TSTP Solution File: SWV761-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV761-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 21:53:12 EDT 2023
% Result : Unsatisfiable 28.68s 28.93s
% Output : Proof 28.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.17 % Problem : SWV761-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.18 % Command : do_cvc5 %s %d
% 0.19/0.39 % Computer : n017.cluster.edu
% 0.19/0.39 % Model : x86_64 x86_64
% 0.19/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.39 % Memory : 8042.1875MB
% 0.19/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40 % CPULimit : 300
% 0.19/0.40 % WCLimit : 300
% 0.19/0.40 % DateTime : Tue Aug 29 04:40:58 EDT 2023
% 0.19/0.40 % CPUTime :
% 0.26/0.58 %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.59 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.D6ZUWtp8Sb/cvc5---1.0.5_23808.p...
% 0.52/0.70 ------- get file name : TPTP file name is SWV761-1
% 0.52/0.70 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23808.smt2...
% 0.52/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.73/10.95 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.78/16.01 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.89/21.07 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.85/26.10 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.68/28.93 % SZS status Unsatisfiable for SWV761-1
% 28.68/28.93 % SZS output start Proof for SWV761-1
% 28.68/28.95 (
% 28.68/28.95 (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy tptp.v_evsf))) (let ((_let_2 (tptp.c_Message_Oanalz _let_1))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey tptp.v_K))) (let ((_let_4 (tptp.hBOOL (tptp.c_in _let_3 _let_2 tptp.tc_Message_Omsg)))) (let ((_let_5 (tptp.c_List_Oset tptp.v_evsf tptp.tc_Event_Oevent))) (let ((_let_6 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK tptp.v_A) (tptp.c_Message_Omsg_OMPair tptp.v_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent tptp.v_B) (tptp.c_Message_Omsg_OMPair _let_3 tptp.v_X)))))) (let ((_let_7 (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer tptp.v_A _let_6))) (let ((_let_8 (tptp.hBOOL (tptp.c_in _let_7 _let_5 tptp.tc_Event_Oevent)))) (let ((_let_9 (tptp.c_Message_Oparts _let_1))) (let ((_let_10 (tptp.c_Message_Omsg_ONonce tptp.v_NB))) (let ((_let_11 (tptp.c_Message_Omsg_OCrypt tptp.v_K _let_10))) (let ((_let_12 (tptp.hBOOL (tptp.c_in _let_11 _let_9 tptp.tc_Message_Omsg)))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.c_Event_Oevent_OSays tptp.v_x tptp.v_B tptp.v_X))) (let ((_let_15 (tptp.hBOOL (tptp.c_in _let_14 _let_5 tptp.tc_Event_Oevent)))) (let ((_let_16 (or _let_15 _let_13 (not _let_8) _let_4))) (let ((_let_17 (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_x tptp.v_B tptp.v_X) (tptp.c_List_Oset (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy tptp.v_Ba tptp.v_Xa) tptp.v_evsf tptp.tc_Event_Oevent) tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (let ((_let_18 (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy tptp.v_Ba tptp.v_Xa))) (let ((_let_19 (tptp.c_List_Olist_OCons _let_18 tptp.v_evsf tptp.tc_Event_Oevent))) (let ((_let_20 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy _let_19))) (let ((_let_21 (tptp.c_Message_Oparts _let_20))) (let ((_let_22 (tptp.hBOOL (tptp.c_in _let_11 _let_21 tptp.tc_Message_Omsg)))) (let ((_let_23 (tptp.c_List_Oset _let_19 tptp.tc_Event_Oevent))) (let ((_let_24 (tptp.hBOOL (tptp.c_in _let_7 _let_23 tptp.tc_Event_Oevent)))) (let ((_let_25 (tptp.c_Message_Oanalz _let_20))) (let ((_let_26 (tptp.hBOOL (tptp.c_in _let_3 _let_25 tptp.tc_Message_Omsg)))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.c_Message_Osynth _let_2))) (let ((_let_29 (tptp.hBOOL (tptp.c_in tptp.v_Xa _let_28 tptp.tc_Message_Omsg)))) (let ((_let_30 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_31 (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)))))) (let ((_let_32 (forall ((V_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (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.hBOOL (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)))))) (let ((_let_33 (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg))))))) (let ((_let_34 (= tptp.c_Message_Oagent_OSpy tptp.c_Message_Oagent_OServer))) (let ((_let_35 (not _let_34))) (let ((_let_36 (forall ((V_y $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_y (tptp.c_List_Oset V_xs T_a) T_a)) (= V_y V_x) (not (tptp.hBOOL (tptp.c_in V_y (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) T_a))))))) (let ((_let_37 (forall ((V_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent1_H $$unsorted) (V_agent2_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_agent1 V_agent1_H))))) (let ((_let_38 (forall ((V_H $$unsorted)) (= (tptp.c_Message_Oparts (tptp.c_Message_Oanalz V_H)) (tptp.c_Message_Oparts V_H))))) (let ((_let_39 (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))))) (let ((_let_40 (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.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))))) (let ((_let_41 (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent))) (let ((_let_42 (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.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))))))) (let ((_let_43 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_Set_Oinsert V_a V_A T_a) V_A) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))) (let ((_let_44 (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (tptp.hBOOL (tptp.c_in V_c V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a))))))) (let ((_let_45 (forall ((V_H $$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))))))) (let ((_let_46 (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.tc_fun T_a tptp.tc_bool))))) (let ((_let_47 (forall ((V_A $$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)))))) (let ((_let_48 (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (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))))))) (let ((_let_49 (tptp.c_Set_Oinsert tptp.v_Xa _let_1 tptp.tc_Message_Omsg))) (let ((_let_50 (= _let_20 _let_49))) (let ((_let_51 (= _let_28 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz _let_49))))) (let ((_let_52 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_53 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_28 _let_9 _let_52))) (let ((_let_54 (tptp.hBOOL (tptp.c_in _let_11 _let_53 tptp.tc_Message_Omsg)))) (let ((_let_55 (tptp.c_Message_Osynth _let_25))) (let ((_let_56 (tptp.hBOOL (tptp.c_in _let_11 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_55 _let_9 _let_52) tptp.tc_Message_Omsg)))) (let ((_let_57 (_let_39))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.c_Message_Oagent_OSpy tptp.v_Ba tptp.v_Xa tptp.v_evsf QUANTIFIERS_INST_E_MATCHING ((tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)))) :args _let_57)) _let_58 :args (_let_50 false _let_39)))) (let ((_let_60 (not _let_29))) (let ((_let_61 (or _let_51 _let_60))) (let ((_let_62 (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (= _let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)))) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (ASSUME :args (_let_29)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_60 _let_51 (not _let_61)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (tptp.v_Xa _let_1 QUANTIFIERS_INST_E_MATCHING ((tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg)))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_51 false _let_29 false _let_61)))) (let ((_let_66 (tptp.c_Set_Oinsert _let_11 _let_21 tptp.tc_Message_Omsg))) (let ((_let_67 (tptp.c_lessequals _let_66 _let_53 _let_52))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_54 _let_68))) (let ((_let_70 (_let_48))) (let ((_let_71 (ASSUME :args _let_70))) (let ((_let_72 (tptp.c_Message_Oparts _let_2))) (let ((_let_73 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_72 _let_28 _let_52))) (let ((_let_74 (= _let_73 (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_28 _let_72 _let_52)))) (let ((_let_75 (= _let_21 (tptp.c_Message_Oparts _let_25)))) (let ((_let_76 (= _let_9 _let_72))) (let ((_let_77 (tptp.c_lessequals (tptp.c_Message_Oparts _let_49) _let_53 _let_52))) (let ((_let_78 (= _let_21 _let_66))) (let ((_let_79 (= (tptp.c_Message_Oparts _let_28) _let_73))) (let ((_let_80 (_let_47))) (let ((_let_81 (ASSUME :args _let_80))) (let ((_let_82 (_let_38))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 ((tptp.c_Message_Oanalz V_H)))) (let ((_let_85 (or _let_77 _let_60))) (let ((_let_86 (_let_42))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 (not _let_22))) (let ((_let_89 (or _let_78 _let_88))) (let ((_let_90 (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (= V_A (tptp.c_Set_Oinsert V_a V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (_let_90))) (let ((_let_93 ((tptp.c_in V_a V_A T_a)))) (let ((_let_94 (_let_45))) (let ((_let_95 (ASSUME :args _let_94))) (let ((_let_96 (and _let_79 _let_78 _let_77 _let_50 _let_76 _let_75 _let_74))) (let ((_let_97 (ASSUME :args (_let_77)))) (let ((_let_98 (APPLY_UF tptp.c_lessequals))) (let ((_let_99 (REFL :args (_let_52)))) (let ((_let_100 (APPLY_UF tptp.c_Lattices_Oupper__semilattice__class_Osup))) (let ((_let_101 (ASSUME :args (_let_76)))) (let ((_let_102 (ASSUME :args (_let_74)))) (let ((_let_103 (ASSUME :args (_let_79)))) (let ((_let_104 (TRANS (SYMM (SYMM _let_103)) (SYMM (SYMM _let_102)) (CONG (REFL :args (_let_28)) (SYMM _let_101) _let_99 :args _let_100)))) (let ((_let_105 (ASSUME :args (_let_50)))) (let ((_let_106 (SYMM _let_105))) (let ((_let_107 (SYMM _let_106))) (let ((_let_108 (CONG _let_107 :args (APPLY_UF tptp.c_Message_Oparts)))) (let ((_let_109 (ASSUME :args (_let_75)))) (let ((_let_110 (TRANS (SYMM _let_109) _let_108))) (let ((_let_111 (ASSUME :args (_let_78)))) (let ((_let_112 (not _let_56))) (let ((_let_113 (tptp.hBOOL (tptp.c_in _let_11 _let_55 tptp.tc_Message_Omsg)))) (let ((_let_114 (or _let_12 _let_113 _let_112))) (let ((_let_115 (_let_44))) (let ((_let_116 (ASSUME :args _let_115))) (let ((_let_117 (tptp.hBOOL (tptp.c_in _let_11 _let_28 tptp.tc_Message_Omsg)))) (let ((_let_118 (not _let_113))) (let ((_let_119 (not _let_117))) (let ((_let_120 (tptp.hBOOL (tptp.c_in _let_11 _let_2 tptp.tc_Message_Omsg)))) (let ((_let_121 (or _let_120 _let_119 _let_4))) (let ((_let_122 (_let_33))) (let ((_let_123 (ASSUME :args _let_122))) (let ((_let_124 (not _let_120))) (let ((_let_125 (or _let_124 _let_12))) (let ((_let_126 (_let_31))) (let ((_let_127 (ASSUME :args _let_126))) (let ((_let_128 (not _let_4))) (let ((_let_129 (or _let_128 _let_26))) (let ((_let_130 (_let_32))) (let ((_let_131 (ASSUME :args _let_130))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_26 _let_128 (not _let_129)))) (ASSUME :args (_let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_131 :args (_let_3 tptp.v_evsf tptp.c_Message_Oagent_OSpy tptp.v_Ba tptp.v_Xa QUANTIFIERS_INST_E_MATCHING ((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)))) :args _let_130)) _let_131 :args (_let_129 false _let_32)) :args (_let_128 true _let_26 false _let_129)))) (let ((_let_133 (not _let_24))) (let ((_let_134 (= _let_18 _let_7))) (let ((_let_135 (or _let_8 _let_134 _let_133))) (let ((_let_136 (_let_36))) (let ((_let_137 (ASSUME :args _let_136))) (let ((_let_138 (not _let_134))) (let ((_let_139 (or _let_138 _let_34))) (let ((_let_140 (_let_37))) (let ((_let_141 (ASSUME :args _let_140))) (let ((_let_142 (not _let_15))) (let ((_let_143 (tptp.c_Set_Oinsert _let_14 _let_5 tptp.tc_Event_Oevent))) (let ((_let_144 (= _let_5 _let_143))) (let ((_let_145 (or _let_144 _let_142))) (let ((_let_146 (tptp.tc_fun tptp.tc_Event_Oevent tptp.tc_bool))) (let ((_let_147 (tptp.c_lessequals _let_5 _let_23 _let_146))) (let ((_let_148 (tptp.c_lessequals _let_143 _let_23 _let_146))) (let ((_let_149 (not _let_144))) (let ((_let_150 (_let_46))) (let ((_let_151 (ASSUME :args _let_150))) (let ((_let_152 (not _let_148))) (let ((_let_153 (tptp.hBOOL (tptp.c_in _let_14 _let_23 tptp.tc_Event_Oevent)))) (let ((_let_154 (or _let_153 _let_152))) (let ((_let_155 (_let_17))) (let ((_let_156 (ASSUME :args _let_155))) (let ((_let_157 (or))) (let ((_let_158 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(tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_List_Oset V_xs T_a) (tptp.c_List_Oset V_ys T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_Z $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_Z) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Olist_ONil T_a) T_a)) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OHash V_X))) (= (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) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor V_H) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) V_H tptp.tc_Message_Omsg))))) (forall ((V_msg $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OHash V_msg_H))) (= V_msg V_msg_H))) (forall ((V_f $$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_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_b T_a) (tptp.c_Set_Oinsert (tptp.hAPP V_f V_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) T_a))) (forall ((V_A $$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_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))) (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp _let_41)) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_ys _let_1)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) _let_1)) (= V_xs _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys _let_1)))) (forall ((T_a $$unsorted) (V_xs $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs _let_1)))) (forall ((V_K $$unsorted)) (or (= (tptp.c_Message_OinvKey V_K) V_K) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in V_ys _let_2 _let_1))) (not (tptp.hBOOL (tptp.c_in V_xs _let_2 _let_1))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_OHPair 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_Set_Oinsert (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oremdups _let_1 T_a) _let_1))) (forall ((V_K $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))))) (forall ((V_K $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_OinvKey V_K) tptp.c_Message_OsymKeys tptp.tc_nat))))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OHash V_X_H))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (tptp.c_lessequals (tptp.c_Set_Oinsert V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg) (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_B $$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_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (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_1))) (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) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Otop__class_Otop _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_B _let_1) _let_2)))) (forall ((T_a $$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_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_bs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Olist__inter _let_1 V_bs T_a) _let_1))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.c_lessequals (tptp.c_Event_OinitState V_A) (tptp.c_Event_Oknows V_A V_evs) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_ys $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.c_List_Odistinct V_ys T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Oappend V_xs V_ys T_a) T_a)))) (forall ((V_ys $$unsorted) (T_a $$unsorted)) (= V_ys (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a))) (forall ((T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_ys T_a) V_ys)) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= V_xs (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (= V_x (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) V_x T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_ONil T_a) T_a) V_xs)) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x)) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)))) (forall ((V_A $$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 $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_evs $$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_x $$unsorted) (V_xa $$unsorted) (V_AA $$unsorted)) (let ((_let_1 (tptp.c_Public_OpublicKey V_x))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP _let_1 V_xa) (tptp.c_Set_Oimage _let_1 V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_xa V_AA tptp.tc_Message_Oagent)))))) (forall ((V_x $$unsorted) (V_AA $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_AA tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (or (= V_b V_c) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_x) (tptp.c_Set_Oimage (tptp.c_Public_OpublicKey V_c) V_AA tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) (tptp.c_List_Oappend V_xs V_zs T_a))) (= V_ys V_zs))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (or (not (= (tptp.c_List_Oappend V_ys V_xs T_a) (tptp.c_List_Oappend V_zs V_xs T_a))) (= V_ys V_zs))) (forall ((V_K $$unsorted) (V_K_H $$unsorted)) (or (not (= (tptp.c_Message_OinvKey V_K) (tptp.c_Message_OinvKey V_K_H))) (= V_K V_K_H))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_ONonce V_N) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_A $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_b V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (not (tptp.c_lessequals (tptp.c_Set_Oimage V_f V_A T_b T_a) V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (not (= (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)))) (forall ((V_b $$unsorted) (V_x $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (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 ((T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_b)) (= (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_f V_g (tptp.tc_fun tptp.t_a T_b)) tptp.v_x) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP V_f tptp.v_x) (tptp.hAPP V_g tptp.v_x) T_b)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_H) _let_1) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_1))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H))) (= V_A V_A_H))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_c $$unsorted) (V_A_H $$unsorted)) (or (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H))) (= V_b V_c))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_OHPair 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_Set_Oinsert (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (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 $$unsorted) (V_Y $$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_X_H (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) (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_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_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_f $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (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 $$unsorted) (V_A $$unsorted)) (tptp.hBOOL (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 $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((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_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= _let_1 (tptp.c_List_Oremdups V_x T_a))) (= V_x _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 ((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)) (let ((_let_1 (tptp.tc_fun 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_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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a) (not (tptp.c_lessequals V_b V_x T_a)) (not (tptp.c_lessequals V_a V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (not (tptp.c_lessequals V_z V_x T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_z T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a))) (forall ((V_x $$unsorted) (V_AA $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_x V_AA tptp.tc_Message_Oagent))))) (forall ((V_x $$unsorted) (V_AA $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_AA tptp.tc_Message_Oagent)) (not (tptp.hBOOL (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 $$unsorted) (V_x $$unsorted)) (= (tptp.c_Message_OHPair V_X V_x) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_x)) V_x))) (forall ((V_X $$unsorted) (V_Y $$unsorted)) (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) V_Y))) (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))) _let_48 (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage V_f V_A T_a T_b))) (or (= (tptp.c_Set_Oinsert (tptp.hAPP V_f V_x) _let_1 T_b) _let_1) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals V_A V_B _let_1) (not (tptp.c_lessequals V_A (tptp.c_Set_Oinsert V_x V_B T_a) _let_1)) (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_X_H $$unsorted) (V_Y_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H) (tptp.c_Message_OHPair V_X V_Y))) (= V_X_H (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y))))) _let_47 (forall ((T_a $$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_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.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor _let_1) tptp.tc_nat)))))) (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_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Set_Oinsert V_x V_A T_a) V_B _let_1) (not (tptp.c_lessequals V_A V_B _let_1)) (not (tptp.hBOOL (tptp.c_in V_x V_B T_a)))))) (forall ((V_K $$unsorted)) (= (tptp.c_Message_OinvKey (tptp.c_Message_OinvKey V_K)) V_K)) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oremdups V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (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_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_xs)) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= V_xs (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_ys (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oappend V_xs V_ys T_a) V_ys)) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((V_ys $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (= V_ys (tptp.c_List_Oappend V_xs V_ys T_a))) (= V_xs (tptp.c_List_Olist_ONil T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a) _let_1))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (tptp.c_List_Odistinct (tptp.c_List_Oremdups V_xs T_a) T_a)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oremdups _let_1 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 $$unsorted)) (= (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) (tptp.c_Event_OinitState V_A))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_y V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) (not (tptp.c_lessequals V_x V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_b V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.c_lessequals V_a V_x T_a) (not (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) V_x T_a)))) (forall ((V_A $$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_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_X $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OHash V_X) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1) _let_1) (not (tptp.hBOOL (tptp.c_in V_X V_G tptp.tc_Message_Omsg)))))) (forall ((V_X $$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_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_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_xs V_ys)))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (or (not (= (tptp.c_List_Oappend V_xs (tptp.c_List_Olist_OCons V_x _let_1 T_a) T_a) (tptp.c_List_Oappend V_ys (tptp.c_List_Olist_OCons V_y _let_1 T_a) T_a))) (= V_x V_y)))) (forall ((V_xs $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.hBOOL (tptp.c_in V_xs _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1))))))) (forall ((V_ys $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist T_a))) (let ((_let_2 (tptp.c_List_Olists V_A T_a))) (or (tptp.hBOOL (tptp.c_in V_ys _let_2 _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_List_Oappend V_xs V_ys T_a) _let_2 _let_1))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= (tptp.c_List_Oappend _let_1 _let_1 T_a) _let_1))) (forall ((V_b $$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_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage V_f V_A T_b T_a) (tptp.c_Set_Oimage V_f V_B T_b T_a) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_X $$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 $$unsorted) (V_G_H $$unsorted) (V_H_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G_H V_H_H _let_1)) _let_1) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H) _let_1)) (not (tptp.c_lessequals (tptp.c_Message_Oanalz V_G) (tptp.c_Message_Oanalz V_G_H) _let_1))))) (forall ((V_xs $$unsorted) (V_ys $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_ys T_a) V_zs T_a) (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_ys V_zs T_a) T_a))) (forall ((V_xs $$unsorted) (V_xs1 $$unsorted) (V_us $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_xs1 V_us T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_xs1 T_a) V_us T_a))) (forall ((V_zs $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Oappend V_zs V_x T_a) V_ys T_a) (tptp.c_List_Oappend V_zs (tptp.c_List_Oappend V_x V_ys T_a) T_a))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (V_ts $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oappend V_xs (tptp.c_List_Oappend V_x V_ts T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Oappend V_xs V_x T_a) V_ts T_a))) (forall ((V_c $$unsorted) (V_A_H $$unsorted) (V_b $$unsorted) (V_A $$unsorted)) (not (= (tptp.hAPP (tptp.c_Public_OpublicKey V_c) V_A_H) (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))))) (forall ((V_X $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Public_OshrK V_X) tptp.c_Message_OsymKeys tptp.tc_nat))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (or (tptp.hBOOL (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 $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)))) (or _let_2 (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) _let_2)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (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_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OGets V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_A $$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))) _let_46 (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_List_Oset V_xs T_a) T_a))) (forall ((V_c $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (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 $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.c_lessequals V_G _let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) _let_1) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_G) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oparts (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_X $$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_c $$unsorted) (V_a $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_a V_G tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_G $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg))))) (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.