V_f11 $$unsorted) (V_f12 $$unsorted) (V_f13 $$unsorted) (V_f14 $$unsorted) (V_f15 $$unsorted) (V_f16 $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onibble_Onibble__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_y V_f10 V_f11 V_f12 V_f13 V_f14 V_f15 V_f16 tptp.c_List_Onibble_ONibble8 T_a) V_y)) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble9 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibbleA tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibbleB tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibbleC tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibbleD tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibbleE tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibbleF tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble0 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble1 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble2 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble3 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble4 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble5 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble6 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble7 tptp.tc_List_Onibble) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_List_Onibble_ONibble8 tptp.tc_List_Onibble) tptp.c_0) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oremove1 V_y V_xs T_a) T_a) T_a)) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (V_I $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Osublist V_xs V_I T_a) T_a) T_a)) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onth (tptp.c_List_Olist_OCons V_y V_xs T_a) tptp.c_0 T_a) V_y)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (= (tptp.c_List_Onth (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_Suc V_n) T_a) (tptp.c_List_Onth V_xs V_n T_a))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_1 tptp.c_0)) (= (tptp.c_List_Onth (tptp.c_List_Olist_OCons V_x V_xs T_a) _let_1 T_a) V_x)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (= (tptp.c_List_Onth (tptp.c_List_Olist_OCons V_x V_xs T_a) _let_1 T_a) (tptp.c_List_Onth V_xs (tptp.c_minus _let_1 tptp.c_1 tptp.tc_nat) T_a)) (= _let_1 tptp.c_0)))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Onth (tptp.c_append V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) T_a) (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) T_a) V_y)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (= (tptp.c_List_Onth (tptp.c_append V_xs V_ys T_a) (tptp.c_plus (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat) T_a) (tptp.c_List_Onth V_ys V_n T_a))) (forall ((V_n $$unsorted) (V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_plus V_n V_i tptp.tc_nat))) (or (not (tptp.c_lessequals _let_1 (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Onth (tptp.c_List_Odrop V_n V_xs T_a) V_i T_a) (tptp.c_List_Onth V_xs _let_1 T_a))))) (forall ((V_i $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_less V_i (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Onth (tptp.c_List_Olist__update V_xs V_i V_y T_a) V_i T_a) V_y))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= V_i V_j) (= (tptp.c_List_Onth (tptp.c_List_Olist__update V_xs V_i V_x T_a) V_j T_a) (tptp.c_List_Onth V_xs V_j T_a)))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_less V_n (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (tptp.c_in (tptp.c_List_Onth V_xs V_n T_a) (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_i $$unsorted) (V_n $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_less V_i V_n tptp.tc_nat)) (= (tptp.c_List_Onth (tptp.c_List_Oreplicate V_n V_y T_a) V_i T_a) V_y))) (forall ((V_i $$unsorted) (V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_less V_i V_n tptp.tc_nat)) (= (tptp.c_List_Onth (tptp.c_List_Otake V_n V_xs T_a) V_i T_a) (tptp.c_List_Onth V_xs V_i T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_plus V_i V_k tptp.tc_nat))) (or (not (tptp.c_less _let_1 V_j tptp.tc_nat)) (= (tptp.c_List_Onth (tptp.c_List_Oupt V_i V_j) V_k tptp.tc_nat) _let_1)))) (forall ((V_i $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_less V_i (tptp.c_Nat_Osize V_ys (tptp.tc_List_Olist T_b)) tptp.tc_nat)) (not (tptp.c_less V_i (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat)) (= (tptp.c_List_Onth (tptp.c_List_Ozip V_xs V_ys T_a T_b) V_i (tptp.tc_prod T_a T_b)) (tptp.c_Pair (tptp.c_List_Onth V_xs V_i T_a) (tptp.c_List_Onth V_ys V_i T_b) T_a T_b)))) (forall ((T_a__1 $$unsorted)) (tptp.c_List_Onull tptp.c_List_Olist_ONil T_a__1)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (not (tptp.c_List_Onull (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted) (V_ys $$unsorted)) (= (tptp.c_append (tptp.c_List_Olist_OCons V_x V_xs T_a__1) V_ys T_a__1) (tptp.c_List_Olist_OCons V_x (tptp.c_append V_xs V_ys T_a__1) T_a__1))) (forall ((V_x $$unsorted) (T_a__1 $$unsorted)) (not (tptp.c_List_Oop_Amem V_x tptp.c_List_Olist_ONil T_a__1))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a__1 $$unsorted)) (or (not (tptp.c_List_Oop_Amem V_x (tptp.c_List_Olist_OCons V_y V_ys T_a__1) T_a__1)) (tptp.c_List_Oop_Amem V_x V_ys T_a__1) (= V_y V_x))) (forall ((V_x $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (tptp.c_List_Oop_Amem V_x (tptp.c_List_Olist_OCons V_x V_ys T_a) T_a)) (forall ((V_x $$unsorted) (V_ys $$unsorted) (T_a__1 $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_List_Oop_Amem V_x V_ys T_a__1)) (tptp.c_List_Oop_Amem V_x (tptp.c_List_Olist_OCons V_y V_ys T_a__1) T_a__1))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a__1) T_a__1)) (= (tptp.c_List_Oremdups (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1) (tptp.c_List_Oremdups V_xs T_a__1)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (or (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a__1) T_a__1) (= (tptp.c_List_Oremdups (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oremdups V_xs T_a__1) T_a__1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oremdups V_x T_a) tptp.c_List_Olist_ONil)) (= V_x tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Oremdups tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_List_Olist_ONil (tptp.c_List_Oremdups V_x T_a))) (= V_x tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= tptp.c_List_Olist_ONil (tptp.c_List_Oremdups tptp.c_List_Olist_ONil T_a))) (forall ((V_x $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Oremove1 V_x tptp.c_List_Olist_ONil T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) V_xs)) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (or (= V_x V_y) (= (tptp.c_List_Oremove1 V_x (tptp.c_List_Olist_OCons V_y V_xs T_a__1) T_a__1) (tptp.c_List_Olist_OCons V_y (tptp.c_List_Oremove1 V_x V_xs T_a__1) T_a__1)))) (forall ((V_x $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Oreplicate tptp.c_0 V_x T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Oreplicate (tptp.c_Suc V_n) V_x T_a__1) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oreplicate V_n V_x T_a__1) T_a__1))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1) (tptp.c_append (tptp.c_List_Orev V_xs T_a__1) (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a__1) T_a__1))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_append V_xs V_ys T_a) T_a) (tptp.c_append (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Orev V_xs T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (= V_xs (tptp.c_append (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a)))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (= (tptp.c_List_Orev (tptp.c_append (tptp.c_List_Orev V_ys T_a) (tptp.c_List_Olist_OCons V_y tptp.c_List_Olist_ONil T_a) T_a) T_a) (tptp.c_List_Olist_OCons V_y V_ys T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) tptp.c_List_Olist_ONil)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Orev tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (not (= (tptp.c_List_Orev V_xs T_a) (tptp.c_List_Orev V_ys T_a))) (= V_xs V_ys))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Oreplicate V_n V_x T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orev (tptp.c_List_Orev V_y T_a) T_a) V_y)) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Orev V_xs T_a) _let_1)) (= V_xs _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Orev _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Orotate1 V_xs T_a) tptp.c_List_Olist_ONil)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Orotate1 tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Nat_Osize V_y (tptp.tc_List_Olist T_a)) tptp.c_1 tptp.tc_nat)) (= (tptp.c_List_Orotate1 V_y T_a) V_y))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate (tptp.c_Suc V_n) V_xs T_a) (tptp.c_List_Orotate1 (tptp.c_List_Orotate V_n V_xs T_a) T_a))) (forall ((V_n $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Divides_Oop_Amod V_n (tptp.c_Nat_Osize V_y (tptp.tc_List_Olist T_a)) tptp.tc_nat) tptp.c_0)) (= (tptp.c_List_Orotate V_n V_y T_a) V_y))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Orotate V_n V_xs T_a) tptp.c_List_Olist_ONil)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Orotate V_n tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_y $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Nat_Osize V_y (tptp.tc_List_Olist T_a)) tptp.c_1 tptp.tc_nat)) (= (tptp.c_List_Orotate V_n V_y T_a) V_y))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_append V_xs V_ys T_a) (tptp.c_append V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_append V_xs V_ys T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_append tptp.c_List_Olist_ONil V_ys T_a))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_append V_xs V_ys T_a))) (= V_ys tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_append V_xs tptp.c_List_Olist_ONil T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a__1) T_a__1) (tptp.c_insert V_x (tptp.c_List_Oset V_xs T_a__1) T_a__1))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_append V_xs V_ys T_a) T_a) (tptp.c_union (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_List_Oset V_xs T_a))) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= tptp.c_emptyset (tptp.c_List_Oset tptp.c_List_Olist_ONil T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oset V_xs T_a) tptp.c_emptyset)) (= V_xs tptp.c_List_Olist_ONil))) (forall ((T_a $$unsorted)) (= (tptp.c_List_Oset tptp.c_List_Olist_ONil T_a) tptp.c_emptyset)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Oremdups V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_List_Odistinct V_xs T_a)) (= (tptp.c_List_Oset (tptp.c_List_Oremove1 V_x V_xs T_a) T_a) (tptp.c_minus (tptp.c_List_Oset V_xs T_a) (tptp.c_insert V_x tptp.c_emptyset T_a) (tptp.tc_set T_a))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= V_n tptp.c_0) (= (tptp.c_List_Oset (tptp.c_List_Oreplicate V_n V_x T_a) T_a) (tptp.c_insert V_x tptp.c_emptyset T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Orev V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Orotate1 V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Orotate V_n V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Orev V_xs T_a))) (= V_xs _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Orev _let_1 T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Osublist V_xs tptp.c_emptyset T_a) tptp.c_List_Olist_ONil)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Osublist tptp.c_List_Olist_ONil V_A T_a) tptp.c_List_Olist_ONil)) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a))) (or (not (tptp.c_in tptp.c_0 V_A tptp.tc_nat)) (= (tptp.c_List_Osublist _let_1 V_A T_a) _let_1)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.c_in tptp.c_0 V_A tptp.tc_nat) (= (tptp.c_List_Osublist (tptp.c_List_Olist_OCons V_x tptp.c_List_Olist_ONil T_a) V_A T_a) tptp.c_List_Olist_ONil))) (forall ((V_l $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Osublist V_l (tptp.c_SetInterval_OlessThan V_n tptp.tc_nat) T_a) (tptp.c_List_Otake V_n V_l T_a))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (not (= _let_1 tptp.c_0)) (= (tptp.c_List_Otake _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) tptp.c_List_Olist_ONil)))) (forall ((V_v $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (= (tptp.c_List_Otake _let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Otake (tptp.c_minus _let_1 tptp.c_1 tptp.tc_nat) V_xs T_a) T_a)) (= _let_1 tptp.c_0)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake (tptp.c_Suc V_n) (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Otake V_n V_xs T_a) T_a))) (forall ((V_y $$unsorted) (T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Nat_Osize V_y (tptp.tc_List_Olist T_a)) V_n tptp.tc_nat)) (= (tptp.c_List_Otake V_n V_y T_a) V_y))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_append V_xs V_ys T_a) T_a) (tptp.c_append (tptp.c_List_Otake V_n V_xs T_a) (tptp.c_List_Otake (tptp.c_minus V_n (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) tptp.tc_nat) V_ys T_a) T_a))) (forall ((V_n $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Otake V_n V_xs T_a) tptp.c_List_Olist_ONil)) (= V_n tptp.c_0) (= V_xs tptp.c_List_Olist_ONil))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake tptp.c_0 V_xs T_a) tptp.c_List_Olist_ONil)) (forall ((V_n $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n tptp.c_List_Olist_ONil T_a) tptp.c_List_Olist_ONil)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_i (tptp.c_List_Oreplicate V_k V_x T_a) T_a) (tptp.c_List_Oreplicate (tptp.c_Orderings_Omin V_i V_k tptp.tc_nat) V_x T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Otake V_n (tptp.c_List_Otake V_m V_xs T_a) T_a) (tptp.c_List_Otake (tptp.c_Orderings_Omin V_n V_m tptp.tc_nat) V_xs T_a))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_plus V_i V_m tptp.tc_nat))) (or (not (tptp.c_lessequals _let_1 V_n tptp.tc_nat)) (= (tptp.c_List_Otake V_m (tptp.c_List_Oupt V_i V_n) tptp.tc_nat) (tptp.c_List_Oupt V_i _let_1))))) (forall ((T_a__1 $$unsorted)) (= (tptp.c_List_Otl tptp.c_List_Olist_ONil T_a__1) tptp.c_List_Olist_ONil)) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_List_Otl (tptp.c_List_Olist_OCons V_x V_y T_a__1) T_a__1) V_y)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (= V_xs tptp.c_List_Olist_ONil) (= (tptp.c_List_Otl (tptp.c_append V_xs V_ys T_a) T_a) (tptp.c_append (tptp.c_List_Otl V_xs T_a) V_ys T_a)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (= V_n tptp.c_0) (= (tptp.c_List_Otl (tptp.c_List_Oreplicate V_n V_x T_a) T_a) (tptp.c_List_Oreplicate (tptp.c_minus V_n tptp.c_1 tptp.tc_nat) V_x T_a)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= (tptp.c_List_Oupt V_i (tptp.c_Suc V_j)) (tptp.c_append (tptp.c_List_Oupt V_i V_j) (tptp.c_List_Olist_OCons V_j tptp.c_List_Olist_ONil tptp.tc_nat) tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_j tptp.tc_nat) (= (tptp.c_List_Oupt V_i (tptp.c_Suc V_j)) tptp.c_List_Olist_ONil))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (= (tptp.c_List_Oupt V_i V_j) tptp.c_List_Olist_ONil)) (tptp.c_lessequals V_j V_i tptp.tc_nat) (= V_j tptp.c_0))) (forall ((V_i $$unsorted)) (= (tptp.c_List_Oupt V_i tptp.c_0) tptp.c_List_Olist_ONil)) (forall ((V_j $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_lessequals V_j V_i tptp.tc_nat)) (= (tptp.c_List_Oupt V_i V_j) tptp.c_List_Olist_ONil))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_xs $$unsorted) (T_a__1 $$unsorted) (T_b__1 $$unsorted)) (= (tptp.c_List_Ozip V_xs tptp.c_List_Olist_ONil T_a__1 T_b__1) tptp.c_List_Olist_ONil)) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Ozip (tptp.c_List_Olist_OCons V_x V_xs T_a) (tptp.c_List_Olist_OCons V_y V_ys T_b) T_a T_b) (tptp.c_List_Olist_OCons (tptp.c_Pair V_x V_y T_a T_b) (tptp.c_List_Ozip V_xs V_ys T_a T_b) (tptp.tc_prod T_a T_b)))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Ozip tptp.c_List_Olist_ONil V_ys T_a T_b) tptp.c_List_Olist_ONil)) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_vs $$unsorted) (T_b $$unsorted) (V_xs $$unsorted) (V_us $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_b))) (let ((_let_2 (tptp.tc_List_Olist T_a))) (or (not (= (tptp.c_Nat_Osize V_ys _let_2) (tptp.c_Nat_Osize V_vs _let_1))) (not (= (tptp.c_Nat_Osize V_xs _let_2) (tptp.c_Nat_Osize V_us _let_1))) (= (tptp.c_List_Ozip (tptp.c_append V_xs V_ys T_a) (tptp.c_append V_us V_vs T_b) T_a T_b) (tptp.c_append (tptp.c_List_Ozip V_xs V_us T_a T_b) (tptp.c_List_Ozip V_ys V_vs T_a T_b) (tptp.tc_prod T_a T_b))))))) (forall ((V_i $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_j $$unsorted) (V_y $$unsorted) (T_b $$unsorted)) (= (tptp.c_List_Ozip (tptp.c_List_Oreplicate V_i V_x T_a) (tptp.c_List_Oreplicate V_j V_y T_b) T_a T_b) (tptp.c_List_Oreplicate (tptp.c_Orderings_Omin V_i V_j tptp.tc_nat) (tptp.c_Pair V_x V_y T_a T_b) (tptp.tc_prod T_a T_b)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)) (not (= (tptp.c_Map_Omap__of (tptp.c_List_Ozip V_xs V_ys T_a T_b) V_x T_a T_b) tptp.c_Datatype_Ooption_ONone)) (not (= (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize V_ys (tptp.tc_List_Olist T_b)))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_Nat_Osize V_xs (tptp.tc_List_Olist T_a)) (tptp.c_Nat_Osize V_ys (tptp.tc_List_Olist T_b)))) (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a) (= (tptp.c_Map_Omap__of (tptp.c_List_Ozip V_xs V_ys T_a T_b) V_x T_a T_b) tptp.c_Datatype_Ooption_ONone))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_lessequals V_k V_j tptp.tc_nat)) (= (tptp.c_plus (tptp.c_minus V_j V_k tptp.tc_nat) V_i tptp.tc_nat) (tptp.c_minus (tptp.c_plus V_j V_i tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_lessequals V_k V_j tptp.tc_nat)) (= (tptp.c_plus V_i (tptp.c_minus V_j V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_minus (tptp.c_plus V_i V_j tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_lessequals V_k V_j tptp.tc_nat)) (= (tptp.c_minus V_m (tptp.c_Suc (tptp.c_minus V_j V_k tptp.tc_nat)) tptp.tc_nat) (tptp.c_minus (tptp.c_plus V_m V_k tptp.tc_nat) (tptp.c_Suc V_j) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_lessequals V_k V_j tptp.tc_nat)) (= (tptp.c_minus (tptp.c_Suc (tptp.c_minus V_j V_k tptp.tc_nat)) V_m tptp.tc_nat) (tptp.c_minus (tptp.c_Suc V_j) (tptp.c_plus V_k V_m tptp.tc_nat) tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_y V_n tptp.tc_nat)) (= (tptp.c_minus V_n (tptp.c_minus V_n V_y tptp.tc_nat) tptp.tc_nat) V_y))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_lessequals V_k V_j tptp.tc_nat)) (= (tptp.c_minus V_i (tptp.c_minus V_j V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_minus (tptp.c_plus V_i V_k tptp.tc_nat) V_j tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_m tptp.tc_nat)) (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_less (tptp.c_minus V_m V_n tptp.tc_nat) V_m tptp.tc_nat))) (forall ((T_a__1 $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a__1)) (= (tptp.c_NatArith_Oof__nat (tptp.c_Suc V_m) T_a__1) (tptp.c_plus (tptp.c_NatArith_Oof__nat V_m T_a__1) tptp.c_1 T_a__1)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= tptp.c_0 (tptp.c_NatArith_Oof__nat V_n T_a))) (= tptp.c_0 V_n))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (= tptp.c_0 (tptp.c_NatArith_Oof__nat tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_NatArith_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_NatArith_Oof__nat V_n T_a) T_a)) (tptp.c_less tptp.c_0 V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_NatArith_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (= (tptp.c_NatArith_Oof__nat tptp.c_1 T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (= (tptp.c_NatArith_Oof__nat (tptp.c_plus V_m V_n tptp.tc_nat) T_a) (tptp.c_plus (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (= (tptp.c_NatArith_Oof__nat (tptp.c_minus V_m V_n tptp.tc_nat) T_a) (tptp.c_minus (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_NatArith_Oof__nat V_m T_a) tptp.c_0)) (= V_m tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (= (tptp.c_NatArith_Oof__nat tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_NatArith_Oof__nat V_m T_a) tptp.c_0 T_a)) (= V_m tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_NatArith_Oof__nat tptp.c_0 T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a) T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (tptp.c_lessequals (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less (tptp.c_NatArith_Oof__nat V_m T_a) tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a) T_a)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less V_m V_n tptp.tc_nat)) (tptp.c_less (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (= (tptp.c_NatArith_Oof__nat (tptp.c_times V_m V_n tptp.tc_nat) T_a) (tptp.c_times (tptp.c_NatArith_Oof__nat V_m T_a) (tptp.c_NatArith_Oof__nat V_n T_a) T_a)))) (forall ((V_v $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Suc (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat)) tptp.c_1))) (forall ((V_v $$unsorted)) (or (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_Suc (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat)) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__succ V_v) tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_plus (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) _let_1 tptp.tc_nat) _let_1)))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_plus _let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) _let_1)))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (or (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_plus (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v V_v_H) tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_div (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) tptp.c_0))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_div (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) (tptp.c_IntDef_Onat (tptp.c_div _let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_x tptp.tc_nat))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_y tptp.tc_nat))) (or (not (tptp.c_Divides_Oop_Advd _let_1 _let_2 tptp.tc_nat)) (= (tptp.c_Divides_Oop_Amod _let_2 _let_1 tptp.tc_nat) tptp.c_0))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_y tptp.tc_nat))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_x tptp.tc_nat))) (or (not (= (tptp.c_Divides_Oop_Amod _let_1 _let_2 tptp.tc_nat) tptp.c_0)) (tptp.c_Divides_Oop_Advd _let_2 _let_1 tptp.tc_nat))))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (= tptp.c_0 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint)))) (forall ((V_v $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= tptp.c_0 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat)))) (forall ((V_v $$unsorted)) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= tptp.c_0 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))) (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint)))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))) (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)))) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) _let_1 _let_1 (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat)))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint))) (or (not (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint))) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat))))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat)))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) tptp.c_0)) (tptp.c_IntDef_Oiszero _let_1 tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint)))) (forall ((V_v $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) tptp.c_0))) (forall ((V_v $$unsorted)) (or (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) tptp.c_0))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_IntDef_Oint (tptp.c_plus V_m V_n tptp.tc_nat)) (tptp.c_plus (tptp.c_IntDef_Oint V_m) (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint))) (forall ((V_v $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_IntDef_Oint (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat)) tptp.c_0))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_IntDef_Oint (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat)) _let_1)))) (forall ((V_v $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) tptp.tc_nat)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__minus V_v) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_v $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__minus V_v) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_less tptp.c_0 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) tptp.tc_nat))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_less (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__minus V_v_H) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_less (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_v_H)) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_less (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__minus V_v_H) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_less (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Obin__minus V_v_H))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v _let_1) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of _let_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_less (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) tptp.c_0))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_Divides_Oop_Amod _let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) _let_1)))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oneg _let_2 tptp.tc_IntDef_Oint) (= (tptp.c_Divides_Oop_Amod (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) (tptp.c_IntDef_Onat (tptp.c_Divides_Oop_Amod _let_2 _let_1 tptp.tc_IntDef_Oint))))))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_times (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) tptp.c_0))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_times (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__mult V_v V_v_H) tptp.tc_nat)))) (forall ((V_w $$unsorted)) (= (tptp.c_IntDef_Onat (tptp.c_Numeral_Onumber__of V_w tptp.tc_IntDef_Oint)) (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (= (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OPls tptp.tc_nat) tptp.c_0) _let_37 (forall ((T_a $$unsorted) (V_v $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_NatArith_Oof__nat (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_v $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (= (tptp.c_NatArith_Oof__nat (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) T_a) (tptp.c_Numeral_Onumber__of V_v T_a)))) (forall ((V_v_H $$unsorted)) (= (tptp.c_div (tptp.c_Suc tptp.c_0) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) (tptp.c_IntDef_Onat (tptp.c_div tptp.c_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)))) (forall ((V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Suc tptp.c_0))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod _let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) _let_1)))) (forall ((V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_IntDef_Oint))) (or (tptp.c_IntDef_Oneg _let_1 tptp.tc_IntDef_Oint) (= (tptp.c_Divides_Oop_Amod (tptp.c_Suc tptp.c_0) (tptp.c_Numeral_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) (tptp.c_IntDef_Onat (tptp.c_Divides_Oop_Amod tptp.c_1 _let_1 tptp.tc_IntDef_Oint)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (= (tptp.c_Nat_Opower tptp.c_1 (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) T_a) tptp.c_1))) (forall ((T_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Power_Orecpower T_b)) (= (tptp.c_Nat_Opower _let_1 (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) T_b) (tptp.c_times _let_1 _let_1 T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_times (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) V_n tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.c_Nat_Opower (tptp.c_uminus V_a T_a) _let_1 T_a) (tptp.c_Nat_Opower V_a _let_1 T_a))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (= (tptp.c_Nat_Opower (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) _let_1 tptp.tc_nat) (tptp.c_Nat_Opower tptp.c_0 _let_1 tptp.tc_nat))))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (tptp.c_IntDef_Oneg _let_2 tptp.tc_IntDef_Oint) (= (tptp.c_Nat_Opower (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat) _let_1 tptp.tc_nat) (tptp.c_IntDef_Onat (tptp.c_Nat_Opower _let_2 _let_1 tptp.tc_IntDef_Oint))))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (= (tptp.c_Nat_Opower tptp.c_0 (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) T_a) tptp.c_0))) (forall ((V_m $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (= (tptp.c_div (tptp.c_Suc (tptp.c_Suc (tptp.c_Suc V_m))) _let_1 tptp.tc_nat) (tptp.c_div (tptp.c_plus (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB1) tptp.tc_nat) V_m tptp.tc_nat) _let_1 tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (= (tptp.c_Divides_Oop_Amod (tptp.c_Suc (tptp.c_Suc (tptp.c_Suc V_m))) _let_1 tptp.tc_nat) (tptp.c_Divides_Oop_Amod (tptp.c_plus (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB1) tptp.tc_nat) V_m tptp.tc_nat) _let_1 tptp.tc_nat)))) (forall ((V_n $$unsorted)) (= (tptp.c_plus (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (= (tptp.c_plus V_n (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) tptp.tc_nat) (tptp.c_Suc (tptp.c_Suc V_n)))) (forall ((V_y $$unsorted)) (= (tptp.c_div (tptp.c_plus V_y V_y tptp.tc_nat) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) tptp.tc_nat) V_y)) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat))) (= (tptp.c_div (tptp.c_Suc (tptp.c_Suc V_m)) _let_1 tptp.tc_nat) (tptp.c_Suc (tptp.c_div V_m _let_1 tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_div V_m (tptp.c_Suc (tptp.c_Suc (tptp.c_Suc V_n))) tptp.tc_nat) (tptp.c_div V_m (tptp.c_plus (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB1) tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (= V_b (tptp.c_times (tptp.c_divide V_b _let_1 T_b) _let_1 T_b)) (= _let_1 tptp.c_0)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (not (= _let_1 tptp.c_0)) (= (tptp.c_divide V_b _let_1 T_b) tptp.c_0)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (= _let_1 tptp.c_0) (= (tptp.c_divide (tptp.c_times V_a _let_1 T_b) _let_1 T_b) V_a)))) (forall ((T_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (= (tptp.c_divide (tptp.c_times tptp.c_0 _let_1 T_b) _let_1 T_b) tptp.c_0)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)) (tptp.c_lessequals tptp.c_0 _let_1 T_b) (tptp.c_lessequals _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)) (tptp.c_lessequals tptp.c_0 V_b T_b) (tptp.c_lessequals tptp.c_0 _let_1 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)) (tptp.c_lessequals V_b tptp.c_0 T_b) (tptp.c_lessequals _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals (tptp.c_divide (tptp.c_Numeral_Onumber__of V_w T_b) V_b T_b) tptp.c_0 T_b)) (tptp.c_lessequals V_b tptp.c_0 T_b) (tptp.c_lessequals tptp.c_0 V_b T_b))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_b tptp.c_0 T_b)) (not (tptp.c_lessequals tptp.c_0 _let_1 T_b)) (tptp.c_lessequals (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals tptp.c_0 V_b T_b)) (not (tptp.c_lessequals _let_1 tptp.c_0 T_b)) (tptp.c_lessequals (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (not (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)) (tptp.c_lessequals V_b (tptp.c_times V_a _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_lessequals (tptp.c_times V_a _let_1 T_b) V_b T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals tptp.c_0 V_a T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals tptp.c_0 V_a T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_lessequals (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals tptp.c_0 V_a T_b)) (not (tptp.c_lessequals (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (not (tptp.c_lessequals V_b (tptp.c_times V_a _let_1 T_b) T_b)) (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_b (tptp.c_times V_a _let_1 T_b) T_b)) (not (tptp.c_lessequals tptp.c_0 V_a T_b)) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_lessequals V_b _let_2 T_b)) (not (tptp.c_lessequals _let_2 V_b T_b)) (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_b _let_2 T_b)) (not (tptp.c_lessequals tptp.c_0 V_a T_b)) (not (tptp.c_lessequals _let_2 V_b T_b)) (tptp.c_lessequals (tptp.c_divide V_b _let_1 T_b) V_a T_b))))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)) (tptp.c_less tptp.c_0 V_b T_b) (tptp.c_less tptp.c_0 _let_1 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)) (tptp.c_less V_b tptp.c_0 T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less (tptp.c_divide (tptp.c_Numeral_Onumber__of V_w T_b) V_b T_b) tptp.c_0 T_b)) (tptp.c_less V_b tptp.c_0 T_b) (tptp.c_less tptp.c_0 V_b T_b))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b tptp.c_0 T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (tptp.c_less (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 V_b T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (tptp.c_less (tptp.c_divide _let_1 V_b T_b) tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (not (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)) (tptp.c_less V_b (tptp.c_times V_a _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less (tptp.c_times V_a _let_1 T_b) V_b T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)) (tptp.c_less tptp.c_0 V_a T_b) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 V_a T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_less (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 V_a T_b)) (not (tptp.c_less (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b (tptp.c_times V_a _let_1 T_b) T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b (tptp.c_times V_a _let_1 T_b) T_b)) (not (tptp.c_less tptp.c_0 V_a T_b)) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b _let_2 T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_less _let_2 V_b T_b)) (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b _let_2 T_b)) (not (tptp.c_less tptp.c_0 V_a T_b)) (not (tptp.c_less _let_2 V_b T_b)) (tptp.c_less (tptp.c_divide V_b _let_1 T_b) V_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide V_x (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) T_a) (tptp.c_uminus V_x T_a)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (= _let_1 tptp.c_0) (= (tptp.c_times (tptp.c_divide V_b _let_1 T_b) _let_1 T_b) V_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (not (= _let_1 tptp.c_0)) (= tptp.c_0 (tptp.c_divide V_b _let_1 T_b))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (= V_a (tptp.c_divide (tptp.c_times V_a _let_1 T_b) _let_1 T_b)) (= _let_1 tptp.c_0)))) (forall ((T_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (= tptp.c_0 (tptp.c_divide (tptp.c_times tptp.c_0 _let_1 T_b) _let_1 T_b))))) (forall ((T_b $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (not (= (tptp.c_uminus V_b T_b) tptp.c_1)) (= V_b (tptp.c_uminus tptp.c_1 T_b)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_uminus (tptp.c_uminus tptp.c_1 T_b) T_b) tptp.c_1))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (not (= _let_1 (tptp.c_uminus V_b T_b))) (= V_b (tptp.c_uminus _let_1 T_b))))) (forall ((T_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= _let_1 (tptp.c_uminus (tptp.c_uminus _let_1 T_b) T_b))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_r T_a)) (tptp.c_less tptp.c_0 (tptp.c_divide V_r (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) T_a) T_a) T_a))) (forall ((T_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Ofield T_b)) (= (tptp.c_HOL_Oinverse _let_1 T_b) (tptp.c_divide tptp.c_1 _let_1 T_b))))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (not (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)) (tptp.c_lessequals (tptp.c_times V_a _let_1 T_b) V_b T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_lessequals V_b (tptp.c_times V_a _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals V_a tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_a tptp.c_0 T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_lessequals V_b (tptp.c_times V_a _let_1 T_b) T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_a tptp.c_0 T_b)) (not (tptp.c_lessequals V_b (tptp.c_times V_a _let_1 T_b) T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (not (tptp.c_lessequals (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_a tptp.c_0 T_b)) (not (tptp.c_lessequals (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_lessequals V_b _let_2 T_b)) (not (tptp.c_lessequals _let_2 V_b T_b)) (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_lessequals V_a tptp.c_0 T_b)) (not (tptp.c_lessequals V_b _let_2 T_b)) (not (tptp.c_lessequals _let_2 V_b T_b)) (tptp.c_lessequals V_a (tptp.c_divide V_b _let_1 T_b) T_b))))) (forall ((T_b $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals tptp.c_1 (tptp.c_uminus V_b T_b) T_b)) (tptp.c_lessequals V_b (tptp.c_uminus tptp.c_1 T_b) T_b))) (forall ((T_b $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals V_b (tptp.c_uminus tptp.c_1 T_b) T_b)) (tptp.c_lessequals tptp.c_1 (tptp.c_uminus V_b T_b) T_b))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals _let_1 (tptp.c_uminus V_b T_b) T_b)) (tptp.c_lessequals V_b (tptp.c_uminus _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals V_b (tptp.c_uminus _let_1 T_b) T_b)) (tptp.c_lessequals _let_1 (tptp.c_uminus V_b T_b) T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oring T_b)) (= (tptp.c_times (tptp.c_minus V_a V_b T_b) _let_1 T_b) (tptp.c_minus (tptp.c_times V_a _let_1 T_b) (tptp.c_times V_b _let_1 T_b) T_b))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Osemiring T_b)) (= (tptp.c_times (tptp.c_plus V_a V_b T_b) _let_1 T_b) (tptp.c_plus (tptp.c_times V_a _let_1 T_b) (tptp.c_times V_b _let_1 T_b) T_b))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (tptp.c_less (tptp.c_times V_a _let_1 T_b) V_b T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (tptp.c_less V_b (tptp.c_times V_a _let_1 T_b) T_b) (tptp.c_less tptp.c_0 _let_1 T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b)) (tptp.c_less V_a tptp.c_0 T_b) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_a tptp.c_0 T_b)) (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b (tptp.c_times V_a _let_1 T_b) T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b) (tptp.c_less tptp.c_0 _let_1 T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_a tptp.c_0 T_b)) (not (tptp.c_less V_b (tptp.c_times V_a _let_1 T_b) T_b)) (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b) (tptp.c_less tptp.c_0 _let_1 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (not (tptp.c_less (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_a tptp.c_0 T_b)) (not (tptp.c_less (tptp.c_times V_a _let_1 T_b) V_b T_b)) (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b _let_2 T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_less _let_2 V_b T_b)) (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (let ((_let_2 (tptp.c_times V_a _let_1 T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_a tptp.c_0 T_b)) (not (tptp.c_less V_b _let_2 T_b)) (not (tptp.c_less _let_2 V_b T_b)) (tptp.c_less V_a (tptp.c_divide V_b _let_1 T_b) T_b))))) (forall ((T_b $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less tptp.c_1 (tptp.c_uminus V_b T_b) T_b)) (tptp.c_less V_b (tptp.c_uminus tptp.c_1 T_b) T_b))) (forall ((T_b $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less V_b (tptp.c_uminus tptp.c_1 T_b) T_b)) (tptp.c_less tptp.c_1 (tptp.c_uminus V_b T_b) T_b))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less _let_1 (tptp.c_uminus V_b T_b) T_b)) (tptp.c_less V_b (tptp.c_uminus _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less V_b (tptp.c_uminus _let_1 T_b) T_b)) (tptp.c_less _let_1 (tptp.c_uminus V_b T_b) T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) V_x