%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV883-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 21:53:38 EDT 2023

% Result   : Unsatisfiable 1.22s 1.46s
% Output   : Proof 1.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17  % Problem    : SWV883-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.19  % Command    : do_cvc5 %s %d
% 0.19/0.40  % Computer : n005.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit   : 300
% 0.19/0.40  % WCLimit    : 300
% 0.19/0.40  % DateTime   : Tue Aug 29 05:32:08 EDT 2023
% 0.19/0.40  % CPUTime    : 
% 0.26/0.59  %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.59  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.zKeYBLgek5/cvc5---1.0.5_30580.p...
% 0.26/0.70  ------- get file name : TPTP file name is SWV883-1
% 0.26/0.70  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30580.smt2...
% 0.26/0.70  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.22/1.46  % SZS status Unsatisfiable for SWV883-1
% 1.22/1.46  % SZS output start Proof for SWV883-1
% 1.29/1.48  (
% 1.29/1.48  (let ((_let_1 (forall ((V_G $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage tptp.v_mgt__call tptp.v_U tptp.tc_Com_Opname tptp.t_a))) (or (not (= (tptp.c_Finite__Set_Ocard V_G tptp.t_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Ocard _let_2 tptp.t_a) tptp.v_na tptp.tc_nat))) (not (tptp.c_lessequals V_G _let_2 _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_G) (tptp.c_Set_Oinsert (tptp.v_mgt V_c) (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.t_a))) (not (tptp.v_wt V_c)))))))) (let ((_let_2 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_3 (tptp.c_Orderings_Obot__class_Obot _let_2))) (let ((_let_4 (tptp.hAPP tptp.v_mgt__call tptp.v_pn))) (let ((_let_5 (tptp.c_Set_Oinsert _let_4 _let_3 tptp.t_a))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P tptp.v_G) _let_5)))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.c_in _let_4 tptp.v_G tptp.t_a))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.c_in tptp.v_pn tptp.v_U tptp.tc_Com_Opname))) (let ((_let_11 (tptp.c_Suc tptp.v_na))) (let ((_let_12 (tptp.c_Set_Oimage tptp.v_mgt__call tptp.v_U tptp.tc_Com_Opname tptp.t_a))) (let ((_let_13 (tptp.c_Finite__Set_Ocard _let_12 tptp.t_a))) (let ((_let_14 (tptp.c_HOL_Ominus__class_Ominus _let_13 _let_11 tptp.tc_nat))) (let ((_let_15 (tptp.c_Finite__Set_Ocard tptp.v_G tptp.t_a))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (tptp.c_lessequals _let_11 _let_13 tptp.tc_nat))) (let ((_let_18 (tptp.c_lessequals tptp.v_G _let_12 _let_2))) (let ((_let_19 (tptp.c_Finite__Set_Ofinite tptp.v_U tptp.tc_Com_Opname))) (let ((_let_20 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.c_in V_a V_A T_a)))))) (let ((_let_21 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard V_A T_a))) (tptp.c_in V_x V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (let ((_let_22 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a)))) (let ((_let_23 (forall ((V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_B T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (let ((_let_24 (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))))) (let ((_let_25 (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))))) (let ((_let_26 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))))) (let ((_let_27 (forall ((V_G $$unsorted) (V_pn $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP tptp.v_mgt__call V_pn))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_G) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.t_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P (tptp.c_Set_Oinsert _let_2 V_G tptp.t_a)) (tptp.c_Set_Oinsert (tptp.v_mgt (tptp.c_Option_Othe (tptp.c_Com_Obody V_pn) tptp.tc_Com_Ocom)) _let_1 tptp.t_a)))))))))) (let ((_let_28 (forall ((V_B $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= V_B (tptp.c_Set_Oimage V_f (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 V_A V_B V_f T_b T_a) T_b T_a)) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))))) (let ((_let_29 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_A) (tptp.c_in V_x V_A T_a)))))) (let ((_let_30 (forall ((V_pn $$unsorted)) (or (tptp.v_wt (tptp.c_Option_Othe (tptp.c_Com_Obody V_pn) tptp.tc_Com_Ocom)) (not (tptp.c_in V_pn tptp.v_U tptp.tc_Com_Opname)))))) (let ((_let_31 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_32 (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_n) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_n)))) (let ((_let_33 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_n tptp.tc_nat))))) (let ((_let_34 (tptp.c_Suc _let_31))) (let ((_let_35 (tptp.c_HOL_Oplus__class_Oplus _let_31 _let_34 tptp.tc_nat))) (let ((_let_36 (tptp.c_HOL_Oplus__class_Oplus _let_34 _let_31 tptp.tc_nat))) (let ((_let_37 (tptp.c_HOL_Oone__class_Oone tptp.tc_nat))) (let ((_let_38 (tptp.c_Set_Oinsert tptp.v_pn tptp.v_U tptp.tc_Com_Opname))) (let ((_let_39 (= tptp.v_U _let_38))) (let ((_let_40 (tptp.c_Set_Oinsert _let_4 _let_12 tptp.t_a))) (let ((_let_41 (= _let_40 (tptp.c_Set_Oimage tptp.v_mgt__call _let_38 tptp.tc_Com_Opname tptp.t_a)))) (let ((_let_42 (tptp.c_Set_Oinsert _let_4 tptp.v_G tptp.t_a))) (let ((_let_43 (tptp.c_lessequals _let_42 _let_40 _let_2))) (let ((_let_44 (tptp.c_lessequals _let_42 _let_12 _let_2))) (let ((_let_45 (not _let_10))) (let ((_let_46 (or _let_39 _let_45))) (let ((_let_47 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.c_Set_Oinsert V_a V_A T_a)) (not (tptp.c_in V_a V_A T_a)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (ASSUME :args (_let_10)))) (let ((_let_50 (_let_25))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (tptp.c_HOL_Ominus__class_Ominus _let_42 _let_5 _let_2))) (let ((_let_53 (tptp.c_lessequals _let_52 _let_12 _let_2))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.c_in _let_4 _let_42 tptp.t_a))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_43 _let_56 _let_54))) (let ((_let_58 (_let_26))) (let ((_let_59 (ASSUME :args _let_58))) (let ((_let_60 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_61 (= tptp.v_G (tptp.c_Set_Oimage tptp.v_mgt__call (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 tptp.v_U tptp.v_G tptp.v_mgt__call tptp.tc_Com_Opname tptp.t_a) tptp.tc_Com_Opname tptp.t_a)))) (let ((_let_62 (= tptp.v_G _let_52))) (let ((_let_63 (tptp.c_Finite__Set_Ofinite tptp.v_G tptp.t_a))) (let ((_let_64 (not _let_63))) (let ((_let_65 (not _let_18))) (let ((_let_66 (or _let_61 _let_65 _let_64))) (let ((_let_67 (_let_28))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (not _let_19))) (let ((_let_70 (or _let_63 _let_65 _let_69))) (let ((_let_71 (_let_23))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 (ASSUME :args (_let_18)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_65 _let_63 (not _let_70)))) (ASSUME :args (_let_19)) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.v_G tptp.t_a tptp.v_mgt__call tptp.v_U tptp.tc_Com_Opname QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) false))))) :args _let_71)) _let_72 :args (_let_70 false _let_23)) :args (_let_63 false _let_19 false _let_18 false _let_70)))) (let ((_let_75 (or _let_62 _let_8))) (let ((_let_76 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1)) (tptp.c_in V_x V_A T_a)))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (ASSUME :args (_let_9)))) (let ((_let_79 (and _let_18 _let_62 _let_61))) (let ((_let_80 (APPLY_UF tptp.c_lessequals))) (let ((_let_81 (REFL :args (_let_2)))) (let ((_let_82 (REFL :args (_let_12)))) (let ((_let_83 (ASSUME :args (_let_61)))) (let ((_let_84 (ASSUME :args (_let_62)))) (let ((_let_85 (_let_22))) (let ((_let_86 (ASSUME :args _let_85))) (let ((_let_87 (tptp.c_Option_Othe (tptp.c_Com_Obody tptp.v_pn) tptp.tc_Com_Ocom))) (let ((_let_88 (tptp.v_wt _let_87))) (let ((_let_89 (not _let_88))) (let ((_let_90 (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P _let_42) (tptp.c_Set_Oinsert (tptp.v_mgt _let_87) _let_3 tptp.t_a))))) (let ((_let_91 (not _let_44))) (let ((_let_92 (tptp.c_Finite__Set_Ocard _let_42 tptp.t_a))) (let ((_let_93 (= (tptp.c_HOL_Ominus__class_Ominus _let_13 tptp.v_na tptp.tc_nat) _let_92))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_94 _let_91 _let_90 _let_89))) (let ((_let_96 (_let_1))) (let ((_let_97 (ASSUME :args _let_96))) (let ((_let_98 (tptp.c_Suc _let_13))) (let ((_let_99 (tptp.c_HOL_Ominus__class_Ominus _let_98 _let_37 tptp.tc_nat))) (let ((_let_100 (= _let_13 _let_99))) (let ((_let_101 (tptp.c_HOL_Ominus__class_Ominus _let_98 _let_11 tptp.tc_nat))) (let ((_let_102 (= _let_101 (tptp.c_HOL_Ominus__class_Ominus _let_99 tptp.v_na tptp.tc_nat)))) (let ((_let_103 (= _let_101 (tptp.c_Suc _let_14)))) (let ((_let_104 (= _let_92 (tptp.c_Suc _let_15)))) (let ((_let_105 (forall ((V_n $$unsorted)) (= V_n (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_n) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (_let_33))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 (not _let_17))) (let ((_let_110 (or _let_103 _let_109))) (let ((_let_111 (_let_24))) (let ((_let_112 (ASSUME :args _let_111))) (let ((_let_113 (or _let_104 _let_8 _let_64))) (let ((_let_114 (_let_21))) (let ((_let_115 (ASSUME :args _let_114))) (let ((_let_116 (ASSUME :args (_let_16)))) (let ((_let_117 (and _let_16 _let_104 _let_103 _let_102 _let_100))) (let ((_let_118 (ASSUME :args (_let_104)))) (let ((_let_119 (ASSUME :args (_let_103)))) (let ((_let_120 (ASSUME :args (_let_102)))) (let ((_let_121 (ASSUME :args (_let_100)))) (let ((_let_122 (or _let_88 _let_45))) (let ((_let_123 (_let_30))) (let ((_let_124 (ASSUME :args _let_123))) (let ((_let_125 (not _let_90))) (let ((_let_126 (or _let_6 _let_125))) (let ((_let_127 (_let_27))) (let ((_let_128 (ASSUME :args _let_127))) (let ((_let_129 (and _let_39 _let_43 _let_41))) (let ((_let_130 (ASSUME :args (_let_43)))) (let ((_let_131 (ASSUME :args (_let_41)))) (let ((_let_132 (ASSUME :args (_let_39)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_129)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_130 _let_131 _let_132) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_42)) (TRANS (CONG (REFL :args (tptp.v_mgt__call)) (SYMM (SYMM _let_132)) (REFL :args (tptp.tc_Com_Opname)) (REFL :args (tptp.t_a)) :args (APPLY_UF tptp.c_Set_Oimage)) (SYMM _let_131)) _let_81 :args _let_80) (TRUE_INTRO _let_130))) :args (_let_43 _let_41 _let_39))) :args (_let_39 _let_43 _let_41))) :args (true _let_129)) :args ((or (not _let_39) _let_44 (not _let_43) (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_90 _let_89 _let_91 _let_94 (not _let_95)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_6 _let_125 (not _let_126)))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_128 :args (tptp.v_G tptp.v_pn QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP tptp.v_P V_G) (tptp.c_Set_Oinsert (tptp.hAPP tptp.v_mgt__call V_pn) _let_3 tptp.t_a))))) :args _let_127)) _let_128 :args (_let_126 false _let_27)) :args (_let_125 true _let_6 false _let_126)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_122)) :args ((or _let_45 _let_88 (not _let_122)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_124 :args (tptp.v_pn QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_in V_pn tptp.v_U tptp.tc_Com_Opname) false))))) :args _let_123)) _let_124 :args (_let_122 false _let_30)) :args (_let_88 false _let_10 false _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_117)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_118 _let_116 _let_119 _let_120 _let_121) (SCOPE (TRANS (CONG (SYMM (SYMM _let_121)) (REFL :args (tptp.v_na)) (REFL :args (tptp.tc_nat)) :args (APPLY_UF tptp.c_HOL_Ominus__class_Ominus)) (SYMM _let_120) (SYMM (SYMM _let_119)) (CONG (SYMM _let_116) :args (APPLY_UF tptp.c_Suc)) (SYMM _let_118)) :args (_let_104 _let_16 _let_103 _let_102 _let_100))) :args (_let_16 _let_104 _let_103 _let_102 _let_100))) :args (true _let_117)) :args ((or (not _let_16) (not _let_104) (not _let_103) _let_93 (not _let_102) (not _let_100)))) _let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_8 _let_64 _let_104 (not _let_113)))) _let_78 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (_let_4 tptp.v_G tptp.t_a QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_in V_x V_A T_a) true))))) :args _let_114)) _let_115 :args (_let_113 false _let_21)) :args (_let_104 true _let_8 false _let_63 false 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(tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1))))) (= (tptp.c_HOL_Oplus__class_Oplus _let_31 _let_31 tptp.tc_nat) _let_31) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc _let_1) tptp.tc_nat))))) (forall ((V_n $$unsorted)) (= (tptp.c_Suc V_n) (tptp.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (= (tptp.c_Suc V_n) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) V_n tptp.tc_nat))) (= _let_36 _let_34) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_i V_m tptp.tc_nat)) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_i tptp.tc_nat)) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_x tptp.tc_nat)) tptp.tc_nat)) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBK _let_1 T_a T_b) V_A T_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_z tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Oplus__class_Oplus V_j V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Oplus__class_Oplus V_m V_j tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_l tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) V_m)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a tptp.tc_nat))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1)) (= V_a _let_1)))) (= _let_37 _let_34) (forall ((V_times $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_times V_a))) (or (= (tptp.hAPP (tptp.hAPP V_times (tptp.hAPP _let_1 V_b)) V_c) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_times V_b) V_c))) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a))))) (forall ((V_times $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_times V_a))) (let ((_let_2 (tptp.hAPP V_times V_b))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c))) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))))) (forall ((V_times $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_times V_a) V_b) (tptp.hAPP (tptp.hAPP V_times V_b) V_a)) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (tptp.c_HOL_Oord__class_Oless _let_31 _let_34 tptp.tc_nat) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat))) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_Suc _let_1) (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat))) (= V_m _let_1) (= V_n _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_Finite__Set_Ofinite V_A T_b))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat) V_n tptp.tc_nat))) (= V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (= _let_34 _let_36) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((V_n $$unsorted)) (or (= (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) V_n) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oplus__class_Oplus V_a V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_u T_a))) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) V_u))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1) _let_2)))) (= _let_34 _let_35) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat))) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat))) (= V_m _let_1) (= V_m _let_2))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Suc V_m) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a)))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_x V_z tptp.tc_nat))) (= V_y V_z))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat))) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a))) (= V_y V_z))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a))) (= V_b V_c))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_2)) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_2)) (= V_m _let_1) (= V_m _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((V_x $$unsorted)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) V_n)) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 