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_Y (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_G) 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_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X (tptp.c_Set_Oinsert V_Y V_H tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (forall ((V_K $$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_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_2 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_2 _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (= (tptp.c_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.hBOOL (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) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_Y _let_2 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_2 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)))))) (forall ((V_N $$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_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_H $$unsorted)) (tptp.c_lessequals (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_Z $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (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_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OHash V_X))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_Y (tptp.c_Message_Osynth (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_G $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth V_G) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash V_X) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (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 $$unsorted) (V_G $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_G) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (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.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) 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.hBOOL (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.hBOOL (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.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg)))))) (forall ((V_N $$unsorted)) (let ((_let_1 (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_N tptp.tc_nat tptp.tc_Message_Omsg))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) _let_45 (forall ((V_agt $$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 $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_C))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$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_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (= (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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_OinvKey V_K) (tptp.c_Message_OkeysFor V_H) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_x $$unsorted)) (= (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_x)) V_x) (tptp.c_Message_OHPair V_X V_x))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (not (= (tptp.c_List_Oremdups V_xs T_a) V_xs)) (tptp.c_List_Odistinct V_xs T_a))) (forall ((V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremdups V_xs T_a) V_xs) (not (tptp.c_List_Odistinct V_xs T_a)))) (forall ((V_b $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A) tptp.c_Message_OsymKeys tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_OCons V_x V_xs T_a))) (= _let_1 (tptp.c_List_Oappend (tptp.c_List_Olist_ONil T_a) _let_1 T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_List_Olist_ONil T_a))) (= _let_1 (tptp.c_List_Oappend _let_1 _let_1 T_a)))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OHash V_X))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_f $$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 $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (= (tptp.c_Message_OkeysFor (tptp.c_Set_Oinsert (tptp.c_Message_Omsg_OMPair V_X V_Y) V_H tptp.tc_Message_Omsg)) (tptp.c_Message_OkeysFor V_H))) (forall ((V_x $$unsorted) (V_b $$unsorted) (V_AA $$unsorted)) (not (tptp.hBOOL (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 ((T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_HOL_Oord T_b)) (tptp.c_lessequals (tptp.hAPP V_f V_x) (tptp.hAPP V_g V_x) T_b) (not (tptp.c_lessequals V_f V_g (tptp.tc_fun T_a T_b))))) (forall ((V_K $$unsorted) (V_evs $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_A T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_B T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a V_B T_a))))) (forall ((V_t $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_t V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_t V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((V_c $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_a))) (not (tptp.c_lessequals V_A V_B (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_A T_a))))) (forall ((V_c $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) T_a)) (not (tptp.hBOOL (tptp.c_in V_c V_B T_a))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_a V_A T_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_b V_A T_a) T_a))))) _let_44 (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun T_a tptp.tc_bool)) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (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 $$unsorted)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_Set_Oinsert V_a V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_Set_Oinsert V_x V_B T_a) T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (or (not (= (tptp.c_Set_Oinsert V_x V_A T_a) (tptp.c_Set_Oinsert V_x V_B T_a))) (tptp.hBOOL (tptp.c_in V_x V_B T_a)) (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (= V_A V_B))) _let_43 (forall ((V_x $$unsorted) (V_A $$unsorted) (T_aa $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_aa))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_aa T_a) T_a)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))) (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP V_f V_x) (tptp.c_Set_Oimage V_f V_A T_b T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_x V_A T_b))))) (forall ((V_f $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_x V_A T_a))))) (forall ((T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (not (= (tptp.c_List_Olist_ONil T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted) (V_zs $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted) (V_ys $$unsorted)) (= (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs T_a) V_ys T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs V_ys T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xa V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xa T_a) V_zs T_a))) (forall ((V_x $$unsorted) (V_xs1 $$unsorted) (V_zs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oappend V_xs1 V_zs T_a) T_a) (tptp.c_List_Oappend (tptp.c_List_Olist_OCons V_x V_xs1 T_a) V_zs T_a))) (forall ((V_x $$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_H $$unsorted) (V_list_H $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_a_H V_list_H T_a) (tptp.c_List_Olist_ONil T_a)))) (forall ((V_xs $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.c_List_Odistinct V_xs T_a) (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OHash V_msg)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_X_H $$unsorted) (V_Y_H $$unsorted)) (or (not (= (tptp.c_Message_OHPair V_X V_Y) (tptp.c_Message_Omsg_OMPair V_X_H V_Y_H))) (= V_Y_H V_Y))) (forall ((V_msg $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (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_Y $$unsorted) (V_G $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (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_xs $$unsorted) (T_a $$unsorted)) (= (tptp.c_List_Oset (tptp.c_List_Oremdups V_xs T_a) T_a) (tptp.c_List_Oset V_xs T_a))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_x V_A tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A tptp.tc_nat)) (not (tptp.hBOOL (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_b $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_OinitState V_B) tptp.tc_Message_Omsg))) (forall ((V_X $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OHash V_X) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_G $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (= (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oparts V_G) (tptp.c_Message_Oparts V_H) _let_1)))) (forall ((V_H $$unsorted)) (tptp.c_lessequals V_H (tptp.c_Message_Oparts V_H) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (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))))) (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)))))) (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_X $$unsorted) (V_G $$unsorted) (V_H $$unsorted)) (or (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz V_G)) (not (tptp.c_lessequals V_H V_G (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (not (tptp.