T_a) (tptp.c_uminus (tptp.c_divide tptp.c_1 V_x T_a) T_a)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (not (= (tptp.c_uminus V_a T_b) _let_1)) (= (tptp.c_uminus _let_1 T_b) V_a)))) (forall ((T_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_uminus (tptp.c_uminus _let_1 T_b) T_b) _let_1)))) (forall ((T_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals (tptp.c_uminus V_a T_b) tptp.c_1 T_b)) (tptp.c_lessequals (tptp.c_uminus tptp.c_1 T_b) V_a T_b))) (forall ((T_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals (tptp.c_uminus tptp.c_1 T_b) V_a T_b)) (tptp.c_lessequals (tptp.c_uminus V_a T_b) tptp.c_1 T_b))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals (tptp.c_uminus V_a T_b) _let_1 T_b)) (tptp.c_lessequals (tptp.c_uminus _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_lessequals (tptp.c_uminus _let_1 T_b) V_a T_b)) (tptp.c_lessequals (tptp.c_uminus V_a T_b) _let_1 T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less (tptp.c_uminus V_a T_b) tptp.c_1 T_b)) (tptp.c_less (tptp.c_uminus tptp.c_1 T_b) V_a T_b))) (forall ((T_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_HOL_Oone T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less (tptp.c_uminus tptp.c_1 T_b) V_a T_b)) (tptp.c_less (tptp.c_uminus V_a T_b) tptp.c_1 T_b))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less (tptp.c_uminus V_a T_b) _let_1 T_b)) (tptp.c_less (tptp.c_uminus _let_1 T_b) V_a T_b)))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_b)) (not (tptp.c_less (tptp.c_uminus _let_1 T_b) V_a T_b)) (tptp.c_less (tptp.c_uminus V_a T_b) _let_1 T_b)))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat))) (= (tptp.c_Divides_Oop_Amod (tptp.c_Suc (tptp.c_Suc V_m)) _let_1 tptp.tc_nat) (tptp.c_Divides_Oop_Amod V_m _let_1 tptp.tc_nat)))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Divides_Oop_Amod V_m (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) tptp.tc_nat))) (or (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_nat)) (= _let_1 tptp.c_1)))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Divides_Oop_Amod V_m (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_nat) tptp.tc_nat))) (or (not (= _let_1 tptp.c_1)) (tptp.c_less tptp.c_0 _let_1 tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Oop_Amod V_m (tptp.c_Suc (tptp.c_Suc (tptp.c_Suc V_n))) tptp.tc_nat) (tptp.c_Divides_Oop_Amod V_m (tptp.c_plus (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB1) tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (not (tptp.c_lessequals (tptp.c_times _let_1 V_a T_b) (tptp.c_times _let_1 V_b T_b) T_b)) (tptp.c_lessequals V_a V_b T_b)))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (not (tptp.c_lessequals (tptp.c_times _let_1 V_a T_b) (tptp.c_times _let_1 V_b T_b) T_b)) (tptp.c_lessequals V_b V_a T_b)))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals (tptp.c_times _let_1 V_a T_b) (tptp.c_times _let_1 V_b T_b) T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_b)) (not (tptp.c_lessequals V_b V_a T_b)) (tptp.c_less tptp.c_0 _let_1 T_b) (tptp.c_lessequals (tptp.c_times _let_1 V_a T_b) (tptp.c_times _let_1 V_b T_b) T_b)))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_b)) (not (tptp.c_lessequals V_a V_b T_b)) (tptp.c_less _let_1 tptp.c_0 T_b) (tptp.c_lessequals (tptp.c_times _let_1 V_a T_b) (tptp.c_times _let_1 V_b T_b) T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not 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(forall ((T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_b)) (not (tptp.c_less V_b V_a T_b)) (not (tptp.c_less V_a V_b T_b)) (tptp.c_less (tptp.c_times V_a _let_1 T_b) (tptp.c_times V_b _let_1 T_b) T_b)))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Oring T_b)) (= (tptp.c_times _let_1 (tptp.c_minus V_b V_c T_b) T_b) (tptp.c_minus (tptp.c_times _let_1 V_b T_b) (tptp.c_times _let_1 V_c T_b) T_b))))) (forall ((T_b $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Osemiring T_b)) (= (tptp.c_times _let_1 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tptp.c_0 _let_1 T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 (tptp.c_divide _let_1 V_b T_b) T_b)) (tptp.c_less V_b tptp.c_0 T_b) (tptp.c_less tptp.c_0 _let_1 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 (tptp.c_divide _let_1 V_b T_b) T_b)) (tptp.c_less tptp.c_0 V_b T_b) (tptp.c_less _let_1 tptp.c_0 T_b)))) (forall ((T_b $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 (tptp.c_divide (tptp.c_Numeral_Onumber__of V_w T_b) V_b T_b) T_b)) (tptp.c_less V_b tptp.c_0 T_b) (tptp.c_less tptp.c_0 V_b T_b))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less tptp.c_0 V_b T_b)) (not (tptp.c_less tptp.c_0 _let_1 T_b)) (tptp.c_less tptp.c_0 (tptp.c_divide _let_1 V_b T_b) T_b)))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w T_b))) (or (not (tptp.class_Numeral_Onumber T_b)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_b)) (not (tptp.class_Ring__and__Field_Oordered__field T_b)) (not (tptp.c_less V_b tptp.c_0 T_b)) (not (tptp.c_less _let_1 tptp.c_0 T_b)) (tptp.c_less tptp.c_0 (tptp.c_divide _let_1 V_b T_b) T_b)))) (= tptp.c_1 _let_36) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_Suc V_m) (tptp.c_Suc V_n))) (= V_m V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_minus (tptp.c_minus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc V_k) tptp.tc_nat) (tptp.c_minus (tptp.c_minus V_m V_n tptp.tc_nat) V_k tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_lessequals V_n V_m tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (tptp.c_less (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) tptp.c_0))) (forall ((V_y $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_y tptp.tc_nat)) (= (tptp.c_Suc (tptp.c_minus V_y (tptp.c_Suc tptp.c_0) tptp.tc_nat)) V_y))) (forall ((V_m $$unsorted)) (not (= tptp.c_0 (tptp.c_Suc V_m)))) (forall ((V_y $$unsorted)) (= (tptp.c_plus V_y tptp.c_0 tptp.tc_nat) V_y)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_plus V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc (tptp.c_plus V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_plus V_m V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_n tptp.tc_nat) (tptp.c_less tptp.c_0 V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_m tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_plus V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_plus V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_plus V_m V_n tptp.tc_nat) tptp.c_0)) (= V_m tptp.c_0))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_plus V_m V_n tptp.tc_nat) tptp.c_0)) (= V_n tptp.c_0))) (= (tptp.c_plus tptp.c_0 tptp.c_0 tptp.tc_nat) tptp.c_0) (forall ((V_n $$unsorted)) (= (tptp.c_minus tptp.c_0 V_n tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_minus (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_minus V_m V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_less (tptp.c_minus V_n (tptp.c_Suc V_i) tptp.tc_nat) V_n tptp.tc_nat))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_minus (tptp.c_minus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_minus V_i (tptp.c_plus V_j V_k tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_minus V_m V_n tptp.tc_nat) tptp.c_0)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (= (tptp.c_minus V_m V_n tptp.tc_nat) tptp.c_0))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_minus V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_m $$unsorted)) (= (tptp.c_minus V_m V_m tptp.tc_nat) tptp.c_0)) (forall ((V_i $$unsorted)) (or (not (tptp.c_lessequals V_i tptp.c_0 tptp.tc_nat)) (= V_i tptp.c_0))) (tptp.c_lessequals tptp.c_0 tptp.c_0 tptp.tc_nat) (forall ((V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_lessequals V_n V_y tptp.tc_nat)) (= (tptp.c_plus (tptp.c_minus V_y V_n tptp.tc_nat) V_n tptp.tc_nat) V_y))) (forall ((V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_lessequals V_n V_y tptp.tc_nat)) (= (tptp.c_plus V_n (tptp.c_minus V_y V_n tptp.tc_nat) tptp.tc_nat) V_y))) (forall ((V_n $$unsorted)) (or (not (tptp.c_less V_n (tptp.c_Suc tptp.c_0) tptp.tc_nat)) (= V_n tptp.c_0))) (tptp.c_less tptp.c_0 _let_36 tptp.tc_nat) (forall ((V_n $$unsorted)) (or (not (tptp.c_less V_n tptp.c_1 tptp.tc_nat)) (= V_n tptp.c_0))) (tptp.c_less tptp.c_0 tptp.c_1 tptp.tc_nat) (forall ((V_y $$unsorted)) (= (tptp.c_Orderings_Omax tptp.c_0 V_y tptp.tc_nat) V_y)) (forall ((V_y $$unsorted)) (= (tptp.c_Orderings_Omax V_y tptp.c_0 tptp.tc_nat) V_y)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Orderings_Omax (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc (tptp.c_Orderings_Omax V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (= (tptp.c_Orderings_Omin tptp.c_0 V_n tptp.tc_nat) tptp.c_0)) (forall ((V_n $$unsorted)) (= (tptp.c_Orderings_Omin V_n tptp.c_0 tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Orderings_Omin (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc (tptp.c_Orderings_Omin V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted)) (= (tptp.c_times V_m tptp.c_0 tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_times V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_plus V_m (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_times V_k V_m tptp.tc_nat) (tptp.c_times V_k V_n tptp.tc_nat))) (= V_m V_n) (= V_k tptp.c_0))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_times tptp.c_0 V_m tptp.tc_nat) (tptp.c_times tptp.c_0 V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_times V_m V_k tptp.tc_nat) (tptp.c_times V_n V_k tptp.tc_nat))) (= V_m V_n) (= V_k tptp.c_0))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_times V_m tptp.c_0 tptp.tc_nat) (tptp.c_times V_n tptp.c_0 tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_times V_m V_n tptp.tc_nat) (tptp.c_Suc tptp.c_0))) (= V_m tptp.c_1))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_times V_m V_n tptp.tc_nat) (tptp.c_Suc tptp.c_0))) (= V_n tptp.c_1))) (= _let_35 _let_36) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_times V_m V_n tptp.tc_nat) tptp.c_0)) (= V_n tptp.c_0) (= V_m tptp.c_0))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_k tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_times V_k V_m tptp.tc_nat) (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_less tptp.c_0 V_k tptp.tc_nat) (tptp.c_lessequals (tptp.c_times V_k V_m tptp.tc_nat) (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (tptp.c_lessequals (tptp.c_times V_k V_m tptp.tc_nat) (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_k tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_times V_m V_k tptp.tc_nat) (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_less tptp.c_0 V_k tptp.tc_nat) (tptp.c_lessequals (tptp.c_times V_m V_k tptp.tc_nat) (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (tptp.c_lessequals (tptp.c_times V_m V_k tptp.tc_nat) (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_times V_k V_m tptp.tc_nat) (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_k tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_times V_k V_m tptp.tc_nat) (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (not (tptp.c_less tptp.c_0 V_k tptp.tc_nat)) (tptp.c_less (tptp.c_times V_k V_m tptp.tc_nat) (tptp.c_times V_k V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_times V_m V_k tptp.tc_nat) (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_k tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_times V_m V_k tptp.tc_nat) (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (not (tptp.c_less tptp.c_0 V_k tptp.tc_nat)) (tptp.c_less (tptp.c_times V_m V_k tptp.tc_nat) (tptp.c_times V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (not (tptp.c_less tptp.c_0 V_m tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_plus V_k V_m tptp.tc_nat) (tptp.c_plus V_k V_n tptp.tc_nat))) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_k V_m tptp.tc_nat) (tptp.c_plus V_k V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus V_k V_m tptp.tc_nat) (tptp.c_plus V_k V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less (tptp.c_plus V_k V_m tptp.tc_nat) (tptp.c_plus V_k V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (tptp.c_less (tptp.c_plus V_k V_m tptp.tc_nat) (tptp.c_plus V_k V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_plus V_m V_k tptp.tc_nat) (tptp.c_plus V_n V_k tptp.tc_nat))) (= V_m V_n))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_less (tptp.c_plus V_i V_j tptp.tc_nat) V_i tptp.tc_nat))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_less (tptp.c_plus V_j V_i tptp.tc_nat) V_i tptp.tc_nat))) (forall ((V_n $$unsorted)) (or (tptp.c_less tptp.c_0 V_n tptp.tc_nat) (= V_n tptp.c_0))) (not (tptp.c_less tptp.c_0 tptp.c_0 tptp.tc_nat)) (forall ((V_n $$unsorted)) (not (tptp.c_less V_n tptp.c_0 tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_Suc tptp.c_0) (tptp.c_times V_m V_n tptp.tc_nat))) (= V_m tptp.c_1))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_Suc tptp.c_0) (tptp.c_times V_m V_n tptp.tc_nat))) (= V_n tptp.c_1))) (= _let_36 _let_35) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Suc tptp.c_0) (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_lessequals tptp.c_1 V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_Suc tptp.c_0) (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat)) (tptp.c_lessequals tptp.c_1 V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_lessequals tptp.c_1 V_n tptp.tc_nat)) (not (tptp.c_lessequals tptp.c_1 V_m tptp.tc_nat)) (tptp.c_lessequals (tptp.c_Suc tptp.c_0) (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (= (tptp.c_times tptp.c_0 V_n tptp.tc_nat) tptp.c_0)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_times (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_plus V_n (tptp.c_times V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_y $$unsorted)) (= (tptp.c_plus tptp.c_0 V_y tptp.tc_nat) V_y)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_plus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_plus V_m V_n tptp.tc_nat)))) (forall ((V_y $$unsorted)) (= (tptp.c_minus V_y tptp.c_0 tptp.tc_nat) V_y)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_minus V_n V_m tptp.tc_nat) tptp.tc_nat)) (tptp.c_less V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_less V_m V_n tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_minus V_n V_m tptp.tc_nat) tptp.tc_nat))) (= (tptp.c_Numeral_OBit tptp.c_Numeral_OMin tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_OMin) (= (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB0) tptp.c_Numeral_OPls) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_plus (tptp.c_Numeral_Onumber__of V_v T_a) (tptp.c_minus V_c (tptp.c_Numeral_Onumber__of V_w T_a) T_a) T_a) (tptp.c_plus (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_w)) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_plus (tptp.c_Numeral_Onumber__of V_v T_a) (tptp.c_plus (tptp.c_Numeral_Onumber__of V_w T_a) V_z T_a) T_a) (tptp.c_plus (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v V_w) T_a) V_z T_a)))) (forall ((V_v $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (= (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit V_v tptp.c_Numeral_Obit_OB0) (tptp.c_Numeral_OBit V_w V_y)) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__add V_v V_w) V_y))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (= (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit V_v tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0)) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__add V_v V_w) tptp.c_Numeral_Obit_OB1))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (= (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit V_v tptp.c_Numeral_Obit_OB1) (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB1)) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__succ V_w)) tptp.c_Numeral_Obit_OB0))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__add tptp.c_Numeral_OMin V_w) (tptp.c_Numeral_Obin__pred V_w))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__add V_w tptp.c_Numeral_OMin) (tptp.c_Numeral_Obin__pred V_w))) (forall ((V_y $$unsorted)) (= (tptp.c_Numeral_Obin__add tptp.c_Numeral_OPls V_y) V_y)) (forall ((V_y $$unsorted)) (= (tptp.c_Numeral_Obin__add V_y tptp.c_Numeral_OPls) V_y)) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_plus (tptp.c_Numeral_Onumber__of V_v T_a) (tptp.c_Numeral_Onumber__of V_w T_a) T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v V_w) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_uminus (tptp.c_Numeral_Onumber__of V_w T_a) T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__minus V_w) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_uminus tptp.c_1 T_a) (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a)))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_times (tptp.c_Numeral_Onumber__of V_v T_a) (tptp.c_Numeral_Onumber__of V_w T_a) T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__mult V_v V_w) T_a)))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_minus (tptp.c_Numeral_Onumber__of V_v T_a) (tptp.c_Numeral_Onumber__of V_w T_a) T_a) (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_v (tptp.c_Numeral_Obin__minus V_w)) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_x T_a))) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less _let_1 tptp.c_0 T_a)) (= (tptp.c_HOL_Oabs _let_1 T_a) (tptp.c_uminus _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_x T_a))) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_less _let_1 tptp.c_0 T_a) (= (tptp.c_HOL_Oabs _let_1 T_a) _let_1)))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0)) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__minus V_w) tptp.c_Numeral_Obit_OB0))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__minus (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB1)) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__pred (tptp.c_Numeral_Obin__minus V_w)) tptp.c_Numeral_Obit_OB1))) (= (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OMin) _let_33) (= (tptp.c_Numeral_Obin__minus tptp.c_Numeral_OPls) tptp.c_Numeral_OPls) (forall ((V_v $$unsorted) (V_w $$unsorted)) (= (tptp.c_Numeral_Obin__mult (tptp.c_Numeral_OBit V_v tptp.c_Numeral_Obit_OB0) V_w) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__mult V_v V_w) tptp.c_Numeral_Obit_OB0))) (forall ((V_v $$unsorted) (V_w $$unsorted)) (= (tptp.c_Numeral_Obin__mult (tptp.c_Numeral_OBit V_v tptp.c_Numeral_Obit_OB1) V_w) (tptp.c_Numeral_Obin__add (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__mult V_v V_w) tptp.c_Numeral_Obit_OB0) V_w))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__mult tptp.c_Numeral_OMin V_w) (tptp.c_Numeral_Obin__minus V_w))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__mult tptp.c_Numeral_OPls V_w) tptp.c_Numeral_OPls)) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__pred (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0)) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__pred V_w) tptp.c_Numeral_Obit_OB1))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__pred (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB1)) (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0))) (= (tptp.c_Numeral_Obin__pred tptp.c_Numeral_OMin) (tptp.c_Numeral_OBit tptp.c_Numeral_OMin tptp.c_Numeral_Obit_OB0)) _let_34 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T_a)) (not (tptp.c_IntDef_Oiszero tptp.c_1 T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w V_x) T_a) T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_w T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of V_w T_a) T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w V_x) T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_y (tptp.c_Numeral_Obin__minus V_x)) T_a) T_a)) (not (tptp.c_lessequals (tptp.c_Numeral_Onumber__of V_x T_a) (tptp.c_Numeral_Onumber__of V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_y (tptp.c_Numeral_Obin__minus V_x)) T_a) T_a) (tptp.c_lessequals (tptp.c_Numeral_Onumber__of