TSTP Solution File: SWV849-1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV849-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 21:53:32 EDT 2023
% Result : Unsatisfiable 4.63s 4.84s
% Output : Proof 4.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16 % Problem : SWV849-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.17 % Command : do_cvc5 %s %d
% 0.16/0.38 % Computer : n003.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Tue Aug 29 05:58:40 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.55 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.55 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.B8mNk4yx7C/cvc5---1.0.5_27589.p...
% 0.45/0.64 ------- get file name : TPTP file name is SWV849-1
% 0.45/0.64 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27589.smt2...
% 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.63/4.84 % SZS status Unsatisfiable for SWV849-1
% 4.63/4.84 % SZS output start Proof for SWV849-1
% 4.63/4.90 (
% 4.63/4.90 (let ((_let_1 (forall ((V_Za $$unsorted) (V_s_Ha $$unsorted) (V_sa $$unsorted) (V_na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Za))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_s_Ha)) (not (tptp.c_Natural_Oevaln tptp.v_c V_sa V_na V_s_Ha)) (not (tptp.hBOOL (tptp.hAPP tptp.v_b V_sa))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_sa))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid V_na (tptp.v_n V_na) tptp.t_a))))))) (let ((_let_2 (forall ((V_Z $$unsorted) (V_s_H $$unsorted) (V_s $$unsorted) (V_na $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Z))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_s_H)) (not (tptp.c_Natural_Oevaln tptp.v_c V_s V_na V_s_H)) (not (tptp.hBOOL (tptp.hAPP tptp.v_b V_s))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_s))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) (tptp.v_n V_na)) tptp.v_G))))))) (let ((_let_3 (forall ((V_Za $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile tptp.v_ba tptp.v_ca) (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (not (tptp.hBOOL (tptp.hAPP tptp.v_b tptp.v_s2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_Za) tptp.v_s1))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na tptp.v_xa tptp.t_a)))))) (let ((_let_4 (forall ((V_Za $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Za))) (or (not (= (tptp.c_Com_Ocom_OWhile tptp.v_ba tptp.v_ca) (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s1))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na tptp.v_xa tptp.t_a))))))) (let ((_let_5 (forall ((V_Z $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile tptp.v_ba tptp.v_ca) (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (not (tptp.hBOOL (tptp.hAPP tptp.v_b tptp.v_s2))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_Z) tptp.v_s1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) tptp.v_xa) tptp.v_G)))))) (let ((_let_6 (forall ((V_Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Z))) (or (not (= (tptp.c_Com_Ocom_OWhile tptp.v_ba tptp.v_ca) (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s1))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) tptp.v_xa) tptp.v_G))))))) (let ((_let_7 (tptp.hAPP tptp.v_P tptp.v_xb))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP _let_7 tptp.v_s2)))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP tptp.v_b tptp.v_s2)))) (let ((_let_10 (or _let_9 (not _let_8)))) (let ((_let_11 (forall ((V_x $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na V_x tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_x) tptp.v_G))))))) (let ((_let_12 (tptp.hBOOL (tptp.hAPP _let_7 tptp.v_s0)))) (let ((_let_13 (= tptp.v_ca tptp.v_c))) (let ((_let_14 (= tptp.v_ba tptp.v_b))) (let ((_let_15 (tptp.c_Com_Ocom_OWhile tptp.v_ba tptp.v_ca))) (let ((_let_16 (tptp.c_Natural_Oevaln tptp.v_ca tptp.v_s0 tptp.v_na tptp.v_s1))) (let ((_let_17 (tptp.hBOOL (tptp.hAPP tptp.v_ba tptp.v_s0)))) (let ((_let_18 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a tptp.tc_bool)))) (let ((_let_19 (tptp.v_n tptp.v_na))) (let ((_let_20 (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na _let_19 tptp.t_a))) (let ((_let_21 (tptp.hBOOL (tptp.hAPP tptp.v_b tptp.v_s0)))) (let ((_let_22 (tptp.c_Natural_Oevaln tptp.v_c tptp.v_s0 tptp.v_na tptp.v_s1))) (let ((_let_23 (not _let_20))) (let ((_let_24 (tptp.hAPP tptp.v_P SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (tptp.hBOOL (tptp.hAPP _let_24 tptp.v_s0)))) (let ((_let_26 (not _let_25))) (let ((_let_27 (not _let_21))) (let ((_let_28 (not _let_22))) (let ((_let_29 (tptp.hBOOL (tptp.hAPP _let_24 tptp.v_s1)))) (let ((_let_30 (or _let_29 _let_28 _let_27 _let_26 _let_23))) (let ((_let_31 (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)))) (let ((_let_32 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_31 _let_19) tptp.v_G)))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_20 _let_33))) (let ((_let_35 (_let_11))) (let ((_let_36 (ASSUME :args _let_35))) (let ((_let_37 ((not (= (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na V_x tptp.t_a) true))))) (let ((_let_38 (not _let_12))) (let ((_let_39 (tptp.hBOOL (tptp.hAPP _let_7 tptp.v_s1)))) (let ((_let_40 (or _let_39 _let_28 _let_27 _let_38 _let_32))) (let ((_let_41 (_let_2))) (let ((_let_42 (ASSUME :args _let_41))) (let ((_let_43 (ASSUME :args (_let_14)))) (let ((_let_44 (ASSUME :args (_let_17)))) (let ((_let_45 (and _let_17 _let_14))) (let ((_let_46 (_let_17 _let_14))) (let ((_let_47 (REFL :args (tptp.v_s0)))) (let ((_let_48 (SYMM _let_43))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_45)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_44 _let_43) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG _let_48 _let_47 :args (APPLY_UF tptp.hAPP)) :args (APPLY_UF tptp.hBOOL)) (TRUE_INTRO _let_44))) :args _let_46)) :args _let_46)) :args (true _let_45)) _let_44 _let_43 :args (_let_21 false _let_17 false _let_14)))) (let ((_let_50 (ASSUME :args (_let_13)))) (let ((_let_51 (ASSUME :args (_let_16)))) (let ((_let_52 (and _let_16 _let_13))) (let ((_let_53 (_let_16 _let_13))) (let ((_let_54 (SYMM _let_50))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_52)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_51 _let_50) (SCOPE (TRUE_ELIM (TRANS (CONG _let_54 _let_47 (REFL :args (tptp.v_na)) (REFL :args (tptp.v_s1)) :args (APPLY_UF tptp.c_Natural_Oevaln)) (TRUE_INTRO _let_51))) :args _let_53)) :args _let_53)) :args (true _let_52)) _let_51 _let_50 :args (_let_22 false _let_16 false _let_13)))) (let ((_let_56 (not _let_39))) (let ((_let_57 (or _let_8 _let_56))) (let ((_let_58 (forall ((V_Z $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_Z) tptp.v_s1)))))) (let ((_let_59 (= _let_15 (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c)))) (let ((_let_60 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_31 tptp.v_xa) tptp.v_G)))) (let ((_let_61 (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na tptp.v_xa tptp.t_a))) (let ((_let_62 (not _let_60))) (let ((_let_63 (or _let_61 _let_62))) (let ((_let_64 (forall ((V_Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Z))) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s1)))))))) (let ((_let_65 (forall ((V_Za $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Za))) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s1)))))))) (let ((_let_66 (ALPHA_EQUIV :args (_let_64 (= V_Z V_Za))))) (let ((_let_67 (and _let_14 _let_13))) (let ((_let_68 (_let_14 _let_13))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_67)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_43 _let_50) (SCOPE (CONG (SYMM _let_48) (SYMM _let_54) :args (APPLY_UF tptp.c_Com_Ocom_OWhile)) :args _let_68)) :args _let_68)) :args (true _let_67)) :args ((or _let_59 (not _let_14) (not _let_13)))) _let_43 _let_50 :args (_let_59 false _let_14 false _let_13)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.v_xa QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_35)) _let_36 :args (_let_63 false _let_11)))) (let ((_let_71 (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_61 _let_62 (not _let_63)))))) (let ((_let_72 (_let_64))) (let ((_let_73 (_let_58))) (let ((_let_74 (MACRO_RESOLUTION_TRUST _let_71 _let_70 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) _let_69 (REORDERING (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args ((or (not _let_59) _let_60 (not _let_9) _let_58))) _let_69 (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_58 (= V_Z V_Za)))) (ASSUME :args (_let_10)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_73) :args (tptp.v_xb QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P V_Z)))) :args _let_73)) (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_8 _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_72) :args (tptp.v_xb QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P V_Z)))) :args _let_72)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_66) (MACRO_RESOLUTION_TRUST _let_71 _let_70 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) _let_69 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_69 (REORDERING (EQUIV_ELIM1 _let_66) :args ((or _let_65 (not _let_64)))) :args (_let_65 false _let_63 false _let_60 false _let_59 true _let_61 false _let_59 true _let_64)) :args (_let_64 false _let_65)) :args (_let_57 false _let_64)) :args (_let_56 false _let_63 true _let_61 false _let_59 false _let_60 false _let_59 true (forall ((V_Za $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_Za) tptp.v_s1)))) false _let_9 true _let_58 false _let_8 false _let_57)))) (let ((_let_75 (ASSUME :args (_let_12)))) (let ((_let_76 (_let_1))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 (or _let_29 _let_26))) (let ((_let_79 (forall ((V_Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Z))) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s0)))))))) (let ((_let_80 (not _let_78))) (let ((_let_81 (or _let_39 _let_38))) (let ((_let_82 (not _let_79))) (let ((_let_83 (not _let_81))) (let ((_let_84 (_let_79))) (let ((_let_85 (or))) (let ((_let_86 (_let_82))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_86)) :args _let_86)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_79))) (REFL :args (_let_80)) :args _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args (tptp.v_xb QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.hAPP tptp.v_P V_Z)))) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_38 _let_39 _let_83))) _let_75 _let_74 :args (_let_83 false _let_12 true _let_39)) :args (_let_82 true _let_81)) :args (_let_80 true _let_79)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_26 _let_28 _let_27 _let_23 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 1)) (CONG (REFL :args (_let_78)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_85)) :args ((or _let_25 _let_78))) _let_87 :args (_let_25 true _let_78)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_78 0)) _let_87 :args ((not _let_29) true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.v_s1 tptp.v_s0 tptp.v_na QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP tptp.v_P V_Za) V_s_Ha) (not (= (tptp.c_Natural_Oevaln tptp.v_c V_sa V_na V_s_Ha) false))))) :args _let_76)) _let_77 :args (_let_30 false _let_1)) _let_55 _let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_20 _let_33 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_38 _let_39 _let_28 _let_27 _let_32 (not _let_40)))) _let_75 _let_74 _let_55 _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.v_xb tptp.v_s1 tptp.v_s0 tptp.v_na QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.hAPP tptp.v_P V_Z) V_s_H) (not (= (tptp.c_Natural_Oevaln tptp.v_c V_s V_na V_s_H) false))))) :args _let_41)) _let_42 :args (_let_40 false _let_2)) :args (_let_32 false _let_12 true _let_39 false _let_22 false _let_21 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_37)) :args _let_35)) _let_36 :args (_let_34 false _let_11)) :args (_let_20 false _let_32 false _let_34)) :args (false false _let_25 true _let_29 false _let_30 false _let_22 false _let_21 false _let_20)) :args ((forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_pname V_pname_H))) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_fun V_fun_H))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_COMBI T_a) V_Y T_a T_a) V_Y)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f3 V_loc) V_fun) V_com) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com T_a)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 tptp.c_Com_Ocom_OSKIP T_a) V_f1)) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_pname $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OBODY V_pname)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B)))))) (forall ((T_b $$unsorted) (V_M $$unsorted) (V_i $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_b)) (tptp.c_lessequals (tptp.hAPP V_M V_i) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_a T_b) T_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) V_A))))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_pname_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_b) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))) (forall ((V_f $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Oid T_a) T_a T_b