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat))))) (or (tptp.hBOOL (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_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)))) (or _let_1 (not (tptp.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat))) _let_1))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_nE $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_nE tptp.tc_nat tptp.tc_Message_Omsg) V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_K V_nE tptp.tc_nat)))))) (forall ((V_K $$unsorted) (V_X_H $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_K V_X_H) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_msg $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OHash V_msg)))) (forall ((V_K $$unsorted) (V_H $$unsorted) (V_G $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Set_Oinsert V_X V_G tptp.tc_Message_Omsg))) tptp.tc_nat))))) (forall ((V_X $$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.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)))) (forall ((V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_K $$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 $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_H $$unsorted) (V_H_H $$unsorted) (V_X $$unsorted)) (or (not (= (tptp.c_Message_Oanalz V_H) (tptp.c_Message_Oanalz V_H_H))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H_H tptp.tc_Message_Omsg))))) (forall ((V_G $$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_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_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_msg_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_agent $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_nat $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OHash V_msg_H)))) (forall ((V_N $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_OHPair V_X V_Y)))) (forall ((V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OHash V_msg_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_agent1 $$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_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 $$unsorted) (V_C $$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_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_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.c_lessequals (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert V_X V_H tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$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.hBOOL (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)))))) _let_42 (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_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 $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (let ((_let_2 (tptp.c_Message_Osynth V_G))) (= (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 V_H _let_1)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Message_Oanalz (tptp.c_Lattices_Oupper__semilattice__class_Osup V_G V_H _let_1)) _let_2 _let_1))))) (forall ((V_agt $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OAgent V_agt))) (= (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 V_H tptp.tc_Message_Omsg)) (tptp.c_Set_Oinsert _let_1 (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)))) (forall ((V_X $$unsorted) (V_K $$unsorted) (V_N $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_X V_K))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_N))) (= (tptp.c_Set_Oinsert _let_1 (tptp.c_Set_Oinsert _let_2 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg) (tptp.c_Set_Oinsert _let_2 (tptp.c_Set_Oinsert _let_1 V_A tptp.tc_Message_Omsg) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_N $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_N))) (= (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 $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (= (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_x $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_x))) (or (tptp.hBOOL (tptp.c_in V_x (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.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert _let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_KAB $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg)) (= V_K V_KAB) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB) _let_1 tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_KAB (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))))) (forall ((V_K $$unsorted) (V_KAB $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Set_Oinsert (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB) _let_1 tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_KAB (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.hBOOL (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) (V_e $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons V_e V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (tptp.hBOOL (tptp.c_in _let_41 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_30)) (forall ((V_A $$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))) (forall ((V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1 V_X V_evs))) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_OinitState tptp.c_Message_Oagent_OSpy) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes _let_2 V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays _let_2 (tptp.c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2 V_X V_evs) V_X) _let_1 tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_OinitState V_A) tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OGets V_A V_X) _let_1 tptp.tc_Event_Oevent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A (tptp.c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1 V_A V_X V_evs) V_X) _let_1 tptp.tc_Event_Oevent)) (= V_A tptp.c_Message_Oagent_OSpy) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_evs $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_OkeysFor (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (not (tptp.c_List_Odistinct V_xs T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremdups (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olist_OCons V_x (tptp.c_List_Oremdups V_xs T_a) T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (not (tptp.c_List_Odistinct (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a)))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Olength__unique (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Olength__unique V_xs T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xb T_a) T_a)))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (V_xb $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset (tptp.c_List_Oappend V_xa (tptp.c_List_Olist_OCons V_x V_xb T_a) T_a) T_a) T_a)) (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xa T_a) T_a)))) (forall ((V_a $$unsorted) (V_as $$unsorted) (T_a $$unsorted) (V_bs $$unsorted)) (or (= (tptp.c_List_Olist__inter (tptp.c_List_Olist_OCons V_a V_as T_a) V_bs T_a) (tptp.c_List_Olist__inter V_as V_bs T_a)) (tptp.hBOOL (tptp.c_in V_a (tptp.c_List_Oset V_bs T_a) T_a)))) (forall ((V_a $$unsorted) (V_as $$unsorted) (T_a $$unsorted) (V_bs $$unsorted)) (or (= (tptp.c_List_Olist__inter (tptp.c_List_Olist_OCons V_a V_as T_a) V_bs T_a) (tptp.c_List_Olist_OCons V_a (tptp.c_List_Olist__inter V_as V_bs T_a) T_a)) (not (tptp.hBOOL (tptp.c_in V_a (tptp.c_List_Oset V_bs T_a) T_a))))) (forall ((V_x $$unsorted) (V_xs $$unsorted) (T_a $$unsorted)) (or (= (tptp.c_List_Oremdups (tptp.c_List_Olist_OCons V_x V_xs T_a) T_a) (tptp.c_List_Oremdups V_xs T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_B $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_xs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_A T_a)) (not (tptp.hBOOL (tptp.c_in V_x (tptp.c_List_Oset V_xs T_a) T_a))) (not (tptp.hBOOL (tptp.c_in V_xs (tptp.c_List_Olists V_A T_a) (tptp.tc_List_Olist T_a)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (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_N $$unsorted) (V_B $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg)))) _let_40 (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_OHPair V_X V_Y) _let_1 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg))))) (forall ((V_x $$unsorted) (V_A $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce V_x) (tptp.c_Set_Oimage tptp.c_Message_Omsg_OKey V_A tptp.tc_nat tptp.tc_Message_Omsg) tptp.tc_Message_Omsg)))) (forall ((V_A $$unsorted)) (tptp.hBOOL (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 $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_OinitState V_B)) tptp.tc_Message_Omsg))))) (forall ((V_K $$unsorted) (V_X $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) tptp.tc_Message_Omsg)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (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_N $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce V_N) (tptp.c_Event_Oused (tptp.c_List_Olist_ONil tptp.tc_Event_Oevent)) tptp.tc_Message_Omsg)))) (forall ((V_evs $$unsorted)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.c_Public_Osko__Public__XNonce__supply1__1__1 V_evs)) (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A))) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))))) (forall ((V_A $$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 $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows V_A V_evs) (tptp.c_Event_Oknows V_A (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A_H V_B V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) _let_39 (forall ((V_A $$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 $$unsorted) (V_evs $$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_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_K_H $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (let ((_let_3 (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)))) (or (tptp.hBOOL (tptp.c_in _let_3 _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_2 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (let ((_let_3 (tptp.c_Message_Omsg_OHash (tptp.c_Message_Omsg_OMPair V_X V_Y)))) (or (tptp.hBOOL (tptp.c_in _let_3 _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_3 _let_1 tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg))))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP (tptp.c_Public_OpublicKey V_b) V_A)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg))) (forall ((V_evs $$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_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$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_OSays V_A V_B V_X) V_evs tptp.tc_Event_Oevent)) (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))) (forall ((V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (tptp.c_lessequals (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.tc_fun tptp.tc_Message_Omsg tptp.tc_bool))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (forall ((V_X $$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.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (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_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.c_Message_Osynth _let_1))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_2 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X _let_2 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.c_Message_OinvKey V_K)) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_b $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (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_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (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.hBOOL (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_X $$unsorted) (V_evs $$unsorted) (V_K $$unsorted) (V_S $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_K (tptp.c_Set_Oimage tptp.c_Public_OshrK (tptp.c_Orderings_Otop__class_Otop (tptp.tc_fun tptp.tc_Message_Oagent tptp.tc_bool)) tptp.tc_Message_Oagent tptp.tc_nat) tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OGets V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (= V_A tptp.c_Message_Oagent_OSpy))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs5 $$unsorted) (V_S $$unsorted) (V_NA $$unsorted) (V_X $$unsorted) (V_B_H $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs5 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_2 _let_2))) V_evs5 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce V_NA) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B_H V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2)) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs5))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs5 $$unsorted) (V_S $$unsorted) (V_NA $$unsorted) (V_X $$unsorted) (V_B_H $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evs5 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_OMPair _let_3 _let_3))) V_evs5 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce 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))))) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B_H V_A (tptp.c_Message_Omsg_OCrypt V_K _let_3)) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (not (tptp.hBOOL (tptp.c_in V_evs5 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Set_Oinsert V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs4 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_1)) V_evs4 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H V_B (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OAgent V_A)))) (tptp.c_List_Oset V_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Event_Oused V_evs4) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs4)))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs4 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2)) V_evs4 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H V_B (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) (tptp.c_Message_Omsg_OAgent V_A)))) (tptp.c_List_Oset V_evs4 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_K tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Event_Oused V_evs4) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_evs4 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))))) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_KAB $$unsorted) (V_evs2 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NA))) (let ((_let_3 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_4 (tptp.c_Message_Omsg_OAgent V_A))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 _let_4))))))) V_evs2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_3 _let_2))) (tptp.c_List_Oset V_evs2 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_KAB tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Event_Oused V_evs2) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs2))))))))) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_KAB $$unsorted) (V_evs2 $$unsorted) (V_A_H $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_KAB))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NA))) (let ((_let_4 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_5 (tptp.c_Message_Omsg_OAgent V_A))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_2 _let_5))))))) V_evs2 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A_H tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair _let_4 _let_3))) (tptp.c_List_Oset V_evs2 tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_KAB tptp.c_Message_OsymKeys tptp.tc_nat))) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Event_Oused V_evs2) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_evs2 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_1 (tptp.c_Message_Omsg_OAgent V_A))))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1 V_A V_B V_K V_evs) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 _let_2))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_B $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_K_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1 V_K V_NA V_evs) _let_2))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (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_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_ONonce V_NB)))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_4 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A _let_2) _let_4 tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1 V_K V_NA V_evs) _let_3))) _let_4 tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_3 V_X)))) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (not (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1 V_K V_NA V_evs) _let_2))) _let_1 tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_B tptp.c_Event_Obad tptp.tc_Message_Oagent)) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (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_2 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_B) (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OAgent V_A)))))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evsf))))) (forall ((V_NA $$unsorted) (V_NB $$unsorted) (V_K $$unsorted) (V_evso $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evso tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_3 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_2 _let_3))) V_evso tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_3 V_X))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_2)) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evso))))))))) (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.