V_x T_a) (tptp.c_Numeral_Onumber__of V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (= (tptp.c_Numeral_Onumber__of V_x T_a) (tptp.c_Numeral_Onumber__of V_y T_a))) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a)) (= (tptp.c_Numeral_Onumber__of V_x T_a) (tptp.c_Numeral_Onumber__of V_y T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OPls T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0) T_a) T_a)) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_w T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of V_w T_a) T_a)) (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0) T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oiszero (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB1) T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less (tptp.c_Numeral_Onumber__of V_x T_a) (tptp.c_Numeral_Onumber__of V_y T_a) T_a)) (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__add V_x (tptp.c_Numeral_Obin__minus V_y)) T_a) T_a)) (tptp.c_less (tptp.c_Numeral_Onumber__of V_x T_a) (tptp.c_Numeral_Onumber__of V_y T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OPls T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg tptp.c_0 T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_IntDef_Oneg tptp.c_1 T_a)))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__succ (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB0)) (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB1))) (forall ((V_w $$unsorted)) (= (tptp.c_Numeral_Obin__succ (tptp.c_Numeral_OBit V_w tptp.c_Numeral_Obit_OB1)) (tptp.c_Numeral_OBit (tptp.c_Numeral_Obin__succ V_w) tptp.c_Numeral_Obit_OB0))) (= (tptp.c_Numeral_Obin__succ tptp.c_Numeral_OMin) tptp.c_Numeral_OPls) (= (tptp.c_Numeral_Obin__succ tptp.c_Numeral_OPls) _let_33) (forall ((V_y $$unsorted) (V_f2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Numeral_Obit_Obit__case V_y V_f2 tptp.c_Numeral_Obit_OB0 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Numeral_Obit_Obit__case V_f1 V_y tptp.c_Numeral_Obit_OB1 T_a) V_y)) (not (= tptp.c_Numeral_Obit_OB0 tptp.c_Numeral_Obit_OB1)) (not (= tptp.c_Numeral_Obit_OB1 tptp.c_Numeral_Obit_OB0)) (forall ((V_y $$unsorted) (V_f2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Numeral_Obit_Obit__rec V_y V_f2 tptp.c_Numeral_Obit_OB0 T_a) V_y)) (forall ((V_f1 $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Numeral_Obit_Obit__rec V_f1 V_y tptp.c_Numeral_Obit_OB1 T_a) V_y)) (= (tptp.c_Nat_Osize tptp.c_Numeral_Obit_OB0 tptp.tc_Numeral_Obit) tptp.c_0) (= (tptp.c_Nat_Osize tptp.c_Numeral_Obit_OB1 tptp.tc_Numeral_Obit) tptp.c_0) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_times (tptp.c_uminus (tptp.c_Numeral_Onumber__of V_w T_a) T_a) V_z T_a) (tptp.c_times (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__minus V_w) T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_times (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) V_z T_a) (tptp.c_uminus V_z T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_times V_z (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) T_a) (tptp.c_uminus V_z T_a)))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_times (tptp.c_Numeral_Onumber__of V_v T_a) (tptp.c_times (tptp.c_Numeral_Onumber__of V_w T_a) V_z T_a) T_a) (tptp.c_times (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_Obin__mult V_v V_w) T_a) V_z T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OPls T_a) tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (= (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_plus (tptp.c_uminus V_a T_a) V_a T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (not (= tptp.c_0 (tptp.c_HOL_Oabs V_a T_a))) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (= tptp.c_0 (tptp.c_HOL_Oabs tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_plus (tptp.c_HOL_Oabs V_a T_a) (tptp.c_HOL_Oabs V_b T_a) T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (= (tptp.c_HOL_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (not (= (tptp.c_HOL_Oabs V_a T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (= (tptp.c_HOL_Oabs tptp.c_0 T_a) tptp.c_0))) _let_32 (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs V_a T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (= (tptp.c_HOL_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oabs V_a T_a) tptp.c_0 T_a)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs tptp.c_0 T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (= (tptp.c_HOL_Oabs (tptp.c_uminus V_a T_a) T_a) (tptp.c_HOL_Oabs V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (not (tptp.c_less (tptp.c_HOL_Oabs V_a T_a) tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (not (tptp.c_lessequals tptp.c_0 V_y T_a)) (= (tptp.c_HOL_Oabs V_y T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (not (tptp.c_lessequals V_a tptp.c_0 T_a)) (= (tptp.c_HOL_Oabs V_a T_a) (tptp.c_uminus V_a T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_plus V_y tptp.c_0 T_a) V_y))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_lessequals (tptp.c_plus V_c V_a T_a) (tptp.c_plus V_c V_b T_a) T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals (tptp.c_plus V_c V_a T_a) (tptp.c_plus V_c V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_lessequals (tptp.c_plus V_a V_c T_a) (tptp.c_plus V_b V_c T_a) T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals (tptp.c_plus V_a V_c T_a) (tptp.c_plus V_b V_c T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_plus V_a V_b T_a) (tptp.c_plus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_less (tptp.c_plus V_c V_a T_a) (tptp.c_plus V_c V_b T_a) T_a)) (tptp.c_less V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_less V_a V_b T_a)) (tptp.c_less (tptp.c_plus V_c V_a T_a) (tptp.c_plus V_c V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_less (tptp.c_plus V_a V_c T_a) (tptp.c_plus V_b V_c T_a) T_a)) (tptp.c_less V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.c_less V_a V_b T_a)) (tptp.c_less (tptp.c_plus V_a V_c T_a) (tptp.c_plus V_b V_c T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_plus V_b V_a T_a) (tptp.c_plus V_c V_a T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_plus tptp.c_0 V_y T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_minus tptp.c_0 V_a T_a) (tptp.c_uminus V_a T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_minus V_y tptp.c_0 T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_minus V_a V_b T_a) tptp.c_0)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals (tptp.c_minus V_a V_b T_a) tptp.c_0 T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals (tptp.c_minus V_a V_b T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less (tptp.c_minus V_a V_b T_a) tptp.c_0 T_a)) (tptp.c_less V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less V_a V_b T_a)) (tptp.c_less (tptp.c_minus V_a V_b T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_minus V_a (tptp.c_uminus V_b T_a) T_a) (tptp.c_plus V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_minus V_a V_a T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals (tptp.c_plus V_a V_a T_a) tptp.c_0 T_a)) (tptp.c_lessequals V_a tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals V_a tptp.c_0 T_a)) (tptp.c_lessequals (tptp.c_plus V_a V_a T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less (tptp.c_plus V_a V_a T_a) tptp.c_0 T_a)) (tptp.c_less V_a tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (tptp.c_less (tptp.c_plus V_a V_a T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (= (tptp.c_LOrder_Ojoin V_a (tptp.c_uminus V_a T_a) T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (= (tptp.c_LOrder_Ojoin tptp.c_0 (tptp.c_uminus tptp.c_0 T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (= (tptp.c_LOrder_Omeet V_a (tptp.c_uminus V_a T_a) T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (= (tptp.c_LOrder_Omeet tptp.c_0 (tptp.c_uminus tptp.c_0 T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_uminus (tptp.c_plus V_a V_b T_a) T_a) (tptp.c_plus (tptp.c_uminus V_a T_a) (tptp.c_uminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_uminus (tptp.c_minus V_a V_b T_a) T_a) (tptp.c_minus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_uminus (tptp.c_uminus V_y T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_times tptp.c_1 V_y T_a) V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_times V_y tptp.c_1 T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= tptp.c_0 (tptp.c_uminus V_a T_a))) (= tptp.c_0 V_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= tptp.c_0 (tptp.c_uminus tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_uminus V_a T_a) T_a)) (tptp.c_lessequals V_a tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals V_a tptp.c_0 T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_uminus V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_uminus V_a T_a) T_a)) (tptp.c_less V_a tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (tptp.c_less tptp.c_0 (tptp.c_uminus V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_uminus V_a T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_uminus tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_uminus V_a T_a) (tptp.c_uminus V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (= (tptp.c_uminus (tptp.c_LOrder_Ojoin V_a V_b T_a) T_a) (tptp.c_LOrder_Omeet (tptp.c_uminus V_a T_a) (tptp.c_uminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals (tptp.c_uminus V_a T_a) tptp.c_0 T_a)) (tptp.c_lessequals tptp.c_0 V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals tptp.c_0 V_a T_a)) (tptp.c_lessequals (tptp.c_uminus V_a T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals (tptp.c_uminus V_b T_a) (tptp.c_uminus V_a T_a) T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals (tptp.c_uminus V_b T_a) (tptp.c_uminus V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less (tptp.c_uminus V_a T_a) tptp.c_0 T_a)) (tptp.c_less tptp.c_0 V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (tptp.c_less (tptp.c_uminus V_a T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less (tptp.c_uminus V_b T_a) (tptp.c_uminus V_a T_a) T_a)) (tptp.c_less V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (tptp.c_less V_a V_b T_a)) (tptp.c_less (tptp.c_uminus V_b T_a) (tptp.c_uminus V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (= (tptp.c_uminus (tptp.c_LOrder_Omeet V_a V_b T_a) T_a) (tptp.c_LOrder_Ojoin (tptp.c_uminus V_a T_a) (tptp.c_uminus V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (= (tptp.c_OrderedGroup_Onprt tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals tptp.c_0 V_x T_a)) (= (tptp.c_OrderedGroup_Onprt V_x T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals V_y tptp.c_0 T_a)) (= (tptp.c_OrderedGroup_Onprt V_y T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (tptp.c_lessequals (tptp.c_OrderedGroup_Onprt V_a T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals (tptp.c_OrderedGroup_Onprt V_a T_a) (tptp.c_OrderedGroup_Onprt V_b T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (= (tptp.c_OrderedGroup_Opprt tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals V_x tptp.c_0 T_a)) (= (tptp.c_OrderedGroup_Opprt V_x T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals tptp.c_0 V_y T_a)) (= (tptp.c_OrderedGroup_Opprt V_y T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals (tptp.c_OrderedGroup_Opprt V_a T_a) (tptp.c_OrderedGroup_Opprt V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_plus V_a (tptp.c_uminus V_a T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_plus V_a V_a T_a) T_a)) (tptp.c_lessequals tptp.c_0 V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (not (tptp.c_lessequals tptp.c_0 V_a T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_plus V_a V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_OrderedGroup_Opprt V_a T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_HOL_Oabs tptp.c_0 T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__abs T_a)) (tptp.c_less tptp.c_0 (tptp.c_HOL_Oabs V_a T_a) T_a) (= V_a tptp.c_0))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less (tptp.c_Orderings_Omax V_x V_y T_a) V_z T_a)) (tptp.c_less V_x V_z T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less (tptp.c_Orderings_Omax V_x V_y T_a) V_z T_a)) (tptp.c_less V_y V_z T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less V_y V_z T_a)) (not (tptp.c_less V_x V_z T_a)) (tptp.c_less (tptp.c_Orderings_Omax V_x V_y T_a) V_z T_a))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less V_z (tptp.c_Orderings_Omin V_x V_y T_a) T_a)) (tptp.c_less V_z V_x T_a))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less V_z (tptp.c_Orderings_Omin V_x V_y T_a) T_a)) (tptp.c_less V_z V_y T_a))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_less V_z V_y T_a)) (not (tptp.c_less V_z V_x T_a)) (tptp.c_less V_z (tptp.c_Orderings_Omin V_x V_y T_a) T_a))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_lessequals V_x (tptp.c_Orderings_Omin V_y V_z T_b) T_b)) (tptp.c_lessequals V_x V_y T_b))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_lessequals V_x (tptp.c_Orderings_Omin V_y V_z T_b) T_b)) (tptp.c_lessequals V_x V_z T_b))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_lessequals V_x V_z T_b)) (not (tptp.c_lessequals V_x V_y T_b)) (tptp.c_lessequals V_x (tptp.c_Orderings_Omin V_y V_z T_b) T_b))) (forall ((T_b $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_Orderings_Omin V_y V_y T_b) V_y))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Omin V_x V_y T_b))) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_Orderings_Omin V_x _let_1 T_b) _let_1)))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_lessequals (tptp.c_Orderings_Omax V_x V_y T_b) V_z T_b)) (tptp.c_lessequals V_x V_z T_b))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_lessequals (tptp.c_Orderings_Omax V_x V_y T_b) V_z T_b)) (tptp.c_lessequals V_y V_z T_b))) (forall ((T_b $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (not (tptp.c_lessequals V_y V_z T_b)) (not (tptp.c_lessequals V_x V_z T_b)) (tptp.c_lessequals (tptp.c_Orderings_Omax V_x V_y T_b) V_z T_b))) (forall ((T_b $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_Orderings_Omax V_y V_y T_b) V_y))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Omax V_x V_y T_b))) (or (not (tptp.class_Orderings_Olinorder T_b)) (= (tptp.c_Orderings_Omax V_x _let_1 T_b) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_less V_x V_x T_a)))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (tptp.c_Parity_Oeven (tptp.c_IntDef_Oint _let_1) tptp.tc_IntDef_Oint)))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_nat))) (or (not (tptp.c_Parity_Oeven (tptp.c_IntDef_Oint _let_1) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (tptp.c_Parity_Oeven _let_1 tptp.tc_IntDef_Oint)) (= (tptp.c_Divides_Oop_Amod _let_1 (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) tptp.c_0)))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_v tptp.tc_IntDef_Oint))) (or (not (= (tptp.c_Divides_Oop_Amod _let_1 (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) tptp.c_0)) (tptp.c_Parity_Oeven _let_1 tptp.tc_IntDef_Oint)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint)) (not (tptp.c_Parity_Oeven (tptp.c_minus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint)) (not (tptp.c_Parity_Oeven (tptp.c_minus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint)) (not (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven (tptp.c_minus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint) (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint) (tptp.c_Parity_Oeven (tptp.c_minus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_nat)) (not (tptp.c_Parity_Oeven (tptp.c_Suc V_x) tptp.tc_nat)))) (forall ((V_x $$unsorted)) (or (tptp.c_Parity_Oeven V_x tptp.tc_nat) (tptp.c_Parity_Oeven (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven (tptp.c_Nat_Opower V_x V_y tptp.tc_nat) tptp.tc_nat)) (tptp.c_Parity_Oeven V_x tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven (tptp.c_Nat_Opower V_x V_y tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_y tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_nat)) (not (tptp.c_less tptp.c_0 V_y tptp.tc_nat)) (tptp.c_Parity_Oeven (tptp.c_Nat_Opower V_x V_y tptp.tc_nat) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven (tptp.c_times V_x V_y tptp.tc_nat) tptp.tc_nat)) (tptp.c_Parity_Oeven V_y tptp.tc_nat) (tptp.c_Parity_Oeven V_x tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_nat)) (tptp.c_Parity_Oeven (tptp.c_times V_x V_y tptp.tc_nat) tptp.tc_nat))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_nat)) (tptp.c_Parity_Oeven (tptp.c_times V_x V_y tptp.tc_nat) tptp.tc_nat))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_nat)) (not (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_nat) tptp.tc_nat)) (tptp.c_Parity_Oeven V_x tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_nat)) (not (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_nat) tptp.tc_nat)) (tptp.c_Parity_Oeven V_y tptp.tc_nat))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_nat)) (not (tptp.c_Parity_Oeven V_x tptp.tc_nat)) (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_nat) tptp.tc_nat))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Parity_Oeven V_y tptp.tc_nat) (tptp.c_Parity_Oeven V_x tptp.tc_nat) (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_nat) tptp.tc_nat))) (tptp.c_Parity_Oeven tptp.c_0 tptp.tc_nat) (forall ((V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven (tptp.c_uminus V_x tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven (tptp.c_uminus V_x tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Parity_Oeven (tptp.c_Nat_Opower V_x V_n tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Parity_Oeven (tptp.c_Nat_Opower V_x V_n tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_less tptp.c_0 V_n tptp.tc_nat))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint)) (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (tptp.c_Parity_Oeven (tptp.c_Nat_Opower V_x V_n tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven (tptp.c_times V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint) (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven (tptp.c_times V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven (tptp.c_times V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint)) (not (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint)) (not (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint)) (not (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint)) (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Parity_Oeven V_y tptp.tc_IntDef_Oint) (tptp.c_Parity_Oeven V_x tptp.tc_IntDef_Oint) (tptp.c_Parity_Oeven (tptp.c_plus V_x V_y tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (tptp.c_Parity_Oeven tptp.c_0 tptp.tc_IntDef_Oint) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (not (tptp.c_Parity_Oeven V_x tptp.tc_nat)) (= (tptp.c_Nat_Opower (tptp.c_uminus tptp.c_1 T_a) V_x T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_uminus tptp.c_1 T_a))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Parity_Oeven V_x tptp.tc_nat) (= (tptp.c_Nat_Opower _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Power_Orecpower T_a)) (not (tptp.c_Parity_Oeven V_x tptp.tc_nat)) (= (tptp.c_Nat_Opower (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a) V_x T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of tptp.c_Numeral_OMin T_a))) (or (not (tptp.class_Numeral_Onumber__ring T_a)) (not (tptp.class_Power_Orecpower T_a)) (tptp.c_Parity_Oeven V_x tptp.tc_nat) (= (tptp.c_Nat_Opower _let_1 V_x T_a) _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Divides_Oop_Amod V_x (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (or (= _let_1 tptp.c_0) (= _let_1 tptp.c_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Divides_Oop_Amod V_x (tptp.c_Numeral_Onumber__of (tptp.c_Numeral_OBit (tptp.c_Numeral_OBit