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_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_c V_A T_a) (not (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (= V_x V_y) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_xa))) (not (tptp.c_in V_xa V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_xa))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.hAPP V_f V_x) (tptp.hAPP V_f V_y))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (= V_x V_y) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a) (not (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b) (not (tptp.c_in (tptp.hAPP V_f V_a) V_A T_a)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_b T_a) T_b) (not (tptp.c_in (tptp.hAPP V_f V_a) V_B T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) V_B T_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_B T_a T_b) T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_a) V_A T_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f V_A T_a T_b) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not 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(tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (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)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_n $$unsorted)) (or (= V_n (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_j V_l tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (not (tptp.c_HOL_Oord__class_Oless _let_31 _let_31 tptp.tc_nat)) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat) V_i tptp.tc_nat))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_j V_i tptp.tc_nat) V_i tptp.tc_nat))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) V_j tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus V_a V_b tptp.tc_nat)))))) (= _let_35 _let_34) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) tptp.tc_nat) V_m) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) (tptp.c_Suc _let_1))) (= V_m _let_1) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_F $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_Set_Oinsert V_a V_F T_a) T_a T_b) (tptp.c_HOL_Oplus__class_Oplus (tptp.hAPP V_f V_a) (tptp.c_Finite__Set_Osetsum V_f V_F T_a T_b) T_b)) (tptp.c_in V_a V_F T_a) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.c_in V_x V_A T_a)) (tptp.c_in V_x V_B T_a) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (tptp.c_in V_x V_B T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_B T_a T_b) T_b)) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_a) tptp.tc_nat)) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_Finite__Set_Ofinite V_B T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_Set_Oinsert V_x (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) 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_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_B T_a)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_in V_a (tptp.c_Inductive_Ocomplete__lattice__class_Ogfp V_f _let_1) T_a) (not (tptp.c_lessequals V_X (tptp.hAPP V_f V_X) _let_1)) (not (tptp.c_in V_a V_X T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b)) (tptp.c_in V_a V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (not (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 V_A V_P T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a) T_a)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)) (tptp.c_in V_x V_B T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) T_b)) (not (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b))))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Fun_Oinj__on V_f (tptp.c_Set_Oinsert V_a V_A T_a) T_a T_b) (tptp.c_in (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMax (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Finite__Set_Olinorder__class_OMin (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Set_Oinsert (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 V_A V_P T_a) (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a) T_a)))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_b) (not (tptp.c_Fun_Oinj__on V_f V_A T_b T_a)) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_x $$unsorted)) (or (not (tptp.c_lessequals V_x V_x tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) _let_1))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oimage V_f (tptp.c_Set_Ovimage V_f V_A T_b T_a) T_b T_a) V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted)) (= (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) _let_33 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_Suc V_m) tptp.tc_nat)) _let_32 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat) V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_c tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_b V_c tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_c V_a tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) V_j tptp.tc_nat) (not (tptp.c_lessequals V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) V_j tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_j (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat) (not (tptp.c_lessequals V_j (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Ovimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_in V_c V_A T_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) V_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (tptp.c_Fun_Oinj__on