%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV734-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 21:53:06 EDT 2023

% Result   : Unsatisfiable 2.54s 2.79s
% Output   : Proof 2.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.16  % Problem    : SWV734-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.17  % Command    : do_cvc5 %s %d
% 0.16/0.38  % Computer : n002.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 06:13:50 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/sandbox2/tmp/tmp.lNZe1RYECS/cvc5---1.0.5_31965.p...
% 0.23/0.64  ------- get file name : TPTP file name is SWV734-1
% 0.23/0.64  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31965.smt2...
% 0.23/0.65  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.54/2.79  % SZS status Unsatisfiable for SWV734-1
% 2.54/2.79  % SZS output start Proof for SWV734-1
% 2.54/2.80  (
% 2.54/2.80  (let ((_let_1 (tptp.class_Lattices_Olattice tptp.tc_bool))) (let ((_let_2 (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)))))) (let ((_let_3 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evsf))) (let ((_let_4 (tptp.c_Message_Oparts _let_3))) (let ((_let_5 (tptp.c_Message_Omsg_OCrypt tptp.v_KAB tptp.v_X))) (let ((_let_6 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_7 (tptp.c_Orderings_Obot__class_Obot _let_6))) (let ((_let_8 (tptp.c_Set_Oinsert tptp.v_X _let_7 tptp.tc_Message_Omsg))) (let ((_let_9 (tptp.c_Message_Oparts _let_8))) (let ((_let_10 (tptp.hAPP tptp.c_Message_Omsg_OKey tptp.v_K))) (let ((_let_11 (tptp.c_in _let_10 _let_9 tptp.tc_Message_Omsg))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.c_Set_Oinsert tptp.v_Xa _let_3 tptp.tc_Message_Omsg))) (let ((_let_14 (tptp.c_Message_Oparts _let_13))) (let ((_let_15 (tptp.c_in _let_10 _let_14 tptp.tc_Message_Omsg))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.c_in _let_5 _let_14 tptp.tc_Message_Omsg))) (let ((_let_18 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_19 (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg))))))) (let ((_let_20 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))))) (let ((_let_21 (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))))) (let ((_let_22 (forall ((V_a $$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)))))) (let ((_let_23 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))))) (let ((_let_24 (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oparts V_H))) (or (tptp.c_lessequals (tptp.c_Message_Oparts V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))))) (let ((_let_25 (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (let ((_let_26 (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))))) (let ((_let_27 (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent))) (let ((_let_28 (tptp.c_in tptp.v_X _let_14 tptp.tc_Message_Omsg))) (let ((_let_29 (tptp.c_lessequals _let_8 _let_14 _let_6))) (let ((_let_30 (not _let_28))) (let ((_let_31 (tptp.c_lessequals _let_7 _let_14 _let_6))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_29 _let_32 _let_30))) (let ((_let_34 (not _let_17))) (let ((_let_35 (or _let_28 _let_34))) (let ((_let_36 (_let_19))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (not _let_29))) (let ((_let_39 (tptp.c_lessequals _let_9 _let_14 _let_6))) (let ((_let_40 (or _let_39 _let_38))) (let ((_let_41 (_let_24))) (let ((_let_42 (ASSUME :args _let_41))) (let ((_let_43 (not _let_39))) (let ((_let_44 (or _let_15 _let_12 _let_43))) (let ((_let_45 (_let_21))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (_let_23))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (tptp.c_Set_Oinsert tptp.v_Xa _let_7 tptp.tc_Message_Omsg))) (let ((_let_50 (tptp.c_lessequals _let_49 _let_14 _let_6))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_31 _let_51))) (let ((_let_53 (_let_26))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_49 _let_3 _let_6))) (let ((_let_56 (tptp.c_lessequals _let_55 _let_14 _let_6))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.class_Lattices_Oupper__semilattice _let_6))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_59 _let_50 _let_57))) (let ((_let_61 (_let_20))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (= _let_13 _let_55))) (let ((_let_64 (tptp.c_lessequals _let_13 _let_14 _let_6))) (let ((_let_65 (_let_22))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (_let_25))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (and _let_64 _let_63))) (let ((_let_70 (_let_64 _let_63))) (let ((_let_71 (ASSUME :args (_let_64)))) (let ((_let_72 (ASSUME :args (_let_63)))) (let ((_let_73 (not _let_1))) (let ((_let_74 (or _let_58 _let_73))) (let ((_let_75 (_let_2))) (let ((_let_76 (ASSUME :args _let_75))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_30 _let_29 _let_32 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_31 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_59 _let_57 _let_50 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_73 _let_58 (not _let_74)))) (ASSUME :args (_let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (tptp.tc_Message_Omsg tptp.tc_bool QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.tc_fun T_2 T_1)))) :args _let_75)) _let_76 :args (_let_74 false _let_2)) :args (_let_58 false _let_1 false _let_74)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_69)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_71 _let_72) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_72) (REFL :args (_let_14)) (REFL :args (_let_6)) :args (APPLY_UF tptp.c_lessequals)) (TRUE_INTRO _let_71))) :args _let_70)) :args _let_70)) :args (true _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Message_Oparts V_H)))) :args _let_67)) _let_68 :args (_let_64 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (tptp.v_Xa _let_3 tptp.tc_Message_Omsg QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Set_Oinsert V_a V_A T_a)))) :args _let_65)) _let_66 :args (_let_63 false _let_22)) :args (_let_56 false _let_64 false _let_63)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_6 _let_49 _let_14 _let_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) false))))) :args _let_61)) _let_62 :args (_let_60 false _let_20)) :args (_let_50 false _let_58 