tptp.c_Numeral_OPls tptp.c_Numeral_Obit_OB1) tptp.c_Numeral_Obit_OB0) tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint))) (or (not (= _let_1 tptp.c_0)) (not (= _let_1 tptp.c_1))))) (not (tptp.c_Parity_Oeven tptp.c_1 tptp.tc_IntDef_Oint)) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (= _let_1 tptp.c_0)) (= (tptp.c_Nat_Opower tptp.c_0 _let_1 T_a) tptp.c_1)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (= (tptp.c_Nat_Opower tptp.c_0 _let_1 T_a) tptp.c_0) (= _let_1 tptp.c_0)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_Nat_Opower V_a (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat) T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_Nat_Opower V_a _let_1 T_a) tptp.c_0)) (tptp.c_less tptp.c_0 _let_1 tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 _let_1 tptp.tc_nat)) (= (tptp.c_Nat_Opower tptp.c_0 _let_1 T_a) tptp.c_0)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (= (tptp.c_Nat_Opower (tptp.c_HOL_Oabs V_x T_a) _let_1 T_a) (tptp.c_Nat_Opower V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.c_Nat_Opower V_x _let_1 T_a) tptp.c_0 T_a)) (not (= _let_1 tptp.c_0))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_Nat_Opower V_x _let_1 T_a) tptp.c_0 T_a)) (= V_x tptp.c_0)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.c_Nat_Opower V_x _let_1 T_a) tptp.c_0 T_a)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat) (tptp.c_lessequals V_x tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.c_Nat_Opower V_x (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat) T_a) tptp.c_0 T_a)) (tptp.c_lessequals V_x tptp.c_0 T_a) (= V_x tptp.c_0))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals V_x tptp.c_0 T_a)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat) (tptp.c_lessequals (tptp.c_Nat_Opower V_x _let_1 T_a) tptp.c_0 T_a) (= _let_1 tptp.c_0)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (tptp.c_lessequals (tptp.c_Nat_Opower tptp.c_0 _let_1 T_a) tptp.c_0 T_a) (= _let_1 tptp.c_0)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (not (tptp.c_less (tptp.c_Nat_Opower V_x _let_1 T_a) tptp.c_0 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less (tptp.c_Nat_Opower V_x (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat) T_a) tptp.c_0 T_a)) (tptp.c_less V_x tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less V_x tptp.c_0 T_a)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat) (tptp.c_less (tptp.c_Nat_Opower V_x _let_1 T_a) tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (not (tptp.c_Parity_Oeven V_n tptp.tc_nat)) (= (tptp.c_Nat_Opower (tptp.c_uminus V_x T_a) V_n T_a) (tptp.c_Nat_Opower V_x V_n T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Parity_Oeven V_n tptp.tc_nat) (= (tptp.c_Nat_Opower (tptp.c_uminus V_x T_a) V_n T_a) (tptp.c_uminus (tptp.c_Nat_Opower V_x V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 T_a) T_a)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat) (tptp.c_lessequals tptp.c_0 V_x T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (tptp.c_lessequals tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals tptp.c_0 V_x T_a)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat) (tptp.c_lessequals tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 T_a) T_a)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat) (tptp.c_less tptp.c_0 V_x T_a) (= _let_1 tptp.c_0)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower tptp.c_0 _let_1 T_a) T_a)) (= _let_1 tptp.c_0)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower tptp.c_0 _let_1 T_a) T_a)) (tptp.c_less tptp.c_0 tptp.c_0 T_a) (= _let_1 tptp.c_0)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 tptp.c_0)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven _let_1 tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 T_a) T_a) (= V_x tptp.c_0)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 V_x T_a)) (tptp.c_Parity_Oeven _let_1 tptp.tc_nat) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 T_a) T_a)))) (forall ((V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 tptp.tc_nat) tptp.tc_nat)) (tptp.c_less tptp.c_0 V_x tptp.tc_nat) (= _let_1 tptp.c_0)))) (forall ((V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat))) (or (not (= _let_1 tptp.c_0)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x _let_1 tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_w $$unsorted)) (or (not (tptp.c_less tptp.c_0 V_x tptp.tc_nat)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x (tptp.c_Numeral_Onumber__of V_w tptp.tc_nat) tptp.tc_nat) tptp.tc_nat))) (forall ((V_i $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals tptp.c_1 V_i tptp.tc_nat)) (tptp.c_lessequals (tptp.c_Suc tptp.c_0) (tptp.c_Nat_Opower V_i V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (or (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower tptp.c_0 V_n tptp.tc_nat) tptp.tc_nat)) (= V_n tptp.c_0))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x V_n tptp.tc_nat) tptp.tc_nat) (= V_x tptp.c_0))) (forall ((V_x $$unsorted)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower V_x tptp.c_0 tptp.tc_nat) tptp.tc_nat)) (forall ((V_p $$unsorted)) (= (tptp.c_Nat_Opower V_p tptp.c_0 tptp.tc_nat) tptp.c_1)) (forall ((V_p $$unsorted) (V_n $$unsorted)) (= (tptp.c_Nat_Opower V_p (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_times V_p (tptp.c_Nat_Opower V_p V_n tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (= (tptp.c_Nat_Opower tptp.c_0 (tptp.c_Suc V_n) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_Nat_Opower V_a V_n T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_Nat_Opower V_a V_n T_a) tptp.c_0)) (tptp.c_less tptp.c_0 V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 V_n tptp.tc_nat)) (= (tptp.c_Nat_Opower tptp.c_0 V_n T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less tptp.c_1 V_b T_a)) (not (tptp.c_lessequals (tptp.c_Nat_Opower V_b V_x T_a) (tptp.c_Nat_Opower V_b V_y T_a) T_a)) (tptp.c_lessequals V_x V_y tptp.tc_nat))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less tptp.c_1 V_b T_a)) (not (tptp.c_lessequals V_x V_y tptp.tc_nat)) (tptp.c_lessequals (tptp.c_Nat_Opower V_b V_x T_a) (tptp.c_Nat_Opower V_b V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less tptp.c_1 V_a T_a)) (not (= (tptp.c_Nat_Opower V_a V_m T_a) (tptp.c_Nat_Opower V_a V_n T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (= (tptp.c_Nat_Opower tptp.c_1 V_n T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (= (tptp.c_Nat_Opower V_y tptp.c_1 T_a) V_y))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less tptp.c_1 V_b T_a)) (not (tptp.c_less (tptp.c_Nat_Opower V_b V_x T_a) (tptp.c_Nat_Opower V_b V_y T_a) T_a)) (tptp.c_less V_x V_y tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less V_x V_y tptp.tc_nat)) (not (tptp.c_less tptp.c_1 V_b T_a)) (tptp.c_less (tptp.c_Nat_Opower V_b V_x T_a) (tptp.c_Nat_Opower V_b V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (= (tptp.c_Nat_Opower V_a tptp.c_0 T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs V_a T_a) V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs tptp.c_0 T_a) V_n T_a) T_a)) (= V_n tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs V_a T_a) V_n T_a) T_a) (= V_a tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Orecpower T_a)) (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_less tptp.c_0 (tptp.c_Nat_Opower (tptp.c_HOL_Oabs V_a T_a) tptp.c_0 T_a) 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 ((V_y $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_fst (tptp.c_Pair V_y V_b T_a T_b) T_a T_b) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Pair (tptp.c_fst V_y T_a T_b) (tptp.c_snd V_y T_a T_b) T_a T_b) V_y)) (forall ((V_a $$unsorted) (V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_snd (tptp.c_Pair V_a V_y T_b T_a) T_b T_a) V_y)) (forall ((V_z $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= V_z (tptp.c_Pair (tptp.c_Main_Osurj__pair__1 V_z T_a T_b) (tptp.c_Main_Osurj__pair__2 V_z T_a T_b) T_a T_b))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ODomain tptp.c_Relation_OId T_a T_a) tptp.c_UNIV)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Relation_Odiag V_y T_a) T_a T_a) V_y)) (forall ((T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_ODomain tptp.c_emptyset T_a T_b) tptp.c_emptyset)) (forall ((V_y $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_Orel__comp tptp.c_Relation_OId V_y T_b T_b T_a) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage tptp.c_Relation_OId V_y T_a T_a) V_y)) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_Relation_OImage (tptp.c_Relation_Odiag V_A T_a) V_B T_a T_a) (tptp.c_inter V_A V_B T_a))) (forall ((V_R $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_OImage V_R tptp.c_emptyset T_b T_a) tptp.c_emptyset)) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_OImage V_r (tptp.c_insert V_a tptp.c_emptyset T_b) T_b T_a) T_a)) (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_b T_a) V_r (tptp.tc_prod T_b T_a))) (tptp.c_in V_b (tptp.c_Relation_OImage V_r (tptp.c_insert V_a tptp.c_emptyset T_b) T_b T_a) T_a))) (forall ((V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Orel__comp V_y tptp.c_Relation_OId T_a T_b T_a) V_y)) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_ORange tptp.c_Relation_OId T_a T_a) tptp.c_UNIV)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Relation_Odiag V_y T_a) T_a T_a) V_y)) (forall ((T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange tptp.c_emptyset T_b T_a) tptp.c_emptyset)) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_Oconverse tptp.c_Relation_OId T_a T_a) tptp.c_Relation_OId)) (forall ((V_y $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Relation_Oconverse (tptp.c_Relation_Oconverse V_y T_a T_b) T_b T_a) V_y)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Relation_Odiag V_A T_a))) (= (tptp.c_Relation_Oconverse _let_1 T_a T_a) _let_1))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_b V_a T_b T_a) V_r (tptp.tc_prod T_b T_a))) (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b)))) (forall ((T_a $$unsorted)) (= (tptp.c_Relation_Odiag tptp.c_emptyset T_a) tptp.c_emptyset)) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_a) tptp.c_Relation_OId (tptp.tc_prod T_a T_a))) (= V_a V_b))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in (tptp.c_Pair V_x V_x T_a T_a) tptp.c_Relation_OId (tptp.tc_prod T_a T_a))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Nat_Opower V_y tptp.c_1 (tptp.tc_set (tptp.tc_prod T_a T_a))) V_y)) (forall ((V_R $$unsorted) (T_a__1 $$unsorted)) (= (tptp.c_Nat_Opower V_R tptp.c_0 (tptp.tc_set (tptp.tc_prod T_a__1 T_a__1))) tptp.c_Relation_OId)) (forall ((V_R $$unsorted) (V_n $$unsorted) (T_a__1 $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_prod T_a__1 T_a__1)))) (= (tptp.c_Nat_Opower V_R (tptp.c_Suc V_n) _let_1) (tptp.c_Relation_Orel__comp V_R (tptp.c_Nat_Opower V_R V_n _let_1) T_a__1 T_a__1 T_a__1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs (tptp.c_divide V_a V_b T_a) T_a) (tptp.c_divide (tptp.c_HOL_Oabs V_a T_a) (tptp.c_HOL_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs (tptp.c_HOL_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse (tptp.c_HOL_Oabs V_a T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs tptp.c_1 T_a) tptp.c_1))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T_a)) (not (= tptp.c_0 tptp.c_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide V_y tptp.c_1 T_a) V_y))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_divide V_c V_a T_a) (tptp.c_divide V_c V_b T_a))) (= V_a V_b) (= V_c tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide tptp.c_0 V_a T_a) (tptp.c_divide tptp.c_0 V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_divide V_a V_c T_a) (tptp.c_divide V_b V_c T_a))) (= V_a V_b) (= V_c tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide V_a tptp.c_0 T_a) (tptp.c_divide V_b tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide (tptp.c_divide V_a V_b T_a) V_c T_a) (tptp.c_divide V_a (tptp.c_times V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide V_a (tptp.c_divide V_b V_c T_a) T_a) (tptp.c_divide (tptp.c_times V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_divide V_a V_b T_a) tptp.c_0)) (= V_b tptp.c_0) (= V_a tptp.c_0))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide tptp.c_0 V_b T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide V_a tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_divide V_a V_b T_a) tptp.c_1)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (= (tptp.c_divide V_b tptp.c_0 T_a) tptp.c_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (= (tptp.c_divide V_b V_a T_a) tptp.c_1)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= V_x tptp.c_0) (= (tptp.c_divide V_x V_x T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals (tptp.c_divide tptp.c_1 V_b T_a) tptp.c_0 T_a)) (tptp.c_lessequals V_b tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals V_b tptp.c_0 T_a)) (tptp.c_lessequals (tptp.c_divide tptp.c_1 V_b T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_lessequals (tptp.c_divide V_b V_a T_a) tptp.c_1 T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals (tptp.c_divide V_b V_a T_a) tptp.c_1 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_lessequals (tptp.c_divide V_b V_a T_a) tptp.c_1 T_a)) (tptp.c_lessequals V_b V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_lessequals V_b V_a T_a)) (tptp.c_lessequals (tptp.c_divide V_b V_a T_a) tptp.c_1 T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not 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(tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide V_a (tptp.c_uminus V_b T_a) T_a) (tptp.c_uminus (tptp.c_divide V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide tptp.c_0 tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (= tptp.c_1 (tptp.c_divide V_b tptp.c_0 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (= tptp.c_1 (tptp.c_divide V_b V_a T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= V_x tptp.c_0) (= tptp.c_1 (tptp.c_divide V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_a tptp.c_0) (= (tptp.c_times (tptp.c_HOL_Oinverse V_a T_a) V_a T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_times V_c V_a T_a) (tptp.c_times V_c V_b T_a))) (= V_a V_b) (= V_c tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_times tptp.c_0 V_a T_a) (tptp.c_times tptp.c_0 V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_times V_a V_c T_a) (tptp.c_times V_b V_c T_a))) (= V_a V_b) (= V_c tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_times V_a tptp.c_0 T_a) (tptp.c_times V_b tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse (tptp.c_divide V_a V_b T_a) T_a) (tptp.c_divide V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse V_x T_a) tptp.c_1)) (= V_x tptp.c_1))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse tptp.c_1 T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse (tptp.c_HOL_Oinverse V_y T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_b T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a)) (tptp.c_lessequals V_b V_a T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_b T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_lessequals V_b V_a T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_b tptp.c_0 T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a)) (tptp.c_lessequals V_b V_a T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_b tptp.c_0 T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_lessequals V_b V_a T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_b T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_less (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a)) (tptp.c_less V_b V_a T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_b V_a T_a)) (not (tptp.c_less tptp.c_0 V_b T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (tptp.c_less (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_b tptp.c_0 T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_less (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a)) (tptp.c_less V_b V_a T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_b V_a T_a)) (not (tptp.c_less V_b tptp.c_0 T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (tptp.c_less (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse (tptp.c_uminus V_a T_a) T_a) (tptp.c_uminus (tptp.c_HOL_Oinverse V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse (tptp.c_times V_a V_b T_a) T_a) (tptp.c_times (tptp.c_HOL_Oinverse V_a T_a) (tptp.c_HOL_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less (tptp.c_HOL_Oinverse V_a T_a) tptp.c_0 T_a)) (tptp.c_less V_a tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (tptp.c_less (tptp.c_HOL_Oinverse V_a T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_HOL_Oinverse V_a T_a) T_a)) (tptp.c_lessequals tptp.c_0 V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals tptp.c_0 V_a T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_HOL_Oinverse V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse V_a T_a) tptp.c_0 T_a)) (tptp.c_lessequals V_a tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals V_a tptp.c_0 T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse V_a T_a) tptp.c_0 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse V_a T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_HOL_Oinverse V_a T_a) T_a)) (tptp.c_less tptp.c_0 V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (tptp.c_less tptp.c_0 (tptp.c_HOL_Oinverse V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_lessequals tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a)) (tptp.c_lessequals V_b V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_lessequals V_b V_a T_a)) (tptp.c_lessequals tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_lessequals tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a)) (tptp.c_lessequals V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)) (tptp.c_lessequals tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (not (tptp.c_less tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a)) (tptp.c_less V_b V_a T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_b V_a T_a)) (not (tptp.c_less V_a tptp.c_0 T_a)) (tptp.c_less tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (not (tptp.c_less tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a)) (tptp.c_less V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less V_a V_b T_a)) (not (tptp.c_less tptp.c_0 V_a T_a)) (tptp.c_less tptp.c_1 (tptp.c_divide V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide (tptp.c_uminus V_a T_a) (tptp.c_uminus V_b T_a) T_a) (tptp.c_divide V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_times (tptp.c_uminus V_a T_a) (tptp.c_uminus V_b T_a) T_a) (tptp.c_times V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= V_c (tptp.c_times V_c V_b T_a))) (= V_c tptp.c_0) (= V_b tptp.c_1))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= tptp.c_0 (tptp.c_times tptp.c_0 V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_c (tptp.c_times V_c tptp.c_1 T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_times V_c V_a T_a) V_c)) (= V_c tptp.c_0) (= V_a tptp.c_1))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= V_c (tptp.c_times V_b V_c T_a))) (= V_c tptp.c_0) (= V_b tptp.c_1))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= tptp.c_0 (tptp.c_times V_b tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_c (tptp.c_times tptp.c_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_times V_a V_c T_a) V_c)) (= V_c tptp.c_0) (= V_a tptp.c_1))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide tptp.c_0 (tptp.c_times tptp.c_0 V_b T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c tptp.c_0) (= (tptp.c_divide V_c (tptp.c_times V_c V_b T_a) T_a) (tptp.c_divide tptp.c_1 V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide (tptp.c_times tptp.c_0 V_a T_a) tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c