T_a) V_f)) (forall ((T_b $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ocomp (tptp.c_Fun_Oid T_b) V_g T_b T_b T_a) V_g)) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f8 V_vname) V_pname) V_fun))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) _let_1) V_A))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_a $$unsorted) (V_P $$unsorted)) (= (tptp.hAPP (tptp.c_COMBI T_a) V_P) V_P)) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1) _let_2)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OAss V_vname V_fun) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_vname) V_fun))) (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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (tptp.c_Com_OWT tptp.c_Com_Ocom_OSKIP) (forall ((V_f $$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_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_s1) (not (tptp.c_Natural_Oevalc V_c0 V_s V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s))))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_c1 $$unsorted) (V_t $$unsorted) (V_c2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (tptp.c_Natural_Oevalc V_c1 V_s V_t) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OSemi V_c0 V_c1) V_s0 V_s2) (not (tptp.c_Natural_Oevalc V_c1 V_s1 V_s2)) (not (tptp.c_Natural_Oevalc V_c0 V_s0 V_s1)))) (forall ((V_X $$unsorted) (V_a $$unsorted)) (tptp.c_Com_OWT (tptp.c_Com_Ocom_OAss V_X V_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_X $$unsorted) (V_pn $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCall V_X V_pn V_a)) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OBODY V_pn))))) (forall ((V_P $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OBODY V_P)) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCall V_X V_P V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H))) (= V_vname V_vname_H))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OSemi V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f4 V_com1) V_com2) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com1 T_a)) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com2 T_a)))) (forall ((T_b $$unsorted)) (or (not (tptp.class_Orderings_Obot T_b)) (= (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Orderings_Obot__class_Obot T_b)))) (forall ((V_pname_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((T_a $$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 $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((V_f $$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_vname $$unsorted) (V_fun $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((T_aa $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) 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)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (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_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_2)) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((V_pname_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$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_Lattices_Olower__semilattice__class_Oinf _let_2 V_B _let_1) _let_2)))) (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))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_A $$unsorted) (V_k $$unsorted) (V_I $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_I V_A T_a _let_1))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_A V_k) _let_2 _let_1) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_k) V_I))))))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (tptp.hAPP (tptp.hAPP V_sup V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (tptp.hAPP (tptp.hAPP V_inf V_a) V_b)) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com2 V_com2_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_com1 V_com1_H))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H))) (= V_fun V_fun_H))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (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_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_f $$unsorted) (V_g $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP V_f (tptp.hAPP V_g V_x)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) V_v))) (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_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_vname $$unsorted) (V_fun $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1)) (not (tptp.c_Com_OWT V_c1)) (not (tptp.c_Com_OWT V_c0)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 tptp.c_Com_Ocom_OSKIP T_a) V_f1)) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Ovimage (tptp.c_COMBI T_a) V_Y T_a T_a) V_Y)) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= _let_2 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1))) (= (tptp.hAPP V_B V_x) _let_2) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (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 ((T_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_A T_b _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) _let_1) V_A))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_C $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_B _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (not (tptp.hBOOL (tptp.hAPP _let_2 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_A))) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a) 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))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))) (forall ((V_s $$unsorted)) (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP V_s V_s)) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (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_u $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (or (= V_u V_t) (not (tptp.c_Natural_Oevalc V_c V_s V_u)) (not (tptp.c_Natural_Oevalc V_c V_s V_t)))) (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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_a $$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_a V_d) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$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_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Natural_Oevalc V_c2 V_s V_t) (tptp.hBOOL (tptp.hAPP V_b V_s)) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_s1) (not (tptp.c_Natural_Oevalc V_c1 V_s V_s1)) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_vname_H $$unsorted) (V_fun_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Set_Oinsert V_a V_A T_b) V_B T_b _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_B V_a) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b _let_1) _let_1)))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun1 V_fun1_H))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_com V_com_H))) (forall ((V_fun1 $$unsorted) (V_com $$unsorted) (V_fun2 $$unsorted) (T_a $$unsorted) (V_fun1_H $$unsorted) (V_com_H $$unsorted) (V_fun2_H $$unsorted)) (or (not (= (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1 V_com V_fun2 T_a) (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_fun1_H V_com_H V_fun2_H T_a))) (= V_fun2 V_fun2_H))) (forall ((V_c2 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT V_c2) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c1 V_c2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_Sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_inf $$unsorted) (V_top $$unsorted) (V_bot $$unsorted)) (or (tptp.c_Complete__Lattice_Ocomplete__lattice V_Sup V_Inf (tptp.c_COMBC V_less__eq T_a T_a tptp.tc_bool) (tptp.c_COMBC V_less T_a T_a tptp.tc_bool) V_sup V_inf V_top V_bot T_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) T_a))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_a $$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_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_xa)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_pname $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_m $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) 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))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Oid T_b) V_c T_b T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c V_v)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)))) (forall ((T_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (not (tptp.class_HOL_Ominus T_b)) (= (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP V_A tptp.v_x) (tptp.hAPP V_B tptp.v_x) T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_a T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_b T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (= (tptp.c_Set_Ovimage (tptp.c_Fun_Oid T_a) V_A T_a T_a) V_A)) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OSemi V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP V_f4 V_com1) V_com2))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((V_g $$unsorted) (V_f $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (= (tptp.c_Set_Ovimage (tptp.c_Fun_Ocomp V_g V_f T_c T_b T_a) V_x T_a T_b) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Ovimage V_g V_x T_c T_b) T_a T_c))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_Fun_Oid T_a) V_Y T_a T_a) V_Y)) (forall ((V_pname $$unsorted) (V_pname_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OBODY V_pname) (tptp.c_Com_Ocom_OBODY V_pname_H))) (= V_pname V_pname_H))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_pname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCall V_vname V_pname V_fun) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f8 V_vname) V_pname) V_fun))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_Y $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OLocal V_Y V_a V_c)) (not (tptp.c_Com_OWT V_c)))) (forall ((V_c $$unsorted) (V_Y $$unsorted) (V_a $$unsorted)) (or (tptp.c_Com_OWT V_c) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OLocal V_Y V_a V_c))))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_pname $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OBODY V_pname) T_a) (tptp.hAPP V_f7 V_pname))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (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_com1 $$unsorted) (V_com2 $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (= V_m _let_1) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m _let_1 tptp.tc_nat))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OAss V_vname V_fun) T_a) (tptp.hAPP (tptp.hAPP V_f2 V_vname) V_fun))) (forall ((V_fun_H $$unsorted) (V_com1_H $$unsorted) (V_com2_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun_H V_com1_H V_com2_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_pname_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OBODY V_pname_H)))) (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_A) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Oid T_a) V_x) V_x)) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f5 V_fun) V_com1) V_com2) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com1 T_a)) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com2 T_a)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (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_t $$unsorted) (V_s $$unsorted)) (or (= V_t V_s) (not (tptp.c_Natural_Oevalc tptp.c_Com_Ocom_OSKIP V_s V_t)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastLessThan V_less__eq V_less V_l V_u T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_A T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_B T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less__eq $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_B)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_c) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_a))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Set_Oinsert V_b V_A T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (not (tptp.hBOOL (tptp.hAPP _let_1 V_B))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XbexI__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XbexE__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_A T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Oinsert V_a V_B T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x V_B T_a)))) (forall ((V_Q $$unsorted) (V_xf $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a))) (or (tptp.hBOOL (tptp.hAPP V_Q V_xf)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xf) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q _let_1))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((V_P $$unsorted) (V_xg $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_xg)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xg) V_A))) (not (tptp.hBOOL (tptp.hAPP V_Q _let_1))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (tptp.hBOOL (tptp.hAPP V_P V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XballE__1__1 V_A V_P T_a)) V_A))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))))))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))))) (forall ((T_a $$unsorted) (V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.c_COMBC (tptp.c_in T_a) T_a (tptp.tc_fun T_a tptp.tc_bool) tptp.tc_bool))) (or (not (= (tptp.hAPP _let_1 V_R) (tptp.hAPP _let_1 V_S))) (= V_R V_S)))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less__eq $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatMost V_less__eq V_k T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_k))))) (forall ((V_c1 $$unsorted) (V_c2 $$unsorted)) (or (tptp.c_Com_OWT V_c1) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c1 V_c2))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_P $$unsorted) (V_xa $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_A)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_B)))))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_sup $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP V_sup V_a) (tptp.hAPP V_Sup V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_inf $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a V_A T_a)) (tptp.hAPP (tptp.hAPP V_inf V_a) (tptp.hAPP V_Inf V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 V_A V_B V_P T_b T_a)) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xa) (tptp.hAPP V_B V_x)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f3 V_loc) V_fun) V_com))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_C)))))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((V_f $$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))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofcomp V_f V_g T_b T_c T_a) V_x) (tptp.hAPP V_g (tptp.hAPP V_f V_x)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (= (tptp.hAPP V_f V_a) V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (not (tptp.c_lessequals V_x V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x T_a))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_h $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ocomp V_f (tptp.c_Fun_Ocomp V_g V_h T_d T_c T_a) T_c T_b T_a) (tptp.c_Fun_Ocomp (tptp.c_Fun_Ocomp V_f V_g T_c T_b T_d) V_h T_d T_b T_a))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H))) (= V_fun V_fun_H))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_vname_H $$unsorted) (V_fun_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H))) (= V_vname V_vname_H))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) V_B T_b _let_1) T_a) (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a)))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_x $$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_n $$unsorted)) (not (tptp.c_lessequals (tptp.c_Suc V_n) V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_com V_com_H))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_fun V_fun_H))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_loc_H $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OLocal V_loc_H V_fun_H V_com_H))) (= V_loc V_loc_H))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OSemi V_c0 V_c1)) (not (tptp.c_Com_OWT V_c1)) (not (tptp.c_Com_OWT V_c0)))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fun_Ofcomp V_f (tptp.c_Fun_Oid T_b) T_a T_b T_b) V_f)) (forall ((T_a $$unsorted) (V_g $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ofcomp (tptp.c_Fun_Oid T_a) V_g T_a T_a T_b) V_g)) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_r $$unsorted)) (= (tptp.c_Set_Oimage (tptp.c_Fun_Ocomp V_f V_g T_c T_a T_b) V_r T_b T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oimage V_g V_r T_b T_c) T_c T_a))) (forall ((V_Sup $$unsorted) (T_a $$unsorted) (V_bot $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_bot) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (T_a $$unsorted) (V_top $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) V_top) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_a $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((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_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_pname $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OBODY V_pname) T_a) (tptp.hAPP V_f7 V_pname))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_C _let_1) _let_1)))) (forall ((V_Sup $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Sup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_Inf $$unsorted) (V_a $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less__eq $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (= (tptp.hAPP V_Inf (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)) V_a) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f5 V_fun) V_com1) V_com2))) (forall ((V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (T_d $$unsorted) (V_v $$unsorted)) (or (not (= (tptp.c_Fun_Ocomp V_a V_b T_c T_b T_a) (tptp.c_Fun_Ocomp V_c V_d T_d T_b T_a))) (= (tptp.hAPP V_a (tptp.hAPP V_b V_v)) (tptp.hAPP V_c (tptp.hAPP V_d V_v))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_f_H $$unsorted) (V_g_H $$unsorted) (V_x_H $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_d $$unsorted) (T_e $$unsorted)) (or (not (= (tptp.hAPP V_f (tptp.hAPP V_g V_x)) (tptp.hAPP V_f_H (tptp.hAPP V_g_H V_x_H)))) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_b T_a T_c) V_x) (tptp.hAPP (tptp.c_Fun_Ocomp V_f_H V_g_H T_d T_a T_e) V_x_H)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_M $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) V_M T_b _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_M T_b _let_1) (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_B V_M T_b _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (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_vname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname_H V_fun_H) tptp.c_Com_Ocom_OSKIP))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c1 $$unsorted) (V_b $$unsorted)) (or (tptp.c_Natural_Oevalc V_c2 V_s V_t) (tptp.c_Natural_Oevalc V_c1 V_s V_t) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_t)))) (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_c2 $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Com_OWT V_c2) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2))))) (forall ((V_c1 $$unsorted) (V_b $$unsorted) (V_c2 $$unsorted)) (or (tptp.c_Com_OWT V_c1) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_a $$unsorted) (T_d $$unsorted) (T_c $$unsorted) (V_h $$unsorted) (T_b $$unsorted)) (= (tptp.c_Fun_Ofcomp (tptp.c_Fun_Ofcomp V_f V_g T_a T_d T_c) V_h T_a T_c T_b) (tptp.c_Fun_Ofcomp V_f (tptp.c_Fun_Ofcomp V_g V_h T_d T_c T_b) T_a T_d T_b))) (forall ((V_com1_H $$unsorted) (V_com2_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OSemi V_com1_H V_com2_H)))) (forall ((V_n $$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 ((V_less__eq $$unsorted) (V_i $$unsorted) (V_k $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatMost V_less__eq V_k