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (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_c $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_X $$unsorted)) (or (not (tptp.hBOOL (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.hBOOL (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_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey (tptp.hAPP tptp.c_Public_OshrK V_A)) (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))) (forall ((V_c $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) _let_1))) V_evs1 tptp.tc_Event_Oevent))) (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Event_Oused V_evs1) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs1)))))) (= (tptp.c_NS__Shared__Mirabelle_Ons__sharedp tptp.v_x) (tptp.c_in tptp.v_x tptp.c_NS__Shared__Mirabelle_Ons__shared _let_30)) (forall ((V_X $$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.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (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_B $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (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 ((V_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (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_A $$unsorted) (V_evs $$unsorted)) (or (tptp.hBOOL (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.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Event_Oused V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oused V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_ONotes V_A V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_A $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (or (= (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes V_A V_X) V_evs tptp.tc_Event_Oevent)) (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)))) (forall ((V_agent_H $$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_agent1 $$unsorted) (V_agent2 $$unsorted) (V_msg $$unsorted) (V_agent_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H)))) (not (tptp.hBOOL (tptp.c_in tptp.c_Message_Oagent_OServer tptp.c_Event_Obad tptp.tc_Message_Oagent))) (forall ((V_agent $$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 $$unsorted)) (or (not (= (tptp.c_Event_Oevent_ONotes V_agent V_msg) (tptp.c_Event_Oevent_ONotes V_agent_H V_msg_H))) (= V_agent V_agent_H))) (tptp.hBOOL (tptp.c_in tptp.c_Message_Oagent_OSpy tptp.c_Event_Obad tptp.tc_Message_Oagent)) (forall ((V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_X $$unsorted) (V_evs $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X)))))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A _let_1) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (tptp.hBOOL (tptp.c_in V_A tptp.c_Event_Obad tptp.tc_Message_Oagent)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_NA $$unsorted) (V_evs1 $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) _let_2))) V_evs1 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Event_Oused V_evs1) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_evs1 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs3 tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs3 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair _let_2 _let_3))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair _let_2 (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_1 tptp.tc_Event_Oevent))) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.hBOOL (tptp.c_NS__Shared__Mirabelle_Ons__sharedp V_evs3)))))))) (forall ((V_NA $$unsorted) (V_NB $$unsorted) (V_K $$unsorted) (V_evso $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evso tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_ONonce V_NB))) (let ((_let_4 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_5 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_ONotes tptp.c_Message_Oagent_OSpy (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair _let_3 _let_4))) V_evso tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_5 (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_4 V_X))))) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A (tptp.c_Message_Omsg_OCrypt V_K _let_3)) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in V_evso tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))))))) (forall ((V_agent $$unsorted) (V_agent_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_OAgent V_agent_H))) (= V_agent V_agent_H))) _let_38 (forall ((V_X $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows V_A V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_Y $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (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 $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (V_a_H $$unsorted) (V_list_H $$unsorted)) (or (not (= (tptp.c_List_Olist_OCons V_a V_list T_a) (tptp.c_List_Olist_OCons V_a_H V_list_H T_a))) (= V_list V_list_H))) (forall ((V_a $$unsorted) (V_list $$unsorted) (T_a $$unsorted) (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_nat_H $$unsorted) (V_msg_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_agent $$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_nat $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H) (tptp.c_Message_Omsg_ONonce V_nat)))) _let_37 (forall ((V_agent1 $$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 $$unsorted)) (or (not (= (tptp.c_Event_Oevent_OSays V_agent1 V_agent2 V_msg) (tptp.c_Event_Oevent_OSays V_agent1_H V_agent2_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X V_H tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_B $$unsorted) (V_X $$unsorted) (V_evsf $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OSpy V_B V_X) V_evsf tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evsf))) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_evsf tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)))))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_S $$unsorted) (V_A $$unsorted) (V_KA $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_K $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt V_KA (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair V_B (tptp.c_Message_Omsg_OMPair V_K V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_nat_H $$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 $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oparts _let_1) _let_1))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H)))) (forall ((V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (= (tptp.c_Message_Oanalz _let_1) _let_1))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_B $$unsorted) (V_A $$unsorted) (V_K $$unsorted) (V_NB $$unsorted) (V_evs $$unsorted) (V_NA $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (let ((_let_3 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_4 (tptp.c_Message_Omsg_OCrypt V_K (tptp.c_Message_Omsg_ONonce V_NB)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_B V_A _let_4) _let_3 tptp.tc_Event_Oevent)) (not (tptp.hBOOL (tptp.c_in _let_4 (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (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_2 V_X))))) _let_3 tptp.tc_Event_Oevent))) (tptp.hBOOL (tptp.c_in _let_2 (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))))))))) (forall ((V_K_H $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_N $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_X $$unsorted)) (or (= V_K_H (tptp.hAPP tptp.c_Public_OshrK V_A)) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_nat_H $$unsorted) (V_agent $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat_H) (tptp.c_Message_Omsg_OAgent V_agent)))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (let ((_let_2 (tptp.hAPP tptp.c_Public_OshrK V_A))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey _let_2) _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt _let_2 V_X) _let_1 tptp.tc_Message_Omsg))))))) (not (= tptp.c_Message_Oagent_OServer tptp.c_Message_Oagent_OSpy)) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A V_B V_X) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oparts V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts _let_1) tptp.tc_Message_Omsg)))))) (forall ((V_Y $$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.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_X $$unsorted) (V_H $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OMPair V_X V_Y))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_A $$unsorted) (V_A_H $$unsorted) (V_evs $$unsorted) (V_NA_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_A V_A_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_NA $$unsorted) (V_NA_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_NA V_NA_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_B $$unsorted) (V_B_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_NA_H $$unsorted) (V_K $$unsorted) (V_X_H $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_B V_B_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_X $$unsorted) (V_X_H $$unsorted) (V_evs $$unsorted) (V_A_H $$unsorted) (V_NA_H $$unsorted) (V_B_H $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (= V_X V_X_H) (not (tptp.