false _let_56 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_7 _let_14 tptp.tc_Message_Omsg tptp.v_Xa QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) false))))) :args _let_53)) _let_54 :args (_let_52 false _let_26)) :args (_let_31 false _let_50 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.v_X _let_7 tptp.tc_Message_Omsg _let_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool)) true))))) :args _let_47)) _let_48 :args (_let_33 false _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_38 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_15 _let_12 _let_43 (not _let_44)))) (ASSUME :args (_let_16)) (ASSUME :args (_let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_10 _let_14 tptp.tc_Message_Omsg _let_9 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in V_x V_B T_a) true)) (not (= (tptp.c_in V_x V_A T_a) false))))) :args _let_45)) _let_46 :args (_let_44 false _let_21)) :args (_let_43 true _let_15 false _let_11 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_8 _let_13 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_6) true))))) :args _let_41)) _let_42 :args (_let_40 false _let_24)) :args (_let_38 true _let_39 false _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_28 (not _let_35)))) (ASSUME :args (_let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.v_X _let_13 tptp.v_KAB QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) false))))) :args _let_36)) _let_37 :args (_let_35 false _let_19)) :args (_let_28 false _let_17 false _let_35)) :args (false false _let_31 false _let_33 true _let_29 false _let_28)) :args ((forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (not (= (tptp.c_Orderings_Otop__class_Otop _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (forall ((V_K $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_AA $$unsorted)) (not (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_b) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_x $$unsorted) (V_AA $$unsorted)) (or (tptp.c_in V_x V_AA tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_AA $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat) (not (tptp.c_in V_x V_AA tptp.tc_Message_Oagent)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) T_a)) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (not (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (or (= V_b V_c) (not (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_AA $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (tptp.c_in V_x V_AA tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_AA $$unsorted)) (let ((_let_1 (tptp.c_Public_OpublicKey V_x))) (or (tptp.c_in (tptp.hAPP _let_1 V_xa) (tptp.c_Set_Oimage _let_1 V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat) (not (tptp.c_in V_xa V_AA tptp.tc_Message_Oagent))))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_AA $$unsorted)) (not (tptp.c_in (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Otop__class_Otop T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((V_K $$unsorted)) (or (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat) (not (tptp.c_in (tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat)))) (forall ((V_K $$unsorted)) (or (tptp.c_in (tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat) (not (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)))) (forall ((V_K $$unsorted)) (or (= (tptp.c_Message_OinvKey V_K) V_K) (not (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) V_x))) (forall ((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_Otop__class_Otop _let_1) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Orderings_Otop__class_Otop _let_1) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Otop T_a)) (tptp.c_lessequals V_x (tptp.c_Orderings_Otop__class_Otop T_a) T_a))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.c_in (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_X $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_X) tptp.c_Message_OsymKeys tptp.tc_nat)) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.c_in V_K (tptp.c_Message_OkeysFor V_H) tptp.tc_nat) (not (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) V_H tptp.tc_Message_Omsg)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (not (tptp.c_in (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage tptp.c_Public_OshrK V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (forall ((V_A $$unsorted)) (not (tptp.c_in (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption) V_A)) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f V_A T_b T_a))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$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 ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a))) (forall ((V_f $$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 $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a) (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_x) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (not (tptp.c_in V_x V_A tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_A tptp.tc_nat) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_x) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_K V_X_H) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_msg1 $$unsorted) (V_msg2 $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2)))) (forall ((V_agent $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H)))) (forall ((V_nat_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Set_Oinsert V_a (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) T_a) V_A) (not (tptp.c_in V_a V_A T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_A) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_B $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_A $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_evs $$unsorted)) (or (not (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) tptp.tc_nat)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (not (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A V_A _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_A _let_1) _let_2)))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= V_A (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_a