T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_c))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_A)))))) (forall ((V_Q $$unsorted) (V_xd $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_Q V_xd)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xd) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a)) V_A))))) (forall ((V_P $$unsorted) (V_xe $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (V_Q $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP V_P V_xe)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_xe) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 V_A V_P V_Q T_a)) V_A))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (V_P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__XballE__1__1 V_A V_P T_a)))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_x))) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.hAPP _let_1 V_B)) (tptp.hBOOL (tptp.hAPP _let_1 V_A)) (= V_A V_B)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XbexI__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A))) (not (tptp.hBOOL (tptp.hAPP V_P V_x)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_a) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_b (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_x)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A)))))) (forall ((T_b $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_in T_b) V_b))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP V_B V_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A)))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThan V_less V_k T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_k) V_i))))) (forall ((V_less $$unsorted) (V_k $$unsorted) (V_i $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_k) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OgreaterThan V_less V_k T_a)))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 V_A V_B V_P T_b T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) (tptp.hAPP V_B V_x)))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_A))))) (forall ((T_b $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_a) (tptp.c_Set_Ovimage V_f V_B T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_a)) V_B))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_B)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_B T_a T_b)))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) (tptp.c_Set_Ovimage V_f V_A T_a T_b)))))) (forall ((V_less__eq $$unsorted) (V_Inf $$unsorted) (V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_Sup $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq (tptp.hAPP V_Inf V_A)) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_x $$unsorted) (V_Sup $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_Inf $$unsorted) (V_less $$unsorted) (V_inf $$unsorted) (V_sup $$unsorted) (V_bot $$unsorted) (V_top $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_x) (tptp.hAPP V_Sup V_A))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))) (not (tptp.c_Complete__Lattice_Ocomplete__lattice V_Inf V_Sup V_less__eq V_less V_inf V_sup V_bot V_top T_a)))) (forall ((V_less__eq $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (T_a $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_i) V_u)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a)))))) (forall ((V_less__eq $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastAtMost V_less__eq V_l V_u T_a)))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_B))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_xa $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 V_A V_B V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_xa))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_xa) V_A))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__XbexE__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((T_a $$unsorted) (V_i $$unsorted) (V_less $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OlessThan V_less V_k T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_k))))) (forall ((V_less $$unsorted) (V_i $$unsorted) (V_k $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OlessThan V_less V_k T_a)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_bool))) V_b) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B V_x) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_x) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b (tptp.tc_fun T_c tptp.tc_bool))) V_b) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.hAPP V_B V_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Complete__Lattice_Ocomplete__lattice__class_OSUPR V_A V_B T_a (tptp.tc_fun T_b tptp.tc_bool)) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_B V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_a) V_A))))) (forall ((V_less $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (T_a $$unsorted) (V_less__eq $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less V_i) V_u)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastLessThan V_less__eq V_less V_l V_u T_a)))))) (forall ((V_less__eq $$unsorted) (V_l $$unsorted) (V_i $$unsorted) (T_a $$unsorted) (V_less $$unsorted) (V_u $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_less__eq V_l) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_i) (tptp.c_SetInterval_Oord_OatLeastLessThan V_less__eq V_less V_l V_u T_a)))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_P $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_in T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 V_A V_P T_a)) V_A)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_A)))))) (forall ((V_P $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 V_A V_P T_a))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((T_aa $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_aa) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_aa T_a))))) (forall ((T_b $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_b T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) V_x) V_A))))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_b) (tptp.hAPP V_f V_x)) (tptp.c_Set_Oimage V_f V_A T_a T_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_A))))) (forall ((V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_in tptp.t_a))) (let ((_let_3 (tptp.c_COMBC _let_2 tptp.t_a _let_1 tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_3 V_R) (tptp.hAPP _let_3 V_S) _let_1) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_2 tptp.v_x) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_R V_S _let_1))))))) (forall ((V_R $$unsorted) (V_S $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.t_a tptp.tc_bool))) (let ((_let_2 (tptp.c_in tptp.t_a))) (let ((_let_3 (tptp.c_COMBC _let_2 tptp.t_a _let_1 tptp.tc_bool))) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_3 V_R) (tptp.hAPP _let_3 V_S) _let_1) tptp.v_x) (tptp.hAPP (tptp.hAPP _let_2 tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_R V_S _let_1))))))) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ocomp V_f V_g T_c T_b tptp.t_a) tptp.v_x) (tptp.hAPP V_f (tptp.hAPP V_g tptp.v_x)))) (= (tptp.hAPP (tptp.c_Fun_Oid tptp.t_a) tptp.v_x) tptp.v_x) (forall ((V_f $$unsorted) (V_g $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Fun_Ofcomp V_f V_g tptp.t_a T_c T_b) tptp.v_x) (tptp.hAPP V_g (tptp.hAPP V_f tptp.v_x)))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_pname_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OBODY V_pname_H)))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_b V_s)) (= V_t V_s) (not (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_t)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OSemi V_com1 V_com2)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__case V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OWhile V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP V_f6 V_fun) V_com))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_vname $$unsorted) (V_fun $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OAss V_vname V_fun)))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= tptp.c_Com_Ocom_OSKIP (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_vname $$unsorted) (V_fun $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OAss V_vname V_fun) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_com1 $$unsorted) (V_com2 $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OSemi V_com1 V_com2) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s $$unsorted)) (or (tptp.c_Natural_Oevalc (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_s) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_loc $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OLocal V_loc V_fun V_com)))) (forall ((V_pname_H $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OBODY V_pname_H) (tptp.c_Com_Ocom_OWhile V_fun V_com)))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) tptp.c_Com_Ocom_OSKIP))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s0 $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevalc _let_1 V_s0 V_s2) (not (tptp.c_Natural_Oevalc _let_1 V_s1 V_s2)) (not (tptp.c_Natural_Oevalc V_c V_s0 V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s0)))))) (forall ((V_vname_H $$unsorted) (V_pname_H $$unsorted) (V_fun_H $$unsorted) (V_fun $$unsorted) (V_com $$unsorted)) (not (= (tptp.c_Com_Ocom_OCall V_vname_H V_pname_H V_fun_H) (tptp.c_Com_Ocom_OWhile V_fun V_com)))) (forall ((V_b $$unsorted) (V_c $$unsorted)) (or (tptp.c_Com_OWT (tptp.c_Com_Ocom_OWhile V_b V_c)) (not (tptp.c_Com_OWT V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted)) (or (tptp.c_Com_OWT V_c) (not (tptp.c_Com_OWT (tptp.c_Com_Ocom_OWhile V_b V_c))))) (forall ((V_fun_H $$unsorted) (V_com_H $$unsorted) (V_fun $$unsorted) (V_com1 $$unsorted) (V_com2 $$unsorted)) (not (= (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H) (tptp.c_Com_Ocom_OCond V_fun V_com1 V_com2)))) (forall ((V_f1 $$unsorted) (V_f2 $$unsorted) (V_f3 $$unsorted) (V_f4 $$unsorted) (V_f5 $$unsorted) (V_f6 $$unsorted) (V_f7 $$unsorted) (V_f8 $$unsorted) (V_fun $$unsorted) (V_com $$unsorted) (T_a $$unsorted)) (= (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 (tptp.c_Com_Ocom_OWhile V_fun V_com) T_a) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f6 V_fun) V_com) (tptp.c_Com_Ocom_Ocom__rec V_f1 V_f2 V_f3 V_f4 V_f5 V_f6 V_f7 V_f8 V_com T_a)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_c1 $$unsorted) (V_b $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s V_n V_t) (tptp.c_Natural_Oevaln V_c1 V_s V_n V_t) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_m $$unsorted) (V_t $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevaln V_c V_s V_m V_t) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_t)))) (forall ((V_s $$unsorted) (V_n $$unsorted)) (tptp.c_Natural_Oevaln tptp.c_Com_Ocom_OSKIP V_s V_n V_s)) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_n V_s1) (not (tptp.c_Natural_Oevaln V_c1 V_s V_n V_s1)) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((V_c2 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_b $$unsorted) (V_c1 $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s V_n V_t) (tptp.hBOOL (tptp.hAPP V_b V_s)) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s_H $$unsorted)) (or (tptp.c_Natural_Oevaln V_c V_s (tptp.c_Suc V_n) V_s_H) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_s_H)))) (forall ((V_c2 $$unsorted) (V_s2 $$unsorted) (V_c1 $$unsorted) (V_s1 $$unsorted) (V_t1 $$unsorted) (V_t2 $$unsorted) (V_n2 $$unsorted) (V_n1 $$unsorted)) (or (tptp.c_Natural_Oevaln V_c2 V_s2 (tptp.c_Natural_Osko__Natural__Xevaln__max2__1__1 V_c1 V_c2 V_s1 V_s2 V_t1 V_t2) V_t2) (not (tptp.c_Natural_Oevaln V_c2 V_s2 V_n2 V_t2)) (not (tptp.c_Natural_Oevaln V_c1 V_s1 V_n1 V_t1)))) (forall ((V_c1 $$unsorted) (V_s1 $$unsorted) (V_c2 $$unsorted) (V_s2 $$unsorted) (V_t1 $$unsorted) (V_t2 $$unsorted) (V_n2 $$unsorted) (V_n1 $$unsorted)) (or (tptp.c_Natural_Oevaln V_c1 V_s1 (tptp.c_Natural_Osko__Natural__Xevaln__max2__1__1 V_c1 V_c2 V_s1 V_s2 V_t1 V_t2) V_t1) (not (tptp.c_Natural_Oevaln V_c2 V_s2 V_n2 V_t2)) (not (tptp.c_Natural_Oevaln V_c1 V_s1 V_n1 V_t1)))) (forall ((V_b $$unsorted) (V_c0 $$unsorted) (V_c1 $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c0 V_c1) V_s V_n V_s1) (not (tptp.c_Natural_Oevaln V_c0 V_s V_n V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s))))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_c1 $$unsorted) (V_n $$unsorted) (V_t $$unsorted) (V_c2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (tptp.c_Natural_Oevaln V_c1 V_s V_n V_t) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OCond V_b V_c1 V_c2) V_s V_n V_t)))) (forall ((V_c0 $$unsorted) (V_c1 $$unsorted) (V_s0 $$unsorted) (V_n $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OSemi V_c0 V_c1) V_s0 V_n V_s2) (not (tptp.c_Natural_Oevaln V_c1 V_s1 V_n V_s2)) (not (tptp.c_Natural_Oevaln V_c0 V_s0 V_n V_s1)))) (forall ((V_t $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (or (= V_t V_s) (not (tptp.c_Natural_Oevaln tptp.c_Com_Ocom_OSKIP V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevalc V_c V_s V_t) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_t)))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_x $$unsorted)) (or (tptp.c_Natural_Oevalc