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A_H (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A_H) (tptp.c_Message_Omsg_OMPair V_NA_H (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B_H) (tptp.c_Message_Omsg_OMPair _let_2 V_X_H))))) _let_1 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_2 V_X))))) _let_1 tptp.tc_Event_Oevent))))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat_H))) (= V_nat V_nat_H))) (forall ((V_agent $$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)))) (forall ((V_X $$unsorted) (V_Y $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth (tptp.c_Message_Oanalz V_H)))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OMPair V_X V_Y) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_Y _let_1 tptp.tc_Message_Omsg))) (not (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_evs $$unsorted) (V_A $$unsorted) (V_NA $$unsorted) (V_B $$unsorted) (V_X $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_K (tptp.c_Message_Oparts (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair V_NA (tptp.c_Message_Omsg_OMPair V_B (tptp.c_Message_Omsg_OMPair V_K V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent))))) (forall ((V_agent $$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_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_msg1 $$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_A $$unsorted) (V_evs $$unsorted)) (tptp.hBOOL (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_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_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Oanalz V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz _let_1) tptp.tc_Message_Omsg)))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_ONonce V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_S $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_x V_S T_a)) (not (tptp.hBOOL (tptp.hAPP V_S V_x))))) (forall ((V_S $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_S V_x)) (not (tptp.hBOOL (tptp.c_in V_x V_S T_a))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (not (= (tptp.c_Message_Omsg_ONonce V_nat) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H)))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_nat V_nat_H))) (forall ((V_nat $$unsorted) (V_msg $$unsorted) (V_nat_H $$unsorted) (V_msg_H $$unsorted)) (or (not (= (tptp.c_Message_Omsg_OCrypt V_nat V_msg) (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H))) (= V_msg V_msg_H))) (forall ((V_X $$unsorted) (V_evs $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_S $$unsorted) (V_NA $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Message_Omsg_OKey V_K))) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz (tptp.c_Event_Oknows tptp.c_Message_Oagent_OSpy V_evs)) tptp.tc_Message_Omsg)) (= 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.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_ONonce 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_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) _let_36 (forall ((V_agent $$unsorted) (V_nat_H $$unsorted)) (not (= (tptp.c_Message_Omsg_OAgent V_agent) (tptp.c_Message_Omsg_ONonce V_nat_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_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_agt $$unsorted) (V_H $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OAgent V_agt) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))) (forall ((V_A $$unsorted) (V_H $$unsorted)) (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg))) _let_35 (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X V_H tptp.tc_Message_Omsg))))) (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.c_Message_Omsg_ONonce V_nat)))) (forall ((V_nat_H $$unsorted) (V_msg_H $$unsorted) (V_msg1 $$unsorted) (V_msg2 $$unsorted)) (not (= (tptp.c_Message_Omsg_OCrypt V_nat_H V_msg_H) (tptp.c_Message_Omsg_OMPair V_msg1 V_msg2)))) (forall ((V_X $$unsorted) (V_B $$unsorted) (V_K $$unsorted) (V_A $$unsorted) (V_evs $$unsorted) (V_K_H $$unsorted) (V_N $$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.hBOOL (tptp.c_in V_evs tptp.c_NS__Shared__Mirabelle_Ons__shared (tptp.tc_List_Olist tptp.tc_Event_Oevent)))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays tptp.c_Message_Oagent_OServer V_A (tptp.c_Message_Omsg_OCrypt V_K_H (tptp.c_Message_Omsg_OMPair V_N (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_B) (tptp.c_Message_Omsg_OMPair _let_1 V_X))))) (tptp.c_List_Oset V_evs tptp.tc_Event_Oevent) tptp.tc_Event_Oevent)))))) (forall ((V_nat $$unsorted) (V_msg1_H $$unsorted) (V_msg2_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat) (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H)))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg))) (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg))))) _let_33 (forall ((V_K $$unsorted) (V_H $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Osynth _let_1) tptp.tc_Message_Omsg)))))) (forall ((V_H $$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 $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (let ((_let_2 (tptp.c_Message_Omsg_OCrypt V_K V_X))) (or (tptp.hBOOL (tptp.c_in V_X _let_1 tptp.tc_Message_Omsg)) (tptp.hBOOL (tptp.c_in _let_2 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_2 _let_1 tptp.tc_Message_Omsg))))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_X $$unsorted) (V_evs3 $$unsorted) (V_NA $$unsorted) (V_S $$unsorted) (V_K $$unsorted)) (let ((_let_1 (tptp.tc_List_Olist tptp.tc_Event_Oevent))) (let ((_let_2 (tptp.c_List_Oset V_evs3 tptp.tc_Event_Oevent))) (let ((_let_3 (tptp.c_Message_Omsg_OAgent V_B))) (let ((_let_4 (tptp.c_Message_Omsg_ONonce V_NA))) (or (tptp.hBOOL (tptp.c_in (tptp.c_List_Olist_OCons (tptp.c_Event_Oevent_OSays V_A V_B V_X) V_evs3 tptp.tc_Event_Oevent) tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1)) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_A tptp.c_Message_Oagent_OServer (tptp.c_Message_Omsg_OMPair (tptp.c_Message_Omsg_OAgent V_A) (tptp.c_Message_Omsg_OMPair _let_3 _let_4))) _let_2 tptp.tc_Event_Oevent))) (not (tptp.hBOOL (tptp.c_in (tptp.c_Event_Oevent_OSays V_S V_A (tptp.c_Message_Omsg_OCrypt (tptp.hAPP tptp.c_Public_OshrK V_A) (tptp.c_Message_Omsg_OMPair _let_4 (tptp.c_Message_Omsg_OMPair _let_3 (tptp.c_Message_Omsg_OMPair (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_X))))) _let_2 tptp.tc_Event_Oevent))) (= V_A tptp.c_Message_Oagent_OServer) (not (tptp.hBOOL (tptp.c_in V_evs3 tptp.c_NS__Shared__Mirabelle_Ons__shared _let_1))))))))) (forall ((V_x $$unsorted) (V_t $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_List_Olist_OCons V_x V_t T_a) V_t))) (forall ((V_xs $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (not (= V_xs (tptp.c_List_Olist_OCons V_x V_xs T_a)))) _let_32 (forall ((V_msg1_H $$unsorted) (V_msg2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Message_Omsg_OMPair V_msg1_H V_msg2_H) (tptp.hAPP tptp.c_Message_Omsg_OKey V_nat)))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (or (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)))))) (forall ((V_N $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_N))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_n $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Omsg_ONonce V_n))) (or (tptp.hBOOL (tptp.c_in _let_1 V_H tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in _let_1 (tptp.c_Message_Osynth V_H) tptp.tc_Message_Omsg)))))) (forall ((V_K $$unsorted) (V_X $$unsorted) (V_H $$unsorted)) (let ((_let_1 (tptp.c_Message_Osynth V_H))) (or (tptp.hBOOL (tptp.c_in (tptp.c_Message_Omsg_OCrypt V_K V_X) _let_1 tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in (tptp.hAPP tptp.c_Message_Omsg_OKey V_K) V_H tptp.tc_Message_Omsg))) (not (tptp.hBOOL (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 $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Public_OshrK V_x) (tptp.hAPP tptp.c_Public_OshrK V_y))) (= V_x V_y))) _let_31 (forall ((V_c $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_c (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (forall ((V_X $$unsorted) (V_H $$unsorted)) (or (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oparts V_H) tptp.tc_Message_Omsg)) (not (tptp.hBOOL (tptp.c_in V_X (tptp.c_Message_Oanalz V_H) tptp.tc_Message_Omsg))))) (tptp.hBOOL (tptp.c_in tptp.v_evsf tptp.c_NS__Shared__Mirabelle_Ons__shared _let_30)) _let_29 _let_27 _let_24 _let_22 _let_17 _let_16 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Lattices_Olattice tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Otop tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (forall ((V_x $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.68/28.95 )
% 28.68/28.95 % SZS output end Proof for SWV761-1
% 28.68/28.96 % cvc5---1.0.5 exiting
% 28.68/28.96 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------