tptp.c_0) (= (tptp.c_divide (tptp.c_times V_c V_a T_a) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide (tptp.c_times tptp.c_0 V_a T_a) (tptp.c_times tptp.c_0 V_b T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c tptp.c_0) (= (tptp.c_divide (tptp.c_times V_c V_a T_a) (tptp.c_times V_c V_b T_a) T_a) (tptp.c_divide V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide tptp.c_0 (tptp.c_times V_b tptp.c_0 T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c tptp.c_0) (= (tptp.c_divide V_c (tptp.c_times V_b V_c T_a) T_a) (tptp.c_divide tptp.c_1 V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide (tptp.c_times V_a tptp.c_0 T_a) tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c tptp.c_0) (= (tptp.c_divide (tptp.c_times V_a V_c T_a) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_divide (tptp.c_times V_a tptp.c_0 T_a) (tptp.c_times V_b tptp.c_0 T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c tptp.c_0) (= (tptp.c_divide (tptp.c_times V_a V_c T_a) (tptp.c_times V_b V_c T_a) T_a) (tptp.c_divide V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.c_times V_a V_b T_a) tptp.c_0)) (= V_b tptp.c_0) (= V_a tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_times (tptp.c_uminus V_a T_a) V_b T_a) (tptp.c_uminus (tptp.c_times V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_times V_a (tptp.c_uminus V_b T_a) T_a) (tptp.c_uminus (tptp.c_times V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T_a)) (= (tptp.c_times tptp.c_0 V_a T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T_a)) (= (tptp.c_times V_a tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals tptp.c_1 tptp.c_0 T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_less tptp.c_1 tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (= (tptp.c_divide tptp.c_1 V_a T_a) tptp.c_0)) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_divide tptp.c_1 tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= tptp.c_1 (tptp.c_divide V_a V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T_a)) (not (= tptp.c_1 tptp.c_0)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_less tptp.c_0 tptp.c_1 T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_a tptp.c_0) (= (tptp.c_times V_a (tptp.c_HOL_Oinverse V_a T_a) T_a) tptp.c_1))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_times V_a (tptp.c_divide V_b V_c T_a) T_a) (tptp.c_divide (tptp.c_times V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_times (tptp.c_divide V_b V_c T_a) V_a T_a) (tptp.c_divide (tptp.c_times V_b V_a T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_times (tptp.c_divide V_b tptp.c_0 T_a) tptp.c_0 T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_a tptp.c_0) (= (tptp.c_times (tptp.c_divide V_b V_a T_a) V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_times tptp.c_0 (tptp.c_divide V_b tptp.c_0 T_a) T_a) tptp.c_0))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_a tptp.c_0) (= (tptp.c_times V_a (tptp.c_divide V_b V_a T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (= tptp.c_0 (tptp.c_divide tptp.c_1 V_a T_a))) (= V_a tptp.c_0))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= tptp.c_0 (tptp.c_divide tptp.c_1 tptp.c_0 T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals tptp.c_0 (tptp.c_divide tptp.c_1 V_b T_a) T_a)) (tptp.c_lessequals tptp.c_0 V_b T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_lessequals tptp.c_0 V_b T_a)) (tptp.c_lessequals tptp.c_0 (tptp.c_divide tptp.c_1 V_b T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals tptp.c_0 tptp.c_1 T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 (tptp.c_divide tptp.c_1 V_b T_a) T_a)) (tptp.c_less tptp.c_0 V_b T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.c_less tptp.c_0 V_b T_a)) (tptp.c_less tptp.c_0 (tptp.c_divide tptp.c_1 V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_uminus (tptp.c_SetInterval_OatLeast V_k T_a) (tptp.tc_set T_a)) (tptp.c_SetInterval_OlessThan V_k T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_uminus (tptp.c_SetInterval_OatMost V_k T_a) (tptp.tc_set T_a)) (tptp.c_SetInterval_OgreaterThan V_k T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_uminus (tptp.c_SetInterval_OgreaterThan V_k T_a) (tptp.tc_set T_a)) (tptp.c_SetInterval_OatMost V_k T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_uminus (tptp.c_SetInterval_OlessThan V_k T_a) (tptp.tc_set T_a)) (tptp.c_SetInterval_OatLeast V_k T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_less V_n V_m T_a)) (= (tptp.c_SetInterval_OatLeastAtMost V_m V_n T_a) tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatLeastAtMost V_l V_u T_a) T_a)) (tptp.c_lessequals V_l V_i T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatLeastAtMost V_l V_u T_a) T_a)) (tptp.c_lessequals V_i V_u T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_lessequals V_i V_u T_a)) (not (tptp.c_lessequals V_l V_i T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OatLeastAtMost V_l V_u T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_OatLeastAtMost V_a V_a T_a) (tptp.c_insert V_a tptp.c_emptyset T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals V_n V_m T_a)) (= (tptp.c_SetInterval_OatLeastLessThan V_m V_n T_a) tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatLeastLessThan V_l V_u T_a) T_a)) (tptp.c_lessequals V_l V_i T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatLeastLessThan V_l V_u T_a) T_a)) (tptp.c_less V_i V_u T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_less V_i V_u T_a)) (not (tptp.c_lessequals V_l V_i T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OatLeastLessThan V_l V_u T_a) T_a))) (forall ((V_m $$unsorted)) (= (tptp.c_SetInterval_OatLeastLessThan V_m (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_insert V_m tptp.c_emptyset tptp.tc_nat))) _let_31 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OatLeast V_x T_a) (tptp.c_SetInterval_OatLeast V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatLeast V_k T_a) T_a)) (tptp.c_lessequals V_k V_i T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_lessequals V_k V_i T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OatLeast V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OatLeast V_x T_a) (tptp.c_SetInterval_OatLeast V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OatLeast V_x T_a) (tptp.c_SetInterval_OatLeast V_y T_a) (tptp.tc_set T_a)))) (= (tptp.c_SetInterval_OatMost tptp.c_0 tptp.tc_nat) (tptp.c_insert tptp.c_0 tptp.c_emptyset tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OatMost V_x T_a) (tptp.c_SetInterval_OatMost V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OatMost V_k T_a) T_a)) (tptp.c_lessequals V_i V_k T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_lessequals V_i V_k T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OatMost V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OatMost V_x T_a) (tptp.c_SetInterval_OatMost V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OatMost V_x T_a) (tptp.c_SetInterval_OatMost V_y T_a) (tptp.tc_set T_a)))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OatLeastAtMost V_l V_u tptp.tc_nat) tptp.tc_nat) (tptp.c_minus (tptp.c_Suc V_u) V_l tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OatLeastAtMost V_l V_u tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Onat (tptp.c_plus (tptp.c_minus V_u V_l tptp.tc_IntDef_Oint) tptp.c_1 tptp.tc_IntDef_Oint)))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OatLeastLessThan V_l V_u tptp.tc_nat) tptp.tc_nat) (tptp.c_minus V_u V_l tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OatLeastLessThan V_l V_u tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Onat (tptp.c_minus V_u V_l tptp.tc_IntDef_Oint)))) (forall ((V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OatMost V_u tptp.tc_nat) tptp.tc_nat) (tptp.c_Suc V_u))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u tptp.tc_nat) tptp.tc_nat) (tptp.c_minus V_u V_l tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Onat (tptp.c_minus V_u V_l tptp.tc_IntDef_Oint)))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u tptp.tc_nat) tptp.tc_nat) (tptp.c_minus V_u (tptp.c_Suc V_l) tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Onat (tptp.c_minus V_u (tptp.c_plus V_l tptp.c_1 tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)))) (forall ((V_y $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_SetInterval_OlessThan V_y tptp.tc_nat) tptp.tc_nat) V_y)) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_lessequals V_l V_k T_a)) (= (tptp.c_SetInterval_OgreaterThanAtMost V_k V_l T_a) tptp.c_emptyset))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u T_a) T_a)) (tptp.c_less V_l V_i T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u T_a) T_a)) (tptp.c_lessequals V_i V_u T_a))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_less V_l V_i T_a)) (not (tptp.c_lessequals V_i V_u T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u T_a) T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u T_a) T_a)) (tptp.c_less V_l V_i T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u T_a) T_a)) (tptp.c_less V_i V_u T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_less V_i V_u T_a)) (not (tptp.c_less V_l V_i T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OgreaterThan V_x T_a) (tptp.c_SetInterval_OgreaterThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThan V_k T_a) T_a)) (tptp.c_less V_k V_i T_a))) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_less V_k V_i T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OgreaterThan V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OgreaterThan V_x T_a) (tptp.c_SetInterval_OgreaterThan V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OgreaterThan V_x T_a) (tptp.c_SetInterval_OgreaterThan V_y T_a) (tptp.tc_set T_a)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_i V_n T_a)) (= (tptp.c_minus (tptp.c_SetInterval_OatLeastLessThan V_i V_m T_a) (tptp.c_SetInterval_OatLeastLessThan V_i V_n T_a) (tptp.tc_set T_a)) (tptp.c_SetInterval_OatLeastLessThan V_n V_m T_a)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OatLeastLessThan V_i V_j T_a) (tptp.c_SetInterval_OatLeastLessThan V_m V_n T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_m V_i T_a) (tptp.c_lessequals V_j V_i T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OatLeastLessThan V_i V_j T_a) (tptp.c_SetInterval_OatLeastLessThan V_m V_n T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_j V_n T_a) (tptp.c_lessequals V_j V_i T_a))) (forall ((T_a $$unsorted) (V_j $$unsorted) (V_i $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_j V_i T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OatLeastLessThan V_i V_j T_a) (tptp.c_SetInterval_OatLeastLessThan V_m V_n T_a) (tptp.tc_set T_a)))) (forall ((T_a $$unsorted) (V_j $$unsorted) (V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_j V_n T_a)) (not (tptp.c_lessequals V_m V_i T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OatLeastLessThan V_i V_j T_a) (tptp.c_SetInterval_OatLeastLessThan V_m V_n T_a) (tptp.tc_set T_a)))) _let_29 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_OlessThan V_x T_a) (tptp.c_SetInterval_OlessThan V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_in V_i (tptp.c_SetInterval_OlessThan V_k T_a) T_a)) (tptp.c_less V_i V_k T_a))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Orderings_Oord T_a)) (not (tptp.c_less V_i V_k T_a)) (tptp.c_in V_i (tptp.c_SetInterval_OlessThan V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals (tptp.c_SetInterval_OlessThan V_x T_a) (tptp.c_SetInterval_OlessThan V_y T_a) (tptp.tc_set T_a))) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_lessequals (tptp.c_SetInterval_OlessThan V_x T_a) (tptp.c_SetInterval_OlessThan V_y T_a) (tptp.tc_set T_a)))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_insert V_k tptp.c_emptyset T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_minus _let_1 (tptp.c_SetInterval_OlessThan V_k T_a) (tptp.tc_set T_a)) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (= (tptp.c_uminus (tptp.c_minus V_A V_B _let_1) _let_1) (tptp.c_union (tptp.c_uminus V_A _let_1) V_B T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (= (tptp.c_uminus (tptp.c_inter V_A V_B T_a) _let_1) (tptp.c_union (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1) T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_uminus tptp.c_UNIV (tptp.tc_set T_a)) tptp.c_emptyset)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (= (tptp.c_uminus (tptp.c_union V_A V_B T_a) _let_1) (tptp.c_inter (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1) T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter (tptp.c_uminus V_A (tptp.tc_set T_a)) V_A T_a) tptp.c_emptyset)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter V_A (tptp.c_uminus V_A (tptp.tc_set T_a)) T_a) tptp.c_emptyset)) (forall ((T_a $$unsorted)) (= (tptp.c_uminus tptp.c_emptyset (tptp.tc_set T_a)) tptp.c_UNIV)) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (= (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1))) (= V_A V_B)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_in V_c (tptp.c_uminus V_A (tptp.tc_set T_a)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c V_A T_a) (tptp.c_in V_c (tptp.c_uminus V_A (tptp.tc_set T_a)) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1) _let_1)) (tptp.c_lessequals V_B V_A _let_1)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_B V_A _let_1)) (tptp.c_lessequals (tptp.c_uminus V_A _let_1) (tptp.c_uminus V_B _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (= (tptp.c_minus V_A (tptp.c_uminus V_B _let_1) _let_1) (tptp.c_inter V_A V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_minus V_A tptp.c_UNIV (tptp.tc_set T_a)) tptp.c_emptyset)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_minus V_A V_A (tptp.tc_set T_a)) tptp.c_emptyset)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter V_A (tptp.c_minus V_B V_A (tptp.tc_set T_a)) T_a) tptp.c_emptyset)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_minus V_y tptp.c_emptyset (tptp.tc_set T_a)) V_y)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (= (tptp.c_minus V_A V_B _let_1) tptp.c_emptyset)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_A V_B _let_1)) (= (tptp.c_minus V_A V_B _let_1) tptp.c_emptyset)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (let ((_let_2 (tptp.c_minus V_A V_B _let_1))) (= (tptp.c_minus _let_2 V_B _let_1) _let_2)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_minus V_A V_B (tptp.tc_set T_a)) T_a)) (tptp.c_in V_c V_A T_a))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c (tptp.c_minus V_A V_B (tptp.tc_set T_a)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (tptp.c_in V_c V_B T_a) (tptp.c_in V_c (tptp.c_minus V_A V_B (tptp.tc_set T_a)) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (tptp.c_in V_x V_A T_a) (= (tptp.c_minus V_A (tptp.c_insert V_x V_B T_a) _let_1) (tptp.c_minus V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_inter V_A V_B T_a) tptp.c_UNIV)) (= V_A tptp.c_UNIV))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_inter V_A V_B T_a) tptp.c_UNIV)) (= V_B tptp.c_UNIV))) (forall ((T_a $$unsorted)) (= (tptp.c_inter tptp.c_UNIV tptp.c_UNIV T_a) tptp.c_UNIV)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter tptp.c_UNIV V_y T_a) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter V_y tptp.c_UNIV T_a) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter V_y V_y T_a) V_y)) (forall ((V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter tptp.c_emptyset V_B T_a) tptp.c_emptyset)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_inter V_A tptp.c_emptyset T_a) tptp.c_emptyset)) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_inter V_A V_B T_a) T_a)) (tptp.c_in V_c V_A T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_inter V_A V_B T_a) T_a)) (tptp.c_in V_c V_B T_a))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c V_A T_a)) (tptp.c_in V_c (tptp.c_inter V_A V_B T_a) T_a))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_C (tptp.c_inter V_A V_B T_a) _let_1)) (tptp.c_lessequals V_C V_A _let_1)))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_C (tptp.c_inter V_A V_B T_a) _let_1)) (tptp.c_lessequals V_C V_B _let_1)))) (forall ((V_C $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_C V_B _let_1)) (not (tptp.c_lessequals V_C V_A _let_1)) (tptp.c_lessequals V_C (tptp.c_inter V_A V_B T_a) _let_1)))) (forall ((T_a $$unsorted)) (= (tptp.c_Inter tptp.c_UNIV T_a) tptp.c_emptyset)) (forall ((V_U $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_U V_A (tptp.tc_set T_a))) (not (= (tptp.c_Inter V_A T_a) tptp.c_UNIV)) (= V_U tptp.c_UNIV))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_Main_OInter__UNIV__conv__1__1 V_A T_a) V_A (tptp.tc_set T_a)) (= (tptp.c_Inter V_A T_a) tptp.c_UNIV))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Main_OInter__UNIV__conv__1__1 V_A T_a) tptp.c_UNIV)) (= (tptp.c_Inter V_A T_a) tptp.c_UNIV))) (forall ((V_U $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_U V_A (tptp.tc_set T_a))) (not (= tptp.c_UNIV (tptp.c_Inter V_A T_a))) (= V_U tptp.c_UNIV))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_Main_OInter__UNIV__conv__2__1 V_A T_a) V_A (tptp.tc_set T_a)) (= tptp.c_UNIV (tptp.c_Inter V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Main_OInter__UNIV__conv__2__1 V_A T_a) tptp.c_UNIV)) (= tptp.c_UNIV (tptp.c_Inter V_A T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_Inter tptp.c_emptyset T_a) tptp.c_UNIV)) (forall ((V_U $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_U V_C (tptp.tc_set T_a))) (not (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a)) (tptp.c_in V_A V_U T_a))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a) (tptp.c_in (tptp.c_Main_OInter__iff__1 V_A V_C T_a) V_C (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Main_OInter__iff__1 V_A V_C T_a) T_a)) (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Inter (tptp.c_insert V_a V_B (tptp.tc_set T_a)) T_a) (tptp.c_inter V_a (tptp.c_Inter V_B T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Pow (tptp.c_inter V_A V_B T_a) T_a) (tptp.c_inter (tptp.c_Pow V_A T_a) (tptp.c_Pow V_B T_a) (tptp.tc_set T_a)))) (forall ((T_a $$unsorted)) (= (tptp.c_Pow tptp.c_UNIV T_a) tptp.c_UNIV)) (forall ((T_a $$unsorted)) (= (tptp.c_Pow tptp.c_emptyset T_a) (tptp.c_insert tptp.c_emptyset tptp.c_emptyset (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A (tptp.c_Pow V_B T_a) _let_1)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_A (tptp.c_Pow V_B T_a) _let_1)))) (not (= tptp.c_UNIV tptp.c_emptyset)) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_union (tptp.c_minus V_B V_A (tptp.tc_set T_a)) V_A T_a) (tptp.c_union V_B V_A T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_union V_A (tptp.c_minus V_B V_A (tptp.tc_set T_a)) T_a) (tptp.c_union V_A V_B T_a))) (forall ((V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_union tptp.c_UNIV V_B T_a) tptp.c_UNIV)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_union V_A tptp.c_UNIV T_a) tptp.c_UNIV)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_union V_y V_y T_a) V_y)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_union V_A V_B T_a) tptp.c_emptyset)) (= V_A tptp.c_emptyset))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_union V_A V_B T_a) tptp.c_emptyset)) (= V_B tptp.c_emptyset))) (forall ((T_a $$unsorted)) (= (tptp.c_union tptp.c_emptyset tptp.c_emptyset T_a) tptp.c_emptyset)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_union tptp.c_emptyset V_y T_a) V_y)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_union V_y tptp.c_emptyset T_a) V_y)) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_union V_A V_B T_a) T_a)) (tptp.c_in V_c V_B T_a) (tptp.c_in V_c V_A T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (tptp.c_in V_c (tptp.c_union V_A V_B T_a) T_a))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (tptp.c_in