V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a T_b)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_i) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_Suc V_n) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_m))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= _let_1 V_n) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_x) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) 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(tptp.c_HOL_Oord__class_Oless V_f V_g _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1) (= V_A V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.c_HOL_Ominus__class_Ominus V_C V_A _let_1) _let_1) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_HOL_Oord__class_Oless V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_b) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_B T_a T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A _let_1))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Ovimage V_f V_A T_b T_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _let_1)) (not (tptp.c_Fun_Oinj__on V_f V_C T_a T_b))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_a) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat)))) (forall ((T_a $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Finite__Set_Ocard (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (tptp.c_lessequals _let_31 _let_31 tptp.tc_nat) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals V_m (tptp.c_HOL_Oplus__class_Oplus V_m V_x tptp.tc_nat) tptp.tc_nat)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals V_n (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) tptp.tc_nat)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals V_n (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat) tptp.tc_nat)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_lessequals V_n _let_1 tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_j V_l tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_k V_l tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i (tptp.c_HOL_Oplus__class_Oplus V_m V_j tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_i (tptp.c_HOL_Oplus__class_Oplus V_j V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_k V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_x V_z tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_x V_y tptp.tc_nat)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Suc V_i) tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Suc _let_1) tptp.tc_nat)) V_n) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) _let_1)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) _let_1)) (= V_m V_n)))) (forall ((V_j $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_j V_n tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)))) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m V_m tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_l tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_b V_x tptp.tc_nat) V_b tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_b V_d tptp.tc_nat) V_b tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_d)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_i (tptp.c_HOL_Oplus__class_Oplus V_j V_k tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_k V_n tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_m V_n tptp.tc_nat) V_n tptp.tc_nat) V_m)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_n V_m tptp.tc_nat) V_n tptp.tc_nat) V_m)) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_HOL_Oplus__class_Oplus (tptp.hAPP V_f V_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) T_b)) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_j V_i tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_i V_k tptp.tc_nat) V_j tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus V_k V_i tptp.tc_nat))) (or (not (tptp.c_lessequals V_i _let_1 tptp.tc_nat)) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_i tptp.tc_nat) V_k)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= V_j (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat) V_i tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.c_HOL_Oplus__class_Oplus V_n (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) tptp.tc_nat) V_m) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_n tptp.tc_nat) V_m) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Oplus__class_Oplus V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_i V_j tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_j V_i tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP V_f V_a) T_b)) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Ring__and__Field_Oring T_b)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a T_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.hAPP V_f V_a) T_b)) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x _let_2 T_a) _let_1) (tptp.c_Set_Oinsert V_y _let_2 T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.c_in V_y V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) (tptp.c_in V_a V_B T_a) (not (tptp.c_in V_a V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) _let_30 (forall ((T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_x T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_x (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMax V_A T_a) V_A T_a) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_in (tptp.c_Finite__Set_Olinorder__class_OMin V_A T_a) V_A T_a) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) _let_29 (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_b $$unsorted) (V_times $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)))) (tptp.c_in V_x V_xa T_b) (not (tptp.c_OrderedGroup_Oab__semigroup__mult V_times T_a)))) (forall ((V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted) (T_aa $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_aa T_a) T_aa)) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.c_in V_a (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) V_A) (not (tptp.c_in V_a V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (tptp.c_in V_x V_B T_a) (not (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a) (tptp.c_in V_x V_B T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_HOL_Oord__class_Oless V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a) (not (tptp.c_HOL_Oord__class_Oless V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_n_H $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1 V_f T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals (tptp.hAPP V_f V_n) (tptp.hAPP V_f V_n_H) T_a) (not (tptp.c_lessequals V_n V_n_H tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP V_f _let_1) (tptp.hAPP V_f (tptp.c_Suc _let_1)) T_a))))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (tptp.c_Finite__Set_Ofinite (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 V_A V_P T_a) T_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 V_A V_B V_f T_a T_b) V_A T_a))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 V_A V_B V_f T_b T_a)) V_B T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 V_A V_B V_f T_b T_a) V_A T_b))) (forall ((V_g $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (V_X $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Set_Oimage V_g V_X T_a T_b))) (or (tptp.c_in (tptp.hAPP V_g V_a) (tptp.c_Inductive_Ocomplete__lattice__class_Ogfp V_f _let_1) T_b) (not (tptp.c_lessequals _let_2 (tptp.hAPP V_f _let_2) _let_1)) (not (tptp.c_in V_a V_X T_a)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 V_A V_B V_f T_a T_b)) V_B T_b)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_HOL_Oone__class_Oone tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_a T_b) V_A T_b T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Fun_Oinj__on V_f V_A T_a T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oimage V_f V_A T_a T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) _let_28 (forall ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 V_A V_B V_f T_b T_a) T_b) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_a))) (or (= _let_1 V_A) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_a)) (not (tptp.c_lessequals _let_1 V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_lessequals (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 V_A V_B V_f T_b T_a) V_A (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_B (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (tptp.c_Fun_Oinj__on V_f V_A T_a T_b))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) V_m tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_j) (tptp.c_HOL_Oplus__class_Oplus V_k V_m tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_m V_k tptp.tc_nat) (tptp.c_Suc V_j) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) _let_27 (forall ((V_P $$unsorted) (V_F $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.hBOOL (tptp.hAPP V_P V_F)) (tptp.c_in (tptp.c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 V_A V_P T_a) V_A T_a) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Orderings_Obot__class_Obot _let_1)))) (not (tptp.c_lessequals V_F V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_F T_a))))) (forall ((T_a $$unsorted) (V_M $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMax V_M T_a) (tptp.c_Finite__Set_Olinorder__class_OMax V_N T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_M V_N _let_1))))) (forall ((T_a $$unsorted) (V_N $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals (tptp.c_Finite__Set_Olinorder__class_OMin V_N T_a) (tptp.c_Finite__Set_Olinorder__class_OMin V_M T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_N T_a)) (= V_M (tptp.c_Orderings_Obot__class_Obot _let_1)) (not (tptp.c_lessequals V_M V_N _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) _let_26 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_x $$unsorted)) (or (= (tptp.c_Set_Oimage (tptp.c_COMBK V_c T_b T_a) V_A T_a T_b) (tptp.c_Set_Oinsert V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b)) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Ocard V_xa T_a))) (or (tptp.c_in V_x V_xa T_a) (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_xa T_a) T_a) (tptp.c_Suc _let_1)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_f $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_b)) (not (tptp.c_Finite__Set_Ofinite V_B T_b)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_g V_B T_b T_a) V_A (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_g V_B T_b T_a)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_a) tptp.tc_nat)) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_Finite__Set_Ofinite V_B T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (tptp.c_in