V_c V_s V_t) (not (tptp.c_Natural_Oevaln V_c V_s V_x V_t)))) (= (tptp.hAPP (tptp.c_COMBI tptp.t_a) tptp.v_P) tptp.v_P) (forall ((V_n $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_t T_a) (not (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_Suc V_n) V_t T_a)))) (forall ((V_n $$unsorted) (V_na $$unsorted) (V_ts $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)))) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_na tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_na) V_ts))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 V_G V_n)) V_G)) (not (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a))))) (forall ((V_n $$unsorted) (V_xa $$unsorted) (V_ts $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_xa tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_xa) V_ts))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.c_Suc V_n) (tptp.v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 V_n V_ts) tptp.t_a)))) (forall ((V_G $$unsorted) (V_ts $$unsorted) (V_x $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a) (tptp.c_Hoare__Mirabelle_Otriple__valid (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 V_G V_ts) V_x tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_x) V_G))))) (forall ((V_n $$unsorted) (V_nb $$unsorted) (V_ts $$unsorted) (V_G $$unsorted)) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_nb tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) V_nb) V_ts))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid V_n (tptp.v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 V_G V_n) tptp.t_a)) (not (tptp.c_Hoare__Mirabelle_Ohoare__valids V_G V_ts tptp.t_a)))) (= (tptp.hAPP _let_18 tptp.v_x) (tptp.hAPP (tptp.hAPP (tptp.c_in tptp.t_a) tptp.v_x) _let_18)) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_n $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevaln _let_1 (tptp.c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 V_b V_c V_n V_s V_t) V_n V_t) (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (not (tptp.c_Natural_Oevaln _let_1 V_s V_n V_t))))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_b $$unsorted) (V_t $$unsorted)) (or (tptp.c_Natural_Oevaln V_c V_s V_n (tptp.c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 V_b V_c V_n V_s V_t)) (= V_t V_s) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_t)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_n $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevaln _let_1 (tptp.c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 V_b V_c V_n V_s V_t) V_n V_t) (= V_t V_s) (not (tptp.c_Natural_Oevaln _let_1 V_s V_n V_t))))) (forall ((V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_b $$unsorted) (V_t $$unsorted)) (or (tptp.c_Natural_Oevaln V_c V_s V_n (tptp.c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1 V_b V_c V_n V_s V_t)) (not (tptp.hBOOL (tptp.hAPP V_b V_s))) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_t)))) (forall ((V_Q $$unsorted) (V_Z $$unsorted) (V_s_H $$unsorted) (V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted) (V_P $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_Q V_Z) V_s_H)) (not (tptp.c_Natural_Oevaln V_c V_s V_n V_s_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_Z) V_s))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid V_n (tptp.c_Hoare__Mirabelle_Otriple_Otriple V_P V_c V_Q tptp.t_a) tptp.t_a)))) (forall ((V_n $$unsorted) (V_x $$unsorted) (V_ts $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)))) (or (tptp.c_Hoare__Mirabelle_Otriple__valid V_n V_x tptp.t_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ts))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 V_n V_ts)) V_ts))))) (forall ((V_b $$unsorted) (V_s $$unsorted) (V_t $$unsorted) (V_c $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_b V_s)) (= V_t V_s) (not (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_t)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s $$unsorted) (V_n $$unsorted)) (or (tptp.c_Natural_Oevaln (tptp.c_Com_Ocom_OWhile V_b V_c) V_s V_n V_s) (tptp.hBOOL (tptp.hAPP V_b V_s)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_S $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in T_a) V_x) V_S))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_s0 $$unsorted) (V_n $$unsorted) (V_s2 $$unsorted) (V_s1 $$unsorted)) (let ((_let_1 (tptp.c_Com_Ocom_OWhile V_b V_c))) (or (tptp.c_Natural_Oevaln _let_1 V_s0 V_n V_s2) (not (tptp.c_Natural_Oevaln _let_1 V_s1 V_n V_s2)) (not (tptp.c_Natural_Oevaln V_c V_s0 V_n V_s1)) (not (tptp.hBOOL (tptp.hAPP V_b V_s0)))))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H))) (= V_fun V_fun_H))) (forall ((V_fun $$unsorted) (V_com $$unsorted) (V_fun_H $$unsorted) (V_com_H $$unsorted)) (or (not (= (tptp.c_Com_Ocom_OWhile V_fun V_com) (tptp.c_Com_Ocom_OWhile V_fun_H V_com_H))) (= V_com V_com_H))) _let_17 _let_16 (tptp.c_Natural_Oevaln _let_15 tptp.v_s1 tptp.v_na tptp.v_s2) _let_14 _let_13 _let_12 _let_11 _let_10 (forall ((V_Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Z))) (or (not (= tptp.v_ca (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s0))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) tptp.v_x) tptp.v_G))))) (forall ((V_Z $$unsorted)) (or (not (= tptp.v_ca (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (not (tptp.hBOOL (tptp.hAPP tptp.v_b tptp.v_s1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_Z) tptp.v_s0))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_in (tptp.tc_Hoare__Mirabelle_Otriple tptp.t_a)) tptp.v_x) tptp.v_G)))) (forall ((V_Za $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.v_P V_Za))) (or (not (= tptp.v_ca (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.v_s0))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na tptp.v_x tptp.t_a))))) (forall ((V_Za $$unsorted)) (or (not (= tptp.v_ca (tptp.c_Com_Ocom_OWhile tptp.v_b tptp.v_c))) (not (tptp.hBOOL (tptp.hAPP tptp.v_b tptp.v_s1))) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.v_P V_Za) tptp.v_s0))) (not (tptp.c_Hoare__Mirabelle_Otriple__valid tptp.v_na tptp.v_x tptp.t_a)))) _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_HOL_Ominus (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Ominus T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Ominus tptp.tc_nat) (tptp.class_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Ominus tptp.tc_bool) (forall ((V_x $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.63/4.90 )
% 4.63/4.91 % SZS output end Proof for SWV849-1
% 4.63/4.92 % cvc5---1.0.5 exiting
% 4.63/4.92 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------