V_c (tptp.c_union V_A V_B T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (= (tptp.c_union (tptp.c_insert V_a V_B T_a) V_C T_a) (tptp.c_insert V_a (tptp.c_union V_B V_C T_a) T_a))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_union V_A (tptp.c_insert V_a V_B T_a) T_a) (tptp.c_insert V_a (tptp.c_union V_A V_B T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals (tptp.c_union V_A V_B T_a) V_C _let_1)) (tptp.c_lessequals V_A V_C _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals (tptp.c_union V_A V_B T_a) V_C _let_1)) (tptp.c_lessequals V_B V_C _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (tptp.c_lessequals (tptp.c_union V_A V_B T_a) V_C _let_1)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Union (tptp.c_Pow V_y T_a) T_a) V_y)) (forall ((T_a $$unsorted)) (= (tptp.c_Union tptp.c_UNIV T_a) tptp.c_UNIV)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Union (tptp.c_union V_A V_B (tptp.tc_set T_a)) T_a) (tptp.c_union (tptp.c_Union V_A T_a) (tptp.c_Union V_B T_a) T_a))) (forall ((T_a $$unsorted)) (= (tptp.c_Union tptp.c_emptyset T_a) tptp.c_emptyset)) (forall ((V_U $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_U V_A (tptp.tc_set T_a))) (not (= (tptp.c_Union V_A T_a) tptp.c_emptyset)) (= V_U tptp.c_emptyset))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_Main_OUnion__empty__conv__1 V_A T_a) V_A (tptp.tc_set T_a)) (= (tptp.c_Union V_A T_a) tptp.c_emptyset))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Main_OUnion__empty__conv__1 V_A T_a) tptp.c_emptyset)) (= (tptp.c_Union V_A T_a) tptp.c_emptyset))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a)) (tptp.c_in (tptp.c_Main_OUnion__iff__1 V_A V_C T_a) V_C (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a)) (tptp.c_in V_A (tptp.c_Main_OUnion__iff__1 V_A V_C T_a) T_a))) (forall ((V_A $$unsorted) (V_U $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (or (not (tptp.c_in V_A V_U T_a)) (not (tptp.c_in V_U V_C (tptp.tc_set T_a))) (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (= (tptp.c_Union (tptp.c_insert V_a V_B (tptp.tc_set T_a)) T_a) (tptp.c_union V_a (tptp.c_Union V_B T_a) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_Main_Oall__not__in__conv__1 V_A T_a) V_A T_a) (= V_A tptp.c_emptyset))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ocontents (tptp.c_insert V_y tptp.c_emptyset T_a) T_a) V_y)) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_a V_B T_a)) (not (= (tptp.c_inter V_B (tptp.c_insert V_a V_A T_a) T_a) tptp.c_emptyset)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_inter V_B (tptp.c_insert V_a V_A T_a) T_a) tptp.c_emptyset)) (= (tptp.c_inter V_B V_A T_a) tptp.c_emptyset))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (not (= (tptp.c_inter V_B V_A T_a) tptp.c_emptyset)) (tptp.c_in V_a V_B T_a) (= (tptp.c_inter V_B (tptp.c_insert V_a V_A T_a) T_a) tptp.c_emptyset))) (forall ((V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_b V_A T_a)) (not (= tptp.c_emptyset (tptp.c_inter V_A (tptp.c_insert V_b V_B T_a) T_a))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_inter V_A (tptp.c_insert V_b V_B T_a) T_a))) (= tptp.c_emptyset (tptp.c_inter V_A V_B T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_inter V_A V_B T_a))) (tptp.c_in V_b V_A T_a) (= tptp.c_emptyset (tptp.c_inter V_A (tptp.c_insert V_b V_B T_a) T_a)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (= (tptp.c_uminus (tptp.c_uminus V_y _let_1) _let_1) V_y))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_minus tptp.c_emptyset V_A (tptp.tc_set T_a)) tptp.c_emptyset)) (forall ((V_U $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_U V_A (tptp.tc_set T_a))) (not (= tptp.c_emptyset (tptp.c_Union V_A T_a))) (= V_U tptp.c_emptyset))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_Main_Oempty__Union__conv__1 V_A T_a) V_A (tptp.tc_set T_a)) (= tptp.c_emptyset (tptp.c_Union V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Main_Oempty__Union__conv__1 V_A T_a) tptp.c_emptyset)) (= tptp.c_emptyset (tptp.c_Union V_A T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_c tptp.c_emptyset T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= tptp.c_emptyset (tptp.c_insert V_a V_A T_a)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_x V_B T_a)) (= (tptp.c_minus (tptp.c_insert V_x V_A T_a) V_B _let_1) (tptp.c_minus V_A V_B _let_1))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_insert V_a (tptp.c_minus V_A (tptp.c_insert V_a tptp.c_emptyset T_a) (tptp.tc_set T_a)) T_a) (tptp.c_insert V_a V_A T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_insert V_x V_A T_a))) (= (tptp.c_insert V_x _let_1 T_a) _let_1))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_a V_B T_a)) (not (= (tptp.c_inter (tptp.c_insert V_a V_A T_a) V_B T_a) tptp.c_emptyset)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_inter (tptp.c_insert V_a V_A T_a) V_B T_a) tptp.c_emptyset)) (= (tptp.c_inter V_A V_B T_a) tptp.c_emptyset))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (not (= (tptp.c_inter V_A V_B T_a) tptp.c_emptyset)) (tptp.c_in V_a V_B T_a) (= (tptp.c_inter (tptp.c_insert V_a V_A T_a) V_B T_a) tptp.c_emptyset))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_a V_B T_a)) (not (= tptp.c_emptyset (tptp.c_inter (tptp.c_insert V_a V_A T_a) V_B T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_inter (tptp.c_insert V_a V_A T_a) V_B T_a))) (= tptp.c_emptyset (tptp.c_inter V_A V_B T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (not (= tptp.c_emptyset (tptp.c_inter V_A V_B T_a))) (tptp.c_in V_a V_B T_a) (= tptp.c_emptyset (tptp.c_inter (tptp.c_insert V_a V_A T_a) V_B T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_a (tptp.c_insert V_b V_A T_a) T_a)) (tptp.c_in V_a V_A T_a) (= V_a V_b))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_insert V_x V_A T_a) T_a)) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (tptp.c_in V_a (tptp.c_insert V_b V_A T_a) T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (tptp.c_inter (tptp.c_insert V_a V_A T_a) (tptp.c_insert V_a V_B T_a) T_a) (tptp.c_insert V_a (tptp.c_inter V_A V_B T_a) T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_insert V_a V_A T_a) tptp.c_emptyset))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_insert V_x V_A T_a) V_B (tptp.tc_set T_a))) (tptp.c_in V_x V_B T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals (tptp.c_insert V_x V_A T_a) V_B _let_1)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_lessequals (tptp.c_insert V_x V_A T_a) V_B _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (not (tptp.c_less V_A tptp.c_emptyset (tptp.tc_set T_a)))) (forall ((V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (= (tptp.c_insert V_b tptp.c_emptyset T_a) (tptp.c_insert V_a V_A T_a))) (= V_a V_b))) (forall ((V_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_insert V_b tptp.c_emptyset T_a))) (or (not (= _let_1 (tptp.c_insert V_a V_A T_a))) (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_insert V_x tptp.c_emptyset T_a))) (or (not (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))) (= _let_1 (tptp.c_insert V_x V_A T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_insert V_a V_A T_a) (tptp.c_insert V_b tptp.c_emptyset T_a))) (= V_a V_b))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_insert V_b tptp.c_emptyset T_a))) (or (not (= (tptp.c_insert V_a V_A T_a) _let_1)) (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_insert V_x tptp.c_emptyset T_a))) (or (not (tptp.c_lessequals V_A _let_1 (tptp.tc_set T_a))) (= (tptp.c_insert V_x V_A T_a) _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A tptp.c_UNIV (tptp.tc_set T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_A tptp.c_emptyset (tptp.tc_set T_a))) (= V_A tptp.c_emptyset))) (forall ((T_a $$unsorted)) (tptp.c_lessequals tptp.c_emptyset tptp.c_emptyset (tptp.tc_set T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Sum__Type_OInl V_x T_a T_b) (tptp.c_Sum__Type_OInl V_y T_a T_b))) (= V_x V_y))) (forall ((V_a $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted)) (not (= (tptp.c_Sum__Type_OInl V_a T_a T_b) (tptp.c_Sum__Type_OInr V_b T_b T_a)))) (forall ((V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Sum__Type_OInr V_x T_b T_a) (tptp.c_Sum__Type_OInr V_y T_b T_a))) (= V_x V_y))) (forall ((V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Sum__Type_OInr V_b T_b T_a) (tptp.c_Sum__Type_OInl V_a T_a T_b)))) (forall ((T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Sum__Type_OPlus tptp.c_UNIV tptp.c_UNIV T_a T_b) tptp.c_UNIV)) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) tptp.c_UNIV)) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Ortrancl V_R T_a) T_a T_a) tptp.c_UNIV)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_union (tptp.c_Transitive__Closure_Otrancl V_r T_a) tptp.c_Relation_OId (tptp.tc_prod T_a T_a)) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl tptp.c_emptyset T_a) tptp.c_Relation_OId)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (= (tptp.c_Transitive__Closure_Ortrancl _let_1 T_a) _let_1))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (= (tptp.c_Relation_Orel__comp _let_1 _let_1 T_a T_a T_a) _let_1))) (forall ((V_R $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Ortrancl (tptp.c_union V_R tptp.c_Relation_OId (tptp.tc_prod T_a T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_R T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ODomain (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ODomain V_r T_a T_a))) (forall ((T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl tptp.c_emptyset T_a) tptp.c_emptyset)) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Relation_ORange (tptp.c_Transitive__Closure_Otrancl V_r T_a) T_a T_a) (tptp.c_Relation_ORange V_r T_a T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (= (tptp.c_Transitive__Closure_Otrancl (tptp.c_union V_r tptp.c_Relation_OId (tptp.tc_prod T_a T_a)) T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_Relation_Oconverse V_r T_a T_a) T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a)) (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Oacyclic V_r T_a)) (tptp.c_Wellfounded__Recursion_Oacyclic (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a) (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r (tptp.tc_prod T_a T_a)) T_a)) (tptp.c_Wellfounded__Recursion_Owf V_r T_a))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Owf (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a)) (not (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_Wellfounded__Recursion_Owf V_r T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_insert (tptp.c_Pair V_y V_x T_a T_a) V_r _let_1) T_a) (tptp.c_in (tptp.c_Pair V_x V_y T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))) (forall ((V_r $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf V_r T_a)) (not (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_nat tptp.tc_nat) tptp.c_Wellfounded__Relations_Oless__than (tptp.tc_prod tptp.tc_nat tptp.tc_nat))) (tptp.c_less V_x V_y tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_less V_x V_y tptp.tc_nat)) (tptp.c_in (tptp.c_Pair V_x V_y tptp.tc_nat tptp.tc_nat) tptp.c_Wellfounded__Relations_Oless__than (tptp.tc_prod tptp.tc_nat tptp.tc_nat)))) (forall ((V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_OLeaf V_x T_a T_b) (tptp.c_Datatype__Universe_OLeaf V_y T_a T_b))) (= V_x V_y))) (forall ((V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Datatype__Universe_ONumb V_x T_a T_b) (tptp.c_Datatype__Universe_ONumb V_y T_a T_b))) (= V_x V_y))) (forall ((V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) (tptp.tc_prod _let_1 _let_1))) (= V_c (tptp.c_Pair (tptp.c_Datatype__Universe_OScons (tptp.c_Main_OdprodE__1 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__2 V_c V_r V_s T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OScons (tptp.c_Main_OdprodE__3 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__4 V_c V_r V_s T_a T_b) T_a T_b) _let_1 _let_1))))) (forall ((V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdprodE__2 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__4 V_c V_r V_s T_a T_b) _let_1 _let_1) V_s _let_2))))) (forall ((V_c $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdprodE__1 V_c V_r V_s T_a T_b) (tptp.c_Main_OdprodE__3 V_c V_r V_s T_a T_b) _let_1 _let_1) V_r _let_2))))) (forall ((V_N $$unsorted) (V_N_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted) (V_M $$unsorted) (V_M_H $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in (tptp.c_Pair V_N V_N_H _let_1 _let_1) V_s _let_2)) (not (tptp.c_in (tptp.c_Pair V_M V_M_H _let_1 _let_1) V_r _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_OScons V_M_H V_N_H T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Odprod V_r V_s T_a T_b) _let_2))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) (tptp.tc_prod _let_1 _let_1))) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) T_a T_b) _let_1 _let_1)) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) T_a T_b) _let_1 _let_1))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) _let_1 _let_1) V_s _let_2) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) T_a T_b) _let_1 _let_1)))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) _let_1 _let_1) V_r _let_2) (= V_w (tptp.c_Pair (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) T_a T_b) (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) T_a T_b) _let_1 _let_1)))))) (forall ((V_w $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in V_w (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__1 V_r V_w T_a T_b) (tptp.c_Main_OdsumE__2 V_r V_w T_a T_b) _let_1 _let_1) V_r _let_2) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OdsumE__3 V_s V_w T_a T_b) (tptp.c_Main_OdsumE__4 V_s V_w T_a T_b) _let_1 _let_1) V_s _let_2))))) (forall ((V_M $$unsorted) (V_M_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in (tptp.c_Pair V_M V_M_H _let_1 _let_1) V_r _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_OIn0 V_M_H T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2))))) (forall ((V_N $$unsorted) (V_N_H $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_s $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (or (not (tptp.c_in (tptp.c_Pair V_N V_N_H _let_1 _let_1) V_s _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b) (tptp.c_Datatype__Universe_OIn1 V_N_H T_a T_b) _let_1 _let_1) (tptp.c_Datatype__Universe_Odsum V_r V_s T_a T_b) _let_2))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (= V_c (tptp.c_Datatype__Universe_OScons (tptp.c_Main_OuprodE__1 V_A V_B V_c T_a T_b) (tptp.c_Main_OuprodE__2 V_A V_B V_c T_a T_b) T_a T_b)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OuprodE__2 V_A V_B V_c T_a T_b) V_B _let_1)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_c (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OuprodE__1 V_A V_B V_c T_a T_b) V_A _let_1)))) (forall ((V_N $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_N V_B _let_1)) (not (tptp.c_in V_M V_A _let_1)) (tptp.c_in (tptp.c_Datatype__Universe_OScons V_M V_N T_a T_b) (tptp.c_Datatype__Universe_Ouprod V_A V_B T_a T_b) _let_1)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (= V_u (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) T_a T_b)) (= V_u (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) T_a T_b)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) V_B _let_1) (= V_u (tptp.c_Datatype__Universe_OIn0 (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) T_a T_b))))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) V_A _let_1) (= V_u (tptp.c_Datatype__Universe_OIn1 (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) T_a T_b))))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_u (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)) (tptp.c_in (tptp.c_Main_OusumE__1 V_A V_u T_a T_b) V_A _let_1) (tptp.c_in (tptp.c_Main_OusumE__2 V_B V_u T_a T_b) V_B _let_1)))) (forall ((V_M $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_M V_A _let_1)) (tptp.c_in (tptp.c_Datatype__Universe_OIn0 V_M T_a T_b) (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)))) (forall ((V_N $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_set (tptp.tc_Datatype__Universe_Onode T_a T_b)))) (or (not (tptp.c_in V_N V_B _let_1)) (tptp.c_in (tptp.c_Datatype__Universe_OIn1 V_N T_a T_b) (tptp.c_Datatype__Universe_Ousum V_A V_B T_a T_b) _let_1)))) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_m tptp.c_0 tptp.tc_nat)) (forall ((V_k $$unsorted)) (tptp.c_Divides_Oop_Advd (tptp.c_Suc tptp.c_0) V_k tptp.tc_nat)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_k V_m tptp.tc_nat) tptp.tc_nat)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_m V_k tptp.tc_nat) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Divides_Oop_Amod V_m V_d tptp.tc_nat) tptp.c_0)) (= V_m (tptp.c_times V_d (tptp.c_Main_Omod__eq__0D__dest__1 V_d V_m) tptp.tc_nat)))) (forall ((T_a $$unsorted)) (tptp.c_in tptp.c_emptyset tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_insert V_a V_A T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_F $$unsorted) (T_a $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_F tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_inter V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_G $$unsorted) (T_a $$unsorted) (V_F $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_G tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_inter V_F V_G T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))) (tptp.c_in (tptp.c_Main_Ofinite__Union__1 V_A T_a) V_A _let_1) (tptp.c_in (tptp.c_Union V_A T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_in V_A tptp.c_Finite__Set_OFinites (tptp.tc_set _let_1))) (not (tptp.c_in (tptp.c_Main_Ofinite__Union__1 V_A T_a) tptp.c_Finite__Set_OFinites _let_1)) (tptp.c_in (tptp.c_Union V_A T_a) tptp.c_Finite__Set_OFinites _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Divides_Oop_Advd (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) V_m tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Divides_Oop_Advd (tptp.c_GCD_Ogcd (tptp.c_Pair V_m V_n tptp.tc_nat tptp.tc_nat)) V_n tptp.tc_nat)) (forall ((V_S $$unsorted) (T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Infinite__Set_Oatmost__one V_S T_a)) (not (tptp.c_in V_y V_S T_a)) (not (tptp.c_in V_x V_S T_a)) (= V_y V_x))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals (tptp.c_uminus (tptp.c_IntDef_Oint V_n) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oint V_m) tptp.tc_IntDef_Oint)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_less (tptp.c_uminus (tptp.c_IntDef_Oint (tptp.c_Suc V_n)) tptp.tc_IntDef_Oint) (tptp.c_IntDef_Oint V_m) tptp.tc_IntDef_Oint)) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_m tptp.c_0 tptp.tc_IntDef_Oint)) (forall ((V_m $$unsorted)) (tptp.c_Divides_Oop_Advd tptp.c_1 V_m tptp.tc_IntDef_Oint)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_k V_m tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (forall ((V_k $$unsorted) (V_m $$unsorted)) (tptp.c_Divides_Oop_Advd V_k (tptp.c_times V_m V_k tptp.tc_IntDef_Oint) tptp.tc_IntDef_Oint)) (forall ((V_m $$unsorted) (V_d $$unsorted)) (or (not (= (tptp.c_Divides_Oop_Amod V_m V_d tptp.tc_IntDef_Oint) tptp.c_0)) (= V_m (tptp.c_times V_d (tptp.c_Main_Ozmod__eq__0D__dest__1 V_d V_m) tptp.tc_IntDef_Oint)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Oremdups V_xs T_a) T_a)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_in (tptp.c_List_Oset V_xs T_a) tptp.c_Finite__Set_OFinites (tptp.tc_set T_a))) (forall ((V_xs $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_U $$unsorted)) (or (not (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))) (not (tptp.c_in V_U (tptp.c_List_Oset V_xs T_a) T_a)) (tptp.c_in V_U V_A T_a))) (forall ((V_xs $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)) (tptp.c_in (tptp.c_Main_Oin__listsI__1 V_A V_xs T_a) (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_A $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Main_Oin__listsI__1 V_A V_xs T_a) V_A T_a)) (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (tptp.c_lessequals (tptp.c_Nat_Osize (tptp.c_List_Oremdups V_xs T_a) _let_1) (tptp.c_Nat_Osize V_xs _let_1) tptp.tc_nat))) (forall ((V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_y V_ys T_a) V_xs _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs (tptp.c_List_Olist_OCons (tptp.c_Main_Olistrel__Cons1__1 V_r V_xs V_y V_ys T_a) (tptp.c_Main_Olistrel__Cons1__2 V_r V_xs V_y V_ys T_a) T_a))))) (forall ((V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olistrel V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_y V_ys T_a) V_xs _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair V_ys (tptp.c_Main_Olistrel__Cons1__2 V_r V_xs V_y V_ys T_a) _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair (tptp.c_List_Olist_OCons V_y V_ys T_a) V_xs _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (tptp.c_in (tptp.c_Pair V_y (tptp.c_Main_Olistrel__Cons1__1 V_r V_xs V_y V_ys T_a) T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs (tptp.c_List_Olist_OCons (tptp.c_Main_Olistrel__Cons2__1 V_r V_xs V_y V_ys T_a) (tptp.c_Main_Olistrel__Cons2__2 V_r V_xs V_y V_ys T_a) T_a))))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.tc_prod _let_1 _let_1))) (let ((_let_3 (tptp.c_List_Olistrel V_r T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) _let_3 _let_2)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Olistrel__Cons2__2 V_r V_xs V_y V_ys T_a) V_ys _let_1 _let_1) _let_3 _let_2)))))) (forall ((V_xs $$unsorted) (V_y $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs (tptp.c_List_Olist_OCons V_y V_ys T_a) _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Olistrel__Cons2__1 V_r V_xs V_y V_ys T_a) V_y T_a T_a) V_r (tptp.tc_prod T_a T_a))))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair tptp.c_List_Olist_ONil V_xs _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs tptp.c_List_Olist_ONil)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (or (not (tptp.c_in (tptp.c_Pair V_xs tptp.c_List_Olist_ONil _let_1 _let_1) (tptp.c_List_Olistrel V_r T_a) (tptp.tc_prod _let_1 _let_1))) (= V_xs tptp.c_List_Olist_ONil)))) (forall ((V_x $$unsorted) (V_l $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in (tptp.c_List_Olist_OCons V_x V_l T_a) _let_2 _let_1)) (tptp.c_in V_l _let_2 _let_1))))) (forall ((V_x $$unsorted) (V_l $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in (tptp.c_List_Olist_OCons V_x V_l T_a) (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))) (tptp.c_in V_x V_A T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_in V_l _let_2 _let_1)) (tptp.c_in (tptp.c_List_Olist_OCons V_a V_l T_a) _let_2 _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in tptp.c_List_Olist_ONil (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf V_r T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_List_Olenlex V_r T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_Wellfounded__Recursion_Owf V_r T_a)) (tptp.c_Wellfounded__Recursion_Owf (tptp.c_List_Olex V_r T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals tptp.c_0 V_n tptp.tc_nat)) (forall ((V_n $$unsorted)) (tptp.c_less V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_n $$unsorted)) (not (tptp.c_less V_n V_n tptp.tc_nat))) (forall ((V_n $$unsorted)) (tptp.c_less tptp.c_0 (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a)) (tptp.c_in (tptp.c_Pair V_a (tptp.c_Main_ODomainE__1 V_a V_r T_a T_b) T_a T_b) V_r (tptp.tc_prod T_a T_b)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b))) (tptp.c_in V_a (tptp.c_Relation_ODomain V_r T_a T_b) T_a))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Main_OIdE__1 V_p T_a))) (or (not (tptp.c_in V_p tptp.c_Relation_OId (tptp.tc_prod T_a T_a))) (= V_p (tptp.c_Pair _let_1 _let_1 T_a T_a))))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a)) (tptp.c_in (tptp.c_Main_OImageE__1 V_A V_b V_r T_b T_a) V_A T_b))) (forall ((V_b $$unsorted) (V_r $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_b T_a) T_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OImageE__1 V_A V_b V_r T_b T_a) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b))) (tptp.c_in V_b (tptp.c_Relation_OImage V_r V_A T_a T_b) T_b))) (forall ((V_b $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_b T_a) T_a)) (tptp.c_in (tptp.c_Pair (tptp.c_Main_ORangeE__1 V_b V_r T_a T_b) V_b T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_r (tptp.tc_prod T_a T_b))) (tptp.c_in V_b (tptp.c_Relation_ORange V_r T_a T_b) T_b))) (forall ((V_yx $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_yx (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_OconverseE__1 V_r V_yx T_b T_a) (tptp.c_Main_OconverseE__2 V_r V_yx T_b T_a) T_b T_a) V_r (tptp.tc_prod T_b T_a)))) (forall ((V_yx $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_yx (tptp.c_Relation_Oconverse V_r T_b T_a) (tptp.tc_prod T_a T_b))) (= V_yx (tptp.c_Pair (tptp.c_Main_OconverseE__2 V_r V_yx T_b T_a) (tptp.c_Main_OconverseE__1 V_r V_yx T_b T_a) T_a T_b)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Main_OdiagE__1 V_A V_c T_a))) (or (not (tptp.c_in V_c (tptp.c_Relation_Odiag V_A T_a) (tptp.tc_prod T_a T_a))) (= V_c (tptp.c_Pair _let_1 _let_1 T_a T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Relation_Odiag V_A T_a) (tptp.tc_prod T_a T_a))) (tptp.c_in (tptp.c_Main_OdiagE__1 V_A V_c T_a) V_A T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Relation_Odiag V_A T_a) (tptp.tc_prod T_a T_a)))) (forall ((V_xz $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_xz (tptp.c_Relation_Orel__comp V_r V_s T_c T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Orel__compE__2 V_r V_s V_xz T_c T_b T_a) (tptp.c_Main_Orel__compE__3 V_r V_s V_xz T_c T_b T_a) T_c T_b) V_r (tptp.tc_prod T_c T_b)))) (forall ((V_xz $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_xz (tptp.c_Relation_Orel__comp V_r V_s T_c T_b T_a) (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair (tptp.c_Main_Orel__compE__1 V_r V_s V_xz T_c T_b T_a) (tptp.c_Main_Orel__compE__2 V_r V_s V_xz T_c T_b T_a) T_a T_c) V_s (tptp.tc_prod T_a T_c)))) (forall ((V_xz $$unsorted) (V_r $$unsorted) (V_s $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_xz (tptp.c_Relation_Orel__comp V_r V_s T_c T_b T_a) (tptp.tc_prod T_a T_b))) (= V_xz (tptp.c_Pair (tptp.c_Main_Orel__compE__1 V_r V_s V_xz T_c T_b T_a) (tptp.c_Main_Orel__compE__3 V_r V_s V_xz T_c T_b T_a) T_a T_b)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_s $$unsorted)) (or (not (tptp.c_in (tptp.c_Pair V_b V_c T_b T_c) V_r (tptp.tc_prod T_b T_c))) (not (tptp.c_in (tptp.c_Pair V_a V_b T_a T_b) V_s (tptp.tc_prod T_a T_b))) (tptp.c_in (tptp.c_Pair V_a V_c T_a T_c) (tptp.c_Relation_Orel__comp V_r V_s T_b T_c T_a) (tptp.tc_prod T_a T_c)))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastAtMost V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastAtMost V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastLessThan V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatLeastLessThan V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_k $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OatMost V_k tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanAtMost V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OgreaterThanLessThan V_l V_u tptp.tc_IntDef_Oint) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_IntDef_Oint))) (forall ((V_k $$unsorted)) (tptp.c_in (tptp.c_SetInterval_OlessThan V_k tptp.tc_nat) tptp.c_Finite__Set_OFinites (tptp.tc_set tptp.tc_nat))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a) (tptp.c_in (tptp.c_Main_OInterI__1 V_A V_C T_a) V_C (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Main_OInterI__1 V_A V_C T_a) T_a)) (tptp.c_in V_A (tptp.c_Inter V_C T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x tptp.c_UNIV T_a)) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a)) (tptp.c_in (tptp.c_Main_OUnionE__1 V_A V_C T_a) V_C (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_A (tptp.c_Union V_C T_a) T_a)) (tptp.c_in V_A (tptp.c_Main_OUnionE__1 V_A V_C T_a) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals tptp.c_emptyset V_A (tptp.tc_set T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_less V_A V_B _let_1)) (not (tptp.c_lessequals V_B V_A _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_less V_A V_B _let_1)) (tptp.c_lessequals V_A V_B _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_less V_A V_B _let_1) (= V_A V_B)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_b (tptp.c_insert V_a tptp.c_emptyset T_a) T_a)) (= V_b V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (tptp.c_in V_a (tptp.c_insert V_a tptp.c_emptyset T_a) T_a)) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_insert V_a tptp.c_emptyset T_a) (tptp.c_insert V_b tptp.c_emptyset T_a))) (= V_a V_b))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_set T_a))) (tptp.c_in V_c V_B T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.c_Main_OsubsetI__1 V_A V_B T_a) V_A T_a) (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in (tptp.c_Main_OsubsetI__1 V_A V_B T_a) V_B T_a)) (tptp.c_lessequals V_A V_B (tptp.tc_set T_a)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_set T_a))) (or (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1)) (= V_A V_B)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_set T_a))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (not (tptp.c_in V_a V_A T_a)) (tptp.c_in (tptp.c_Sum__Type_OInl V_a T_a T_b) (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b)))) (forall ((V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_b V_B T_a)) (tptp.c_in (tptp.c_Sum__Type_OInr V_b T_a T_b) (tptp.c_Sum__Type_OPlus V_A V_B T_b T_a) (tptp.tc_sum T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (= V_u (tptp.c_Sum__Type_OInl (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) T_a T_b)) (= V_u (tptp.c_Sum__Type_OInr (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) V_B T_b) (= V_u (tptp.c_Sum__Type_OInl (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) T_a T_b)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) V_A T_a) (= V_u (tptp.c_Sum__Type_OInr (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) T_b T_a)))) (forall ((V_u $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (tptp.c_in V_u (tptp.c_Sum__Type_OPlus V_A V_B T_a T_b) (tptp.tc_sum T_a T_b))) (tptp.c_in (tptp.c_Main_OPlusE__1 V_A V_u T_a T_b) V_A T_a) (tptp.c_in (tptp.c_Main_OPlusE__2 V_B V_u T_b T_a) V_B T_b))) (forall ((V_p $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (or (not (tptp.c_in V_p V_r _let_1)) (tptp.c_in V_p (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (tptp.c_in (tptp.c_Pair V_a V_a T_a T_a) (tptp.c_Transitive__Closure_Ortrancl V_r T_a) (tptp.tc_prod T_a T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (not (tptp.c_in _let_2 V_r _let_1)) (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.tc_prod T_a T_a))) (let ((_let_2 (tptp.c_Pair V_a V_b T_a T_a))) (or (not (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Otrancl V_r T_a) _let_1)) (tptp.c_in _let_2 (tptp.c_Transitive__Closure_Ortrancl V_r T_a) _let_1))))) (forall ((T_a $$unsorted)) (tptp.c_Wellfounded__Recursion_Owf tptp.c_emptyset T_a)) (tptp.c_Relation_Otrans 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(tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_LOrder_Omeet__semilorder tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__comm__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__comm__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Divides_Odiv tptp.tc_nat) (tptp.class_Power_Orecpower tptp.tc_nat) (tptp.class_Numeral_Onumber tptp.tc_nat) (tptp.class_Parity_Oeven__odd tptp.tc_nat) (tptp.class_LOrder_Ojoin__semilorder tptp.tc_nat) (tptp.class_LOrder_Olorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Wellfounded__Recursion_Owellorder tptp.tc_nat) (tptp.class_HOL_Ominus tptp.tc_nat) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_prod T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite T_2)))) (forall ((T_1 $$unsorted)) (tptp.class_HOL_Ominus (tptp.tc_set T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Oord (tptp.tc_set T_1))) (forall ((T_1 $$unsorted)) (tptp.class_Orderings_Oorder (tptp.tc_set T_1))) (forall ((T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_set T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)))) (forall ((T_1 $$unsorted)) (tptp.class_Nat_Opower (tptp.tc_set T_1))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite (tptp.tc_sum T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite T_1)) (not 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(tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oordered__semiring__strict T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Orderings_Olinorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_LOrder_Olorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_LOrder_Omeet__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Opordered__cancel__comm__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Oab__group__add T))) _let_27 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Opordered__comm__semiring T))) _let_26 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T))) _let_25 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oaxclass__abs__if T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oordered__ring__strict T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Olordered__ring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Opordered__ring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_HOL_Ominus T))) _let_24 (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Olordered__ab__group__meet T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Olordered__ab__group__join T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Olordered__ab__group T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Opordered__ab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oordered__semidom T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oaxclass__no__zero__divisors T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Oidom T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Ocomm__semiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_OrderedGroup_Ocomm__monoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T)) (tptp.class_Ring__and__Field_Osemiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Oring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Oab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Oordered__semiring__strict T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Orderings_Olinorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_LOrder_Olorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_HOL_Ominus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_LOrder_Omeet__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Opordered__cancel__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Opordered__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Oaxclass__abs__if T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Olordered__ab__group T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Opordered__ab__group__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Olordered__ring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Opordered__ring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Olordered__ab__group__abs T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Olordered__ab__group__meet T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Olordered__ab__group__join T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Oaxclass__no__zero__divisors T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Ocomm__semiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Ocomm__semiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Ocomm__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Oab__semigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Ocomm__monoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Oordered__semiring__strict T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Orderings_Olinorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_LOrder_Olorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Osemiring__1__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_LOrder_Omeet__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Opordered__cancel__comm__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Opordered__cancel__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Opordered__comm__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Opordered__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Osemiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Ocomm__semiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T)) (tptp.class_Ring__and__Field_Ocomm__semiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Orderings_Olinorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_LOrder_Olorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_LOrder_Omeet__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Ring__and__Field_Opordered__cancel__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_Ring__and__Field_Opordered__semiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T)) (tptp.class_OrderedGroup_Oordered__cancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not 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$$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0__cancel T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Oaxclass__0__neq__1 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Oone T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Osemigroup__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Otimes T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Ocancel__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring__0__cancel T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring__0 T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_Ring__and__Field_Osemiring T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Ocomm__monoid__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Ozero T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Oab__semigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Osemigroup__add T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_HOL_Oplus T))) (forall ((T $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1__cancel T)) (tptp.class_OrderedGroup_Omonoid__mult T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_Orderings_Oord T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_Orderings_Oorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_LOrder_Omeet__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_LOrder_Ojoin__semilorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_LOrder_Olorder T))) (forall ((T $$unsorted)) (or (not (tptp.class_Wellfounded__Recursion_Owellorder T)) (tptp.class_Orderings_Olinorder T))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Osemigroup__mult T_a)) (= (tptp.c_times (tptp.c_times V_a V_b T_a) V_c T_a) (tptp.c_times V_a (tptp.c_times V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_times V_a V_b T_a) (tptp.c_times V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_times V_a (tptp.c_times V_b V_c T_a) T_a) (tptp.c_times V_b (tptp.c_times V_a V_c T_a) T_a)))) _let_23 _let_22 _let_21 _let_20 (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_SetsAndFunctions_Oelt__set__times tptp.c_1 V_y T_a) V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_SetsAndFunctions_Oelt__set__plus tptp.c_0 V_y T_a) V_y))) _let_19 (tptp.c_less tptp.c_0 tptp.v_ca tptp.t_b) _let_18 _let_16 _let_14 _let_9 _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.78/28.04 )
% 27.78/28.05 % SZS output end Proof for ANA034-1
% 27.78/28.06 % cvc5---1.0.5 exiting
% 27.78/28.06 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------