V_x V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a))) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_b) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_B T_b)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) V_B (tptp.tc_fun T_b tptp.tc_bool))) (not (tptp.c_Fun_Oinj__on V_f V_A T_a T_b)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Suc (tptp.c_Finite__Set_Ocard (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a)) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a))))) (forall ((V_G $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_2 (tptp.hAPP tptp.v_P V_G))) (or (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Set_Oinsert (tptp.v_mgt V_c) _let_1 tptp.t_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Set_Oinsert (tptp.hAPP tptp.v_mgt__call (tptp.v_sko__local__Xassms__3__1 V_G tptp.v_P tptp.v_U tptp.v_mgt__call)) _let_1 tptp.t_a)))) (not (tptp.v_wt V_c)))))) (forall ((V_G $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_G) (tptp.c_Set_Oinsert (tptp.v_mgt V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)) tptp.t_a))) (tptp.c_in (tptp.v_sko__local__Xassms__3__1 V_G tptp.v_P tptp.v_U tptp.v_mgt__call) tptp.v_U tptp.tc_Com_Opname) (not (tptp.v_wt V_c)))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_t V_B T_a) (not (tptp.c_in V_t V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a) (not (tptp.c_in V_a V_B T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) (tptp.c_Suc V_m) tptp.tc_nat) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))) (forall ((V_n $$unsorted)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_n tptp.tc_nat))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) _let_25 (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) (tptp.c_Finite__Set_Ocard V_A T_a)) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_h $$unsorted) (V_F $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oimage V_h V_F T_a T_b) T_b) (not (tptp.c_Finite__Set_Ofinite V_F T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_in V_a V_A T_a) (= V_a V_b) (not (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (= V_A V_B) (not (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_B T_a) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x V_A T_a) T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (or (tptp.c_Finite__Set_Ofinite V_A T_a) (not (tptp.c_Finite__Set_Ofinite (tptp.c_Set_Oinsert V_a V_A T_a) T_a)))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) _let_24 (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) _let_23 (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a) (not (tptp.c_in V_x V_A T_b)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)))) _let_22 (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a)) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a)) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x V_S T_a) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.c_in V_x V_S T_a)))) _let_21 (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (tptp.c_in V_x _let_1 T_a) (= (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Suc (tptp.c_Finite__Set_Ocard _let_1 T_a)))))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_l tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_l tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat))) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)) (= V_m V_n))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_k tptp.tc_nat) V_j tptp.tc_nat))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.c_in V_x V_xa T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Suc V_n) V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.c_in V_x V_B T_a) (tptp.c_in V_x V_A T_a) (= V_A V_B))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Suc V_k) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_k tptp.tc_nat))) (forall ((V_G $$unsorted) (V_ts $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_G) V_ts)) (not (tptp.c_lessequals V_ts V_G (tptp.tc_fun tptp.t_a tptp.tc_bool))))) _let_20 (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard V_A T_a) (tptp.c_Finite__Set_Ocard V_B T_a) tptp.tc_nat) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_Finite__Set_Ofinite V_B T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_lessequals (tptp.c_Finite__Set_Ocard (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (tptp.c_Finite__Set_Ocard V_A T_a) tptp.tc_nat) (not (tptp.c_Finite__Set_Ofinite V_A T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Ominus__class_Ominus V_n V_i tptp.tc_nat) tptp.tc_nat) V_i) (not (tptp.c_lessequals V_i V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (= V_m _let_1) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m _let_1 tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_aa)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_b)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a) (not (tptp.c_in V_x V_A T_b)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (not (tptp.c_in V_x V_A T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) _let_19 _let_18 _let_17 _let_16 _let_10 _let_9 _let_7 _let_1 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.29/1.49  )
% 1.29/1.49  % SZS output end Proof for SWV883-1
% 1.29/1.50  % cvc5---1.0.5 exiting
% 1.29/1.50  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------