T_b) T_b) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a) (not (tptp.c_in V_x V_A T_b)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_b)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_in V_x V_A T_aa)) (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_c V_A T_a) (not (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.c_in V_c V_B T_a)) (not (tptp.c_in V_c (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OMPair V_X V_Y) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg)))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_X) (not (tptp.c_Message_Oanalzp V_H (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_H $$unsorted) (V_Y $$unsorted) (V_X $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_Y) (not (tptp.c_Message_Oanalzp V_H (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H) (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg)))) (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_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1)))) (forall ((V_B $$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_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_xa T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_A $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OAgent V_A) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg2 V_msg2_H))) (forall ((V_msg1 $$unsorted) (V_msg2 $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H))) (= V_msg1 V_msg1_H))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_A _let_1))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) _let_1) (tptp.c_Set_Oimage V_f (tptp.c_HOL_Ominus__class_Ominus V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((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 ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1))) (= (tptp.c_HOL_Ominus__class_Ominus _let_2 V_B _let_1) _let_2)))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_X_H V_X))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_Y_H V_Y))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_X_H $$unsorted) (V_Y_H $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H))) (= V_Y_H V_Y))) (forall ((V_agent $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (tptp.c_NS__Shared__Mirabelle_Ons__sharedp _let_27) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_OGets V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_D V_B _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OGets V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_agent V_agent_H))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (= (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)) (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))) (forall ((V_agent_H $$unsorted) (V_msg_H $$unsorted) (V_agent $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H) (tptp.c_Event_Oevent_OGets V_agent V_msg)))) (forall ((V_A $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) (tptp.c_Event_OinitState V_A))) (forall ((V_H $$unsorted) (V_X $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_X) (not (tptp.hBOOL (tptp.hAPP V_H V_X))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus V_B (tptp.c_HOL_Ominus__class_Ominus V_C V_A _let_1) _let_1) V_A) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((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_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_OHPair V_X V_Y) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_B $$unsorted)) (or (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_a T_b) (tptp.c_Set_Oimage V_f V_B T_a T_b) (tptp.tc_fun T_b tptp.tc_bool)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.c_lessequals V_x V_A (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_x T_b T_a) (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_f $$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_agent $$unsorted) (V_agent_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OAgent V_agent_H))) (= V_agent V_agent_H))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_2 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_K (tptp.c_Message_OkeysFor _let_1) tptp.tc_nat))))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.c_in (tptp.c_Message_OinvKey V_K) (tptp.c_Message_OkeysFor V_H) tptp.tc_nat) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) V_H tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_Set_Oinsert V_x (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) T_a)) (tptp.c_in V_x V_B T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.c_in V_x V_A T_a))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1)) (not (tptp.c_in V_x V_B T_a))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a) (not (tptp.c_in V_x V_A T_b)) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_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) (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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_HOL_Ominus__class_Ominus V_B V_A _let_1) _let_1) V_B) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_H $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (tptp.c_in (tptp.c_Message_Omsg_OAgent V_agt) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_N $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_N tptp.tc_nat tptp.tc_Message_Omsg))) (= (tptp.c_Message_Oparts _let_1) _let_1))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_agt))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_C))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_Y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X_H V_Y))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_N $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_N tptp.tc_nat tptp.tc_Message_Omsg))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_agt))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_K $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_C))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (not (tptp.c_in V_K V_nE tptp.tc_nat))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg) (not (tptp.c_in V_K V_nE tptp.tc_nat)) (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg))) (or _let_1 (not (tptp.c_in V_K V_nE tptp.tc_nat)) _let_1))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (not (tptp.c_in V_K V_nE tptp.tc_nat)))) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg) _let_1 _let_1))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_OinitState V_A) (tptp.c_Event_Oknows V_A V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) (tptp.c_Event_Oused V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oused V_evs))) (tptp.c_in _let_27 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_18) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (or (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_OinitState V_B) tptp.tc_Message_Omsg)) (forall ((V_K $$unsorted) (V_X $$unsorted)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) tptp.tc_Message_Omsg))) (forall ((V_H $$unsorted) (V_X $$unsorted) (V_K $$unsorted)) (or (tptp.c_Message_Oanalzp V_H V_X) (not (tptp.c_Message_Oanalzp V_H (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)))) (not (tptp.c_Message_Oanalzp V_H (tptp.c_Message_Omsg_OCrypt V_K V_X))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (forall ((V_A $$unsorted) (V_B $$unsorted)) (not (= (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey tptp.c_Public_Okeymode_OEncryption) V_A)) (tptp.hAPP tptp.c_Public_OshrK V_B)))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A_H V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A_H V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_A (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) _let_1) V_B _let_1) (not (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg))) (or _let_2 (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) _let_2)))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (or (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg) _let_2 _let_2)))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_G $$unsorted) (V_X $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) tptp.tc_nat) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg)) (not (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg))) tptp.tc_nat)))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (forall ((V_X $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_X (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A)))) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Event_Oused V_evs) _let_1)))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (or (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent)) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg)) (not (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evsf)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (= V_A _let_2) (not (tptp.c_lessequals V_A _let_2 _let_1)))))) (forall ((V_A $$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_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot _let_1) V_A _let_1))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((V_a $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_a V_C T_a) (tptp.c_Set_Oinsert V_a V_D T_a) _let_1) (not (tptp.c_lessequals V_C V_D _let_1))))) (forall ((V_B $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_B (tptp.c_Set_Oinsert V_a V_B T_a) (tptp.tc_fun T_a tptp.tc_bool))) (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_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 $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) _let_26 (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1)))) _let_25 (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) _let_24 (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oparts V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oparts V_G) _let_2 _let_1)))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) _let_2 _let_1)))))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Oanalz V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz V_G) V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1))))) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_G $$unsorted) (V_G_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (not (= (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_G_H))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G_H V_H_H _let_1)))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Osynth V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Osynth V_G) (tptp.c_Message_Osynth V_H) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1) (not (tptp.c_lessequals V_G _let_2 _let_1)))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_H))) (or (tptp.c_lessequals V_G _let_2 _let_1) (not (tptp.c_lessequals (tptp.c_Message_Osynth V_G) _let_2 _let_1)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C)))) (forall ((V_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C) (tptp.hAPP tptp.c_Public_OshrK V_A)))) (forall ((V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Public_OshrK V_A))) (= (tptp.c_Message_OinvKey _let_1) _let_1))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) _let_1) (not (tptp.c_in V_X V_G tptp.tc_Message_Omsg))))) (forall ((V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.c_Event_Oused V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))) _let_23 (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.c_in V_x V_A T_a) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.c_in V_x V_A T_a)))) (forall ((V_A $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (let ((_let_3 (tptp.c_Set_Oinsert V_x _let_2 T_a))) (or (= V_A _let_3) (= V_A _let_2) (not (tptp.c_lessequals V_A _let_3 _let_1))))))) _let_22 (forall ((V_H $$unsorted) (V_X $$unsorted)) (or (tptp.c_in (tptp.c_Message_Osko__Message__Xparts__singleton__1__1 V_H V_X) V_H tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_G $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Osynth V_G) tptp.tc_Message_Omsg))))) (forall ((V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_G)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_2)) _let_2) _let_2) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Oparts _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_H) _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_G))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_2 _let_1))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Oanalz _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz V_H) _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_G)) (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) _let_1) (not (tptp.c_lessequals V_G V_H _let_1))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent))) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_evs))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_2) tptp.tc_Message_Omsg)) _let_1 _let_2) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) _let_2) _let_2) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_Y $$unsorted) (V_G $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.c_in V_Y (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (not (tptp.c_in V_Y (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz V_G)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_B $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_B)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (tptp.c_lessequals _let_2 _let_2 _let_1)))) (forall ((T_a $$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 ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$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 $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$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 ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (tptp.c_in V_c V_A T_a) (not (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_in V_c V_B T_a)))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a) (not (tptp.c_in V_c V_A T_a)))) _let_21 (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_c V_B T_a) (not (tptp.c_in V_c V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_x V_B T_a) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_in V_x V_A T_a)))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.c_in V_t V_B T_a) (not (tptp.c_in V_t V_A T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Event_Oused (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Event_Oused V_evs) _let_1)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A_H V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((T_a $$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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((V_A $$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 $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_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 ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((V_A $$unsorted) (V_evs $$unsorted) (V_e $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons V_e V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$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 ((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_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 $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) 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T_a tptp.tc_bool))) (tptp.c_lessequals V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_1))) (forall ((V_B $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (tptp.c_lessequals V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A 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))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_C _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_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_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 ((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 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _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 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_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 ((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 ((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_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H))) (= V_b V_c))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP 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$$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Osynth V_G) (tptp.c_Message_Osynth V_H) _let_1) (tptp.c_Message_Osynth (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (= V_A V_B) (not (tptp.c_lessequals V_B V_A _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or 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(tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_in tptp.c_Message_Oagent_OSpy tptp.c_Event_Obad tptp.tc_Message_Oagent) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_D _let_1) _let_1) (not (tptp.c_lessequals V_B V_D _let_1)) (not (tptp.c_lessequals V_A V_C _let_1))))) (forall ((V_K $$unsorted)) (= (tptp.c_Message_OinvKey (tptp.c_Message_OinvKey V_K)) V_K)) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent2 V_agent2_H))) (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent1 V_agent1_H))) (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)))) _let_20 (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 ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _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))) (or (tptp.c_lessequals V_B V_C _let_1) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1))))) (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_x $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_x V_x (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (tptp.c_lessequals V_A V_A (tptp.tc_fun T_a tptp.tc_bool))) (forall ((V_A $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_C _let_1) (not (tptp.c_lessequals V_B V_C _let_1)) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_Q $$unsorted) (V_x $$unsorted) (V_P $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_Q V_x)) (not (tptp.c_lessequals V_P V_Q (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_a V_a_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_C $$unsorted)) (not (= (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C))))) (forall ((V_b $$unsorted) (V_C $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_C)) (tptp.hAPP tptp.c_Public_OshrK V_A)))) (forall ((V_G $$unsorted) (V_H $$unsorted) (V_G_H $$unsorted) (V_H_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G_H V_H_H _let_1)) _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H) _let_1)) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_G_H) _let_1))))) (forall ((V_c $$unsorted) (V_A_H $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H) (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) V_X) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (let ((_let_2 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_2) tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) _let_2) _let_2) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts V_H) _let_1)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_Y _let_2 tptp.tc_Message_Omsg)) _let_1) (tptp.c_Message_Oparts V_H) _let_1))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (or (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg)) (not (tptp.c_in V_evsf tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_c (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Set_Oinsert (tptp.c_Message_Osko__Message__Xparts__singleton__1__1 V_H V_X) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows V_A V_evs))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts _let_2) _let_1))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg) (not (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_2 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.tc_Message_Omsg)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))))) (forall ((V_Z $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_Z (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_1 (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_Z (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_G $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X _let_2 tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) (tptp.c_Message_Oparts _let_2) _let_1))))) (forall ((V_c $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 (tptp.c_Message_Oparts V_H) _let_1) tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)) (not (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Orderings_Obot__class_Obot _let_1) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg)))) (forall ((V_H $$unsorted)) (= (tptp.c_Message_Oparts (tptp.c_Message_Oanalz V_H)) (tptp.c_Message_Oparts V_H))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_X $$unsorted)) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H_H tptp.tc_Message_Omsg))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a) (not (tptp.c_in V_a V_B T_a)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (= (tptp.c_Message_Oanalz _let_7) _let_7) (forall ((V_x $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P V_x)) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_c (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (not (tptp.c_in V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oparts _let_1) _let_1))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_in V_a V_A T_a) (= V_a V_b) (not (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_K_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_X V_K_H))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))))) _let_19 (forall ((V_X $$unsorted) (V_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.hAPP tptp.c_Public_OshrK V_A))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey _let_2) _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_2 V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H))) (= V_nat V_nat_H))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_Y (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_in V_Y (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (= V_b V_a) (not (tptp.c_in V_b (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a)))) (forall ((V_X $$unsorted)) (not (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_A T_a) T_a)) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a)) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a)) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.c_in V_x V_S T_a) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.c_in V_x V_S T_a)))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_nat V_nat_H))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_a $$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_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_P $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_in V_x (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_xa T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (tptp.c_in V_x V_xa T_a))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.c_in V_x V_B T_a) (tptp.c_in V_x V_A T_a) (= V_A V_B))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X V_H tptp.tc_Message_Omsg)))) (= (tptp.c_Message_Oparts _let_7) _let_7) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg) (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Osynth _let_1) tptp.tc_Message_Omsg))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.c_in V_a V_A T_a)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (= (tptp.c_Message_Osynth _let_1) _let_1))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg) (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg) (not (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg) (not (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (= (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg))) _let_1) (not (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.hAPP tptp.c_Public_OshrK V_y))) (= V_x V_y))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (not (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted)) (not (= tptp.v_Kab (tptp.hAPP tptp.c_Public_OshrK V_x)))) (tptp.c_in tptp.v_evsf tptp.c_NS__Shared__Mirabelle_Ons__shared _let_18) (tptp.c_in tptp.v_Xa (tptp.c_Message_Osynth (tptp.c_Message_Oanalz _let_3)) tptp.tc_Message_Omsg) _let_17 _let_11 _let_16 (or (tptp.c_in _let_10 _let_4 tptp.tc_Message_Omsg) _let_12 (not (tptp.c_in _let_5 _let_4 tptp.tc_Message_Omsg))) _let_2 (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Orderings_Otop (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Otop T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) _let_1 (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.54/2.80  )
% 2.62/2.81  % SZS output end Proof for SWV734-1
% 2.62/2.81  % cvc5---1.0.5 exiting
% 2.62/2.82  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------